My Experience as a Communication Officer at La Française des Jeux (FDJ)

December 28, 2023December 9, 2023 by Lou PERRONE

My Experience as a Communication Officer at La Française des Jeux (FDJ)

In this article, Lou PERRONE (ESSEC Business School, Global Bachelor of Business Administration (GBBA), 2019-2023) shares her professional experience as a Communication Officer at La Française des Jeux (FDJ).

About the company

La Française des Jeux, more widely recognized by its acronym FDJ, stands as an iconic pillar in the French lottery and gambling arena. Established in 1976, FDJ is not just a corporate entity but an embodiment of French heritage and communal festivities. Over the decades, it has ingrained itself into the very fabric of French culture and tradition, offering a diverse portfolio that encompasses lottery games, instant scratch tickets, and an array of sports betting services.
Functioning as a public entity, FDJ’s significance goes beyond entertainment. It plays a pivotal role in the nation’s economic framework, channeling a substantial portion of its revenues into the state’s coffers. This financial contribution has been instrumental in bolstering various sectors, including social welfare programs, sports development, and numerous cultural endeavors that enrich the French way of life.

Recognizing the winds of change and the digital transformation of the entertainment industry, FDJ has not remained complacent. In recent years, it has undertaken a digital metamorphosis. By harnessing the latest technological advancements, FDJ has unveiled a suite of online gaming experiences and user-friendly mobile applications. This digital leap is a testament to FDJ’s commitment to evolving with the times and catering to the preferences of a wide-ranging user base, from traditionalists who have been with the company since its inception to the tech-savvy younger generations seeking on-the-go entertainment solutions.

Logo of FDJ
Source: the company.

My apprenticeship

Embarking on my journey with FDJ as a Communication Officer wasn’t just the beginning of a new job; it signified my induction into a vibrant ecosystem, pulsating with innovation, challenges, and endless learning opportunities. FDJ, with its rich history and significant national footprint, presented a unique landscape where tradition intertwined with modernity. This duality was reflected in every facet of my work, whether communicating the time-honored joy of a lottery win or promoting the cutting-edge digital interfaces of our latest gaming apps.

In the heart of this dynamic environment, my role was multifaceted. While the title ‘Communication Officer’ might evoke images of drafting press releases or handling social media, the reality was a tapestry of responsibilities that spanned across strategic planning, content creation, media relationship management, and more. The position was a constant balancing act: upholding the legacy and values of FDJ while simultaneously pushing the envelope, striving for innovation, and setting new benchmarks in the realm of corporate communication.

Each day presented its unique set of challenges. From navigating the intricate nuances of communicating gaming responsibly to orchestrating large-scale promotional events during national festivals, my role was as much about creativity as it was about strategy and meticulous planning.

One of the most enriching aspects of my apprenticeship was the diversity of people I interacted with. From seasoned professionals who had witnessed FDJ’s transformation over decades to young innovators brimming with fresh ideas, every interaction was a lesson in itself. These encounters not only honed my communication skills but also broadened my perspective, enabling me to view challenges as opportunities and to approach problems with a multifaceted lens.

My missions

Strategy Formulation

Every campaign began with in-depth brainstorming sessions. Collaborating with various internal teams, I led ideation stages, where we’d evaluate current market trends, assess FDJ’s positioning, and devise innovative communication strategies. For each campaign, we identified our target demographics, created tailored messages, and chose the most effective communication channels – from traditional billboards to emerging social media platforms.

Content Creation

This wasn’t simply about drafting text; it involved creating a narrative. Each press release or promotional material told a story, resonating with our audience’s aspirations and emotions. I also collaborated closely with our in-house graphic design team, ensuring visual elements impeccably echoed our narratives. For digital campaigns, A/B testing became a routine, helping us fine-tune our content for maximum engagement.

Event Coordination

FDJ’s presence at exhibitions and conferences wasn’t just about setting up a booth. Each event was an opportunity to entrench our brand deeper into the public consciousness. I meticulously planned every detail, from the booth’s design to the merchandise distributed. Training the staff for these events became pivotal; ensuring they not only knew about FDJ’s offerings but also imbibed the company’s ethos in every interaction.

