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

January 6, 2026 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 Private peers, even when strategically closest, usually cannot be used directly because they do not publish sufficiently detailed or standardized financial statements.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

Written in December 2025 by Ian DI MUZIO, ESSEC Business School.

Understanding WACC: a student-friendly guide

January 3, 2026January 2, 2026 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.

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

January 1, 2026December 31, 2025 by Prof. François LONGIN

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.

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

December 30, 2025December 30, 2025 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.

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

December 28, 2025 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

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.

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.

Principal Component Analysis (PCA) in Quantitative Finance

December 30, 2025December 28, 2025 by Bryan BOISLEVE

In this article, Bryan BOISLEVE (CentraleSupélec – ESSEC Business School, Data Science, 2025-2027) explores Principal Component Analysis (PCA), a dimensionality reduction technique widely used in quantitative finance to identify the hidden drivers or risk factors of market returns.

Introduction

Financial markets generate large volumes of high-dimensional data, as asset prices and returns evolve continuously over time. For instance, analysing the daily returns of the S&P 500 involves studying 500 distinct but related time series. Treating these series independently is often inefficient, as asset returns exhibit strong cross-sectional correlations driven by common systematic factors (for example: macroeconomic conditions, interest rate movements, and sector-specific shocks).

This why we have the Principal Component Analysis (PCA) which is a powerful statistical method used to simplify this complexity. It transforms a large set of correlated variables into a smaller set of uncorrelated variables called Principal Components (PCs). By retaining only the most significant components, quants can filter out the “noise” of individual stock movements and isolate the “signal” of broad market drivers.

The Mathematics: Eigenvectors and Eigenvalues

PCA is an application of linear algebra to the covariance (or correlation) matrix of asset returns. The goal is to find a new coordinate system that best preserves the variance of the data.

If we have a matrix X of standardized returns (where each asset has a mean of 0 and variance of 1), we compute the correlation matrix C. We then perform an eigendecomposition:

Cv = λv

Eigenvectors (v) define the direction of the principal components. In finance, these vectors act as “weights” for constructing synthetic portfolios.
Eigenvalues (λ) represent the magnitude of variance explained by each component. The ratio $ \lambda_i / \sum \lambda $ tells us the percentage of total market risk explained by the i-th component.

A key property of PCA is orthogonality: the resulting principal components are mathematically uncorrelated with each other. This is very useful for risk modeling, as we can sum up the variances of individual components to estimate total portfolio risk without worrying about cross-correlations.

Classic Application: Decomposing the Yield Curve

The most famous application of PCA in finance is in Fixed Income markets. A yield curve consists of interest rates at many maturities (1M, 2Y, 5Y, 10Y, 30Y). As shown in the image below, the history of US yield curves forms a complex “surface” that evolves over time.

Figure 1. PCA of a multivariate Gaussian distribution

Source: Wikimedia Commons.

While the data in Figure 1 appears complex, PCA consistently reveals that 95-99% of these movements are driven by just three factors:

1. Level (PC1)

The first component typically explains 80-90% of the variance. It corresponds to a parallel shift in the yield curve: all rates across the surface go up or down together. Traders use this factor to manage Delta or duration risk. When the Federal Reserve raises rates, the entire surface tends to shift upward, in fact this is PC1 in action.

2. Slope (PC2)

The second component explains most of the remaining variance. It corresponds to a tilting of the curve: steepening or flattening. A “curve trade” (e.g., long 2Y, short 10Y) is essentially a bet on this specific principal component.

3. Curvature (PC3)

The third component captures the “butterfly” movement: short and long ends move in one direction, while the belly (medium term) moves in the opposite direction. While it explains little variance (often <2%), it is crucial for pricing convex instruments like swaptions or constructing fly trades (e.g., long 2Y, short 5Y, long 10Y).

Application to Equities: Eigen-Portfolios and Statistical Arbitrage

In equity markets, PCA is used to identify “Eigen-Portfolios”, synthetic portfolios constructed using the eigenvector weights.

The First Principal Component (PC1) almost always represents the Market Mode. Since stocks generally move up and down together, the weights in PC1 are usually all positive. This synthetic portfolio looks very similar to the S&P 500 or a broad market index.

The subsequent components (PC2, PC3, etc.) often represent Sector Modes or other macroeconomic factors (e.g., Oil vs. Tech, or Value vs. Growth). For example, PC2 might be long energy stocks and short technology stocks by capturing the rotation between these sectors.

