Contributors

My AMF Journey from preparing for the exam to receiving the certificate

by
Mathilde JANIK

In this article, Mathilde JANIK (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2021-2025) shares her experience taking the AMF Exam.

First of all let’s begin by presenting what the AMF (Autorité des Marchés Financiers) is and how the entity AMF differs from the AMF certification. The AMF is the Financial Markets Authority in France and its main mission is to ensure the proper functioning of financial markets, protect the savings invested in them, and ensure that investors are provided with adequate information.The AMF is the second regulatory authority for financial institutions, alongside the ACPR. The ACPR is responsible for the approval and prudential supervision of insurance companies, pension funds, credit institutions, and investment firms. The ACPR is also responsible for protecting the customers of these institutions with regard to banking and insurance transactions, as well as ensuring compliance with anti-money laundering and counter-terrorist financing rules.

The AMF missions, powers, and operating procedures are defined in the Monetary and Financial Code (Code Monétaire et Financier or CMF). A great part of regulation on financial markets and the investment services industry is defined at the European level with the ESMA (European Securities and Markets Authority). The AMF completes them within its General Regulations with rules of good conduct and organization, particularly for portfolio management companies. It monitors compliance with regulations by regulated professionals.

Brief introduction to the AMF certifications

The AMF issues professional licenses to compliance officers at investment firms. Here, we will focus on the actual AMF exam and its importance for professionals working with financial markets in France. In order to provide financial market participants with a consistent and common foundation of knowledge in the areas of finance, regulation, ethics, and sustainable finance, two certification systems have been implemented. The first certification, called “l’Examen AMF” is recognized everywhere in France and is a professional certification. There is also what’s called an internal certification provided by some employers in France, this option, which is only available to investment service providers, including management companies, is only valid within the same group. If the person who has passed the internal assessment changes groups, they will have to take the internal assessment organized by their new employer again, or take the AMF exam. There is another certification delivered by the AMF which is called “L’examen AMF Finance Durable” which is specifically tailored to professionals providing services or products linked to sustainable finance. It provides general knowledge on the regulative and economic side of sustainable finance and prepares to gather durability and sustainability preferences of customers in order to offer tailored solutions adapted to their needs. This article is made to provide a bit more information and to share my experience taking this exam, as it may be of interest to many of you who want to work in finance in France.

About the AMF Certification

The exam consists of a MCQ of 120 questions and to pass this exam and receive the certification you need at least 80% of good answers for questions relating to financial literacy and for questions relating to knowledge deemed essential to the practice of the profession (mainly legal knowledge or knowledge relating to professional ethics). The exam length is 2 hours but you don’t have to stay during the whole exam if you finish earlier. On the date where this article is published, 13 organizations in France are certified to organize the exam. I will provide the links under the section “useful resources” below. I personally prepared for this exam with Lefebvre Dalloz Education. As they provide a partnership with ESSEC we have a discount on the package for the course as well as the exam session.

The professionals who need to pass the exam are professionals exercising under the authority of an investment service provider, including portfolio management companies, or act as financial investment advisors.

Within the investment service provider, not all positions require the AMF Exam or the internal equivalent exam, there are 8 functions that require this exam; salespeople, managers, financial instrument clearing officers, post-trade officers, financial analysts, financial instrument traders, compliance and internal control officers (RCCI), and compliance officers for investment services (RCSI). On top of that, independent or employed financial advisors are now required to pass the AMF exam to advise customers on financial products. Something very important to mention is also that no diploma in France is equivalent to the AMF, therefore, no matter which educational background you may have, you need the AMF certificate to work in the functions aforementioned.

My personal experience

First of all, I would like to explain why I decided to apply for this certificate. I’m currently finishing my apprenticeship as a personal banker in a regional bank in France, during which I discovered financial advisory for personal customers and small businesses. This apprenticeship has driven a strong interest towards portfolio management and how to tailor financial products as solutions depending on the client’s needs and wants. That’s the reason why I decided to pursue a future career in wealth management and to take a step in that direction. I’m doing an internship as a wealth manager assistant from January 2026 onwards. In order to make this experience more efficient, I decided to take the exam before the start of my internship in order to be operational by January 2026 in my functions.

I registered for the AMF in late August 2025 and I passed the exam in late September. I tried to keep a steady study schedule each week and practice lessons at least 3 times a week. I reviewed each theme in details with quizzes at the end of each section, here is the list of themes present in the exam:

  • French, European, and international institutional and regulatory framework
  • Ethics, compliance, and ethical organization of institutions
  • Financial security
  • Market abuse regulations
  • Marketing of financial instruments: rules governing banking and financial solicitation, distance selling, and customer advice Customer relations and information
  • Financial instruments, crypto-assets, and their risks
  • Collective management and management on behalf of third parties
  • Market functioning and organization
  • Post-market and market infrastructure
  • Issues and transactions in securities
  • Accounting and financial fundamentals

Key Takeaways: Skills and Mindset

In terms of studying, depending on your background with finance, it may be more difficult to remember everything if the subjects mentioned are completely new. Personally, I did 3 weeks of studying before passing the exam, but most of the notions to be acquired were already familiar to me as I saw them throughout my apprenticeship.

The themes where I struggled the most were the ones related to the different institutions, jurisdictions and their areas of applications, sometimes I mixed the different institutions and what they were responsible for. The section on collective management or on third parties’ behalf was also a bit of a struggle to me as they were not the usual financial solutions we offered to clients.

The most useful study techniques for me were constant practice and quizzes, first I would read all the information per theme, then I would quiz myself on as many questions as possible, and I also did an “error log” in which I would write every time I made a mistake what the mistake was and what was the right answer. It helped me tailor my study session depending on where my weaknesses were. Once I finished the exam, the most exciting part was the email confirming I passed the exam. When I saw the green “Successfully Passed” sentence, it was a moment of true relief and accomplishment. I received my official certificate shortly after, marking the end of my AMF journey and the start of a new chapter where I can apply this critical knowledge.

Key Takeaways: Skills and Mindset

My preparation for the AMF exam highlighted two essential professional skills: discipline and the ability to embrace regulation as a foundation, not a barrier. The exam is less about innate intelligence and more about consistent, structured effort. The disciplined three-week schedule, combined with the detailed “error log,” was crucial. This study strategy translates directly to the finance world: successful wealth management or banking relies not on a single spectacular trade or transaction, but on the daily, meticulous adherence to process and continuous learning from mistakes. This consistency is the greatest soft skill I gained from the process. Before the exam, it’s easy to view the complex institutional and legal frameworks as merely regulatory hurdles. The real takeaway, however, is that this knowledge is the absolute foundation of professional trust. Understanding the nuances of customer relations and information, market abuse regulations, and professional ethics isn’t just about passing a test, it is about ensuring the integrity of the financial advice provided. For my future role as a wealth manager assistant, the AMF certificate means I can confidently structure solutions knowing they are compliant, ethical, and designed to protect the client’s interests first.

Why should I be interested in this post?

I would strongly advise any student interested in client-facing or advisory roles in French finance to approach this exam with a structured plan and a focus on understanding the spirit of the law rather than just memorizing facts. The certificate doesn’t just grant you the right to advise; it grants you the responsibility to do so ethically.

Related posts on the SimTrade blog

   ▶ Akshit GUPTA AMF

   ▶ Mahé FERRET Selling Structured Products in France

Useful resources

Autorité des Marchés Financiers (AMF) The AMF at a glance.

Autorité des Marchés Financiers (AMF) Guide sur l’examen AMF généraliste et finance durable .

Autorité des Marchés Financiers (AMF) Certification professionnelle AMF en matière de Finance durable .

Autorité des Marchés Financiers (AMF) Certification professionnelle AMF en matière de Finance durable Transcription textuelle.

Lefebvre Dalloz Compétences. Certification professionnelle AMF

Autorité des Marchés Financiers (AMF) European supervision of capital markets: the AMF calls for an enhanced role for ESMA to promote a true Savings and Investments Union

Autorité de contrôle prudentiel et de résolution (ACPR) (2024) Rapport annuel du pôle commun AMF-ACPR 2024

Autorité de contrôle prudentiel et de résolution (ACPR) (2024) Qui sommes-nous ?

About the author

The article was written in February 2026 by Mathilde JANIK (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2021-2025).

   ▶ Discover all articles written by Mathilde JANIK.

Randomness game

by

Randomness Game

The pedagogical objective of this game is to help you become familiar with randomness. At each trial, you must choose between Head and Tail. At the same time, the simulator independently chooses Head or Tail with equal probability (50%). If the two choices coincide, you win the trial. You have trials in total. Try to beat randomness. Good luck.

Your choice
Simulator choice
?
Head or Tail
Trial 0 /
Your last choice—
Simulator last choice—
Result—
Score 0 / 0

My Personal Experience in Marketing, and How It Links to Finance

by
Guylan ABBOU

In this article, Guylan ABBOU (ESSEC Business School, Global Bachelor’s in Business Administration (GBBA) – Exchange Student, 2025) shares his professional experience in marketing and explains how it connects to finance.

Introduction

Hello, my name is Guylan. While studying marketing in Spain, I completed several internships across marketing departments. I interned in four roles across internal marketing, content, and B2B growth: at Bolletje (Netherlands), I created factory-floor packaging norm sheets to reduce errors and waste; at Rejolt (France), I helped onboard partners to a B2B2B catering/events platform and contributed to a CSR label; at Descapada/Grupo Masala (Spain), I prospected B2B partners in new markets and supported targeted campaigns; and in a local clinic in Granada, I produced content and campaign materials for social channels. Those roles taught me how to navigate a professional environment and, more importantly, how different areas of a company connect: marketing, Human Resources (HR), finance, and operations don’t sit in silos; they shape each other’s outcomes every day. I decided to take the SimTrade course at ESSEC to practice disciplined decision-making under pressure and to build habits I could apply back to marketing.

When marketing picks up the HR baton (internal marketing)

In many firms, headcount pressures have shrunk traditional HR teams. Some companies outsource HR; others reassign parts of it, culture initiatives, internal communication, and employer branding to marketing. Marketers are trained to communicate clearly, align people, and move them to action. What works just as well inside the company as outside it.

At Bolletje for example, my internal marketing work focused on aligning teams on quality and execution. In practice, this included organizing cross-department discussions to reduce friction between production, quality, and operations; translating quality standards and product updates into clear, usable guidelines for factory teams; and supporting internal communication to clarify priorities, reinforce standards, and make expectations visible on the production floor.

Consumers rarely see this work, yet it’s critical. Internal marketing improves employee perception and strengthens execution: clearer priorities, faster coordination, and fewer dropped handoffs. That “invisible” efficiency shows up later in lower churn, better customer experience, and higher lifetime value. And that is exactly where finance enters the story.

Marketing ↔ Finance bridge

Finance focuses on cash flows and risk; marketing shapes both. The points below describe how common marketing situations translate into finance-oriented views.

Demand signals and market depth

In digital marketing, demand appears through search trends, click-through rates, and conversions. In finance, the order book displays supply and demand at each price level. Looking beyond surface metrics to factors such as audience saturation, competitive pressure, and funnel health provides an analogue to market depth.

Pricing, promotion and order types

In marketing, discounts and launch timing influence volume and margin. In trading, the contrast between market and limit orders represents urgency versus price discipline. The parallel highlights how conditions and thresholds determine when value is created or eroded.

The execution gap (slippage)

The difference between plan and live results constitutes an execution gap. In markets, this is slippage between expected and actual fill; in campaigns, it appears as divergence between forecast and realized metrics, often tied to targeting, timing, or creative constraints.

Risk management & guardrails

Marketing spends, like a portfolio, aggregates position-level risks. Guardrails, such as budget caps, pause thresholds (e.g., a customer acquisition cost level sustained over several days), time boxes, and brand-safety filters; define the acceptable risk envelope before execution begins.

Experimentation discipline

Attribution depends on isolating variables. Changing a single factor at a time and documenting a brief hypothesis, metric, result, and follow-up preserves causal clarity. Clean experimentation produces forecasts that map more directly into credible budgets.

Marketing and the economy

Marketing is more than ads or catchy lines. It is how useful ideas travel from creators to people who need them. When a product’s promise is explained in simple words, what it is, who it helps, and why it’s better, adoption speeds up. Faster adoption of good solutions raises productivity for everyone: households save time and money, and companies run more efficiently. New products often fail because no one understands them; good marketing teaches the market about the problem, the solution, and the proof. Clear, repeated messaging shortens the education curve and helps innovations become normal faster.

Case study: Bolletje, an internal marketing project

Last summer, I was employed by a Dutch company named Bolletje for an internal marketing task: how to communicate the standards of the company to all employees, to increase the quality of all products made, and to reduce waste by giving clear guidelines and instructions.

Logo of Bolletje.
Bolletje logo
Source: the company.

Company snapshot

Bolletje is a long-standing Dutch bakery brand best known for Beschuit (rusk), crackers/crispbread, and seasonal biscuits like kruidnoten, usually sold between September and December (for Sinterklaas, Dutch St-Nicolas). The brand’s roots trace back to the 19th century; today, it operates from Almelo in the east of the Netherlands. Beyond rusks, Bolletje’s range spans everyday “bread replacers” Dutch consumers keep in the pantry, as well as sweet treats. In 2013, Bolletje joined Germany’s Borggreve group.

Selected Bolletje products.

Bolletje logo
Source: the company.

My task (more depth)

My task, very concretely, was to design a packaging norm sheet, a clear, visual reference displayed for all factory employees on the production floor. The goal was twofold: first, to help operators correctly adjust the different types of packaging machines they use every day; second, to make sure everyone shares the same understanding of the quality standards expected from a brand that is widely recognized in the country for its high quality. The sheet set out, in simple terms and with pictures where useful, what “good” looks like for each product and pack, so that a worker can quickly check settings, compare what they see in hand to the standard, and correct issues before they become waste.

Just as important, the norm sheet explained when a product must be rejected and why. For example, if a seal is incomplete, a label is misaligned, or a pack is damaged, even if the food inside seems fine. For each type of defect, it also included a short “what to do next” section, describing the remediation steps to fix the root cause: which knob to adjust, which sensor to clean, which film tension to change, or when to call a line leader or maintenance. By making the decision rules explicit (keep, rework, or discard) and by linking each rule to a practical fix, the sheet helped reduce both food waste and packaging waste. In short, it turned quality standards into everyday actions: the right settings up front, faster problem detection, smarter corrections, and fewer products thrown away.

What I learned

I learned that clarity beats volume. People don’t need a thick manual; they need one clear page that shows exactly what “good” looks like. When the standards are written in plain words and supported by photos, operators can check, adjust, and move on without guessing. Because the company employs some foreign workers, photos and simple phrases were far more helpful than complex written instructions. Putting the norm sheet at the point of work, right next to the machine, also matters. If the guide is visible where decisions happen, it actually gets used.

I also saw that rules work better when they include the reason, not just the instruction. The “why” increases compliance. Alongside that, making the choices explicit (keep, rework, or discard) reduces hesitation. For each defect, pairing the decision with a short fix (adjust heat, clean the sensor, change film tension, call maintenance) turns standards into action and cuts waste.

Another lesson was to build the standard with the people who use it. Operators and line leaders know the real problems and edge cases. Co-creating the sheet with them made it more accurate and kept it alive after my project ended. Small visuals were surprisingly powerful: a couple of photos of correct and incorrect packs removed long debates on the line, sped up decisions, and reduced stoppages.

Measurement closed the loop. Tracking a few simple indicators and the most common defect types showed where the process truly struggled and which fixes worked. Training also worked best in the flow of work: two-minute huddles at the machine were more effective than long classroom sessions far from the line, because people could apply the information immediately.

Finally, I learned the importance of small details, and the importance in general of having as much information as possible. One example of a small detail was that products could have lower quality just because of one small change in the quality of the ingredients, like having less protein in the flour bought, or the heat of the oven not being perfectly evenly distributed. Those small details, those small pieces of information, can cause great change in the perception consumers might have over a company, changing, of course, the perception investors will have of it. To conclude, many people in the financial industry claim that the stock market is uncertain, changing without apparent reason. I would reply that maybe the information wasn’t used well enough, or that we didn’t look for it carefully enough. Like a butterfly effect, one very small event can cause great damage to the financial structure of the company. For example, a person with influence online could have an unlucky experience with your company, and by talking about it and by rumors, a company could suffer greatly.

Closing: how the SimTrade habits transfer

I took SimTrade to practice decisions under pressure. The habits I use every day now are simple: define entry conditions before spending, set guardrails to control risk, measure the gap between plan and reality, and write short post-mortems so the team learns fast. Those same habits made my factory-floor project calmer, clearer, and more effective, and they make marketing outcomes easier for finance to trust.

Find related posts on the SimTrade blog

   ▶ All posts about Professional experiences

   ▶ Alexandre VERLET Classic brain teasers from real-life interviews

Useful resources

bolletje Company’s website

About the author

The article was written in January 2026 by Guylan ABBOU (ESSEC Business School, Global Bachelor’s in Business Administration (GBBA) – Exchange Student, 2025).

   ▶ Discover all articles by Guylan ABBOU

From IAS to IFRS: How International Accounting Standards Shape Financial Reporting

by
Maxime PIOUX

In this article, Maxime PIOUX (ESSEC Business School, Global Bachelor in Business Administration (GBBA) – 2022-2026) explains the importance of international accounting standards and highlights the key differences that finance and business students should be aware of.

Why International Accounting Standards

Financial statements are the primary source of information used by investors, managers, and other stakeholders to assess a company’s financial position and performance. However, without common accounting rules, it would be difficult to compare the results of two companies operating in different countries and industries. International accounting standards were developed to address this challenge.

In a context of globalization in financial markets, international accounting standards aim to harmonize accounting practices in order to ensure better comparability between companies regardless of their country or sector. These rules also play a key role in financial transparency. By defining how transactions should be recorded, measured, and presented, they enhance transparency and reduce information asymmetries (situations in which some parties, such as investors, have less information than others about a company’s actual financial situation).

Finally, international accounting standards help improve the quality of financial reporting by imposing disclosure requirements in the financial statements and their notes. These guidelines therefore provide more reliable and consistent financial information, facilitating economic decision-making and strengthening market confidence, as highlighted by Richard Grasso, former Chairman of the NYSE (New York Stock Exchange, the main American stock exchange), “It should strengthen investors’ confidence. This is done through transparency, high quality financial reports, and a standardized economic market.”

IAS: First International Accounting Standards and reference framework

The first international accounting standards to emerge were the IAS (International Accounting Standards), developed from 1973 by the International Accounting Standards Committee (IASC). This international organisation, composed of representatives from multiple countries, was responsible for developing accounting rules applicable worldwide by proposing a common accounting framework.

The IAS were created to meet the needs of investors and markets for reliable, transparent, and consistent information. They cover numerous areas and provide detailed rules on how to account for and present financial transactions and events. Initially, they primarily concerned multinational companies and listed entities seeking to publish financial statements comparable internationally. At the beginning, their application was often voluntary, but some jurisdictions gradually required their adoption.

IFRS: the emergence of a modern international accounting framework

In 2001, the International Accounting Standards Board (IASB) replaced the IASC, representing a significant shift with the former committee. While the IASC focused mainly on developing voluntary standards to harmonize accounting practices, the IASB introduced a more structured, rigorous, and coherent framework, with a mission to supervise and continuously develop international standards in order to strengthen their adoption and credibility worldwide. The IFRS (International Financial Reporting Standards) were born from this process. Their primary objective is similar to that of the IAS: to improve the reliability and comparability of financial statements. However, IFRS go further by imposing a uniform framework with precise principles. They aim to provide a single accounting reference, ensuring that all relevant companies present their financial transactions and events transparently and in a standardized way.

Today, IFRS apply to a wide range of companies, mainly listed and multinational entities, but some countries have adopted them for all companies. In the European Union, for example, all listed companies must prepare their consolidated financial statements according to IFRS, while in other countries, such as the United States, IFRS may be applied voluntarily or for certain subsidiaries of international groups.

To better understand the purpose of IFRS, it is useful to remember three fundamental principles these standards adhere to:

  • Completeness: Financial statements must reflect the company’s entire activity and limit off-balance-sheet information.
  • Comparability: Financial statements are standardized and identical for all companies.
  • Neutrality: Standards should not allow companies to manipulate their accounts.

The application of these standards today

Today, IFRS constitute the main framework for international accounting standards, used in 147 countries (98% of European countries and 92% of Middle Eastern countries). Some IAS, developed before 2001, continue to apply (such as IAS 1 on the presentation of financial statements) as long as they have not been replaced by an equivalent IFRS.

In France, the application of IFRS is mandatory for all listed companies, particularly for the preparation of their consolidated financial statements. Large unlisted companies and certain mid-sized enterprises can also choose to apply them in order to harmonize their international reporting, although this is not compulsory. In contrast, SMEs remain largely subject to the French General Accounting Plan (PCG “Plan Comptable Général”), which provides simplified rules suited to their size and structure.