Media Relations

Building and nurturing relationships with journalists, bloggers, and influencers was crucial. Regular media briefings were organized, where we’d discuss FDJ’s latest ventures, answer queries, and sometimes even handle challenging questions regarding industry controversies. Managing media relations was not just about promoting our brand but also about ensuring FDJ’s voice was accurately represented in the public domain.

Required skills and knowledge

In my dynamic role as a Communication Officer at FDJ, I quickly realized the vast spectrum of responsibilities and the ever-evolving landscape of skills required. Central to my role was the art of communication, both written and oral. Crafting press releases, coordinating with media personnel, or pitching fresh ideas, I always aimed for clarity and resonance with the audience. It was equally important to adapt my tone and style to match the specific audience and occasion.

But communication wasn’t just about creating the message; it was also about measuring its impact. Here, the world of data analytics became an invaluable ally. Metrics like engagement rates and conversion rates offered a window into the effectiveness of our campaigns and highlighted areas ripe for improvement. As the digital world expanded, I delved deeper into tools like Search Engine Optimization (SEO) and Search Engine Marketing (SEM) to ensure FDJ’s prominence in the vast online landscape.

One of the most critical facets of my role was crisis management. While not every day brought a storm, being prepared for them was essential. Specialized workshops in crisis communication provided the knowledge and tactics to manage challenges and ensure FDJ’s reputation remained impeccable.

Understanding FDJ’s brand essence allowed for the creation of cohesive narratives across all communication platforms, fostering consistency and a deeper connection with the audience. The world of communications is vast, and every project came with its timelines and nuances. Efficiently organizing, prioritizing, and monitoring became second nature to me, aided by tools and platforms that ensured timely delivery and informed stakeholders.

Visual storytelling, an integral part of modern communication, often saw me collaborating closely with graphic designers. A foundational understanding of design tools ensured that our visual campaigns harmoniously merged with our narratives. Beyond internal collaborations, my role also demanded external networking. Building genuine relationships with media representatives, influencers, and other industry stakeholders was pivotal. Regular participation in industry events kept me connected and informed about the latest trends.

The digital realm further expanded with platforms like WordPress and Joomla playing a pivotal role. Even a basic grasp of these Content Management Systems smoothed interactions with the IT team, ensuring our online content was always up to date. Given FDJ’s diverse audience, cultural awareness was of paramount importance. Recognizing and respecting cultural nuances ensured our communications were not just well-received but also deeply resonated with our varied demographic.

This journey was more than just a job; it was a continuous learning experience, ensuring I stayed abreast with the best practices and evolving trends in the world of corporate communication.

What I learned

Adaptability

Thriving in a dynamic environment like FDJ was an exercise in adaptability. The rapidly shifting terrain of the gaming and gambling industry, influenced by evolving market trends, customer behavior, and technological breakthroughs, taught me that flexibility wasn’t just an asset—it was a necessity. Whether it was adjusting campaign strategies in response to unexpected market shifts or incorporating feedback from real-time analytics, I learned the importance of being agile, proactive, and receptive to change. It wasn’t just about adjusting to change but leveraging it to foster innovation and drive growth.

Collaboration

My role at FDJ was not siloed; it was deeply intertwined with various departments, from marketing and digital to events and customer service. This cross-functional collaboration was a masterclass in teamwork. I realized that the success of a campaign or project was often the culmination of diverse inputs, insights, and expertise. Engaging with colleagues from different backgrounds and specializations enriched my perspective, helping me appreciate the value of collective brainstorming and problem-solving. It emphasized the importance of open communication, mutual respect, and the synergies created when individuals come together with a shared purpose.

Strategic Thinking

Beyond the day-to-day tasks and immediate goals lay the broader vision of FDJ. My tenure taught me the significance of strategic foresight. It wasn’t enough to create impactful campaigns; these campaigns needed to be aligned with FDJ’s long-term objectives and brand ethos. I learned to view projects not as standalone endeavors but as interconnected pieces of a larger puzzle. By keeping an eye on the bigger picture and anticipating future trends, I could make decisions that not only addressed immediate challenges but also positioned FDJ for sustained success in the years to come.