Quantitative traders use this for Statistical Arbitrage. For example, by regressing a single stock’s returns against the top factors (e.g., the first 5 PCs), they can decompose the return into a “systematic” part (explained by the market) and a “residual” part (idiosyncratic). If the residual deviates significantly from zero, it implies the stock is mispriced relative to its usual correlation structure, traders then buy the stock and hedge the systematic risk using the Eigen-Portfolios, betting that the residual will revert to zero.

Critical limitations of PCA

While being very useful, PCA is not a magic bullet. Quants must be aware of its limitations:

1. PCA only detects linear correlations as it cannot capture complex, non-linear dependencies (like tail dependence during a crash) where correlations tend to spike toward 1.
2. The principal components are statistical constructs, not fundamental laws. They can be unstable over time: what looks like a “Tech factor” today might blend into a “Momentum factor” tomorrow. The eigenvectors can “flip” signs or mix, requiring constant re-estimation.
3. PCA is a “blind” algorithm. It tells you that a factor exists, but not what it is. It is up to the analyst to interpret PC2 as “Slope” or “Inflation Risk.” Without careful interpretation, it can lead to wrong correlations.

Why should I be interested in this post?

For students in Data Science and Finance, PCA is the perfect bridge between machine learning theory and asset management practice. It moves beyond simple diversification (“don’t put all eggs in one basket”) to a mathematical rigor that quantifies exactly how many independent baskets actually exist.

Whether you want to work in Fixed Income (managing curve risk), Equity Derivatives (managing volatility surfaces), or Quantitative Hedge Funds (building neutral alpha signals), PCA is a foundational tool that appears in almost every risk model.

Useful resources

Statistics

Laloux, L., Cizeau, P., Bouchaud, J.P., and Potters, M. (2000). Random matrix theory and financial correlations, International Journal of Theoretical and Applied Finance, 3(03), 391-397.

d’Aspremont, A., El Ghaoui, L., Jordan, M. I., and Lanckriet, G. R. (2007). A direct formulation for sparse PCA using semidefinite programming, SIAM review, 49(3), 434-448.

Applications in finance

Litterman, R., & Scheinkman, J. (1991). Common factors affecting bond returns, The Journal of Fixed Income, 1(1), 54-61.

Avellaneda, M., & Lee, J. H. (2010). Statistical arbitrage in the US equities market, Quantitative Finance, 10(7), 761-782.

Cont, R., & da Fonseca, J. (2002). Dynamics of implied volatility surfaces, Quantitative Finance, 2(1), 45-60.

Python code

Bryan Boislève Principal Component Analysis (PCA) on S&P 500 Sector ETFs (Python code)

About the author

The article was written in December 2025 by Bryan BOISLEVE (CentraleSupélec – ESSEC Business School, Data Science, 2025-2027).

▶ Read all articles by Bryan BOISLEVE.

My internship experience as a Counterparty Risk Analyst at Société Générale

December 28, 2025December 28, 2025 by Bryan BOISLEVE

In this article, Bryan BOISLEVE (CentraleSupélec – ESSEC Business School, Data Science, 2025-2027) shares his professional experience as a Counterparty Risk Analyst intern within Société Générale’s investment banking division.

About the company

Société Générale is one of the largest European banking groups, offering retail banking, corporate and investment banking, and specialised financial services in over 60 countries. As of 31 December 2024, the Group had around 119,000 employees, served more than 26 million clients in 62 countries, and reported total assets of EUR 1,573.5bn, with total equity of EUR 79.6bn. In 2024, revenues (net banking income) amounted to EUR 26.8bn and group net income (Group share) reached EUR 4.2bn.

Logo of Société Générale

Source: the company.

Its Corporate & Investment Banking (CIB) branches serve corporates and institutional investors with financing, capital markets, and risk-management solutions on a diverse range of asset classes (equities, fixed income, derivatives…).

The bank is a major clearing member at leading central counterparties (CCPs), acting as an intermediary between clients and clearing houses for listed and cleared OTC derivatives. This activity is supported by a structured process of daily margining, exposure monitoring, and default fund contributions, embedded within risk management and control functions. The chart below helps illustrate the distribution and scale of OTC derivatives activity, and how a CCP simplifies OTC operations.

Chart of derivatives market structure with CCP

Source: Bank Of Australia

During my internship, I worked in the front office counterparty risk team (counterparty risk has also a team in middle office) in Paris, which monitors exposures to central counterparties and major clearing brokers, analyses margin models, and challenges the robustness of CCP risk frameworks used for derivatives clearing.