Impact of IFRS

The impacts of IFRS on companies have been numerous and have varied by industry. However, overall, these impacts have remained relatively limited. For instance, according to a FinHarmony study on the transition to IFRS, the equity of CAC 40 companies changed by only 1.5%.

Three IFRS standards that have led to significant changes in corporate accounting are presented below.

IFRS 16: Leases in the Balance Sheet

Before the introduction of IFRS 16 in January 2019, the accounting treatment of leases was governed by IAS 17 (leases). This standard distinguished between two types of leases:

  • Finance leases, for example when a company leases a machine with a purchase option, for which the company recognized an asset corresponding to the leased item and a liability corresponding to future lease payments.
  • Operating leases, for example when a company rents office space, which were recorded as expenses in the income statement and remained off-balance-sheet.

With IFRS 16, this distinction disappears for most leases: now, all leases must be recognized in the balance sheet as a “right-of-use” asset and a lease liability. The only exceptions are short-term leases (less than 12 months) or leases of low-value assets (less than 5,000 USD). This reform aims to improve the transparency and comparability of financial statements by reflecting all lease obligations on the balance sheet.

As a result, companies with numerous operating leases, such as retail chains or airlines, have seen their assets and liabilities increase significantly, thereby affecting certain financial ratios and indicators (such as debt-to-assets or EBITDA).

Let’s take the example of an airline that leases 10 aircraft under operating lease contracts, with a total annual rent of €10 million over a 10-year period. The company generates revenue of €500 million, an EBITDA of €100 million, and has debt of €250 million.

  • Before IFRS 16, these contracts were classified as operating leases, with an annual lease expense of €10 million recorded in the income statement and no recognition on the balance sheet, despite this significant long-term financial commitment.
  • With IFRS 16, the company must now recognize a right-of-use asset on the balance sheet (corresponding to the present value of future lease payments) along with a lease liability of the same amount. Assuming a discount rate of 2%, the present value of the lease payments over 10 years is approximately €90 million, recorded as both an asset and a liability.
    In the income statement, the lease expense is replaced by depreciation expenses on the right-of-use asset and interest expenses on the lease liability.

The EBITDA, which excludes depreciation and interest, therefore increases to €110 million, compared to €100 million under the previous treatment. The former annual lease expense of €10 million no longer affects EBITDA because it has been replaced by depreciation and interest. However, the apparent leverage increases significantly, as the lease liability rises by €90 million (from €250 million to €340 million). Consequently, the debt-to-EBITDA ratio, for example, moves from 2.5 (250/100) to 3.1 (340/110), which can affect the perception of investors and banks.

This example illustrates that the increase in EBITDA and debt results from a change in accounting standards rather than a real improvement in the company’s economic performance.

IFRS 13: Historical Cost vs Fair Value

A significant change introduced by IFRS 13 in January 2013 concerns the measurement of assets and liabilities. Indeed, under certain IAS and in many national practices, assets were often recorded at historical cost, meaning their original purchase price.

By contrast, IFRS 13 promotes the concept of fair value, which represents the price at which an asset could be sold in a market at the closing date.

Fair value accounting can lead to significant fluctuations in the balance sheet and income statement, particularly for companies holding financial assets, securities, or significant real estate, as it reflects market variations. Companies in sectors such as finance, real estate or hotel industry may thus see their balance sheets and financial ratios change from one period to another, reflecting market realities. However, this approach provides a more realistic and transparent view of the financial situation.

Let’s take the example of a real estate group that owns a portfolio of buildings recorded at a historical cost of €500 million. In other words, the total purchase price of all the group’s buildings amounts to €500 million, whether they were acquired recently or several years ago. The company also has a bank debt of €200 million.

  • Before IFRS 13, the buildings were recorded under “property, plant, and equipment” in non-current assets at their historical cost of €500 million, regardless of changes in the real estate market. Equity and financial ratios therefore reflected this fixed value, without taking market fluctuations into account.
  • With the application of fair value as defined by IFRS 13, buildings are now valued at their market value at the reporting date. This fair value corresponds to the price at which the asset could be sold under normal market conditions and is generally estimated using real estate appraisals or comparable transactions.

Let’s assume that the current market value of the portfolio is €600 million. The balance sheet increases by €100 million in assets and equity. In practice, this revaluation directly affects certain financial ratios. For example, the debt-to-equity ratio decreases from 0.4 (200/500) to 0.33 (200/600). Investors and banks then perceive the company as less leveraged and with a larger asset base, even though the company’s actual operating activity has not changed.
By contrast, if the market value drops to €400 million, equity decreases by €100 million, and the debt-to-equity ratio rises from 0.4 to 0.5 (200/400), which could negatively affect the perceived risk of the company.

This example illustrates that fair value accounting more accurately reflects the current economic situation of assets, but leads to visible fluctuations in the balance sheet and financial ratios.

IFRS 15: Revenue from Contracts with Customers

IFRS 15, which came into effect in January 2018, replaced IAS 18 (Revenue) and IAS 11 (Construction Contracts), introducing a single and standardized approach to revenue recognition.

Before IFRS 15, revenue was recognized differently depending on its nature:

  • Under IAS 18, revenue from goods was recognized at delivery, and revenue from services was recognized at the time they were performed.
  • Under IAS 11, revenue from construction contracts was recognized over time based on the percentage of completion of the project.

With IFRS 15, revenue recognition is based on a single principle: the transfer of control of the good or service to the customer, regardless of physical delivery. In other words, revenue is recognized when the customer obtains control of the good or service. In practical terms, this means:

  • For goods sold, revenue is recognized when the customer can use the item and benefit economically from it.
  • For services (subscriptions or IT services for instance), revenue is recognized progressively as the service is provided, in proportion to the progress or consumption by the customer, rather than at the end of the contract or at invoicing.
  • For construction contracts, revenue is allocated to each stage of the contract as the customer gains control of the corresponding performance.

This approach standardizes revenue treatment across all sectors and reduces discrepancies between companies and countries. IFRS 15 has changed the way companies record revenue in the income statement. Some transactions must now be spread over time, while others can be recognized more quickly, depending on when the customer obtains control of the good or service. The most affected sectors are construction, technology, telecommunications, and services. This standard therefore improves comparability and transparency of revenue, enabling investors and financial analysts to better understand a company’s actual economic performance.

Let’s take the example of a construction company that signs a contract to renovate a residential complex for a total amount of €50 million, over a period of 2 years. Let’s suppose the total estimated cost of the project is €20 million.

  • Before IFRS 15, revenue recognition could differ depending on the applicable standard: under IAS 11, revenue was generally recognized progressively based on the percentage of completion of the project, but some companies could wait until invoicing or delivery to record revenue. This could lead to divergent practices, for example recognizing revenue too early to artificially improve performance, or on the contrary, postponing revenue to smooth results.
  • With IFRS 15, revenue recognition is based on the unique principle of transfer of control to the customer. In practice, this means that the company must recognize revenue as the customer obtains control of the work performed, even if payment has not yet been received.

Let’s assume that, at the end of the first year, 60% of the work is completed and the customer can use this part of the complex: the company will then record €30 million of revenue (60% of the total contract) in its income statement, and the corresponding costs of €12 million (60% of the project costs). The net profit for this part of the project is therefore €18 million (30 – 12).
On the balance sheet, assets increase by €30 million: in cash if the customer has already paid, or in accounts receivable if payment has not yet been received. Equity increases by €18 million, corresponding to the net income from this portion of the project. On the liabilities side, a trade payable of €12 million is recorded, corresponding to costs incurred but not yet paid. This debt will disappear when the company pays its suppliers, reducing cash and maintaining the balance sheet equilibrium.

This approach allows the financial statements to more accurately reflect the economic reality of the contract and makes results more transparent for investors. Without this method, revenue for the first year could have been zero, thus hiding the true performance of the project.

What about US GAAP ?

In addition to IFRS, there are also US GAAP (Generally Accepted Accounting Principles), which constitute the accounting framework used in the United States (US). US GAAP are mandatory for all U.S. listed companies, as IFRS are not permitted for the preparation of financial statements of domestic companies. However, foreign companies listed in the United States may publish their financial statements under IFRS without reconciliation to US GAAP.

US GAAP have existed since 1973 and are developed by the Financial Accounting Standards Board (FASB). They are based on a more rules-based approach, with a much larger volume of standards and interpretations than IFRS, often estimated at several thousand pages (compared with only a few hundred pages for IFRS). This approach reduces the degree of judgment and interpretation but makes the framework more complex.

Why should I be interested in this post?

Understanding the differences between IAS and IFRS standards is essential for any student in finance, accounting, auditing, or corporate finance who wishes to pursue a career in finance. International accounting standards directly influence how companies present their financial performance, measure their assets and liabilities, and communicate with investors. Mastering these concepts makes it easier to read and understand financial statements and to develop a more critical view on a company’s actual performance.

Related posts on the SimTrade blog

   ▶ Samia DARMELLAH My experience as an accounting assistant at Dafinity

   ▶ Louis DETALLE A quick review of the accountant job in France

   ▶ Alessandro MARRAS My professional experience as a financial and accounting assistant at Professional Services

   ▶ Louis DETALLE A quick review of the Audit job

Useful resources

IFRS

FASB

US GAAP vs IFRS

YouTube IFRS 16

YouTube IFRS 13

YouTube IFRS 15

Academic resources

Colmant B., Michel P., Tondeur H., 2013, Les normes IAS-IFRS : une nouvelle comptabilité financière Pearson.

Raffournier B., 2021, Les normes comptables internationales IFRS, 8th edition, Economica.

Richard J., Colette C., Bensadon D., Jaudet N., 2011, Comptabilité financière : normes IFRS versus normes françaises, Dunod.

André P., Filip A., Marmousez S., 2014, L’impact des normes IFRS sur la relation entre le conservatisme et l’efficacité des politiques d’investissement, Comptabilité Contrôle Audit, Vol.Tome 20 (3), p.101-124

Poincelot E., Chambost I., 2015, L’impact des normes IFRS sur les politiques de couverture des risques financiers : Une étude des groupes côtés en France, Revue française de gestion, Vol.41 (249), p.133-144

About the author

The article was written in February 2026 by Maxime PIOUX (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2022-2026).

   ▶ Read all articles by Maxime PIOUX.

My internship as a Junior Financial Auditor at KPMG

by
Maxime PIOUX

In this article, Maxime PIOUX (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2022-2026) shares his professional experience as a junior financial auditor at KPMG.

About the company

KPMG is an international audit and advisory firm founded in 1987, operating in more than 145 countries and employing over 275,000 professionals worldwide. It is part of the Big Four, alongside Deloitte, PwC and EY, which represent the leading global players in audit and advisory services.

The KPMG network supports organizations of all sizes, from small and medium-sized enterprises to large international groups, as well as public sector institutions. Its activities are primarily structured around three core business lines: audit, advisory, and accounting and tax services. Audit represents a central pillar of the firm, playing a key role in the reliability of financial information and in maintaining investor confidence in financial markets. In addition, KPMG has expanded its expertise into areas such as artificial intelligence, digital transformation, risk management and innovation, in order to address the evolving challenges of the contemporary economic environment.

In 2024, KPMG International generated revenues of USD 38.4 billion, distributed across advisory (42.5%), audit (35%), and tax and legal services (22.5%). In France, the firm reported revenues of EUR 1.55 billion, representing approximately 4% of global revenues.

Finally, KPMG became a mission-driven company in 2022, with the objective of contributing to a more sustainable and responsible form of prosperity by integrating social, environmental and ethical considerations into its activities.

Logo of KPMG.
Logo of KPMG
Source: KPMG

My internship

I completed a six-month internship at KPMG Audit, in the Consumer, Media & Telecommunications (CMT) Business Unit. This department is key and dynamic within the firm, bringing together a significant number of partners and professionals specialized in audit engagements for companies operating in these sectors. Due to the size and diversity of its client portfolio, I have worked with different teams for companies of various sizes and with different business models.

A specific feature of working within an audit firm such as KPMG is the dual work environment, which combines assignments carried out directly at clients’ premises and tasks performed at KPMG’s offices, located at the Eqho Tower in La Défense. This organization facilitates better interaction with client teams while providing a collaborative working environment.

My missions

The tasks assigned to me were those typically entrusted to a junior auditor. They mainly consisted of internal control testing, which represents a core responsibility at the junior level and involves designing and formalizing controls, collecting information from client teams, and documenting the results in audit working papers. I worked across all audit cycles, with a particular focus on operating expenses (OPEX), revenues and fixed assets. I also participated in analytical reviews, aimed at analyzing the company’s business activity over a financial year, as well as impairment tests, which involved identifying and proposing potential accounting adjustments to clients. Finally, I was also asked to suggest improvements and automation solutions for Excel files used in certain time-consuming audit procedures, with the objective of smoothing audit work and improving overall efficiency.

Required skills and knowledge

Working in audit requires both strong technical skills and behavioural qualities suited to a demanding environment. At the beginning of an internship, it is essential to demonstrate commitment, rigor, and patience, as some tasks assigned to junior staff can be repetitive but are crucial to the proper execution of audit engagements, particularly tick-and-tie procedures and internal control testing. These initial assignments represent a key step in the learning process and provide an opportunity to demonstrate professionalism, reliability and work quality, which subsequently determines access to more stimulating and higher value-added tasks.

From a hard skills perspective, strong proficiency in Excel is essential, as this tool is used daily to analyze, structure, and process financial data. Solid foundations in financial accounting and a good understanding of financial statements are also required. Rigor in the preparation of clear, well-structured, and well-documented working papers is critical, as these documents constitute the core support of audit work.

In terms of soft skills, flexibility and adaptability are key. Junior auditors are required to work with different teams, on multiple engagements sometimes in parallel, and to adapt to new tools and software, whether internal to the firm or client specific. Communication is also essential, particularly to keep his in-charge informed of the progress of the work. Finally, a strong willingness to learn, commitment, and a sense of responsibility are essential qualities for progressing quickly in such a demanding environment.

What I learned

Audit is a particularly formative field, allowing to develop a rigorous work methodology and processes applicable in many professional environments. During my internship, I first developed strong technical and analytical skills. I used Excel and the firm’s internal workflows on a daily basis to document and report audit work. I also occasionally used tools such as SAP or BFC during client missions.

Beyond technical skills, this experience taught me how to structure my reasoning and develop a critical mindset when analyzing financial information. Audit work required me to question the numbers, understand their origin, and analyze their consistency across different cycles.

The internship also allowed me to develop essential professional and interpersonal skills, such as rigor, adaptability and team spirit. Working within different teams and on multiple missions taught me how to organize myself efficiently, manage priorities, and perform effectively in demanding periods, particularly during phases of high intensity related to the finalization of audit work before the signing and certification of the accounts.

Audit concepts related to my internship

I present below three concepts related to my internship:

The central role of training

I was impressed by the importance placed on training at KPMG. Every employee, regardless of their level, begins their journey with an intensive one-week training, followed by several days of online modules and numerous e-learnings throughout the year. For instance, during my internship, in addition to the initial training week for interns, I completed around ten e-learning modules over the six months, which enabled me to deepen my technical and regulatory knowledge while familiarising me with the company’s expectations. These trainings cover technical skills, such as accounting standards, obligations for listed companies, as well as ethics and compliance rules. Additional sessions are also provided at each promotion to further deepen knowledge and skills.

Completing these trainings is considered as important as the quality of daily work. In cases of repeated delays or missed deadlines, an employee’s bonus may be adjusted downwards, illustrating how seriously KPMG takes the continuous development of its teams. This constant focus on training is part of the firm’s strategy to maintain excellence in the quality of its work and to remain a trusted partner for its clients.

Completing these trainings is considered as important as the quality of daily work. In cases of repeated delays or missed deadlines, an employee’s bonus may be adjusted downwards, illustrating how seriously KPMG takes the continuous development of its teams. This constant focus on training is part of the firm’s strategy to maintain excellence in the quality of its work and to remain a trusted partner for its clients.

Audit Methodology

Another key aspect of my internship was the audit methodology. Each firm has its own methodology, a set of systematic procedures and steps that every employee must follow to analyze and evaluate a company’s financial statements. This approach ensures that the work is carried out rigorously, consistently, and in compliance with professional standards.

The methodology covers all phases of the audit, from planning to analyzing the results obtained, including risk assessment, sample selection, and the performance of tests. It allows auditors to gather sufficient and relevant evidence to form a reliable opinion on the accuracy and compliance of the financial statements. During my internship, I learned to systematically refer to it in order to organize my work and ensure that each step was properly followed.

Each firm also implements internal workflows to structure and document all work performed on an engagement. These workflows allow the harmonization of work conclusions among different team members, ensuring the consistency and clarity of the entire audit file.

The control approach

In audit, several types of approaches can be adopted, including the balance sheet approach, the systems-based approach, and the control approach. Each approach offers a structured method for identifying risks, testing transactions and ensuring that the accounts accurately reflect the company’s financial position. The choice of approach depends on the auditor’s professional judgement, the size and complexity of the company, the level of internal control in place and, in some cases, a combination of several approaches is used to best suit the engagement. During my internship, all the engagements I worked on were performed using the control approach. This method consists of assessing the effectiveness of the company’s internal procedures and controls to reduce the risk of errors or misstatements in the financial statements. In fact, the auditor determines the sample size to be tested in order to obtain a sufficient level of assurance without having to check all transactions. The sample size depends on the risk of significant misstatements, the materiality threshold, the nature of the tests performed, and the characteristics of the population being audited. This approach allows the collection of reliable audit evidence while optimizing the time and resources required for the audit.

For example, if an internal control is performed monthly (12 occurrences) by a company and the risk of misstatement is considered normal by the auditor (“base risk”), the methodology will indicate the number of occurrences to test in that specific situation (for example 5 instead of testing all 12 occurrences).

Why should I be interested in this post?

Audit is a particularly interesting option for student wishing to pursue a career in finance. It allows you to develop a rigorous work methodology, strong organizational skills, and a deep understanding of financial statements and accounting mechanisms. Working with multiple clients across different sectors also enhances open-mindedness, flexibility, and the ability to quickly adjust to various situations; qualities that are highly valued in corporate finance, consulting, or M&A roles.

Moreover, an increasing number of M&A and Transaction Services firms seek candidates with audit experience to ensure they have solid foundations (technical, analytical and professional skills). For these reasons, considering an internship or apprenticeship in audit is not only intellectually rewarding, but can also open many doors for a future career in finance.

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   ▶ Annie YEUNG My Audit Summer Internship experience at KPMG

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   ▶ Louis DETALLE A quick review of the Audit job…

Useful resources

About KPMG and the consulting sector

KPMG

Financial Times KPMG tax business pushes firm to faster growth than Big Four rivals

FinTech Magazine KPMG: What can Uniphore bring to financial services ?

Les Echos Concurrence : soupçons d’entente chez les géants de l’audit

Le Figaro (2025) Pourquoi les cabinets d’audit recrutent-ils désormais des ingénieurs ?

Academic resources

Appercel R., 2022, Audit et contrôle interne

Boccon-Gibod S., Vilmint E., 2020, La boite à outils de l’auditeur financier

About the author

The article was written in February 2026 by Maxime PIOUX (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2022-2026).

   ▶ Discover all articles by Maxime PIOUX.

Discovering Financial Controlling within a Media Group

by
Maxime PIOUX

In this article, Maxime PIOUX (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2022-2026) shares his professional experience as a financial controller assistant at Altice Media.

About the company

Altice Media was a major French media group owned by the Altice Group, founded and controlled by billionaire Patrick Drahi. The group operated across television, radio, and digital media, gathering some of the most important brands in the French audiovisual landscape, including BFM TV, BFM Business, RMC, and RMC Sport. Through these channels, Altice Media played a central role in continuous diffusion of economic, politic and sport news and content, addressing a wide audience.

In July 2024, Altice Media was sold at 100% to the French shipping and logistics group CMA CGM, led by its CEO Rodolphe Saadé, for an estimated amount of €1.5 billion. This acquisition marked CMA CGM’s ambition to diversify its activities beyond transport and logistics, notably by strengthening its presence in the media and information sector.

Logo of Altice.
Logo of Altice
Source: Altice

My internship

I completed a three-month operational internship within the Finance and Administration Department of Altice Media, more specifically in the central management control team. This department plays a key role in monitoring the group’s financial performance and provides essential support for decision-making, particularly by tracking results, analyzing variances, and consolidating data from the different entities.

I worked within the central team, collaborating directly with the two management controllers responsible for consolidating the figures of all the group’s subsidiaries before they were reported to the Chief Financial Officer (CFO), then to the group’s executive management and the shareholder. This position offered a comprehensive view of the performance of the group’s various entities and allowed me to understand how the consolidated data was used in reporting to both the finance department and the shareholder.

My missions

This internship gave me a practical understanding of the role of a management controller and allowed me to participate in a wide range of tasks. My main responsibilities were focused on monthly closing activities, including updating financial reporting, analyzing variances between actual and budgeted figures, performing intra-group reconciliations, and integrating certain companies not yet included in the reporting systems.