Financial concepts related my internship

Return on Investment (ROI )

In the intricate realm of communication, the concept of Return on Investment (ROI) transcends its traditional financial boundaries. For every campaign I led or contributed to at FDJ, the metrics weren’t limited to immediate financial returns. We delved deep into intangible metrics like brand recall, media impressions, and customer sentiment analysis. Parameters such as engagement rates, share of voice in media, and other key performance indicators (KPIs) served as compasses, guiding our strategic adjustments. These metrics, while not directly financial, held significant implications for FDJ’s long-term revenue potential. An impactful campaign with high brand recall, for instance, could drive customer loyalty, leading to repeat purchases and sustained revenue streams.

Budget Management

Managing a campaign’s budget wasn’t just about allocation; it was a strategic endeavor in its own right. With every campaign at FDJ, we had to ensure that the funds were deployed where they’d yield the most impact. This involved making tough decisions, prioritizing certain channels over others, and sometimes innovating cost-effective solutions without compromising the campaign’s efficacy. Regular tracking of expenses, juxtaposed against campaign milestones and KPIs, ensured that we remained within the stipulated budgetary confines. Through continuous monitoring and adaptive allocation strategies, I learned the delicate art of optimizing returns while maintaining fiscal discipline.

Risk Management

Operating in the gambling and lottery sector came with its unique set of challenges, the most paramount being the responsibility towards our customers and stakeholders. While the overarching goal was to promote FDJ’s offerings, it was crucial to strike a balance with responsible gaming narratives. Every promotional message was meticulously crafted to ensure it didn’t inadvertently promote irresponsible gambling behavior. This not only mitigated potential reputational risks but also preempted regulatory backlash. Beyond communications, risk management also extended to assessing financial vulnerabilities in our campaigns, such as over-reliance on a single promotional channel or unforeseen market fluctuations that could impact campaign outcomes.

In conclusion, my apprenticeship at FDJ was a deeply immersive journey, one that sharpened my skills in corporate communication while concurrently highlighting its symbiotic relationship with core business and financial principles. Every campaign, every message, and every budgetary decision was a lesson in strategic foresight, underscoring the intricate balance between effective communication and fiscal responsibility.

Why should I be interested in this post?

If the world of finance and a company’s profitability pique your interest, this article is tailored for you. Through my experience at FDJ, I unveil the communication strategies of a major company and the financial impact of every decision made. From ROI to risk management, and budgetary control, this deep dive provides you with a tangible insight into how communication is shaped by financial imperatives.

Useful resources

La Française des Jeux (FDJ)

About the author

The article was written in December 2023 by Lou PERRONE (ESSEC Business School, Global Bachelor of Business Administration (GBBA), 2019-2023).

My experience as a Self-employed Business Owner

December 2, 2023 by Magnus NIELSEN

My experience as a Self-employed Business Owner

In this article, Magnus NIELSEN (ESSEC Business School, European Management Track, 2023-2024) shares his professional experience as an entrepreneur and Business Owner.

About the company

Pilot Education ApS is a Danish aviation consultancy company that I founded in 2019.
The company originated as a vision to establish a flight school. Specializing in pilot training and revalidation services, my company initially focused on ensuring the continued proficiency of pilots through regular license revalidation processes, as well as the training of new student pilots.

As I delved deeper into the aviation industry and advanced in my studies at Copenhagen Business School, the company’s scope evolved. Expanding beyond traditional pilot training, the company began to establish connections with various stakeholders in the aviation sector. This growing network allowed me to provide valuable non-pilot services, transforming the company into a small dynamic aviation consultancy.