My internship

Over three months, I focused on cleared derivatives exposures, supporting the team in monitoring house and client portfolios across several CCPs and in assessing whether margin and default fund resources were sufficient under stressed market conditions.

My missions

My main tasks were to analyze house and client risk exposures using Initial Margin (IM), Default Fund (DF), Variation Margin (VM), Value at Risk (VaR) and Conditional VaR (CVaR), to automate DF estimations for two CCPs in Python, to draft annual credit reviews for major central counterparty, and to investigate daily IM and DF breaches together with traders and the wider risk department.

I also implemented an Almgren–Chriss optimal execution model on a client book to better estimate liquidation costs in the Default Management Process, improving the bank’s view on how quickly and at what cost a defaulted portfolio could be unwound.

Required skills and knowledge

This internship required strong quantitative skills (statistics, VaR/CVaR, optimisation), solid understanding of derivatives and CCP mechanics, and programming abilities in Python to automate risk calculations, as well as proficiency with Excel and internal risk systems.

On the soft-skill side, I had to communicate complex risk topics clearly to traders and senior risk managers, work accurately under time pressure when margin breaches occurred, and be proactive in proposing model improvements or new monitoring dashboards.

A good example of how I applied these skills is when my manager asked me to create a dashboard available for key managers that could show the historical exposition and an estimate of this exposition on a specific CCP. After my internship ended, the team decided to implement the model used for the estimation as well as the dashboard for all the CCP where Société Générale was a clearing member.

What I learned

I learned a lot during my internship: how CCPs use margin models, default funds and stress tests to ensure they can withstand the default of major clearing members, and how a bank as a clearing member independently challenges those frameworks to protect its balance sheet.

This experience also taught me to question model assumptions, to combine quantitative analysis with qualitative judgement on CCP governance and transparency, and it confirmed my interest in pursuing a career in quantitative risk management. I also learned how to work with colleage from different countries and different backgrounds which is a soft skills that can really be helpful in a professional environment.

Economic, financial, and business concepts related to my internship

I believe these are three financial concepts related to my internship which are very important: central counterparty default waterfalls, initial margin models, and the Almgren–Chriss optimal execution framework.

Central counterparty default waterfall

The CCP default waterfall is the sequence of financial resources used to absorb losses when a clearing member defaults: the member’s IM, then its DF contribution, then the CCP’s own capital (“skin‑in‑the‑game”), and finally the mutualised default fund and any additional loss-allocation tools.

Understanding this waterfall was crucial in my role, because my analyses assessed whether Société Générale’s exposures and contributions at each CCP were consistent with its risk appetite and with regulatory “Cover‑2” stress-test standards.

Initial margin models (VaR / SPAN)

CCPs typically compute IM with either VaR-based models or SPAN-style scenario approaches, which aim to cover potential losses over a margin period of risk at high confidence levels (often 99% or more).

In my reviews of multiple CCPs, I compared how their IM methodologies capture product risk, concentration risk and wrong-way risk, and how model choices translate into the level and procyclicality of margin calls for the bank and its clients.

Almgren–Chriss optimal execution

The Almgren–Chriss model provides an optimal schedule to liquidate large positions by balancing market impact costs against price risk, typically leading to front‑loaded execution for risk‑averse traders.

By calibrating this model on client portfolios, I helped the team estimate realistic liquidation costs that would arise in a CCP default management auction, improving the calibration of IM add‑ons and internal stress scenarios.

Why should I be interested in this post?

For a student in finance, counterparty risk at a global investment bank like Société Générale, offers a great opportunity on how derivatives markets, CCPs and regulation interact between each other, and shows how quantitative models directly influence daily risk decisions and capital usage.

This type of internship is particularly valuable if you are interested in careers in market risk, XVA, clearing risk or quantitative research, because it combines modelling, coding and discussions with trading desks on real portfolios and real constraints. Overall it is a great internship to have a first step in the trading floor.

Useful resources

Financial regulation

European Securities and Market Authority (ESMA) Clearing obligation and risk mitigation techniques under EMIR.

Bank of International Settlements (BIS) (April 2012) Principles for financial market infrastructure.

Bank of England (November 2025) Central Counterparty (CCP) policy and rules.

Boudiaf, I., Scheicher, M., Vacirca, F., (April 2023) CCP initial margin models in Europe, Occasional Paper Series, European Central Bank (ECB).

International Swaps and Derivatives Association (ISDA) (August 2013) CCP Loss Allocation at the End of the Waterfall.