In a context of understaffing due to high turnover within the department, I quickly gained autonomy and was entrusted with more challenging tasks, such as participating in reforecasting exercises for two entities, building tracking dashboards, and preparing summary presentations for the Finance Department and Group Management.

In parallel, I contributed to various ad hoc assignments for the Finance Department, such as weekly analysis of unpaid invoices and updating regulated agreements.

Required skills and knowledge

This internship required me to mobilize a wide range of skills. On the hard skills side, proficiency in Excel was essential, as it is the main tool used daily by the management controller. It was also necessary to be flexible and able to quickly learn how to use new financial software such as SAP, an Enterprise Resource Planning (ERP) system, which centralizes and automates the main processes of a company, including accounting and financial transactions. The use of Hyperion was also required: this financial performance management tool is commonly used for budgeting, forecasting and consolidated reporting, and is often directly connected to Excel. Finally, being comfortable with numbers is strongly recommended to succeed in this type of role.

On the soft skills side, rigor and organization were crucial to deliver accurate data for the Finance Department and the management teams of the different entities. A management controller must also demonstrate strong communication and collaboration skills, as the role involves constant interaction with operational teams as well as with the finance departments of the various entities in order to collect, monitor, and analyze financial information.

What I learned

This immersion in the world of finance allowed me to gain a better understanding of the day-to-day operations of a Finance Department within a multi-entity group. I discovered the role of a management controller through the key processes that structure this function, notably monthly closing, consolidated financial reporting, and reforecasting work, which then serve as a basis for performance analysis and strategic decision-making.

I was also exposed to challenges related to financial consolidation, a complex area that requires both strong technical skills and a high level of rigor. I was able to understand the importance of adjustments, intra-group reconciliations, and data consistency in order to produce reliable financial information that can be effectively used by management.

Financial concepts related to my internship

I present below three concepts related to my internship:

Budget and Reforecast

Budgeting and reforecasting are essential tools in management control for anticipating and driving a company’s financial performance. On the one hand, the budget corresponds to a projection of expected financial results over a given period (generally one year) and serves as a benchmark against which actual performance is measured. The process begins with numerous discussions between the management controller and operational teams in order to understand business needs, identify potential cost savings, and estimate revenue. This information is then consolidated and analyzed by the Finance Department before being submitted to Group Management for review and comments, and ultimately validated by the shareholder.

On the other hand, reforecasting, consists of updating these projections during the year by incorporating actual data and changes in business activity or market conditions. These exercises are generally carried out on a monthly basis and allow management to anticipate the year-end outcome (an estimate of final performance at the end of the year). In practice, this work is often performed using Excel, with the support of financial software directly connected to Excel, such as Hyperion, in order to quickly consolidate data from the various entities and monitor performance against targets.

Investment Decisions (CAPEX)

Investment decisions, or CAPEX (Capital Expenditures), are a core pillar of management control and financial strategy, as they enable a company to finance strategic projects while maintaining control over its resources. These expenditures are essential for growth and long-term competitiveness, as they allow the company to renew equipment, develop new activities, or improve operational efficiency: “Wealth generation requires investments, which must be financed and be sufficiently profitable” From Vernimmen, Corporate Finance, 6th edition.

The process generally begins with the identification of needs and projects by operational teams, who define the objectives, estimated costs, and expected impact on the business. The management controller then assesses the financial relevance of each project by evaluating the return on investment, the financing plan, and potential cost savings. These proposals are subsequently submitted to the Finance Department and then to Group Management for strategic validation, before being approved by the shareholder when amounts are significant (approval thresholds are defined within each company).

CAPEX is monitored throughout the year, as shareholders typically pay close attention to these expenditures. Indeed, in certain circumstances, it may be tempting to reclassify OPEX as CAPEX in order to artificially improve the company’s financial presentation, which makes strict monitoring essential.

Workforce Cost Control

Payroll cost management is another central aspect of management control, as it enables the company to monitor one of its main expenses while ensuring that human resources are used effectively to support strategy and operational performance. This process involves collecting workforce data from the Human Resources department on a monthly basis, then analyzing costs, identifying potential variances compared to the budget, and anticipating changes in payroll expenses based on operational needs, new hires, departures, or salary adjustments.

Effective payroll cost control is crucial to maintaining the company’s competitiveness and profitability. This is why it is closely monitored by management and shareholders to avoid any cost overruns or financial imbalances.

Why should I be interested in this post?

A position in management control is an excellent opportunity for any finance student looking to become familiar with corporate financial management and performance monitoring. It allows the development of strong technical skills, particularly in financial analysis, while also strengthening essential soft skills such as rigor, organization, and communication. This type of role also provides a comprehensive view of a company’s operations, as it involves close collaboration with all departments. Finally, working in management control is formative and can serve as a stepping stone toward careers in corporate finance, internal audit, or consulting.

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   ▶ Emma LAFARGUE Mon expérience en contrôle de gestion chez Chanel

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Useful resources

About Altice

Altice

Acquisition de la branche media du groupe Altice par CMA CGM : l’Autorité de la concurrence conditionne la réalisation de l’opération à des engagements

Le rachat d’Altice Media, maison mère de BFMTTV et RMC, par l’armateur CMA CGM est finalisé

CMA CGM acquiert Altice Media, propriétaire de BFMTV : les détails de l’accord

Financial and management techniques

Vernimmen P., 2022, Corporate Finance, 6th edition

Alcouffe S., Boitier M., Rivière A., Villesèque-Dubus F., 2013, Contrôle de gestion sur mesure : industrie, grande distribution, banque, culture, secteur publique

Cappelletti L., Baron P., Desmaison G., Ribiollet F., 2014, Contrôle de gestion

About the author

The article was written in February 2026 by Maxime PIOUX (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2022-2026).

   ▶ Discover all articles by Maxime PIOUX.

January 2026: Most Read Posts on the SimTrade Blog

by

Top Most Read Finance Articles on the SimTrade Blog

Based on WordPress statistics, the following ranking presents the five most read articles on the SimTrade blog in January 2026. These posts cover key topics in financial markets, quantitative finance, risk management, derivatives pricing, and macroeconomic analysis.

   ▶ Anant JAIN Top 12 FMCG Companies Worldwide: Growth, Market Share, and Investment Opportunities

   ▶ Federico DE ROSSI Understanding the Order Book: How It Impacts Trading

   ▶ Alessandro MARRAS Top 5 Private Equity firms

   ▶ Anant JAIN The Ongoing Hyperinflation In Turkey And Its Ripple Effects On European Union

   ▶ Akshit GUPTA Analysis of the Margin Call movie

SimTrade Editorial Picks in Quantitative Finance and Corporate Finance

In addition to the most read posts, I highlight the following articles for their strong educational value in quantitative finance, corporate finance, and financial risk modeling.

   ▶ Saral BINDAL Implied Volatility and Option Prices

   ▶ Michel VERHASSELT Difference between market profile and volume profile

   ▶ Alberto BORGIA EBITDA: Uses, Benefits and Limitations

Measures and statistics of business activity in global derivative markets

by
Saral BINDAL

In this article, Saral BINDAL (Indian Institute of Technology Kharagpur, Metallurgical and Materials Engineering, 2024-2028 & Research assistant at ESSEC Business School) explains how the business of derivatives markets has evolved over time and the pivotal role of the Black–Scholes–Merton option pricing model in their development.

Introduction

The derivatives market is among the most dynamic segments of global finance, serving as a tool for risk management, speculation, and price discovery across diverse asset classes. Spanning from bespoke over-the-counter contracts to standardized exchange-traded instruments, derivatives have become indispensable for investors, institutions, and corporations alike.

This post explores the derivatives landscape, examining market structures, contract types, underlying assets, and key statistics of business activity. It also highlights the pivotal role of the Black–Scholes–Merton model, which provided a theoretical framework for options pricing and catalysed the growth of derivatives markets.

Types of derivatives markets

The derivatives market can be categorized according to their market structure (over-the-counter derivatives and exchange-traded derivatives), the types of derivatives contracts traded (futures/forward, options, swaps), and the underlying asset classes involved (equities, interest rates, foreign exchange, commodities, and credit), as outlined below.

Market structure: over-the-counter derivatives and exchange-traded derivatives

Over-the-counter derivatives are privately negotiated, customized contracts between counterparties like banks, corporates, and hedge funds, traded via phone or electronic networks. OTC derivatives offer high flexibility in terms (price, maturity, quantity, delivery) but are less regulated, with decentralized credit risk management, no central clearing, low price transparency, and higher counterparty risk. They suit specialized or low-volume trades and often incubate new products.

Exchange-traded derivatives are standardized contracts traded on organized exchanges with publicly reported prices. Trades are cleared through a central clearing house that guarantees settlement, with daily marking-to-market and margining to reduce counterparty risk. ETDs are more regulated, transparent, and liquid, making them ideal for high-volume, widely traded instruments, though less flexible than OTC contracts.

Types of derivatives contracts

A derivative contract is a financial instrument that derives its values from an underlying asset. The four major types of such instruments are explained below.

A forward contract is a private agreement to buy or sell an asset at a fixed future date and price. It is traded over the counter between two counterparties (e.g., banks or clients). One party takes a long position (agrees to buy), the other a short position (agrees to sell). Settlement happens only at maturity, and contracts are customized, unregulated, and expose parties to direct counterparty risk.

A futures contract has the same economic purpose as a forward, future delivery at a fixed price, but is traded on an exchange with standardized terms. A clearing house stands between buyers and sellers and guarantees performance. Futures are marked to market daily so gains and losses are realized continuously. They are regulated, more transparent, and carry lower counterparty risk than forwards.

Options are contracts that give the holder the right but not the obligation to buy (call) or sell (put) an asset at a fixed strike price by a given expiration date. The buyer pays an upfront premium to the writer. If the option expires unexercised, the buyer loses only the premium. If exercised, the writer bears the payoff. Options can be American (exercise anytime) or European (exercise only at expiry) and are traded both on exchanges (standardized) and OTC (customized).

Swaps are bilateral contracts to exchange streams of cash flows over time, typically based on fixed versus floating interest rates or other reference indices. Payments are calculated on a notional principal that is not exchanged. Swaps are core OTC instruments for managing interest rate and financial risk.

Types of underlying asset classes

Underlying assets are the products on which a derivative instrument or contract derives its value. The most commonly traded underlying assets are explained below.

Equity derivatives include futures and options on stock indices, such as the S&P 500 Index. These instruments offer capital-efficient ways to manage market risk and enhance returns. Through index futures, institutional investors can achieve cost-effective hedging by locking in prices, while index options provide a non-linear, asymmetric payoff structure that protects against tail risk. Furthermore, equity swaps allow for the seamless exchange of total stock returns for floating interest rates, providing exposure to specific market segments without the capital requirements of direct physical ownership.

Interest rate derivatives include swaps and futures that help manage interest rate risk. Interest rate swaps involve exchanging fixed and floating payments, protecting banks against mismatches between loan income and deposit costs. Interest rate futures allow investors to lock in future borrowing or investment rates and provide insight into market expectations of monetary policy.

Commodity derivatives hedge price risk arising from storage, delivery, and seasonal supply-demand fluctuations. Forwards and futures on crude oil, natural gas, and power are widely used.

Foreign exchange derivatives include forward contracts and cross-currency swaps, allowing firms to hedge currency risk. Cross-currency swaps also support local currency bond markets by enabling hedging of interest and exchange rate risk.

Credit derivatives transfer the risk of default between counterparties. The most widely used is the credit default swap (CDS), which acts like insurance: the buyer pays a premium to receive compensation if a reference entity default.

Quantitative measures of derivatives market activity and size

This section presents the principal measures or statistics used to evaluate the size of the derivatives markets, covering both over-the-counter and exchange-traded instruments, the different derivatives products, and asset classes.

Notional outstanding and gross market value are the primary measures used to assess the size and economic exposure of OTC derivatives markets, while ETDs are typically evaluated using indicators such as open interest and trading volume.

Notional amount

Notional amount, or notional outstanding, is the total principal or reference value of all outstanding derivatives contracts. It captures the overall scale of positions in the derivatives market without reflecting actual market risk or cash exchanged.

For example let us consider a FX forward contract in which two parties agree to exchange $50 for euros in three months at a predetermined exchange rate. The notional amount is $50, because all cash flows (and gains or losses) from the contract are calculated with reference to this amount. No money is exchanged when the contract is initiated, and at maturity only the difference between the agreed exchange rate and the prevailing market rate determines the gain or loss computed on the $50 notional.

Now consider a call option on a stock with a strike price of $50. The notional amount is $50. The option buyer pays only an upfront premium, which is much smaller than $50, but the payoff of the option at maturity depends on how the market price of the stock compares to this $50 reference value.

When measuring notional outstanding in the derivatives market, the notional amounts of all individual contracts are simply added together. For example, one FX forward with a notional of $50 and two option contracts each with a notional of $50 result in a total notional outstanding of $150. This aggregated figure indicates the overall scale of derivatives activity, but it typically overstates actual economic risk because contracts may offset each other and only a fraction of the notional is ever exchanged.

Gross market value

Gross market value is the sum of the absolute values of all outstanding derivatives contracts with either positive or negative replacement (mark-to-market) values, evaluated at market prices prevailing on the reporting date. It reflects the potential scale of market risk and financial risk transfer, showing the economic exposure of a dealer’s derivatives positions in a way that is comparable across markets and products.

To continue the previous FX forward example, suppose a dealer has two outstanding FX forward contracts, each with a notional amount of $50. Due to movements in exchange rates, the first contract has a positive replacement value of $0.50 (the dealer would gain $0.50 if the contract were replaced at current market prices), while the second contract has a negative replacement value of –$0.40. The gross market value is calculated as the sum of the absolute values of these replacement values: |0.50| + |−0.40| = $0.90. Although the total notional outstanding of the two contracts is $100, the gross market value is only $0.90. This measure therefore reflects the dealer’s actual economic exposure to market movements at current prices, rather than the contractual size of the positions.

When this concept is extended to the entire derivatives market, the same distinction becomes apparent at a global scale. While the global derivatives market is often described as having hundreds of trillions of dollars in notional outstanding (approximately USD 850 trillion for OTC derivatives), the economically meaningful exposure is an order of magnitude smaller when measured using gross market value. Unlike notional amounts, gross market value aggregates current mark-to-market exposures, making it a more meaningful and comparable indicator of market risk and financial risk transfer across products and markets.

Open Interest

Open interest refers to the total number of outstanding derivative contracts that have not been closed, expired, or settled. It is calculated by adding the contracts from newly opened trades and subtracting those from closed trades. Open interest serves as an important indicator of market activity and liquidity, particularly in exchange-traded derivatives, as it reflects the level of active positions in the market. Measured at the end of each trading day, open interest is widely used as an indicator of market sentiment and the strength behind price trends.

For example on an exchange, a total of 100 futures contracts on crude oil are opened today. Meanwhile, 30 existing contracts are closed. The open interest at the end of the day would be: 100 (new contracts) − 30 (closed contracts) = 70 contracts. This indicates that 70 contracts remain active in the market, representing the total number of positions that traders are holding.

Trading Volume

Trading volume measures the total number of contracts traded over a specific period, such as daily, monthly, or annually. It provides insight into market liquidity and activity, reflecting how actively derivatives contracts are bought and sold. For OTC markets, trading volume is often estimated through surveys, while for exchange-traded derivatives, it is directly reported.

Consider the same crude oil futures market. If during a single trading day, 50 contracts are bought and 50 contracts are sold (including both new and existing positions), the trading volume for the day would be: 50 + 50 = 100 contracts

Here, trading volume shows how active the market is on that day (flow), while open interest shows how many contracts remain open at the end of the day (stock). High trading volume with low open interest may indicate rapid turnover, whereas high open interest with rising prices can signal strong bullish sentiment.

Key sources of statistics on global derivatives markets

Bank for International Settlements (BIS)

The Bank for International Settlements (BIS) provides quarterly statistics on exchange-traded derivatives (open interest and turnover in contracts, and notional amounts) and semiannual data on OTC derivatives outstanding (notional amounts and gross market values across risk categories like interest rates, FX, equity, commodities, and credit). All the data used in this post has been sourced from the BIS database.

Data are collected from over 80 exchanges for ETDs and via surveys of major dealers in 12 financial centers for OTC derivatives. BIS ensures comparability by standardizing definitions, consolidating country-level data, halving inter-dealer positions to avoid double counting, and converting figures into USD. Interpolations are used to fill gaps between triennial surveys, ensuring consistent time series for analysis.

International Swaps and Derivatives Association (ISDA)

ISDA develops and maintains standardized reference data and contractual frameworks that underpin global OTC derivatives markets. This includes machine-readable definitions and value lists for core market terms such as benchmark rates, floating rate options, currencies, business centers, and calendars, primarily derived from ISDA documentation (notably the ISDA Interest Rate Derivatives Definitions). The data are distributed via the ISDA Library and increasingly designed for automated, straight-through processing.

ISDA’s standards are created and updated through industry working groups and are widely used to support trade documentation, confirmation, clearing, and regulatory reporting. Initiatives such as the Common Domain Model (CDM) and Digital Regulatory Reporting (DRR) translate market conventions and regulatory requirements across multiple jurisdictions into consistent, machine-executable logic. While ISDA does not publish comprehensive market volume statistics, its frameworks play a central role in harmonizing OTC derivatives markets and enabling reliable post-trade transparency.

Futures Industry Association (FIA)

Futures Industry Association (FIA), via FIA Tech, provides comprehensive derivatives data including position limits, exchange fees, contract specifications, and trading volumes for futures/options across global products.

Sources aggregate from exchanges, indices (1,800+ products, 100,000+ constituents), and regulators for reference data like symbologist and corporate actions. The process involves standardizing data into consolidated formats with 500+ attributes, automating regulatory reporting (e.g., CFTC ownership/control), and ensuring compliance via databanks.

How to get the data

The data discussed in this article is drawn from the BIS, FIA and Visual Capitalist. For comprehensive statistics on global derivatives markets (both over-the-counter (OTC) and exchange-traded derivatives (ETDs)), the data are available at https://data.bis.org/ and for exchange-traded derivatives specifically, detailed data are provided by the Futures Industry Association (FIA) through its ETD volume reports, accessible at https://www.fia.org/etd-volume-reports. Data on equity spot market and real economy sectors are sourced from Visual Capitalist.

Derivatives market business statistics

Global derivatives market

In this section, we focus on two core measures of derivatives market activity and size: the notional amount outstanding and the gross market value, which together provide complementary perspectives on the scale of contracts and the associated economic exposure.

As of 30th July 2025, the global derivatives market is estimated to have an outstanding notional value of approximately USD 964 trillion, according to the Bank for International Settlements (BIS). As illustrated in the figure below, the market is largely dominated by over-the-counter (OTC) derivatives, which account for nearly 88% of total notional amounts, whereas exchange-traded derivatives (ETDs) represent a comparatively smaller share of about USD 118 trillion.

Figure 1. Derivatives Markets: OTC versus ETD (2025)
Derivatives Markets: OTC and ETD (2025)
Source: computation by the author (BIS data of 2025).

Figure 2 below compares the scale of the global equity derivatives market with that of the underlying equity spot market as of mid-2025. The figure shows that, although equity derivatives represent a sizeable market in notional terms, they are still much smaller than the equity spot market measured by market capitalization. This suggests that the primary locus of economic value in equities remains in the spot market, while the derivatives market mainly represents contingent claims written on that underlying value rather than a comparable pool of market wealth. The relatively small gross market value of equity derivatives further indicates that only a limited portion of derivative notional translates into actual market exposure.

Figure 2. Equity Markets: Spot versus Derivatives (2025)
Equity Markets: Spot versus Derivatives (2025)
Source: computation by the author (BIS and Visual Capitalist data of 2025).

Data sources: global derivatives notional outstanding as of mid-2025 BIS OTC and exchange traded data; global equity spot market capitalization as of 2025 (Visual Capitalist).

Figure 3 below juxtaposes the global derivatives market with selected real-economy sectors to provide an intuitive comparison of scale. Values are reported in USD trillions and plotted on a logarithmic axis, such that equal distances along the horizontal scale correspond to ten-fold (×10) changes in magnitude rather than linear increments. This representation allows quantities that differ by several orders of magnitude to be meaningfully displayed within a single chart.

Interpreted in this manner, the figure illustrates that the notional size of derivatives markets far exceeds the market capitalization of major real-economy sectors, including technology, financials, energy, fast moving consumer goods (FMCG), and luxury. The comparison is illustrative rather than like-for-like, and is intended to contextualize the scale of financial contract exposure rather than to imply equivalent economic value or direct risk.

Figure 3. Scale of Global Derivatives Relative to Major Real-Economy Sectors (2025)
Scale of Global Derivatives Relative to Major Real-Economy Sectors (2025)
Source: computation by the author (BIS and Visual Capitalist data).

Data sources: BIS OTC derivatives statistics (June 2025) for notional outstanding; Visual Capitalist global stock market sector data (2025) for sector market capitalizations; companies market cap / Visual Capitalist for luxury company market caps.