Presently, Pilot Education ApS is still a new player in the aviation consulting landscape, offering a range of services to small and medium-sized companies within the industry, and mostly to Danish firms. The company’s core areas of expertise include cost optimization, addressing strategic concerns, streamlining operational processes, and focusing on services that enhance overall value for its clients. As one might hear, this comprises typical and commonly encountered elements within the consulting sector. Nothing different about it, just in a much smaller scale compared to the large consulting firms, such as McKinsey and Bain and Company.

Pilot Education ApS has carved a niche for itself by combining practical aviation knowledge with business acumen. This unique approach has positioned the company as a trusted advisor in the Danish aviation sector, providing tailored solutions to meet the diverse needs of its clients.

I attempted to gradually foster the growth of the company; however, this endeavor was swiftly hindered by the impact of COVID-19 (which hit the aviation sector extremely hard) and time constraints arising from my academic commitments. Consequently, I faced a dilemma between maintaining academic performance and pursuing the expansion of the small consulting firm specializing in aviation. I choose the first option.

Working with the company has provided me with diverse experience across a variety of segments within the sector. This includes involvement with entities engaged in air travel (airlines), aviation mechanics, ground handling, and even organizations contributing to the education of air traffic controllers.

Similarly, through the company and its connections with clients and customers, I have had the opportunity to travel not only within Denmark but also to various parts of Scandinavia and Northern Europe. This has all been very valuable for me personally, and a unique way to work besides my university studies, allowing me to integrate practical experiences with theoretical knowledge and giving a holistic approach to my professional development.

Evolution and Expertise

“Be the master of one’s own destiny.”

As the company grew, I encountered the need for a deeper understanding of Danish tax law, and corporate law particularly during the transition from “sole proprietorship to a limited liability company”. This strategic shift was prompted by the company’s growth, underscoring the importance of adapting to evolving business needs and legal considerations. As Denmark is the best country for business in (Forbes 2021), it is easy to get advice from the government and municipalities. In the beginning I did all accounting myself, but quickly found it difficult to cope with all the tax rules and tax deduction/credit. Thus, I found the need to employ an accountant and a bookkeeper. I could then focus on core business tasks, while getting advice on financials by the accountant. Likewise, the annual report is also prepared and filled by the accountant.

Operating a consultancy firm demands a versatile skill set, as one must navigate various aspects of the aviation sector, handle client interactions directly, and manage the complexities of Danish business regulations. This multifaceted role involves not only consulting services but also to understand and comply with legal frameworks governing business structures and taxation.

Entrepreneurial Responsibilities

In contrast to traditional student assistant roles, where tasks may be more narrowly defined, the responsibility of running a small consultancy falls squarely on the entrepreneur. Direct client engagement is a key aspect, requiring a proactive approach to meet client expectations, secure projects, and ensure the successful delivery of services.

The entrepreneurial journey involves not just technical expertise but also resilience, adaptability, and a relentless commitment to client satisfaction. In the competitive field of aviation consultancy, success is contingent upon the ability to proactively pursue opportunities, work diligently, and deliver tangible results. It’s a journey where the dedication to achieving professional goals goes hand in hand with the responsibility of running a business. One must be the

My missions

Client Engagement

Directly responsible for client interactions
Proactively pursue opportunities to secure projects
Ensure client satisfaction through attentive and responsive interactions

Evolution and connections

Expanded the company’s scope beyond traditional pilot training
Establish connections with various stakeholders in the aviation sector

Entrepreneurial Responsibilities

Manage diverse aspects of the aviation sector
Navigate legal frameworks and comply with business regulations

Adaptability and Resilience

Demonstrate adaptability in response to challenges, such as the impact of COVID-19
Balancing academic commitments while fostering company growth

Required skills and knowledge

Operating a small company requires skills and knowledge that extend beyond conventional boundaries. One must not merely adhere to established norms but instead think innovatively, always ready to step out of the box and explore uncharted territories. The ability to think creatively is paramount, to uncover solutions and pathways that may not have been immediately apparent. In my experience I’ve learned that the capacity to think beyond traditional approaches is a key driver of success. Initially I didn’t expect to end up in the consulting world. But, when I saw the opportunity, I went for it.