Academic research

Almgren, R., Chriss, N., 2000. Optimal execution of portfolio transactions, Working Paper.

Duffie, D., Scheicher, M., Vuillemey, G., 2014. Central Clearing and Collateral Demand, Working Paper.

Pirrong, C., 2013. A Bill of Goods: CCPs and Systemic Risk, Working paper, Bauer College of Business University of Houston.

Berndsen, R., 2021. Fundamental questions on central counterparties: A review of the literature, The Journal of Futures Markets, 41(12) 2009-2022.

About the author

The article was written in December 2025 by Bryan BOISLEVE (CentraleSupélec – ESSEC Business School, Data Science, 2025-2027).

▶ Read all articles by Bryan BOISLEVE .

EBITDA: Uses, Benefits and Limitations

December 30, 2025December 28, 2025 by Alberto BORGIA

In this article, Alberto BORGIA (ESSEC Business School, Global Bachelor in Business Administration (GBBA), Exchange student, Fall 2025) explains about EBITDA, how it can be used, its advantages and disadvantages.

Introduction

Earning Before Interest, Taxes, Depreciation and Amortization (EBITDA) is ones of the most used financial metric and its goal is to understand a company’s operating performance before considering the effects of financial choices (interests), taxation and non-cash accounting charges related to long-lived asset and acquired intangibles.

So in intuition behind it is that if two or more firms sell similar products, the analyst should be able to compare their “core operating engine”, even if they differ from a debt (higher debt), tax (different tax jurisdiction) or asset base prospective.

Because EBITDA is a key component capable of influence valuation and decisions, it is crucial to understand both how it is obtained and what it does.

How it is obtained

To calculate this metric, we begin with the income statement and add back the expenses that are excluded by the EBITDA definition:

EBITDA = Net Income + Interest + Taxes + Depreciation + Amortization

Another way is to start from the EBIT:

EBITDA = EBIT + Depreciation + Amortization

Using Carrefour as a real-case example, I calculated EBITDA starting from the company’s income-statement figures. First, I reproduced an “operating-style” EBITDA by taking Gross Margin and subtracting selling, general and administrative expenses, which gives a core operating profit measure before financing and taxes. Then, for a second approach, I computed EBITDA as Recurring Operating Income + Depreciation + Amortization. This shows how EBITDA is obtained in practice from published financial statement components.

These two formulae can look clean and easy, but the real computation is messier, depending on how the company structure his income statement and on what is included in the amortization and depreciation class. For these reasons EBITDA is usually accompanied by a set of clear definitions and reconciliations.

Another key factor is that the “earnings” are not always interpreted in the same way, that is why the SEC has decided that in the context of EBITDA and EBIT described in its adopting release, “earnings” means GAAP net income as presented in the statement of operations. So, if a measure is calculated differently, it should not be labeled EBITDA, but Adjusted EBITDA.

Adjusted EBITDA

For many documents we see the term Adjusted EBITDA, because it modifies the measure by excluding values that are considered by the management as “non-core” or “non-recurring”. These adjustments typically include items such as restructuring costs, acquisition-related expenses, unusual or non-recurring gains and losses, and stock-based compensation. The goal is to estimate a normalized operating result. This can however create risks when comparing different firms or the same one in different years.

What it is used for

The reasons why EBITDA is one of the metrics most taken into account by financial analysts are multiple as its ways of use. First of all, by excluding interest rates, it is suitable as a proxy for comparing companies from an operating perspective, even when they have different tax or capital structures. It is then used to compare various risk indicators or to limit leverage and protect lenders (in the debt market).

It is also used for company valuation and for the calculation of multiples, such as EV/EBITDA. Here, EV indicates the total value of the firm. According to the technical literature, the reasons why this multiple is particularly useful and widely used include, for example, the possibility of calculating it even when net income is negative, for this reason, it is extremely common in markets where significant infrastructure investments are present and in leveraged buyouts and naturally because it allows the comparison of companies with totally different levels of financial leverage.

They are also particularly useful (EBITDA and its variants) for communicating to investors and analysts, even though it is necessary to be especially careful about any modifications aimed at “inflating” the results.

Last it is considered by analysts as a starting point, pairing it with cash-flow measures, such as free cash flow, for a fuller view.

Advantages

There are several advantages to using EBITDA; for instance, it can be calculated quickly from publicly available financial statements or is often directly disclosed by companies. In industries where leverage varies a lot it is useful to analyze companies in it or when assessing a target in M&A where capital structure can change immediately after the acquisition. Finally operating results are less sensitive to life assigned to asset when we add back depreciation and amortization.