OTC derivatives market

Figures 4 and 5 below illustrate the evolution of the OTC derivatives market from 1998 to 2025 using the two measures discussed above: outstanding notional amounts (Figure 4) and gross market value (Figure 5). As the data show, notional outstanding tends to overstate the effective economic size of the market, as it reflects contractual face values rather than actual risk exposure. By contrast, gross market value provides a more economically meaningful measure by capturing the current cost of replacing outstanding contracts at prevailing market prices.

Figure 4. Size of the OTC Derivatives Market (Notional amount)
Size of the OTC derivative market (Notional amount)
Source: computation by the author (BIS data).

Figure 5. Size of the OTC Derivatives Market (Gross market value)
Size of the OTC derivative market (Gross market value)
Source: computation by the author (BIS data).

The figure below illustrates the OTC derivatives market data as of 30th July 2025 based on the two metrics discussed above: outstanding notional amounts and gross market value. As the data show, Gross market value (GMV) represents only about 2.6% of total notional outstanding, highlighting the large gap between contractual face values and economically meaningful exposure.

Figure 6. Size measure of the OTC derivatives market (2025)
Size of the OTC derivative market (2025)
Source: computation by the author (BIS data).

Exchange-traded derivatives market

Figure 7 below illustrates the growth of the exchange-traded derivatives market from 1993 to 2025, based on outstanding notional amounts (open interest) and turnover notional amounts (trading volume). For comparability across contracts and exchanges, open interest is expressed in notional terms by multiplying the number of open contracts by their contract size, yielding US dollar equivalents. Turnover is defined as the notional value of all futures and options traded during the period, with each trade counted once.

Figure 7. Size of the Exchange-Traded Derivatives Market
Size of the exchange traded derivatives market
Source: computation by the author (BIS data).

The figure below illustrates the exchange-traded derivatives market data as of 30th July 2025 based on the two metrics discussed above: open interest and turnover (trading volume). The chart shows that only about 12%, of the open positions is actively traded, highlighting the difference between market size and the trading activity.

Figure 8. Size of the Exchange traded derivatives market (2025)
Size of the exchange traded derivatives market (2025)
Source: computation by the author (BIS data).

Figure 9 below illustrates the evolution of the global exchange-traded derivatives market from 1993 to 2025, measured by outstanding notional amounts across major regions. The figure reveals a pronounced concentration of activity in North America and Europe, which drives most of the market’s expansion over time, while Asia-Pacific and other regions play a more modest role. Despite cyclical fluctuations, the overall trajectory is one of sustained long-run growth, underscoring the increasing importance of exchange-traded derivatives in global risk management and price discovery.

Figure 9. Size of the Exchange-Traded Derivatives Market by geographical locations
Size of the exchange traded derivatives market by geographic location
Source: computation by the author (BIS data).

Underlying asset classes

This section analyzes underlying asset-class statistics for derivatives traded in exchange-traded (ETD) and over-the-counter (OTC) markets.

Figure 10 below presents the distribution of exchange-traded derivatives (ETDs) activity across major underlying asset classes. When measured by the number of contracts traded (volume), the market is highly concentrated, with Equity derivatives dominating and accounting for the vast majority of activity. This is followed at a significant distance by Interest Rate and Commodity derivatives. However, this distribution reverses when measured by the notional value of outstanding contracts, where Interest Rate derivatives represent the largest share of the market due to the high underlying value of each contract.

Figure 10. Size of the exchange-traded derivatives market by asset classes
Size of the exchange traded derivatives market
Source: computation by the author (FIA data).

Figure 11 below presents the distribution of OTC derivatives activity across major underlying asset classes, measured by the outstanding notional amounts and displayed on a logarithmic scale. Read in this way, the chart shows that OTC activity is broadly diversified across interest rates, equity indices, commodities, foreign exchange, and credit, with interest rate and foreign exchange derivatives accounting for the largest contract volumes.

Figure 11. Size of the OTC derivatives market by asset classes
Size of the exchange traded derivatives market
Source: computation by the author (BIS data).

Role of the Black–Scholes–Merton (BSM) model

The Black–Scholes–Merton (BSM) model played a role in financial markets that extended well beyond option pricing. As argued by MacKenzie and Millo (2003), once adopted by traders and exchanges, it actively shaped how options markets were organized, priced, and operated rather than merely describing pre-existing price behaviour. Its use at the Chicago Board Options Exchange (CBOE) helped standardize quoting practices, enabled model-based hedging, and supported the rapid growth of liquidity in listed options markets.

At a broader level, MacKenzie (2006) shows that BSM contributed to a transformation in financial culture by embedding theoretical assumptions about risk, volatility, and rational pricing into everyday market practice. In this sense, BSM acted as an “engine” that reshaped markets and economic behaviour, not simply a “camera” recording them.

Beyond markets and firms, the diffusion of the BSM model also had wider societal implications. By formalizing risk as something that could be quantified, priced, and hedged, BSM contributed to a broader cultural shift in how uncertainty was perceived and managed in modern economies (MacKenzie, 2006). This reframing reinforced the view that complex economic risks could be controlled through mathematical models, with public perceptions of financial stability.

Why should you be interested in this post?

For anyone aiming for a career in finance, understanding the derivatives market is essential, as it is currently one of the most actively traded markets and is expected to grow further. Studying the statistics and business impact of derivatives provides valuable context on past challenges and the solutions developed to manage risks, offering a solid foundation for analyzing and navigating modern financial markets.

Related posts on the SimTrade blog

   ▶ Jayati WALIA Derivatives Market

   ▶ Alexandre VERLET Understanding financial derivatives: options

   ▶ Alexandre VERLET Understanding financial derivatives: forwards

   ▶ Alexandre VERLET Understanding financial derivatives: futures

   ▶ Akshit GUPTA Understanding financial derivatives: swaps

   ▶ Akshit GUPTA The Black Scholes Merton model

   ▶ Luis RAMIREZ Understanding Options and Options Trading Strategies

Useful resources

Academic research on option pricing

Black F. and M. Scholes (1973) The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.

Merton R.C. (1973) Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4(1), 141–183.

Hull J.C. (2022) Options, Futures, and Other Derivatives, 11th Global Edition, Chapter 15 – The Black–Scholes–Merton model, 338–365.

Academic research on the role of models

MacKenzie, D., & Millo, Y. (2003). Constructing a Market, Performing Theory: The Historical Sociology of a Financial Derivatives Exchange. American Journal of Sociology, 109(1), 107–145.

MacKenzie, D. (2006). An Engine, not a Camera: How Financial Models Shape Markets. MIT Press.

Data

Bank for International Settlements (BIS). Retrieved from BIS Statistics Explorer.

Futures Industry Association (FIA). Retrieved from ETD Volume Reports.

Visual Capitalist. Retrieved from The Global Stock Market by Sector.

Visual Capitalist. Retrieved from Piecing Together the $127 Trillion Global Stock Market.

About the author

The article was written in February 2026 by Saral BINDAL (Indian Institute of Technology Kharagpur, Metallurgical and Materials Engineering, 2024-2028 & Research assistant at ESSEC Business School).

   ▶ Discover all articles written by Saral BINDAL

Beyond price: The wisdom of Warren Buffett and Napoleon Hill on investment and self-growth

by
Mathilde JANIK

In this article, Mathilde JANIK (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2021-2025) comments on two quotes that bridge the gap between financial philosophy and personal development: one from the world’s most successful investor, Warren Buffett, and another from the self-help pioneer, Napoleon Hill. These quotes collectively highlight the profound truth that success in finance, much like success in life, is less about quick wins and more about the quality of the long-term compounding investments we make in businesses and ourselves.

About the Quoted Authors

This post draws on the wisdom of two influential figures: Warren Buffett, the chairman and CEO of Berkshire Hathaway, widely regarded as one of the most successful investors in history and the architect of the Value Investing philosophy; and Napoleon Hill (1883–1970), the American author of the classic 1937 self-help book Think and Grow Rich, whose work focused on the power of belief and consistent, long-term personal discipline.

The selection of these two quotes is deliberate: the first establishes the principle of quality over price in capital allocation (finance), while the second extends this exact same principle to the allocation of time and effort in personal life (self-growth). Together, they form a complete roadmap for achieving sustainable success, reminding us that both financial and personal wealth are built patiently through consistent, high-quality choices.

Quotes

The quote by Warren Buffett

“It’s far better to buy a wonderful company at a fair price than a fair company at a wonderful price.” – Warren Buffett

The quote by Napoleon Hill

“Tell me how you use your spare time, and how you spend your money, and I will tell you where and what you will be in ten years from now.” – Napoleon Hill

Analysis of the quotes

The first quote, from Warren Buffett, is the cornerstone of Value Investing. It focuses on the financial market and how to choose a company to invest in. It makes a lot of sense to always take into account not only the stock price of the company but also everything that goes beyond its market capitalization. Factors like the management and leadership within the company, the cash flows (and their robustness and stability), and the market share compared to competitors are really important. Investing in a robust company that does good things every day may be more profitable than investing in a company that may be cheaper and more appealing for one specific innovation but may not be profitable at all.

This is why I also wanted to include the second quote, which applies the same long-term quality principle to personal development. I came across this quote shortly after reading the book “Think and Grow Rich” by Napoleon Hill, an American author widely known for his self-help books, first published in 1937. He asserted that desire, faith, and persistence can propel one to great heights if one can suppress negative thoughts and focus on long-term goals. I like this quote because it shows that, depending on what we focus on, we can become anything we want. It also shows that it’s about the little things you do every day that will bring you where you want to be in life. I appreciate how this quote shows that spending money is not a deliberate act and we should think this through, questioning ourselves on our own goals and how making specific spending decisions may or may not bring us towards them and what our future self would think of our present decision.

Financial concepts related to the quotes

We can relate these quotes to three core concepts that govern both capital and personal allocation: intrinsic value vs. market price, economic moats and competitive advantage, and the power of compounding.

Intrinsic value vs. Market price

Buffett’s quote directly addresses the difference between a stock’s intrinsic value (the true, underlying economic worth of a business, determined by its future cash flows and qualitative factors like management quality and competitive advantage) and its volatile market price (the price at which it trades publicly). He emphasizes that while price is what you pay, value is what you get. A “wonderful company” has a high intrinsic value, meaning its quality justifies the price, whereas a “fair company” may trade at a low price, but its lack of quality means that price is likely justified by its poor prospects.

Economic moats and competitive advantage

The concept of a “wonderful company” is often defined by its economic moat: a structural feature that protects a company’s long-term profits and market share from competition. Taken from moats that protect castles, certain advantages help protect companies from their competitors. Moats can come from high switching costs for customers, network effects, or intangible assets like brand strength (e.g., Coca-Cola). A company with a strong moat has robust and stable cash flows, which, as I noted, are crucial. Hill’s quote is a mirror: investing in personal skills and knowledge creates a personal “moat” around your career and future earning potential.

The power of compounding

Both quotes relates to the principle of compounding. In finance, it’s the ability of an asset to generate earnings that are then reinvested to generate their own earnings. Buffett seeks companies that compound capital effectively over decades. Napoleon Hill’s quote speaks to compounding in personal life: the cumulative effect of small, positive daily actions (how you use your spare time and spending decisions) that, over ten years, leads to exponential growth in skills, wealth, and character. This continuous, patient investment, whether in a stock or a skill, is the ultimate driver of long-term success. Other authors, such as the best-selling author James Clear in his widely known self-help book Atomic Habits, also present this idea of compounding specifically for everyday skills.

My opinion about this quote

I chose these two quotes because they provide a complete roadmap for success. The Buffett quote provides the external strategy: be disciplined, patient, and focus on quality when allocating capital. The Hill quote provides the internal strategy: be disciplined, patient, and focus on quality when allocating time and effort. As a student of finance, it’s easy to get fixated on technical analysis and short-term movements, but these quotes remind us that the biggest returns come from long-term vision and consistent commitment to fundamental excellence, whether we’re analyzing a company’s leadership or assessing our own daily habits. This dual focus is the best preparation for a successful career in finance and beyond, emphasizing that personal growth and investment success are deeply intertwined.

Why should I be interested in this post?

If you’re a student interested in business and finance, this post is essential. It moves beyond the mechanics of valuation to address the philosophy of investment, a core requirement for success in roles like asset management, portfolio management, and private equity. Understanding Buffett’s principle demonstrates a mature, long-term mindset often tested in interviews. Furthermore, Napoleon Hill’s insight offers a blueprint for personal development, showing that the same consistency and discipline required to choose a “wonderful company” are needed to build a successful professional self through thoughtful allocation of your time and money.

Related posts on the SimTrade blog

Quotes

   ▶ All posts about Quotes

   ▶ Hadrien PUCHE “Price is what you pay, value is what you get“ – Warren Buffett

   ▶ Federico DE ROSSI The Power of Patience: Warren Buffett’s Advice on Investing in the Stock Market

   ▶ Hadrien PUCHE “The big money is not in the buying and selling, but in the waiting.” – Charlie Munger

Financial techniques

   ▶ All posts about Financial Techniques

   ▶ Andrea ALOSCARI Valuation methods

   ▶ Maite CARNICERO MARTINEZ How to compute the net present value of an investment in Excel

Useful resources

Cunningham, L.A (1997) The Essays of Warren Buffett: Lessons for Corporate America, Fourth Edition.

Hill, N. (1937). Think and Grow Rich. New York: The Ralston Society.

Graham, B., & Dodd, D. L. (1934). Security Analysis. New York: McGraw-Hill.

Autorité des Marchés Financiers (AMF) Guide d’élaboration des prospectus et de l’information à fournir en cas d’offre au public ou d’admission de titres financiers

Autorité des Marchés Financiers (AMF) (January 2026) Les obligations d’information des sociétés cotées

Autorité des Marchés Financiers (AMF) Guides épargnants

U.S. Securities and Exchange Commission (SEC) Resources for Investors

U.S. Securities and Exchange Commission (SEC) Beginners Guide to Investing

About the author

The article was written in January 2026 by Mathilde JANIK (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2021-2025).

   ▶ Discover all articles written by Mathilde JANIK.

Volatility curves: smiles and smirks

by
Saral BINDAL

In this article, Saral BINDAL (Indian Institute of Technology Kharagpur, Metallurgical and Materials Engineering, 2024-2028 & Research assistant at ESSEC Business School) analyzes the various shapes of volatility curves observed in financial markets and explains how they reveal market participants’ beliefs about future asset price distributions as implied by option prices.

Introduction

In financial markets characterized by uncertainty, volatility is a fundamental factor shaping the dynamics of the prices of financial instruments. Implied volatility stands out as a key metric as a forward-looking measure that captures the market’s expectations of future price fluctuations, as reflected in current market prices of options.

Implied volatility is inherently a two-dimensional object, as it is indexed by strike K and maturity T. The collection of these implied volatilities across all strikes and maturities constitutes the volatility surface. Under the Black–Scholes–Merton (BSM) framework, volatility is assumed to be constant across strikes and maturities, in which case the volatility surface would degenerate into a flat plane. Empirically, however, the volatility surface is highly structured and varies significantly across both strike and maturity.

Accordingly, this post focuses on implied volatility curves across moneyness for a fixed maturity (i.e. cross-sections of the volatility surface), examining their canonical shapes, economic interpretation, and the insights they reveal about market beliefs and risk preferences.

Option pricing

Option pricing aims to determine the fair value of options (calls and puts). One of the most widely used frameworks for this purpose is the Black–Scholes–Merton (BSM) model, which expresses the option value as a function of five key inputs: the underlying asset price S, the strike price K, time to maturity T, the risk-free interest rate r, and volatility σ. Given these parameters, the model yields the theoretical value of the option under specific market assumptions. The details of the BSM option pricing formulas along with variable definitions can be found in the article Black-Scholes-Merton option pricing model.

Implied volatility

In the Black–Scholes–Merton (BSM) model, volatility is an unobservable parameter, representing the expected future variability of the underlying asset over the option’s remaining life. In practice, implied volatility is obtained by inverting the BSM pricing formula (using numerical methods such as the Newton–Raphson algorithm) to find the specific volatility that equates the BSM theoretical price to the observed market price. The details for the mathematical process of calculation of implied volatility can be found in Implied Volatility and Option Prices.

Moneyness

Moneyness describes the relative position of an option’s strike price K with respect to the current underlying asset price S. It indicates whether the option would have a positive intrinsic value if exercised at the current moment. Moneyness is typically parameterized using ratios such as K/S or its logarithmic transform.


Moneyness formula

In practice, moneyness classifies an option based on its intrinsic value. An option is said to be in-the-money (ITM) if it has positive intrinsic value, at-the-money (ATM) if its intrinsic value is zero, and out-of-the-money (OTM) if its intrinsic value is zero and immediate exercise would not be optimal. In terms of the relationship between the underlying asset price (S) and the strike price (K), a call option is ITM when S > K, ATM when S = K, and OTM when S < K. Conversely, a put option is ITM when S < K, ATM when S = K, and OTM when S > K.

The payoff, that is the cash flow realized upon exercising the option at maturity T, is given for call and put options by:


Payoff formula for call and put options

where ST is the underlying asset price at the time the option is exercised.

Figure 1 below illustrates the payoff of a call option, that is the call option value at maturity as a function of its underlying asset price. The call option’s strike price is assumed to be equal to $4,600. For an underlying price of $3,000, the call option is out-of-the-money (OTM); for a price of $4,600, the call option is at-the-money (ATM); and for a price of $7,000, the call option is in-the-money (ITM) and worth $2,400.

Figure 1. Payoff for a call option and its moneyness (OTM, ATM and ITM)
Payoff for a call option and its moneyness (OTM, ATM and ITM)
Source: computation by the author.

Similarly, Figure 2 below illustrates the payoff of a put option, that is the put option value at maturity as a function of its underlying asset price. The put option’s strike price is assumed to be equal to $4,600. For an underlying price of $3,000, the put option is in-the-money (ITM) and worth $1,600; for a price of $4,600, the put option is at-the-money (ATM); and for a price of $7,000, the put option is out-of-the-money (OTM).

Figure 2. Payoff for a put option and its moneyness (OTM, ATM and ITM)
Payoff for a put option and its moneyness (OTM, ATM and ITM)
Source: computation by the author.

Figure 3 below illustrates the temporal dynamics of moneyness for a European call option with a strike price of $4,600, showing how the option transitions between out-of-the-money, at-the-money, and in-the-money states as the underlying asset price moves relative to the strike over its lifetime.

Figure 3. Evolution of a call option moneyness
Evolution of a call option moneyness
Source: computation by the author.

Similarly, Figure 4 below illustrates the temporal dynamics of moneyness for a European put option with a strike price of $4,600, showing how the option transitions between out-of-the-money, at-the-money, and in-the-money states as the underlying asset price moves relative to the strike over its lifetime.

Figure 4. Evolution of a put option moneyness
Evolution of a put option moneyness
Source: computation by the author.

You can download the Excel file below for the computation of moneyness of call and put options as discussed in the above figures.

Download the Excel file.

Empirical observation: implied volatility depends on moneyness

Smiles and smirks

Volatility curves refer to plots of implied volatility across different strikes for options with the same maturity. Two distinct shapes are commonly observed: the “volatility smile” and the “volatility smirk”.

A volatility smile is a symmetric pattern commonly observed in options markets. For a given underlying asset and expiration date, it is defined as the mapping of option strike prices to their Black–Scholes–Merton implied volatilities. The term “smile” refers to the distinctive shape of the curve: implied volatility is lowest near the at-the-money (ATM) strike and rises for both lower in-the-money (ITM) strikes and higher out-of-the-money (OTM) strikes.

A volatility smirk (also called skew) is an asymmetric pattern in the implied volatility curve and is mainly observed in the equity markets. It is characterized by high implied volatilities at lower strikes and progressively lower implied volatilities as the strike increases, resulting in a downward-sloping profile. This shape reflects the uneven distribution of implied volatility across strikes and stands in contrast to the more symmetric volatility smile observed in other markets.

Stylized facts about the implied volatility curve across markets

Stylized facts characterizing implied volatility curves are persistent and statistically robust empirical regularities observed across financial markets. Below, I discuss the key stylized facts for major asset classes, including equities, foreign exchange, interest rates, commodities, and cryptocurrencies.

Equity market: For major equity indices, the implied volatility curve at a given maturity is typically a negatively sloped smirk: IV is highest for out of the money puts and declines as the strike moves up, rather than forming a symmetric smile (Zhang & Xiang, 2008). This left skew is persistent across maturities and provides useful signals at the individual stock level, where steeper smirks (higher OTM put vs ATM IV) forecast lower subsequent returns, consistent with markets pricing crash risk into downside options (Xing, Zhang & Zhao, 2010).

FX market: For foreign currency options, implied volatility curves most often display a U shaped smile: IV is lowest near at the money and higher for deep in or out of the money strikes, especially for major FX pairs (Daglish, Hull & Suo, 2007). The degree of symmetry depends on the correlation between the FX rate and its volatility, so near zero correlation gives a roughly symmetric smile, while non zero correlations generate skews or smirks that have been empirically documented in options on EUR/USD, GBP/USD and AUD/USD (Choi, 2021).

Commodity market: For commodity options, cross market evidence shows that implied volatility curves are generally negatively skewed with positive curvature, meaning they exhibit smirks rather than flat surfaces, with higher IV for downside strikes but still some smile like curvature (Jia, 2021). Studies on crude oil and related commodities also find pronounced smiles and smirks whose strength varies with fundamentals such as inventories and hedging pressure, reinforcing it is a core stylized fact in commodity derivatives (Soini, 2018; Vasseng & Tangen, 2018).

Fixed income market: Swaption markets display smiles and skews on their volatility curves: for a given expiry and tenor, implied volatility typically curves in moneyness and may tilt up or down depending on the correlation between the underlying rate and volatility (Daglish, Hull & Suo, 2007). Empirical work on the swaption volatility cube shows that simple one factor or SABR lifted constructions do not capture the full observed smile, indicating that a rich, strike and maturity dependent IV surface is itself a stylized feature of interest rate options (Samuelsson, 2021).

Crypto market: Bitcoin options exhibit a non flat implied volatility smile with a forward skew, and short dated options can reach very high levels of implied volatility, reflecting heavy tails and strong demand for certain strikes (Zulfiqar & Gulzar, 2021). Because of this forward skew, the paper concludes that Bitcoin options “belong to the commodity class of assets,” although later studies show that the Bitcoin smile can change shape across regimes and is often flatter than equity index skew (Alexander, Kapraun & Korovilas, 2023).

Summary of stylized facts about implied volatility
Summary of stylized facts about implied volatility

An Empirical Analysis of S&P 500 Implied Volatility

This section describes the data, methodology, and empirical considerations for the analysis of implied volatility of put options written on the S&P 500 index. We begin by highlighting a classical challenge in cross-sectional option data: asynchronous trading.

Asynchronous trading and measurement error

In empirical option pricing, the non-synchronous observation of option prices and the underlying asset price generates measurement errors in implied volatility estimation, as the building of the volatility curve based on an option pricing model relies on option prices with the underlying price observed at the same point of time.

Formally, let the option price C be observed at time tc, while the underlying asset price S is observed at time ts with ts ≠ tc. The observed option price therefore satisfies


Asynchronous call option price and underlying asset price

Since the option price at time tc depends on the latent spot price S(tc), rather than the asynchronously observed price S(ts), this mismatch introduces measurement error in the underlying price variable and implied volatility at the end.

Various standard filters including no-arbitrage, liquidity, moneyness, maturity, and implied-volatility sanity checks are typically applied to mitigate errors-in-variables arising from asynchronous observations of option prices and their underlying assets.

Example: options on the S&P 500 index

Consider the following sample of option data written on the S&P 500 index. Data can be obtained from FirstRate Data.

Download the Excel file.

Figure 5 below illustrates the volatility smirk (or skew) for an option chain (a series of option prices for the same maturity) written on the S&P 500 index traded on 3rd July 2023 with time to maturity of 2 days after filtering it out from the above data.

Figure 5. Volatility smirk for put option prices on the S&P 500 index
Volatility smirk computed for put option on the S&P 500 index
Source: computation by the author.

You can download the Excel file below to compute the volatility curve for put options on the S&P 500 index.

Download the Excel file.

Economic Insights

This section explains how the shape of the implied volatility curve reveals key economic forces in options markets, including demand for crash protection, leverage-driven volatility feedback effects, and the role of market frictions and limits to arbitrage.

Demand for crash protection:

Out-of-the-money put options serve as insurance against market crashes and hedge tail risk. Because this demand is persistent and largely one-sided, put options become expensive relative to their Black–Scholes-Merton values, resulting in elevated implied volatilities at low strikes. This excess pricing reflects the market’s willingness to pay a premium to insure against rare but severe losses.

Leverage and volatility feedback effects:

When equity prices fall, firms become more leveraged because the value of equity declines relative to debt. Higher leverage makes equity riskier, increasing expected future volatility. Anticipating this effect, markets assign higher implied volatility to downside scenarios than to upside moves. This endogenous feedback between price declines, leverage, and volatility naturally produces a negative volatility skew, even in the absence of crash-risk preferences.

Market frictions and limits to arbitrage:

In practice, option writers are subject to capital constraints, margin requirements, and exposure to jump and tail risk. These constraints limit their capacity to supply downside protection at low prices. As a result, downside options embed not only compensation for fundamental crash risk, but also a risk premium reflecting the balance-sheet costs and risk-bearing capacity of intermediaries. The observed volatility skew therefore arises endogenously from limits to arbitrage rather than purely from differences in underlying return distributions.

Conclusion

The dependence of implied volatility on moneyness is neither an anomaly nor a technical artifact. It reflects market expectations, risk preferences, and the perceived probability of extreme outcomes. For both pedagogical and investment applications, the implied volatility curve is a central tool for understanding how markets price tail and downside risk.

Why should I be interested in this post?

Understanding implied volatility and its relationship with moneyness extends beyond option pricing, offering insights into how markets perceive risk and assess the likelihood of extreme events. Patterns such as volatility smiles and skews reflect investor behavior, the demand for protection, and the asymmetric emphasis on potential losses over gains, providing a clearer view of both pricing anomalies and the economic forces that shape financial markets.

Related posts on the SimTrade blog

Option price modelling

   ▶ Jayati WALIA Brownian Motion in Finance

   ▶ Saral BINDAL Modeling Asset Prices in Financial Markets: Arithmetic and Geometric Brownian Motions

   ▶ Jayati WALIA Black-Scholes-Merton option pricing model

   ▶ Jayati WALIA Monte Carlo simulation method

Volatility

   ▶ Saral BINDAL Historical Volatility

   ▶ Saral BINDAL Implied Volatility and Option Prices

   ▶ Jayati WALIA Implied Volatlity

Useful resources

Academic research on Option pricing

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities, Journal of Political Economy, 81(3), 637–654.

Hull J.C. (2015) Options, Futures, and Other Derivatives, Ninth Edition, Chapter 15 – The Black-Scholes-Merton model, 343-375.

Merton, R.C. (1973). Theory of rational option pricing, The Bell Journal of Economics and Management Science, 4(1), 141–183.

Academic research on Stylized facts

Alexander, C., Kapraun, J. & Korovilas, D. (2023) Delta hedging bitcoin options with a smile, Quantitative Finance, 23(5), 799–817.

Bakshi, G., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models, The Journal of Finance, 52(5), 2003–2049.

Bates, D. S. (1991). The crash of ’87: Was it expected? The evidence from options markets, The Journal of Finance, 46(5), 1777–1819.

Bates, D. S. (2000). Post-’87 crash fears in the S&P 500 futures option market, Journal of Econometrics, 94(1–2), 181–238.

Choi, K. (2021) Foreign exchange rate volatility smiles and smirks, Applied Stochastic Models in Business and Industry, 37(3), 405–425.

Daglish, T., Hull, J. & Suo, W. (2007) Volatility surfaces: theory, rules of thumb, and empirical evidence, Quantitative Finance, 7(5), 507–524.

Jia, G. (2021) The implied volatility smirk of commodity options, Journal of Futures Markets, 41(1), 72–104.

Samuelsson, A. (2021) Empirical study of methods to complete the swaption volatility cube. Master’s thesis, Uppsala University.

Soini, E. (2018) Determinants of volatility smile: The case of crude oil options. Master’s thesis, University of Vaasa.

Xing, Y., Zhang, X. & Zhao, R. (2010) What does individual option volatility smirk tell us about future equity returns? Review of Financial Studies, 23(5), 1979–2017.

Zhang, J.E. & Xiang, Y. (2008) The implied volatility smirk, Quantitative Finance, 8(3), 263–284.

Zulfiqar, N. & Gulzar, S. (2021) Implied volatility estimation of bitcoin options and the stylized facts of option pricing, Financial Innovation, 7(1), 67.

About the author

The article was written in January 2026 by Saral BINDAL (Indian Institute of Technology Kharagpur, Metallurgical and Materials Engineering, 2024-2028 & Research assistant at ESSEC Business School).

   ▶ Discover all articles written by Saral BINDAL

Leverage in LBOs: How Debt Creates and Destroys Value in Private Equity Transactions

by
Ian DI MUZIO

In this article, Ian DI MUZIO (ESSEC Business School, Master in Finance (MiF), 2025–2027) explores the economics of leverage in leveraged buyouts (LBOs) from an investment banking perspective.

Rather than treating debt as a purely mechanical input in an Excel model, the article explains—both conceptually and technically—how leverage amplifies equity returns, reshapes risk, affects pricing, and constrains deal execution.

The ambition is to provide junior analysts with a realistic framework they can use when building or reviewing LBO models during internships, assessment centres, or live mandates.

Context and objective

Most students encounter leverage for the first time through a simplified capital structure slide: a bar divided into senior debt, subordinated debt, and equity, followed by a formula showing that higher debt and lower equity mechanically increase the internal rate of return (IRR, the discount rate that sets net present value to zero).

In the abstract, the story appears straightforward. If a company generates stable cash flows, a sponsor can finance a large share of the acquisition with relatively cheap debt, repay that debt over time, and magnify capital gains on a smaller equity cheque.

In reality, this mechanism operates only within a narrow corridor. Too little leverage and the financial sponsor struggles to compete with strategic buyers. Too much leverage and the business becomes fragile: covenants tighten, financial flexibility disappears, and relatively small shocks in performance can wipe out the equity.

The objective of this article is therefore not to restate textbook identities, but to describe how investment bankers think about leverage when advising financial sponsors and corporate sellers, drawing on market practice and transaction experience (see, for example, Kaplan & Strömberg).

The focus is on the interaction between free cash flow generation, debt capacity, pricing, and exit scenarios, and on how analysts should interpret LBO outputs rather than merely producing them.

What an LBO really is

At its core, a leveraged buyout is a change of control transaction in which a financial sponsor acquires a company using a combination of equity and a significant amount of borrowed capital, secured primarily on the target’s own assets and cash flows.

The sponsor is rarely a long-term owner. Instead, it underwrites a finite investment horizon—typically four to seven years—during which value is created through a combination of operational improvement, deleveraging, multiple expansion, and sometimes add-on acquisitions, before exiting via a sale or initial public offering emphasises.

From a financial perspective, an LBO is effectively a structured bet on the spread between the company’s return on invested capital and the cost of debt, adjusted for the speed at which that debt can be repaid using free cash flow.

In other words, leverage only creates value if operating performance is sufficiently strong and stable to service and amortise debt. When performance falls short, the rigidity of the capital structure becomes a source of value destruction rather than enhancement.

How leverage amplifies equity returns

The starting point for understanding leverage is the identity that equity value equals enterprise value minus net debt. If enterprise value remains constant while net debt declines over time, equity value must mechanically increase.

This is the familiar deleveraging effect: as free cash flow is used to repay borrowings, the equity slice of the capital structure expands even if EBITDA growth is modest and exit multiples remain unchanged.

Figure 1 illustrates this mechanism in a stylised LBO. The company is acquired with high initial leverage. Over the holding period, EBITDA grows moderately, but the primary driver of equity value creation is the progressive reduction of net debt.

Figure 1. Evolution of capital structure in a simple LBO.
Evolution of capital structure in a simple LBO
Source: the author.

Figure 1 illustrates the evolution of capital structure in a simple LBO. Debt is repaid using free cash flow, causing the equity portion of enterprise value to increase even if valuation multiples remain unchanged.

To enhance transparency and pedagogical value, the Excel model used to generate Figure 1—allowing readers to adjust leverage, cash flow, and amortisation assumptions—can be made available alongside this article.

This dynamic explains why LBO IRRs can appear attractive even with limited operational growth. It also highlights the fragility of highly levered structures: when EBITDA underperforms or exit multiples contract, equity value erodes rapidly because the initial leverage leaves little margin for error.

Debt capacity and the role of free cash flow

For investment bankers, the key practical question is not “how much leverage maximises IRR in Excel?” but “how much leverage can the business sustainably support without breaching covenants or undermining strategic flexibility?”.

This shifts the focus from headline EBITDA to the quality, predictability, and cyclicality of free cash flow. In an LBO context, free cash flow is typically defined as EBITDA minus cash taxes, capital expenditure, and changes in working capital, adjusted for recurring non-operating items.

A business with recurring revenues, limited capex requirements, and stable working capital can support materially higher leverage than a cyclical, capital-intensive company, even if both report similar EBITDA today.

Debt capacity is assessed using leverage and coverage metrics such as net debt to EBITDA, interest coverage, and fixed-charge coverage, tested under downside scenarios rather than a single base case. Lenders focus not only on entry ratios, but on how those ratios behave when EBITDA compresses or capital needs spike.

Pricing, entry multiples, and the leverage trade-off

Leverage interacts with pricing in a non-linear way. At a given entry multiple, higher leverage reduces the equity cheque and tends to increase IRR, provided exit conditions are favourable.

However, aggressive leverage also constrains bidding capacity. Lenders rarely support structures far outside market norms, which means sponsors cannot indefinitely substitute leverage for price. In competitive auctions, sponsors must choose whether to compete through valuation or capital structure, knowing that both dimensions feed directly into risk.

Figure 2 presents a stylised sensitivity of equity IRR to entry multiple and starting leverage, holding exit assumptions constant.

Figure 2. Sensitivity of equity IRR to entry valuation and starting leverage.
Sensitivity of equity IRR to entry valuation and starting leverage
Source: the author.

Figure 2 illustrates the sensitivity of equity IRR to entry valuation and starting leverage. Outside a moderate corridor, IRR becomes highly sensitive to small changes in operating or exit assumptions.

Providing the Excel file behind Figure 2 would allow readers to stress-test entry pricing and leverage assumptions interactively.

Risk, scenarios, and the distribution of outcomes

A mature view of leverage focuses on the full distribution of outcomes rather than a single base case. Downside scenarios quickly reveal how leverage concentrates risk: when performance weakens, equity absorbs losses first.

Figure 3 illustrates how higher leverage increases expected IRR but also widens dispersion, creating both a fatter upside tail and a higher probability of capital loss.

Figure 3. Distribution of equity returns under low, moderate, and high leverage.
Distribution of equity returns under low, moderate, and high leverage
Source: the author.

Higher leverage raises expected returns but materially increases downside risk.

For junior bankers, the key lesson is that leverage is a design choice with consequences. A robust analysis interrogates downside resilience, covenant headroom, and the coherence between capital structure and strategy.

The role of investment banks

Investment banks play a central role in structuring and advising on leverage. On buy-side mandates, they assist sponsors in negotiating financing packages and ensuring proposed leverage aligns with market appetite. On sell-side mandates, they help sellers compare bids not only on price, but on financing certainty and execution risk.

Conclusion

Leverage sits at the heart of LBO economics, but its effects are often oversimplified. For analysts, the real skill lies in linking model outputs to a coherent economic narrative about cash flows, debt service, and downside resilience.

Related posts on the SimTrade blog

   ▶ Alexandre VERLET Classic brain teasers from real-life interviews

   ▶ Emanuele BAROLI Interest Rates and M&A: How Market Dynamics Shift When Rates Rise or Fall

   ▶ Bijal GANDHI Interest Rates

Useful resources

Academic references

Fama, E. F., & MacBeth, J. D. (1973). Risk, Return, and Equilibrium: Empirical Tests. Journal of Political Economy, 81(3), 607–636.

Koller, T., Goedhart, M., & Wessels, D. (2020). Valuation: Measuring and Managing the Value of Companies (7th ed.). Hoboken, NJ: John Wiley & Sons.

Axelson, U., Jenkinson, T., Strömberg, P., & Weisbach, M. S. (2013). Borrow Cheap, Buy High? The Determinants of Leverage and Pricing in Buyouts. The Journal of Finance, 68(6), 2223–2267.

Kaplan, S. N., & Strömberg, P. (2009). Leveraged Buyouts and Private Equity. Journal of Economic Perspectives, 23(1), 121–146.

Gompers, P. A., & Lerner, J. (1996). The Use of Covenants: An Empirical Analysis of Venture Partnership Agreements. Journal of Law and Economics, 39(2), 463–498.

Business data

PitchBook

About the author

The article was written in January 2026 by Ian DI MUZIO (ESSEC Business School, Master in Finance (MiF), 2025–2027).

   ▶ Read all posts written by Ian DI MUZIO

Quantifying the Gap: Why AI Productivity will fail to Move the Market

by
Andrei DONTU

In this article, Andrei DONTU (ESSEC Business School, Global Bachelor in Business Administration (GBBA) 2025-2026) explains the gap between the productivity gains and the unrealized returns of the investors regarding the investments in AI.

Introduction

In the current market landscape, “Artificial Intelligence” has become the magic word used to justify almost any valuation. The narrative is simple: AI will trigger a productivity explosion, fundamentally altering the unit economics of global business and ushering in a new era of equity growth. However, when we cut away the marketing icing and look at the underlying economic data, a much more sobering economic reality emerges, one that I call the AI Productivity Myth.

Distributions of Correlations: Stock Growth vs Industrial Stock Growth
”Distributions
Source: ECB data.

The core of this myth is the macroeconomic assumption that a more efficient workforce naturally results in a more valuable stock market. This myth has been debunked on numerous occasions(1) (2), but the disruption created by AI creates new challenges that have to be addressed. To test this, I conducted an extensive analysis on the correlation between labor productivity and stock market returns across European Union countries. The results were startling. The correlation value was only 0.063.

The 0.063 Reality Check

In the world of statistics, a correlation of 0.063 is effectively zero. This figure reveals a profound “missing link” in our economic understanding. For decades, workers in the EU became more efficient and had almost no direct impact on the country’s stock market performance.

In conducting this study, I took the data for the EU member states starting from 2005 until 2025. This time-lapse represents the period following the “.com bubble” and the beginning of the mass adoption of informational systems by many companies. As the cost of owning, operating, and managing these systems became more accessible, it represented a fresh start.

Productivity Trend
Productivity Trend
Source: ECB data.

By computing the productivity with the return on the EURO STOXX, a clear result can be seen: working harder is not making the enterprise more valuable if everyone is capable of implementing similar strategies. At an individual level, some countries can excel in the implementation if the governance facilitates the projection of technology by liberating and promoting innovation. Some good examples would be the Netherlands, a leader in innovation in the technology and information sector, benefiting heavily from the adoption of the internet and outsourcing, and Italy, a counter-example in productivity growth with similarly low growth in the stock market.

Sectoral Correlation
Sectoral Productivity
Source: ECB data.

Although many countries exhibit a significant correlation between growth and productivity, the reality shows that some sectors are driving the general growth. The benefits of the new technologies implemented in the information sector led to a process simplification, reducing the due diligence and accelerating the globalization of the product and market access. While some sectors directly benefited from the implementation of the internet in the processes, the industrial process lagged in showing a similar impact from the internet adoption.

The implementation of the internet resulted in winners and losers, affecting individual companies differently and consolidating the position of global leaders in the industry. Following the .com bubble, many companies disappeared or were acquired by the companies that successfully bypassed the fast-paced changes of the new demands of the customers that encountered a truly global world for the first time (3).

Stock Market Trends
Stock Market Trends
Source: ECB data.

This finding is the “missing link” for the AI Productivity Myth. If thirty years of digital and industrial evolution failed to bridge this gap, investors must ask why AI will be the exception and close the gap. My research suggests that productivity is a measure of how hard an economy works, whereas stock growth is a measure of how much of that work shareholders actually get to keep. In the EU, these two variables operate in parallel universes and vary vastly from one country to another.

Individual Correlation: Productivity vs Stock Growth
Stock Market Trends
Source: ECB data.

Echoes of the Internet Boom

In the late 1990s, the Internet was the “disruptive power” that promised a new era of high profits from internet sales, showing positive sentiment in the new technology (4). Specialists discussed the exponential implementation of the internet and how all companies will use it in maximizing their profits and directly impacting the prices of the stocks. Many investors were unaware of the risk involved in the investments in new technologies, and focused solely on the possible returns from their investments. The promise was very similar to the AI’s, the internet will revolutionize the world, creating a massive leap in how we exchange information.

Although the information travelled faster and everyone was benefiting from the effects of a “smaller world”, it backfired. While the technology succeeded, the investments often failed. When the bubble burst in 2000, it wasn’t because the internet stopped working; it was because the market momentum had far outpaced the actual ability of companies to turn that efficiency into profit.

Today, AI is facing the same exaggerated expectations. Investors are paying premium prices for the hope of future productivity, but they are ignoring thehardships of the adoption gap: the period where companies spend billions on Graphic Processing Units(GPU), the core of the AI systems, and energy without seeing a single cent of increased margin. This gold rush after the current stock of GPUs is leading to a speculative movement over their importance and short product cycles, leading to slow amortizations for ⅚ years, while in reality they become obsolete in ⅔ years(5).