Disadvantages

However, EBITDA is also associated with several notable drawbacks. Even by adding back depreciation and amortization, the value does not take into account changes in working capital and capex needed to increase or maintain productive capacity, it is more like a “rough” measure of operating cash flows.

As previously noted, EBITDA is also susceptible to manipulation, as it is inherently open to interpretation. Consequently, it should be complemented with other financial metrics to provide a more comprehensive and balanced assessment, thereby reducing the risk of misinterpretation driven by management’s attempts to influence investors’ perceptions..

EBITDA Margin

To express the EBITDA relative to revenue, we can use EBITDA margin:

EBITDA Margin = EBITDA / Revenue

It is calculated to understand how much operating earnings the firm generates per unit of sales, in particular it can be used to compare a firm’s profitability with its peers or to track trends. Even though it is particularly useful in financial analysis, the EBITDA margin presents the same issues as the original metric. If the first value is defined incorrectly, then this one will also be wrong. Just like normal EBITDA, this metric can be used best when it is accompanied by Operating Cash Flow (OCF), which reflects the cash generated by a company’s core operating activities, and Free Cash Flow (FCF), which represents the cash available after capital expenditures necessary to maintain or expand the asset base, and by an industry context.

Example

I provide below an example for the computation of EBITDA based on Carrefour, a French firm operating in the retail sector, more precisely in mass-market distribution (retail grocery).

Example of EBITDA calculation: Carrefour

You can download the Excel file provided below, which contains the calculations of EBITDA for Carrefour.

Why should I be interested in this post?

EBITDA represents a fundamental concept for anyone who wants to build their career in the financial field, but not only. Understanding how it works, as well as its weaknesses and strengths, is necessary in order to build the knowledge required to become a competent and respected professional. This article, in fact, starts from the basics in order to explain the principles behind this metric even to those who are not in the field, helping them understand it.

Useful resources

Non-GAAP Financial Measures

Deloitte Accounting Research Tool (DART) 3.5 EBIT, EBITDA, and adjusted EBITDA

Damodaran EBITDA concept, margins, interpretation

Moody’s (202/11/2024) EBITDA: Used and Abused

Faria-e-Castro, M., Gopalan R., Pal, A, Sanchez J.M., and Yerramilli V. (2021) EBITDA Add-backs in Debt Contracting: A Step Too Far? Working paper.

Damodaran EBITDA vs cash flow logic; reinvestment/capex relevance

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.

2025: The 10 Most Searched Finance Articles on the SimTrade Blog

December 28, 2025 by Prof. François LONGIN

SimTrade Editorial Picks in Quantitative Finance and Corporate Finance

In addition to the most searched posts, the SimTrade editorial team highlights the following articles for their strong educational value in quantitative finance, corporate finance, and financial risk modeling.

▶ Nithisha CHALLA Calculation of financial indexes

▶ Snehasish CHINARA Optimal capital structure with taxes: Modigliani and Miller 1963

▶ Shengyu ZHENG Extreme Value Theory: the Block-Maxima approach and the Peak-Over-Threshold approach

My Experience as a Wealth Management Intern at Nextam Partners

December 30, 2025December 26, 2025 by Alberto BORGIA

In this article, Alberto BORGIA (ESSEC Business School, Global Bachelor in Business Administration (GBBA), Exchange student, Fall 2025) shares his professional experience as a Wealth Management Intern at Nextam Partners.

About the company

During the summer between my second and third year of my Bachelor’s degree, I had the opportunity to join the Nextam Partners team for two months. Founded in 2001 by a group of professionals with decades of experience behind them and billions under management, Nextam is currently a family office that also provides financial advisory and wealth management services for Ultra High Net Worth Individuals and private foundations, with over 6 billion in assets under management. The company used to operate in the asset management sector as well, before being acquired by Banca Generali and then was partly taken back over by the founding partners, with regard to the segments that are still active.

Logo of NEXTAM.

Source: Nextam Partners.

My internship

I joined Nextam in June 2025 as a Summer Analyst in order to pursue my interest in wealth management and finally obtain a concrete experience that would allow me to learn first-hand both the more technical and the more practical concepts of the sector that are not covered in university lectures. and my role consisted mainly in supporting the various team members in their analysis and research functions for the development and modification of multi-asset portfolios through market screening, Bloomberg-based analysis and portfolio risk simulation using Windham.