The “Blurriness” of AI Returns

The “blurriness” of Large Language Models (LLMs) refers to the difficulty in measuring their return on investment (ROI). The investment in AI chips, developing agents, and managing data centers comes into effect without prior benchmarks on how such investments should be estimated, and it is hard to quantify their success in monetary terms or advantages against the competitors. Unlike a new factory machine that produces 10% more widgets, an LLM’s impact on knowledge and streamlining is harder to capture on a balance sheet.

  • The CapEx Trap: Companies are engaged in an “Arms Race,” spending record amounts on infrastructure. Firms are paying considerable amounts on implementation costs (licensing, retraining, power, cloud, cybersecurity,etc.), but often eats up the savings the AI was supposed to generate.
  • The Perfect Competition Paradox: If every firm uses AI to work 50% faster, no single firm has a competitive advantage. Competition forces them to lower prices, passing the productivity gain to the consumer while the investor is left with higher tech costs and lower retention of both earnings and customers.
  • Front-Running the Gains: The stock market is forward-looking. Most expected gains are already baked into today’s prices. When a company finally reports a “good” productivity increase, the stock may drop because it wasn’t the “miraculous” increase the market demanded to justify its valuation.

Conclusion: Why the Low Correlation Matters

The key takeaway is the danger of the 0.063 correlation. It proves that efficiency is the tool for survival, but not a guaranteed engine for wealth. In the European Union (EU), efficiency gains are frequently absorbed by regulatory compliance, labor costs, and competitive pricing before they ever reach the bottom line.

Why should I be interested in this post?

As we move through 2026, the “blurriness” of AI will likely resolve into a clear picture of high costs and incremental gains. For everyone, the lesson should be clear: do not mistake a technological revolution for a guaranteed stock market return. In an environment where the correlation between productivity and returns is as low, the “AI Myth” is a luxury that few can afford to believe in.

Other SimTrader Blogs:

   ▶ Mahé FERRET Behavioral Finance

References

(1) Chun, H., Kim, J. W., & Morck, R. (2016). Productivity growth and stock returns: firm-and aggregate-level analyses. Applied Economics, 48(38), 3644-3664.

(2) Pellegrini, C. B., Romelli, D., & Sironi, E. (2011). The impact of governance and productivity on stock returns in European industrial companies. Investment management and financial innovations, (8, Iss. 4), 20-28.

(3) Johansen, A., & Sornette, D. (2000). The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash. The European Physical Journal B-Condensed Matter and Complex Systems, 17(2), 319-328.

(4) Bandyopadhyay, S., Lin, G., & Zhang, Y. (2001). A critical review of pricing strategies for online business models.

(5) Lifespan of AI chips- the 300 billion question

Data sources:

European Central Bank EURO STOXX

European Central Bank~Productivity Growth

MSCI Report

About the author

The article was written in January 2026 by Andrei DONTU (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2025-2026).

   ▶ Read all posts written by Andrei DONTU

“The big money is not in the buying and selling, but in the waiting.” – Charlie Munger

by

In an era dominated by instant trading for individuals, high-frequency trading firms, ever-faster market infrastructures, and social-media-driven market narratives, patience has become an underrated virtue.

Hadrien PUCHE

In this article, Hadrien PUCHE (ESSEC Business School, Grande École Program, Master in Management, 2023-2027) comments on Charlie Munger’s famous quote about the role of patience and discipline in long-term investing, and what it teaches us about the power of compounding, temperament, and time.

About Charlie Munger

Charlie Munger (1924–2023) was the long-time vice chairman of Berkshire Hathaway, and Warren Buffett’s closest business partner for over 50 years. Munger profoundly influenced Buffett’s philosophy, steering him toward buying high-quality businesses and holding them for the long run.

Munger’s wisdom combined principles from psychology, economics, and philosophy to form a timeless view of markets and human behavior.

Charlie Munger
Source: Wikimedia Commons

About the quote

“The big money is not in the buying and selling, but in the waiting.”

This quote is one of Charlie Munger’s most enduring lessons, though its origins date back to the 1923 classic Reminiscences of a Stock Operator by Jesse Livermore. Munger adopted and popularized this wisdom throughout his career, most notably during the Berkshire Hathaway annual shareholder meetings, to explain the firm’s extraordinary success.

The quote encapsulates the essence of long-term investing: wealth is not built through frequent market timing, but through the quiet power of patience and compounding. Munger and Buffett repeatedly emphasized that the most successful investors are not those who move the fastest, but those who possess the “temperament” to sit still when the rest of the market is acting impulsively.

Ultimately, this principle suggests that time, rather than timing, is the real driver of wealth creation. In Munger’s view, “waiting” is an active strategy. It is the disciplined choice to let your initial thesis play out without the interference of market noise or emotional reactions.

Analysis of the quote

This quote highlights a key principle of investing: activity is not the same as value creation. Many investors confuse motion with progress, feeling the urge to trade constantly in response to news, trends, or short-term price fluctuations.

Munger’s philosophy reminds us that wealth is not “generated” by the act of trading; it is accumulated by letting compounding do its work, a process that rewards patience and conviction far more than speed. Charlie Munger’s observation, “The first rule of compounding is to never interrupt it unnecessarily,” distills decades of investing wisdom into a single principle: long-term wealth creation depends less on brilliance than on consistency and emotional endurance.

Every time an investor exits a position due to short-term fear or a desire to “lock in” small gains, they “reset” the clock and sacrifice the exponential growth that occurs in the final years of a holding period. Furthermore, frequent activity creates “leakage” through trading costs and taxes, which act as a constant drag on returns.

In essence, Munger’s rule is a call for consistency over cleverness, emphasizing that compounding rewards time and temperament, qualities far rarer and more valuable than momentary flashes of insight.

Financial concepts related to the quote

I present below three financial concepts: the power of compounding, opportunity cost and value of inactivity, and the patience premium of investor behavior.

The Power of Compounding

Compounding is the process by which returns themselves begin to generate further returns: a self-reinforcing cycle of growth. Its effect is exponential rather than linear: small, steady gains, that accumulate dramatically over time.

For instance, at a 10% annual return, an investment of 100 grows to 110 after one year, 259 after ten years, and 1,745 after thirty years. The formula for the future value Vf is:

Vf = Vi × (1 + ρ / n)n × t

Where ρ (rho) is the interest rate and n is the number of times that interest is compounded every year. The key variable is time (t): the longer the compounding process continues uninterrupted, the greater the growth. Interruptions through withdrawals or frequent trading can significantly reduce the ultimate value of the investment.

Opportunity Cost and the value of inactivity

In behavioral and financial terms, opportunity cost is what one sacrifices by choosing one action over another. Many investors mistakenly equate activity with progress, yet frequent transactions often lead to higher costs, taxes, and emotional errors. As Buffett and Munger emphasize, strategic inactivity (allowing quality investments to compound) is often the most effective decision one can make.

The “Goalkeeper Syndrome”: A Lesson from the Pitch

This tendency to favor motion over stillness is driven by action bias. A study by Bar-Eli et al. (2007) on elite soccer goalkeepers found that while goalkeepers have the highest probability of stopping a penalty by staying in the center of the goal, they only do so 6.3% of the time. In over 93% of cases, they dive to the left or right.

This “Goalkeeper Syndrome” is best explained by Daniel Kahneman’s Norm Theory (Thinking, Fast and Slow, 2011). Kahneman demonstrates that humans feel more intense regret when a bad outcome results from an action than from an inaction—unless the action is the norm.

In the goalkeeper’s case, jumping is the social norm. If a goal is scored while the keeper stands still, they appear to have “done nothing,” which is socially and emotionally harder to bear. If they dive and miss, they have “tried.” For investors, this creates a dangerous paradox. In the investment industry, “activity” is often the norm. A fund manager who does nothing during a market shift risks being seen as lazy or incompetent. By “diving” into a new trade, they protect themselves from the intense regret of being wrong while being inactive.

Recognizing this bias is essential for any finance professional. True discipline lies in knowing when to act, and having the courage to stay in the center of the net when everyone else is jumping.

The Patience Premium and Investor Behavior

Behavioral finance demonstrates that human psychology often works against long-term success. Biases like overconfidence, loss aversion, and herd behavior push investors to buy high and sell low. The ability to stay rational when others panic — to maintain conviction in one’s analysis rather than react to market noise — creates a powerful advantage.

This discipline produces what can be called a patience premium: higher long-term returns earned simply by avoiding costly mistakes. As Warren Buffett summarized, “The stock market is a device for transferring money from the impatient to the patient.”

Private equity provides a practical illustration of the patience premium. Investments in private companies are typically illiquid for many years, forcing investors to maintain a long-term perspective. This “forced patience” comes with a reward: private equity funds historically deliver higher returns than public markets, reflecting both the illiquidity premium and the benefits of disciplined, long-term value creation.

Illiquidity vs average expected returns graph
In general, more illiquid investments offer higher expected returns, as investors are compensated for the additional illiquidity risk. Note: Values are illustrative.

Beyond the financial premium, illiquidity serves as a vital behavioral guardrail. In public markets, the ability to sell an asset instantly makes it far easier to succumb to panic during market turbulence. You cannot “panic sell” an asset that you cannot sell quickly. By removing the option for impulsive exits, illiquid structures protect investors from their own emotional reactions, ensuring that compounding is never interrupted unnecessarily.

My opinion about this quote

I believe this quote captures one of the hardest truths in investing: sometimes the most profitable action is to do nothing. In today’s world of trading apps, meme stocks, and 24-hour market news, patience feels almost countercultural. Investors are constantly nudged to act, reacting to every headline or social media hype. Yet, this very activity often erodes long-term returns.

One concrete way to see this principle in action is through passive investing. Actively managed funds exist with the goal of outperforming their benchmark indexes, yet studies like SPIVA (S&P Indices Versus Active) show that most fail to do so over long periods. For instance, over 10-year periods, roughly 80% of U.S. equity funds underperformed the S&P 500 index.

underperformance rates over time SPIVA
This SPIVA graph illustrates that most actively managed funds underperform their benchmark index over the long term, highlighting the advantage of passive investing.

However, this debate between active and passive management leads us to a fascinating theoretical tension: the Grossman-Stiglitz Paradox. If every investor followed the “sweet fruit” of passive investing because it is statistically superior, the market would cease to function properly and make active investment worth it again.

The paradox, formulated by Sanford Grossman and Joseph Stiglitz in 1980, suggests that markets cannot be perfectly efficient. If a market were perfectly efficient (meaning all information is already reflected in the price), no one would have an incentive to spend time uncovering new information. But if no one uncovers information, the market becomes inefficient. Therefore, the market must remain “efficiently inefficient”: it requires active managers to do the “bitter” work of research, even if they often fail to beat the index, so that passive investors can enjoy the “sweet” ride of a mostly accurate market price.

Yet, the lesson is clear: staying invested in a broadly diversified index often beats trying to “time” the market. The patient investor harnesses compounding without the friction of trading costs, taxes, and emotional mistakes. As Munger famously noted, “the big money is not in the buying and selling, but in the waiting.” It’s not about inactivity for its own sake; it’s about informed, disciplined inactivity.

Why should you be interested in this post?

Beyond investing, this quote is about cultivating a mindset of patience, discipline and rational thinking that can separate successful individuals from the crowd. Mastering the art of waiting will give you an edge, no matter which industry you desire to work in.

Careers, skills, and personal growth all compound like investments; building expertise takes time. Quick wins may feel gratifying, but long-term impact comes to those who embrace patience and persist through the quiet, unglamorous work that others sometimes avoid.

Related posts

   ▶ All posts about Quotes

   ▶ Hadrien PUCHE “The stock market is filled with individuals who know the price of everything, but the value of nothing.” – Philip Fisher.

   ▶ Hadrien PUCHE “Most people overestimate what they can do in a year and underestimate what they can do in ten.” – Bill Gates

   ▶ Hadrien PUCHE “Patience is bitter, but its fruit is sweet.” – Aristotle

Useful resources

Berkshire Hathaway’s website: www.berkshirehathaway.com

Munger, Charlie. Poor Charlie’s Almanack, 2005.

Buffett, Warren. Berkshire Hathaway Shareholder Letters.

Kahneman, Daniel. Thinking, Fast and Slow, 2011. (especially Chapter 32 on regret and norm theory).

Bar-Eli, M., Azar, O. H., Ritov, I., Keidar-Levin, Y., & Schein, G. (2007) Action bias among elite soccer goalkeepers: The case of penalty kicks. Journal of Economic Psychology, 28(5), 606-621.

About the Author

This article was written in January 2026 by Hadrien PUCHE (ESSEC Business School, Grande École Program, Master in Management, 2023-2027).

   ▶ Read all posts written by Hadrien PUCHE

Patience is bitter, but its fruit is sweet – Aristotle

by

Waiting is never easy. In life, at work, and certainly in finance, we are naturally drawn to quick outcomes and instant gratification. This preference for immediacy is built into our psychology, a leftover from a time when obtaining resources in the present meant survival.

This is why the quote resonates so strongly. It expresses a universal tension between the comfort of the present and the rewards that arrive only through the passage of time. The analogy with food captures the idea beautifully: most of us choose what tastes good now, such as a sugary treat or a risky trade, instead of what will benefit us later, like a healthy meal or a disciplined investment. Markets consistently reward discipline, yet human nature urges us toward the immediate emotional release provided by action.

Hadrien PUCHE

In this article, Hadrien PUCHE (ESSEC, Grande École Program, Master in Management, 2023-2027) comments on Aristotle’s famous quote about the discipline required for long-term success.

Aristotle

Aristotle
Source: Wikimedia Commons

Aristotle was one of the most influential thinkers in ancient Greece and a foundational figure of Western philosophy. Born in the fourth century BCE in Stagira, he studied under Plato and later tutored Alexander the Great. He founded the Lyceum, emphasizing careful observation and reason across logic, ethics, and metaphysics.

In ethics, Aristotle focused on character development through deliberate practice. He believed virtues like patience are not natural gifts, but habits formed through repeated disciplined actions. This connects directly with long-term investing, which rewards consistent behaviors and emotional mastery. While the quote is often misattributed, its message stands at the center of successful investing: the true test is not intelligence, but emotional endurance.

Analysis of the Quote

This quote encompasses the central tension in investing: the difficulty of the present versus the reward of the future. In markets, patience is an active discipline. It requires staying invested through volatility and resisting popular trends. These moments of discomfort represent the “bitter” side of patience.

The “sweet fruit” is compounding—a force that transforms small, consistent gains into extraordinary outcomes. It only rewards those who give it time. Legendary investors like Buffett, Lynch, and Munger insist that patience, not genius, accounts for their success. The investor who endures temporary discomfort for long-term clarity exercises patience exactly as Aristotle would have understood it.

Short term vs long term trends
Short-term variations matter less than the long-term average trend. Source: Wikimedia Commons.

Historical Failures of Patience

History shows that impatience fueled many financial catastrophes. During the 17th-century **Tulip Mania**, prices soared as traders flipped bulbs for quick profits, only to see the market collapse in days. The same pattern repeated in the **South Sea Bubble** and the **Dot-Com Bubble**, where speculation displaced fundamentals. Across these episodes, short-term excitement overshadowed long-term thinking, turning promising opportunities into costly lessons.

Financial Concepts Tied to the Quote

Time Horizon: The Power of μ over σ

Having a long time horizon allows investors to rely on fundamentals rather than hype. Quantitatively, this is the battle between the expected return ($\mu$) and volatility ($\sigma$). While market prices are dominated by $\sigma$ (random swings) in the short term, the long-term outcome is driven by $\mu$ (intrinsic growth).

Probability of loss depending on time

Viewing decisions through a 10 or 20-year perspective reframes downturns as opportunities. This is due to time diversification: as the holding period ($t$) expands, the annualized volatility decreases at a rate of $1/\sqrt{t}$. Time reduces the “noise,” making the fundamental $\mu$ eventually overwhelm the temporary $\sigma$.

Risk and Reward Balance

Patience does not remove risk, but it improves emotional endurance. Impatient investors often understand risk in theory but panic when it appears on a statement, leading to selling at the worst time. Patient investors focus on long-term goals, allowing time to work as a risk management tool.

Opportunity Cost and the Value of Inactivity

In behavioral finance, opportunity cost is what one sacrifices by choosing one action over another. Many investors mistakenly equate activity with progress, yet frequent transactions lead to higher costs and taxes. Buffett and Munger emphasize that strategic inactivity is often the most effective decision.

This tendency to favor motion is driven by action bias, or the “Goalkeeper Syndrome.” A study by Bar-Eli et al. (2007) found that goalkeepers have the highest probability of stopping a penalty by staying in the center of the goal, yet they do so only 6.3% of the time. They dive because the regret of “doing nothing” feels worse than the regret of a failed action. This carries over to investment management, where investors churn portfolios during volatility just to feel in control.

My Opinion in a Modern Context

This quote is especially relevant today. Trading apps encourage activity, and social media amplifies FOMO (Fear of Missing Out). In this environment, patience is a competitive advantage. Successful investors are often not the smartest, but the most consistent. In a world that rewards speed, the courage to wait becomes rare and extremely valuable.

Why This Quote Should Matter to You

Patience isn’t just a pleasant virtue; it’s a tool that shapes results. Whether building a career or managing finances, patience allows you to:

  • Make thoughtful choices grounded in clarity rather than impulse.
  • Avoid stress-driven errors.
  • Stay aligned with long-term goals despite short-term distractions.

Related Posts on the SimTrade Blog

   ▶ All posts about Quotes

   ▶ Hadrien PUCHE “Most people overestimate what they can do in a year…” – Bill Gates

   ▶ Hadrien PUCHE “Price is what you pay, value is what you get” – Warren Buffett

Useful resources

Aristotle. Nicomachean Ethics. Translated by Terence Irwin. Hackett Publishing, 1999.

Bar-Eli, M., Azar, O. H., Ritov, I., Keidar-Levin, Y., & Schein, G. (2007). Action bias among elite soccer goalkeepers: The case of penalty kicks. Journal of Economic Psychology, 28(5), 606-621.

Kindleberger, Charles P., and Robert Aliber. Manias, Panics, and Crashes. Palgrave Macmillan, 2011.

Mackay, Charles. Extraordinary Popular Delusions and the Madness of Crowds. Wordsworth Editions, 1995.

About the Author

The article was written in January 2026 by Hadrien PUCHE (ESSEC, Grande École Program, Master in Management – 2023-2027).

Modeling Asset Prices in Financial Markets: Arithmetic and Geometric Brownian Motions

by
Saral BINDAL

In this article, Saral BINDAL (Indian Institute of Technology Kharagpur, Metallurgical and Materials Engineering, 2024-2028 & Research assistant at ESSEC Business School) presents two statistical models used in finance to describe the time behavior of asset prices: the arithmetic Brownian motion (ABM) and the geometric Brownian motion (GBM).

Introduction

In financial markets, performance over time is governed by three fundamental variables: the drift (μ), volatility (σ), and maybe most importantly time (T). The drift represents the expected growth rate of the price and corresponds to the expected return of assets or portfolios. Volatility measures the uncertainty or risk associated with price fluctuations around this expected growth and corresponds to the standard deviation of returns. The relationship between these variables reflects the trade-off between risk and return. Time, which is related to the investment horizon set by the investor, determines how both performance and risk accumulate. Together, these variables form the foundation of asset pricing to model the behavior of market price over time, and in fine the performance of the investor at their investment horizon.

Modeling asset prices

Asset price modeling is used to understand the expected return and risk in asset management, risk management, and the pricing of complex financial products such as options and structured products. Although asset prices are influenced by countless unpredictable risk factors, quants in finance always try to find a parsimonious way to model asset prices (using a few parameters only).

The first study of asset price modelling dates from Louis Bachelier in 1900, in his doctoral thesis Théorie de la Spéculation (The Theory of Speculation), where he modelled stock prices as a random walk and applied this framework to option valuation. Later, in 1923, the mathematician Norbert Wiener formalized these ideas as the Wiener process, providing the rigorous stochastic foundation that underpins modern finance.

In the 1960s, Paul Samuelson refined Bachelier’s model by introducing the geometric Brownian motion, which ensures positive stock prices following a lognormal statistical distribution. His 1965 paper “Rational Theory of Warrant Pricing” laid the groundwork for modern asset price modelling, showing that discounted stock prices follow a martingale.

We detail below the two models usually used in finance to model the evolution of asset prices over time: the arithmetic Brownian motion (ABM) and the geometric Brownian motion (GBM). We will then use these models to simulate the evolution of asset prices over time with the Monte Carlo simulation method.

Arithmetic Brownian motion (ABM)

Theory

One of the most widely used stochastic processes in financial modeling is the arithmetic Brownian motion, also known as the Wiener process. It is a continuous stochastic process with normally distributed increments. Using the Wiener process notation, an asset price model in continuous time based on an ABM can be expressed as the following stochastic differential equation (SDE):


SDE for the arithmetic Brownian motion

where:

  • dSt = infinitesimal change in asset price at time t t
  • μ = drift (growth rate of the asset price)
  • σ = volatility (standard deviation)
  • dWt = infinitesimal increment of wiener process (N(0,dt))

Note that the standard Brownian motion is a special case of the arithmetic Brownian motion with a mean equal to zero and a variance equal to one.

In this model, both μ and σ are assumed to be constant over time. It can be shown that the probability distribution function of the future price is a normal distribution implying a strictly positive (although negligible in most cases) probability for the price to be negative.

Integrating the SDE for dSt over a finite interval (from time 0 to time t), we get:


Integrated SDE for the arithmetic Brownian motion

Here, Wt is defined as Wt = √t · Zt, where Zt is a normal random variable drawn from the standard distribution N(0, 1) with mean equal to 0 and variance equal to 1.

At any date t, we can also compute the expected value and a confidence interval such that the asset price St lies between the lower and upper bound of the interval with probability equal to 1-α.


Theoritical formulas for mean, upper and lower limits of ABM model

Where S0 is the initial asset price and zα.

The z-score for a confidence level of (1 – α) can be calculated as:


z-score formula

where Φ-1 denotes the inverse cumulative distribution function (CDF) of the standard normal distribution.

For example the statistical z-score (zα) values for 66%, 95%, and 99% confidence intervals are as the following:


z-score examples

Monte Carlo simulations with ABM

Since Monte Carlo simulations are performed in discrete time, the underlying continuous-time asset price process (ABM) is approximated using the Euler–Maruyama discretization of SDEs (see Maruyama, 1955), as shown below.


Discretization formula for the arithmetic Brownian motion (ABM)

where Δt denotes the time step, expressed in the same time units as the drift parameter μ and the volatility parameter σ (usually the annual unit). For example, Δt may be equal to one day (=1/252) or one month (=1/12).

Figure 1 below illustrates a single simulated asset price path under an arithmetic Brownian motion (ABM), sampled at monthly intervals (Δt = 1/12) over a 10-year horizon (T = 10). Alongside the simulated path, the figure shows the expected (mean) price trajectory and the corresponding upper and lower bounds of a 66% confidence interval. In this example, the model assumes an annual drift (μ) of $8, representing the expected growth rate, and an annual volatility (σ) of $15, capturing random price fluctuations. The initial asset price (S0) is equal to $100.

Figure 1. Single Monte Carlo–simulated asset price path under an Arithmetic Brownian Motion model.
A Monte Carlo–simulated price path under an arithmetic Brownian motion model
Source: computation by the author (with Excel).

Figure 2 below illustrates 1,000 simulated asset price paths generated under an arithmetic Brownian motion (ABM). In addition to the simulated paths, the figure displays the expected (mean) price trajectory along with the corresponding upper and lower bounds of a 66% confidence interval, using the same parameter settings as in Figure 1.

Figure 2. Monte Carlo–simulated asset price paths under an Arithmetic Brownian Motion model.
Monte Carlo–simulated price paths under an arithmetic Brownian motion model.
Source: computation by the author (with R).

Geometric Brownian motion (GBM)

Theory

Since an arithmetic Brownian motion (ABM) can take negative values, it is unsuitable for directly modeling stock prices if we assume limited liability for investors. Under limited liability, an investor’s maximum possible loss is indeed confined to their initial investment, implying that asset prices cannot fall below zero. To address this limitation, financial models instead use geometric Brownian motion (GBM), a non-negative stochastic process that is widely employed to describe the evolution of asset prices. Using the Wiener process notation, an asset price model in continuous time based on a GBM can be expressed as the following stochastic differential equation (SDE):


SDE for the geometric Brownian motion (GBM)

where:

  • St = asset price at time t t
  • μ = drift (growth rate of the asset price)
  • σ = volatility (standard deviation)
  • dWt = infinitesimal increment of wiener process (N(0,dt))

Integrating the SDE for dSt/St over a finite interval, we get:


Integrated SDE for the geometric Brownian motion (GBM)

The theoretical expected value and confidence intervals are given analytically by the following expressions:


Theoritical formulas for mean, upper and lower limits of GBM model

Monte Carlo simulations with GBM

To implement Monte Carlo simulations, we approximate the underlying continuous-time process in discrete time, yielding:


Asset price under discrete GBM

where Zt is a standard normal random variable drawn from the distribution N(0, 1) and Δt denotes the time step, chosen so that it is expressed in the same time units as the drift parameter μ and the volatility parameter σ.

Figure 3 below illustrates a single simulated asset price path under a geometric Brownian motion (GBM), sampled at monthly intervals (Δt = 1/12) over a 10-year horizon (T = 10). Alongside the simulated path, the figure shows the expected (mean) price trajectory and the corresponding upper and lower bounds of a 66% confidence interval. In this example, the model assumes an annual drift (μ) of 8%, representing the expected growth rate, and an annual volatility (σ) of 15%, capturing random price fluctuations. The initial asset price is S0 €100.

Figure 3. Monte Carlo–simulated asset price path under a Geometric Brownian Motion model.
Monte Carlo–simulated asset price path under a GBM model.
Source: computation by the author (with Excel).

Figure 4 below illustrates 1,000 simulated asset price paths generated under a geometric Brownian motion (GBM). In addition to the simulated paths, the figure displays the expected (mean) price trajectory along with the corresponding upper and lower bounds of a 66% confidence interval, using the same parameter settings as in Figure 3.

Figure 4. Monte Carlo–simulated asset price paths under a Standard Brownian Motion model.
Monte Carlo–simulated asset price paths under a Geometric Brownian Motion model.
Source: computation by the author (with R).

Discussion

The drift μ represents the expected rate of growth of asset prices, so its cumulative contribution increases linearly with time as μT. In contrast, volatility σ captures investment risk, and its cumulative impact scales with the square root of time as σ√T. As a result, over short horizons stochastic shocks tend to dominate the deterministic drift, whereas over longer horizons the expected growth component becomes increasingly prominent.

When many paths for the asset price are simulated and plotted over time, the resulting trajectories form a cone-shaped region, commonly referred to as a fan chart. The center of this fan traces the smooth expected path governed by the drift μ, while the widening envelope reflects the growing dispersion of outcomes induced by volatility σ.

This representation underscores a key implication for long-term investing and risk management: uncertainty expands with the investment horizon even when model parameters remain constant. While the expected value evolves predictably and linearly through time, the range of plausible outcomes broadens at a slower, square-root rate, shaping the risk–return trade-off across different time scales.

You can download the Excel file provided below for generating Monte Carlo Simulations for asset prices modeled on arithmetic and geometric Brownian motion.

Download the Excel file.

You can download the Python code provided below, for generating Monte Carlo Simulations for asset prices modeled on arithmetic and geometric Brownian motion.

Download the Python code.

Alternatively, you can download the R code below with the same functionality as in the Python file.

Download the R code.

Link between the ABM and the GBM

The ABM and GBM models are fundamentally different: the drift for the ABM is additive while the drift for the GBM is multiplicative. Moreover, the statistical distribution for the price for the ABM is a normal distribution while the statistical distribution for the GBM is a log-normal distribution. However, we can study the relationship between the two models as they are both used to model the same phenomenon, the evolution of asset prices over time in our case.

We can especially study the relationship between the two parameters of the two models, μ and σ. In the presentation above, we used the same notations for μ and σ for the two models, but the values of these parameters for the two models will be different when we apply these models to the same phenomenon. There is no mapping of the ABM and GBM in the price space such that we get the same results as the two models are fundamentally different.

Let us rewrite the two models (in terms of SDE) by differentiating the parameters for each model:


SDE for the ABM and GBM

To model the same phenomenon, we can use the following relationship between the parameters of the ABM and GBM models:


Link between the ABM and GBM parameters.

To make the two models comparable in terms of price behavior, an ABM can locally approximate GBM by matching instantaneous drift and volatility such that:


Local link between the ABM and GBM parameters.

This local correspondence is state-dependent and time-varying, and therefore not a true parameter equivalence.

Figure 5 below compares the asset price path for an ABM, monthly adjusted ABM and a GBM.


Simulated asset price paths for ABM, adjusted ABM and GBM.

Why should I be interested in this post?

Understanding how asset prices are modeled, and in particular the difference between additive and multiplicative price dynamics, is essential for building strong intuition about how prices evolve over time under uncertainty. This understanding forms the foundation of modern risk management, as it directly informs concepts such as capital protection, downside risk, and the long-term behavior of investment portfolios.

Related posts on the SimTrade blog

   ▶ Saral BINDAL Historical Volatility

   ▶ Saral BINDAL Implied Volatility and Option Prices

   ▶ Jayati WALIA Brownian Motion in Finance

   ▶ Jayati WALIA Monte Carlo simulation method

Useful resources

Academic research

Bachelier L. (1900) Théorie de la spéculation. Annales scientifiques de l’École Normale Supérieure, 3e série, 17, 21–86.

Kataoka S. (1963) A stochastic programming model. Econometrica, 31, 181–196.

Lawler G.F. (2006) Introduction to Stochastic Processes, 2nd Edition, Chapman & Hall/CRC, Chapter “Brownian Motion”, 201–224.

Maruyama G. (1955) Continuous Markov processes and stochastic equations. Rendiconti del Circolo Matematico di Palermo, 4, 48–90.

Samuelson P.A. (1965) Rational theory of warrant pricing. Industrial Management Review, 6(2), 13–39.

Telser L. G. (1955) Safety-first and hedging. Review of Economic Studies, 23, 1–16.

Wiener N. (1923) Differential-space. Journal of Mathematics and Physics, 2, 131–174.

Other

H. Hamedani, Brownian Motion as the Limit of a Symmetric Random Walk, ProbabilityCourse.com Online chapter section.

About the author

The article was written in January 2026 by Saral BINDAL (Indian Institute of Technology Kharagpur, Metallurgical and Materials Engineering, 2024-2028 & Research assistant at ESSEC Business School).

   ▶ Discover all articles written by Saral BINDAL

Valuation in Niche Sectors: Using Trading Comparables and Precedent Transactions When No Perfect Peers Exist

by
Ian DI MUZIO

In this article, Ian DI MUZIO (ESSEC Business School, Master in Finance (MiF), 2025–2027) discusses how valuation practitioners use trading comparables and precedent transactions when no truly “perfect” peers exist, and how to build a defensible valuation framework in Mergers & Acquisitions (M&A) for hybrid or niche sectors.

Context and objective

In valuation textbooks, comparable companies and precedent transactions appear straightforward: an analyst selects a sector in a database, obtains a clean peer group, computes an EV/EBITDA range, and applies it to the target. In practice, this situation is rare.

In real M&A mandates, the target often operates at the intersection of several activities (e.g. media intelligence, marketing technology, and consulting), across multiple geographies, with competitors that are mostly private or poorly disclosed.

Practitioners typically rely on databases such as Capital IQ, Refinitiv, PitchBook or Orbis. While these tools are powerful, they often return peer groups that are either too broad (mixing unrelated business models) or too narrow (excluding relevant private competitors). Private peers, even when strategically closest, usually cannot be used directly because they do not publish sufficiently detailed or standardized financial statements.

The objective of this article is therefore to provide an operational framework for valuing companies in such conditions. It explains:

  • What trading comparables and precedent transactions really measure;
  • Why “perfect” peers almost never exist in practice;
  • How to construct and clean a comps set in hybrid sectors;
  • How to use precedent transactions when listed peers are scarce;
  • How to combine these tools with discounted cash-flow (DCF) analysis and professional judgment.

The target reader is a student or junior analyst who already understands the intuition behind EV/EBITDA (enterprise value divided by earnings before interest, taxes, depreciation and amortisation), but wants to understand how experienced deal teams reason when databases do not provide obvious answers.

Trading comparables: what they measure in practice

Trading comparables rely on the idea that listed companies with similar risk, growth and operating characteristics should trade at comparable valuation multiples.

The construction of trading multiples follows three technical steps.

First, equity value is converted into enterprise value (EV):

Enterprise Value = Equity Value + Net Debt + Preferred Equity + Minority Interests – Non-operating Cash and Investments.

This adjustment ensures consistency between the numerator (EV) and the denominator (operating metrics such as EBITDA), which reflect the performance of the entire firm.

Second, the denominator is selected and cleaned. Common denominators include LTM or forward revenue, EBITDA or EBIT. EBITDA is typically adjusted to exclude non-recurring items such as restructuring costs, impairments or exceptional litigation expenses.

Third, analysts interpret the distribution of multiples rather than relying on a simple average. Dispersion reflects differences in growth, margins, business quality and risk. When peers are imperfect, this dispersion becomes a key analytical input.

EV/EBITDA distribution
Figure 1 – Distribution of EV/EBITDA multiples for a selected peer group in the media and marketing technology space. The figure is based on a simulated dataset constructed to mirror typical outputs from Capital IQ and Refinitiv for educational purposes. The target company is positioned within the range based on its growth, margin and risk profile.

Precedent transactions: what trading comps do not capture

Precedent transactions analyse valuation multiples paid in actual M&A deals. While computed in a similar way to trading multiples, they capture additional economic dimensions, as explained below.

Transaction multiples typically include a control premium, as buyers obtain control over strategy and cash flows. They also embed expected synergies and strategic considerations, as well as prevailing credit-market conditions at the time of the deal.

From a technical standpoint, transaction enterprise value is reconstructed at announcement using the offer price, fully diluted shares, and the target’s net debt and minority interests. Careful alignment between balance-sheet data and LTM operating metrics is essential.

Trading vs precedent multiples
Figure 2 – Comparison between trading comparables and precedent transaction multiples (EV/EBITDA). The illustration is based on a simulated historical sample consistent with PitchBook and Capital IQ deal data. Precedent transactions typically trade at higher multiples due to control premia, synergies and financing conditions.

Why perfect peers almost never exist

Teaching in business schools often presents comparables as firms with identical sector, geography, size and growth. In real M&A practice, this situation is exceptional.

Business models are frequently hybrid. A single firm may combine SaaS subscriptions, recurring managed services and project-based consulting, each with different margin structures and risk profiles.

Accounting reporting rules, such as International Financial Reporting Standards (IFRS) or US GAAP, further reduce comparability. Differences in revenue recognition (IFRS 15), lease accounting (IFRS 16) or capitalization of development costs can materially affect reported EBITDA.

Finally, many relevant competitors are private or embedded within larger groups, making transparent comparison impossible.

Building a defensible comps set in hybrid sectors

When similarity is weak, the analysis should begin with a decomposition of the target’s business model. Revenue streams are separated into functional blocks (platform, services, consulting), each benchmarked against the most relevant public proxies.

Peer groups are therefore modular rather than homogeneous. Geographic constraints are relaxed progressively, prioritising business-model similarity over local proximity.

Comps workflow
Figure 3 – Bottom-up workflow for constructing a defensible comps set in niche sectors. The figure illustrates the analytical sequence used by practitioners: business-model decomposition, peer clustering, financial cleaning and positioning within a valuation range.

When comparables fail: the role of DCF

When no meaningful peers exist, discounted cash-flow (DCF) analysis becomes the primary valuation tool.

A DCF estimates firm value by projecting free cash flows and discounting them at the weighted average cost of capital (WACC), which reflects the opportunity cost for both debt and equity investors.

Key valuation drivers include unit economics, operating leverage and realistic assumptions on growth and margins. Sensitivity analysis is essential to reflect uncertainty.

Corporate buyers versus private equity sponsors

Corporate acquirers focus on strategic fit and synergies, while private equity sponsors are constrained by required internal rates of return (IRR) and money-on-money multiples (MOIC).

Despite different objectives, both rely on the same principle: when comparables are imperfect, the narrative behind the multiples matters more than the multiples themselves.

How to communicate limitations effectively

From the analyst’s perspective, the key is transparency. Clearly stating the limitations of the comps set and explaining the analytical choices strengthens credibility rather than weakening conclusions.

Useful resources

Damodaran, A. (NYU), Damodaran Online.

Rosenbaum, J. & Pearl, J. (2013), Investment Banking: Valuation, Leveraged Buyouts, and Mergers & Acquisitions, Wiley.

Koller, T., Goedhart, M. & Wessels, D. (2020), Valuation: Measuring and Managing the Value of Companies, McKinsey & Company, 7th edition.

About the author

This article was written in January 2025 by Ian DI MUZIO (ESSEC Business School, Master in Finance (MiF), 2025–2027).

Understanding WACC: a student-friendly guide

by
Daniel LEE

In this article, Daniel LEE (ESSEC Business School, Global Bachelor in Business Administration (GBBA) – 2023-2027) explains the Weighted Average Cost of Capital (WACC).

Introduction

The Weighted Average Cost of Capital (WACC) is one of the most important concepts in corporate finance and valuation. I know that for some students, it feels abstract or overly technical. In reality, WACC is simpler than we think.

Whether it is a DCF, investment decision or assessing long-term value creation, understanding WACC is essential to interpret the financial world. In a DCF, WACC is used as the discount rate applied for FCF. Moreover, a higher WACC lowers the PV of future cashflows whereas a lower WACC increases the firm value. That is why WACC is a benchmark for value creation.

What is the cost of capital?

Every company needs funding to operate, which comes from two main sources: debt and equity. Debt is provided by banks or bondholders and equity is provided by shareholders. Both expect to be compensated for the risk they take. Shareholders typically require a higher return because they bear greater risk, as they are paid only after all other obligations have been met. In contrast, debt investors mainly expect regular interest payments and face lower risk because they are paid before shareholders in case of financial difficulty. The cost of capital represents the return required by each group of investors, and the Weighted Average Cost of Capital (WACC) combines these required returns into a single percentage.

The cost of capital is the return required by each investor group and WACC combines these two expectations with a simple %.

Breaking down the WACC formula

WACC is calculated with this formula:

Formula for the WACC

To gather these elements, we use several methods such as:

Cost of Equity: CAPM model

Cost of equity = Risk-free rate + β (Expected market return – Risk-free rate)

Beta measures how sensitive a company’s returns are to movements in the overall market. It captures systematic risk, meaning the risk that cannot be eliminated through diversification. A beta above 1 indicates that the firm is more volatile than the market, while a beta below 1 means it is less sensitive to market changes.

It is important to distinguish between unlevered beta and levered beta. The unlevered beta reflects only the risk of the firm’s underlying business activities, assuming the company has no debt. It represents the pure business risk of the firm and is especially useful when comparing companies within the same industry, as it removes the effect of different financing choices. This is why analysts often unlever betas from comparable firms and then relever them to match a target capital structure.

The levered beta, on the other hand, includes both business risk and financial risk created by the use of debt. When a company takes on more debt, shareholders face greater risk because interest payments must be made regardless of the firm’s performance. This increases the volatility of equity returns, leading to a higher levered beta and a higher cost of equity.

The risk-free rate represents the return investors can earn without taking any risk and is usually approximated by long-term government bond yields. It acts as the baseline return in the CAPM, since investors will only accept risky investments if they offer a return above this rate. Choosing the correct risk-free rate is important: it should match the currency and the time horizon of the cash flows. Changes in the risk-free rate have a direct impact on the cost of equity and, therefore, on firm valuation.

Cost of Debt

The interest payments are tax-deductible. That’s why we include 1-T in the formula. For example: if a company pays 5% interest annually and the corporate tax rate is 30% then the net cost of debt is 5%*(1-0.3) = 3.5%.

Capital Structure Weights

The weights Equity/(Equity+Debt) and Debt/(Equity+Debt) represents the proportion of equity and debt in the company’s balance sheet. We can then assume that a firm with more debt will have a lower WACC because debt is cheaper, but too much debt is risky. That is why the balance is very important for valuation and that usually you use a “target capitalization”. Target capitalization is an assumption of the level of debt and equity that a company is expected to have in the long term, rather than the current one.

Understanding risk through the WACC

WACC is a measure of risk. A higher WACC means the company is riskier and a lower WACC means it’s safer.

WACC is also closely linked to a firm’s capability to create value. If ROIC > WACC then the company creates value, but if ROIC < WACC, the company destroys value. This rule is widely used by CFO and investors to take decisions.

How is WACC used in practice?

  • WACC is the discount rate applied to FCF in the DCF > Lower WACC = Higher valuation; Higher WACC = Lower Valuation
  • As said before, it helps to assess value creation and find NPV
  • Assessing capital structure > helps to find the optimal balance between debt and equity
  • Comparing companies > good preliminary step to look at similar companies in the same company, the WACC will tell you a lot about their risk

Example

To illustrate how the WACC formula is used in practice, let us take the DCF valuation for Alstom that I made recently. In this valuation, WACC is used as the discount rate to convert future free cash flows into present value.

Alstom’s capital structure is defined using a target capitalization, that was chosen on the industry and the comps. Equity represents 75% of total capital and debt 25%. The cost of equity is estimated using the CAPM. Based on the base-case assumptions, Alstom has a levered beta that reflects both its industrial business risk and its use of debt. Combined with a risk-free rate and an equity risk premium, this leads to a cost of equity of 8.3%.

The cost of debt is estimated using Alstom’s borrowing conditions. Alstom pays an average interest rate of 4.12% on its debt. Since interest expenses are tax-deductible, we adjust for taxes. With a corporate tax rate of 25.8%, the after-tax cost of debt is:

4.12%×(1-0.258)=3.05%

We can now compute the WACC:

WACC=75%×8.3%+25%×3.05%=6.98%

This WACC represents the minimum return Alstom must generate on its invested capital to satisfy both shareholders and lenders. In the DCF, this rate is applied to discount future free cash flows. A higher WACC would reduce Alstom’s valuation, while a lower WACC would increase it, highlighting how sensitive valuations are to financing assumptions.

Conclusion

To conclude, WACC may look a bit complicated, but it represents a simple idea: the company must generate enough to reward its investors for the risk they take. Understanding WACC allows people to interpret valuations, understand how capital structure influences risk and compare businesses across industries. Once you master the WACC, it is one of the best tools to dig your intuition about risk and valuation.

Related posts on the SimTrade blog

   ▶ Snehasish CHINARA Academic perspectives on optimal debt structure and bankruptcy costs

   ▶ Snehasish CHINARA Optimal capital structure with corporate and personal taxes: Miller 1977

   ▶ Snehasish CHINARA Optimal capital structure with no taxes: Modigliani and Miller 1958

Useful resources

Damodaran, A. (2001) Corporate Finance: Theory and Practice. 2nd edn. New York: John Wiley & Sons.

Modigliani, F., M.H. Miller (1958) The Cost of Capital, Corporation Finance and the Theory of Investment, American Economic Review, 48(3), 261-297.

Modigliani, F., M.H. Miller (1963) Corporate Income Taxes and the Cost of Capital: A Correction, American Economic Review, 53(3), 433-443.

Vernimmen, P., Quiry, P. and Le Fur, Y. (2022) Corporate Finance: Theory and Practice, 6th Edition. Hoboken, NJ: Wiley.

About the author

The article was written in January 2026 by Daniel LEE (ESSEC Business School, Global Bachelor in Business Administration (GBBA) – 2023-2027).

   ▶ Read all articles by Daniel LEE.

December 2025: The 10 Most Read Articles about Financial Culture

by

From an educational perspective, financial culture plays a central role in the training of students and early-career professionals. It fosters critical thinking toward financial narratives by corporates, financial institutions, and governments. Beyond technical mastery of valuation methods, risk models, or portfolio theory, financial culture encompasses the ability to interpret markets through historical events, narratives, symbols, and representations conveyed by films, books, and broader cultural artefacts. This objective lies at the core of the SimTrade Blog, which aims to provide accessible yet rigorous content at the intersection of academic finance, market practice, and financial/economic/business literacy. You will find articles about financial culture deals with books, movies, paintings, sculpture…

Improving financial culture is also an effective way to prepare for interviews, as it enables candidates to contextualize technical knowledge, articulate personal opinions on markets and institutions, and demonstrate intellectual curiosity and critical thinking beyond purely quantitative skills.

Top 10 Read Articles about Financial Culture on the SimTrade Blog

   ▶ Akshit GUPTA Movie Analysis: Margin Call (2011)

   ▶ Akshit GUPTA Movie Analysis: Wall Street: Money Never Sleeps (2010)

   ▶ Federico MARTINETTO “Money never sleeps” – Wall Street Movie

   ▶ Marie POFF Film analysis: The Big Short

   ▶ William LONGIN Religious imagery in finance: analysis of the book ‘Money’ by Émile Zola

   ▶ Mohamed Dhia KHAIROUNI Analyse de film : Margin Call (2011)

   ▶ Nakul PANJABI Charging Bull on Wall Street

   ▶ Akshit GUPTA Movie Analysis: Other People’s Money (1991)

   ▶ Marie POFF Film analysis: Rogue Trader

   ▶ Akshit GUPTA Movie Analysis: The Hummingbird Project (2018)

SimTrade Editorial Picks in Financial Culture

In addition to the most read articles, we would like to highlight the following articles for their strong educational value in quantitative finance, corporate finance, and financial risk modeling.

   ▶ Lucas BAURIANNE The Golden Boy: Une immersion dans l’univers des banques d’investissement

   ▶ Nakul PANJABI Art as an asset class

   ▶ Marie POFF Book review: Barbarians at the gate

Crypto ETP

by
Alberto BORGIA

In this article, Alberto BORGIA (ESSEC Business School, Global Bachelor in Business Administration (GBBA), Exchange student, Fall 2025) explains about ETPs on crypto.

Introduction

An Exchange-Traded Product (ETP) is a type of regulated financial instrument, which is traded on stock exchanges and allows exposure to the price movements of an underlying asset or a benchmark without requiring direct ownership of the asset.

Crypto ETPs are instruments that provide regulated access to all market participants. Since their inception, they have become the main access point for traditional investors seeking exposure to digital assets. Every year, the value of assets in this category continues to grow and in their latest report, 21Shares analysts agree that by 2026 these assets will be able to surpass $400 billion globally.

The picture shows how rapidly crypto ETPs have scaled from early 2024 to late 2025. Assets under management (blue area) rise in successive waves, moving from roughly the tens of billions to just under the $300B range by late October 2025, while cumulative net inflows (yellow line) trend steadily upward toward ~$100B, signaling that growth has been supported by persistent new capital in addition to market performance.

As regulated access expands through mainstream distribution channels and more jurisdictions formalize frameworks for crypto investment vehicles, ETPs increasingly become the default wrapper for exposure. As the market deepens, secondary-market liquidity typically improves and execution costs compress, reducing short-term dislocations around the product and reinforcing further allocations.

Crypto ETP Asset under Management (AUM)
Crypto ETP AUM
Source: 21Shares.

This trend is driven not only by retail clients’ demand, but also by an increasing openness of traditional markets toward these types of products, meaning that established exchanges, broker-dealers, custodians and market-makers are increasingly willing to list, distribute and support crypto-linked ETPs within the same governance, disclosure and risk-management frameworks used for other exchange-traded instruments. In the US, more and more structural barriers are being removed thanks to new approval processes for crypto investment vehicles, as regulators and exchanges have been moving toward clearer, more standardized filing and review pathways and more predictable disclosure expectations.

By the end of 2025, more than 120 ETP applications were pending review in the USA, under assessment by the SEC and, where relevant, by the national securities exchanges seeking to list these products, positioning the market for significant inflows beyond Bitcoin and Ethereum in the new year.

We see this trend in other countries as well: the UK has removed the ban for retail investors, Luxembourg’s sovereign fund has invested as much as 1% of its portfolio in Bitcoin ETPs, while countries such as the Czech Republic and Pakistan have even started using such assets for national reserves. In Asia and Latin America, regulatory frameworks are also being formed, making crypto ETPs the global standard for regulated access.

This will lead to a virtuous cycle that will attract more and more capital: AUM growth enables a reduction in spreads, volatility decreases and liquidity increases, improving price efficiency and execution quality and reducing short-term dislocations, thereby supporting the growth of the asset class.

ETP o ETF

An Exchange-Traded Product is a broad category of regulated instruments that give investors transparent, tradable exposure to an underlying asset, index or a strategy. An Exchange-Traded Fund is a specific type of ETP that is legally structured as an investment fund, typically holding the underlying assets and calculating a net asset value. The key difference is therefore the legal form and the risk profile: ETFs are fund vehicles with segregated assets held for investors, whereas many non-ETF ETPs (such as ETNs) are debt instruments whose performance can also depend on the issuer’s creditworthiness. So, all ETFs are ETPs, but not all ETPs are ETFs.

Structure

There are two methods for replicating the underlying: physical and synthetic. Physical ETPs are created through the purchase and holding of the asset by the issuing entity, thus allowing a replication directly linked to the performance of the underlying. As for synthetic ETPs instead, they are created from a SWAP contract with a counterparty, for example a bank, in order to provide the return of that asset. To protect the liquidity of the daily return, the counterparty is required to post liquid collateral with the issuer and the amount of this collateral then fluctuates based on the value of the underlying asset and its volatility profile. Based on the data shown by Vanguard’s discussion of physical vs. synthetic ETF structures and with industry evidence showing that physical replication dominates European ETF AUM, we can say that in recent years investors have generally preferred physical ETPs, thanks to their transparency, the absence of counterparty risk and their relative simplicity rather than synthetic structures. In particular with regard to crypto, given the simplicity of holding the asset and their liquidity, almost all of these derivatives on cryptocurrencies are physical.

For this reasons, when you purchase this type of financial asset, you do not directly own the physical cryptocurrency (the underlying), but rather a debt security of the issuer, backed by the crypto and with a guarantee provided by the relationship with the trustee (This entity’s task is to represent the interests of investors, receiving all rights over the physical assets that collateralize the ETP. It therefore acts as a third and independent party that protects the ETP’s assets and ensures that it is managed in accordance with the terms and conditions established beforehand.)

Structure of Exchange Traded Product
ETP’s structure
Source: Sygnum Bank.

Single or diversified

Depending on the exposure the investor wants to obtain, various types of these assets can be purchased:

  • Some may replicate a specific cryptocurrency by tracking the value of a single digital coin. Their task is therefore only to replicate the market of the underlying asset in a simple and efficient way.
  • Other ETPs can replicate a basket or an index of cryptocurrencies; this is done to gain exposure simultaneously to different markets, diversifying risk.
  • We can find an example of this in the products offered by 21Shares. Part of it is represented by diversified products, such as the 21Shares Crypto Basket Equal Weight ETP, where several cryptocurrencies make up the product. The majority, however, both in terms of AUM and number of products, is single-asset, with only one underlying. Examples include the 21Shares Bitcoin ETP or the 21Shares Bitcoin Core ETP.
  • When speaking specifically about these two products, there is a distinctive feature that makes 21Shares unique. The company was the first to bring these products to market and, for this reason, having a “monopoly” at the time, it was able to charge extremely high fees. With the arrival of new players, however, it was forced to reduce them and, thanks to its structure and competitive advantages, was able to offer extremely low fees, the lowest on the market, without delisting the previous products, as they remained profitable. In fact, the two products mentioned above have no differences of any kind, except for their costs.

BTC ETP
21Shares BTC ETP
Source: 21Shares.

Advantages compared to traditional crypto

The reasons that may lead to the purchase of this type of financial instrument can be multiple. First of all, navigating the world of cryptocurrencies can seem difficult, but ETPs remove much of the complexity. Instead of relying on unregulated platforms or paying extremely high fees to traditional funds that invest only marginally in cryptocurrencies, investors have the opportunity to buy this asset directly as they would with other securities. ETPs will then sit alongside all other investments in the portfolio, thus enabling a simpler analysis of it and also comparison with other products. Moreover, even if these intermediaries do not offer true financial advice, they provide investor support that is far higher than that of classic crypto platforms.

Another element in their favor is the security and transparency on which they are based. In particular in Europe, these instruments are subject to stringent financial regulations and are required to comply with accounting, disclosure, and transparency rules. Then, since they are predominantly physically collateralized, their structure makes it possible to protect the client and the asset itself in the event of bankruptcy or insolvency of the issuer, limiting exposure to the underlying.

Why should I be interested in this post?

The crypto market is a complex world and constantly changing. This article can be read by anyone who intends even just to deepen their understanding or discover concepts that nowadays are becoming increasingly important and fundamental in financial markets and in everyday life, not only by those who want to pursue a career in the cryptocurrency sector.

Related posts on the SimTrade blog

   ▶ Snehasish CHINARA Top 10 Cryptocurrencies by Market Capitalization

   ▶ Hugo MEYER The regulation of cryptocurrencies: what are we talking about

Useful resources

CoinShares

21Shares

Swem, N. and F. Carapella (28/03/2025) Crypto ETPs: An Examination of Liquidity and NAV Premium FEDS Notes.

sygnum

Vanguard: Replication methodology / ETF knowledge

About the author

The article was written in December 2025 by Alberto BORGIA (ESSEC Business School, Global Bachelor in Business Administration (GBBA), Exchange student, Fall 2025).

   ▶ Read all articles by Alberto BORGIA.

Understanding the Almgren-Chriss Model for Optimal Trade Execution

by
Bryan BOISLEVE

In this article, Bryan BOISLEVE (CentraleSupélec – ESSEC Business School, Data Science, 2023-2025) explains the Almgren-Chriss model, a fundamental framework in quantitative finance for optimal execution of large trading orders.

Introduction

Imagine you are a portfolio manager at a large asset management firm, and you need to sell 1 million shares of a stock. If you sell everything right now, you will significantly move the market price against yourself which comes with massive transaction costs. However, if you spread the trades over a too long a period, you expose yourself to the risk of adverse price movements due to market volatility. This dilemma between these two scenarios is one of the major optimal execution problems in finance.

The Almgren-Chriss model, developed by Robert Almgren and Neil Chriss in 2000, provides a mathematical framework to solve this problem. It has become an important model of algorithmic trading strategies used by investment banks, hedge funds, and asset managers worldwide. The model balances two competing objectives: minimizing transaction costs caused by market impact and minimizing the risk from price volatility during the execution period.

The liquidation trajectory after the use of Almgren-Chriss model
The liquidation trajectory after the use of Almgren-Chriss model
Source: Github (joshuapjacob)

The Core Problem: Market Impact and Execution Risk

When institutional investors execute large orders, they face two types of market impact. The first is the permanent market impact which is the lasting changes in the equilibrium price caused by the information revealed through trading. For example, a large sell order might signal negative information about the stock, causing the price to drop permanently. The second impact is temporary market impact, which represents the immediate price concession required to find liquidity for the trade, which typically reverts after the order is completed.

In market microstructure, the canonical microfoundation for price impact is Kyle (1985). In Kyle’s model, an informed trader optimally splits a large order across time to hide private information, while competitive market makers update prices from the signed order flow. This generates a linear price impact: the price change is proportional to order flow, with the slope (Kyle’s lambda, λ) capturing how sensitive prices are to trading pressure. This provides a useful economic interpretation for the linear permanent-impact term in Almgren–Chriss: the “depth” parameter can be seen as an equilibrium measure of how quickly information get incorporated into prices, rather than as a purely statistical coefficient.

In addition to these costs, traders face execution risk or volatility risk, which is the uncertainty about future price movements while the order is being executed. A slow execution strategy minimizes market impact but increases exposure to this uncertainty, while rapid execution reduces volatility risk but amplifies market impact costs.

However, rather than assuming permanent impact persists indefinitely because of information content, Bouchaud (2009) shows that individual trade impacts follow a power-law decay governed by the market’s order flow dynamics and latent liquidity structure. The critical distinction is that this decay pattern emerges mechanically from how order books replenish and how traders split their orders across time, not because other participants are updating their valuations based on information signals.

The Mathematical Framework

The Almgren-Chriss model formulates optimal execution as a mean-variance optimization problem. Suppose we want to liquidate X shares over a time horizon T, divided into N discrete intervals. The model assumes that the stock price follows an arithmetic random walk with volatility, and our trading activity affects the price through both permanent and temporary impact functions.

Price Dynamics

The price evolves according to the discrete-time equation. At each step k, the mid-price moves because of an exogenous shock and the permanent impact of selling qk shares during [tk, tk+1]. The execution price also includes a temporary impact term that depends on v_k. The actual execution price we receive includes an additional temporary impact that depends on how quickly we are trading in that interval.

In the simplest linear case, the permanent impact is proportional to the number of shares we sell, with a coefficient representing the depth of the market. The temporary impact includes both a fixed cost (such as half the bid-ask spread) and a variable component proportional to our trading speed.

Expected Cost and Variance

The total expected cost of execution consists of three components: the permanent impact cost, the fixed cost proportional to the total shares traded, and the temporary impact cost that depends on how we split the order over time. Meanwhile, the variance of the trading cost is driven by price volatility and increases with the square of the inventory we hold at each point in time.

The optimization problem seeks to minimize a combination of expected cost and a risk-adjusted penalty for variance. A higher risk aversion parameter indicates greater concern about execution risk and leads to faster trading to reduce exposure.

The Optimal Strategy and Efficient Frontier

One of the most elegant results of the Almgren-Chriss model is the closed-form solution for the optimal trading trajectory. Under linear market impact assumptions, the optimal number of shares to hold at time t follows a hyperbolic sine function that decays from the initial position X to zero at the terminal time T.

The Half-Life of a Trade

A key insight from the model is the concept of the trade’s half-life, which represents the intrinsic time scale over which the position is naturally liquidated, independent of any externally imposed deadline T. This parameter is determined by the trader’s risk aversion, the stock’s volatility, and the temporary market impact coefficient.

If the required execution time T is much shorter than the half-life, the optimal strategy looks nearly linear which spreads trades evenly over time to minimize transaction costs. But, if T is much longer than the half-life, the trader will liquidate most of the position quickly to reduce volatility risk, with the trajectory looking as an immediate execution.

The Efficient Frontier

The Almgren-Chriss model produces an efficient frontier which is a curve in the space of expected cost versus variance where each point represents the minimum expected cost achievable for a given level of variance. This frontier is smooth and convex, as the efficient frontier in portfolio theory.

At one extreme lies the minimum-variance strategy (selling everything immediately), which has zero execution risk but very high transaction costs. At the other extreme is the minimum-cost strategy (the naive strategy of selling uniformly over time), which has the lowest expected costs but maximum exposure to volatility. The optimal strategy for any risk-averse trader lies somewhere along this frontier, determined by their risk aversion parameter.

Interestingly, the efficient frontier is differentiable at the minimum-cost point, meaning that one can achieve significant reductions in variance with only a marginal increase in expected cost. This mathematical property justifies moving away from the naive linear strategy toward more front-loaded execution schedules.

Practical Applications in Financial Markets

The Almgren-Chriss framework is behind many real-world algorithmic execution strategies used by institutional investors. VWAP (Volume-Weighted Average Price) strategies, which aim to execute trades in proportion to market trading volume, can be shown to be optimal for risk-neutral traders in certain extensions of the model. Also, TWAP (Time-Weighted Average Price) strategies, which execute at a constant rate over time, correspond to the minimum-cost solution when trading volume is constant.

Investment banks and electronic trading platforms use variations of the Almgren-Chriss model to power their execution algorithms. By calibrating the model parameters (volatility, market impact coefficients, risk aversion) to historical data and client preferences, these algorithms automatically determine the optimal trading schedule for large orders. The model also informs decisions about whether to use dark pools, limit orders, or aggressive market orders at different stages of the execution.

Beyond equity markets, the framework has been adapted to optimal execution in foreign exchange, fixed income, and derivatives markets, where liquidity conditions and market microstructure differ but the fundamental tradeoff between cost and risk remains central.

More broadly, the need for optimal execution fits naturally with Pedersen’s idea of markets being “efficiently inefficient”. Even when sophisticated investors detect mispricing or believe they have an informational edge, trading aggressively is limited by real frictions: transaction costs, market impact, funding constraints, and risk limits. These frictions imply that profit opportunities can persist because fully arbitraging them away would be too costly or too risky. From this perspective, Almgren–Chriss is not only a practical trading tool: it is a mechanism that quantifies one of the key forces behind “efficiently inefficient” markets, namely that the act of trading to exploit information or rebalance portfolios moves prices and creates costs that rationally slow down execution.

Why should I be interested in this post?

If you are a student interested in quantitative finance, algorithmic trading, or market microstructure, understanding the Almgren-Chriss model is essential. It represents an important application of stochastic optimization and control theory to real-world financial problems. By having a good understanding of this framework will prepare you for roles in proprietary trading, electronic market making, or quantitative research at investment banks and hedge funds.

Moreover, the model illustrates the broader principle of balancing multiple competing objectives under uncertainty which is a skill valuable across many areas of business and finance. The ability to formulate and solve such optimization problems is a key competency in quant finance.

Related Posts on the SimTrade Blog

   ▶ Raphael TRAEN Volume-Weighted Average Price (VWAP)

   ▶ Martin VAN DER BORGHT Market Making

   ▶ Jayati WALIA Implied Volatility

Useful Resources – Scientific articles

Almgren, R., & Chriss, N. (2000) Optimal execution of portfolio transactions Journal of Risk, 3(2), 5–39.

Almgren, R., & Chriss, N. (2001) Value under liquidation. Risk Journal of Mathematical Finance, 12(12), 61–63.

Bouchaud, J.-P. (2017) Price impact.

Bouchaud, J.-P., & Potters, M. (2003) Theory of financial risk and derivative pricing: From statistical physics to risk management Second Edition, Cambridge University Press.

Kyle, A. S. (1985) Continuous auctions and insider trading, Econometrica, 53(6), 1315–1335.

Kyle, A. S. (1989). Informed speculation with imperfect competition, Review of Economic Studies, 56(3), 317–355.

Useful Resources – Python code

Sébastien David, Arthur Bagourd, Mounah Bizri. Solving the Almgren-Chriss framework through dynamic programming

Sébastien David, Arthur Bagourd, Mounah Bizri. Solving the Almgren-Chriss framework through quadratic/nonlinear programming

About the Author

The article was written in December 2025 by Bryan BOISLEVE (CentraleSupélec – ESSEC Business School, Data Science, 2023-2025).

   ▶ Read all articles by Bryan BOISLEVE.