Whether navigating legal transitions, devising strategies for cost optimization, or engaging with clients in the aviation sector, thinking outside the box has proven essential. It involves not just following a set path but actively seeking unexplored avenues, fostering adaptability, and finding solutions to challenges that may not have been initially apparent. If you do not like to do so, the lifestyle may not be for you.

It is crucial to bear in mind that in a small company, you represent the face of the business. You are intricately connected to every facet of the company’s operations and must actively participate in all activities that the company undertakes.

What I learned

Tax advantages in a limited liability company

Investment tax credit
Income split. One can choose to pay salary to the owner but may instead focus on the benefits to distribute profit as “dividends”
Tax deferral delay paying taxes on income until a later date, provides additional cash flow, that can be used in projects or in passive investments such as treasury bills

Financial Management and Planning:

Owning a company has provided insights into effective financial management, including budgeting, forecasting, and strategic allocation of resources to ensure sustained growth.

Regulatory Compliance and Legal Understanding:

Managing a business involves navigating legal frameworks and ensuring compliance with regulations. Learning about legal structures, and industry-specific regulations has become integral to the day-to-day operations. While it requires time to grasp, once mastered, it can become a valuable asset for the owner’s advantage.

Financial concepts related my internship

Game Theory Analysis

Game Theory, a branch of mathematics that analyzes strategic interactions between rational decision-makers, provides an advanced framework to model and understand the complex dynamics of airline alliances in the aviation sector. Despite the high level of competitiveness in the industry, and despite the impact of inflation leading to overall price increases, the cost of plane tickets has remained relatively stable, comparable to the prices observed three years ago.

The application of Game Theory to airline alliances involves the study of strategic interactions among airlines. Each client (airline) pursues its own interest in a very competitive environment.

Modeling the Strategic Interaction

The Nash Equilibrium, a central concept in Game Theory, represents a state in which no player has an incentive to unilaterally deviate from their chosen strategy. In the context of alliances, the Nash Equilibrium can be determined by analyzing the reaction functions of each airline to the other’s strategy.

The strategic considerations go beyond quantity decisions. Airlines must also strategically determine pricing, route allocation, and capacity sharing. These decisions can be incorporated into the game model to provide a more comprehensive analysis of the strategic landscape. Sometimes I try to quantify the Nash equilibrium, other times you should just keep it in your mind, and then look into strategy in a broader sense (not quantified). For instance, Ryanair is extremely good at providing low-cost air fares. While a customer choosing Air France, might expect more quality or at least a larger selection of flights to his/her destination.

Capital Structure optimization

Within the industry, a growing trend among airlines is the preference for leasing over direct purchases. This shift in approach calls for a thorough reassessment of fundamental business operations. The utilization of foundational financial modeling techniques, such as Discounted Cash Flow (DCF) analysis, becomes essential in making well-informed decisions when weighing the options between leasing and purchasing.

While calculating the Net Present Value (NPV) might be straightforward, accurately estimating the relevant parameters and acknowledging their uncertainties poses a more intricate challenge. To address this, I designate each parameter as a stochastic variable and conduct multiple simulations to compare NPVs across various leasing and acquisition scenarios.

By integrating statistical methodologies into corporate finance, a more nuanced and informed decision-making process emerges. This approach enhances the accuracy of predictions, allowing for a more robust evaluation of leasing versus acquiring propositions in the dynamic landscape of the aviation industry. Navigating the details of debt financing terms and adhering to covenants is also paramount in the process. The objective is not only to secure operational flexibility for aviation-related activities but also to ensure alignment with financial agreements and covenants.

In the end, it is the management of the respective company that makes decisions based on their strategic intuition, complemented by data and suggestions compiled by my company.

Why should I be interested in this post?

Entrepreneurial Exposure: The entrepreneurial journey of a business owner, and how you should shed light on the challenges and triumphs of managing your own firm. This firsthand experience is invaluable for anyone interested in finance, as it provides insights into the financial intricacies of running your own business.

Financial Management: The aspects of running a company, including budgeting, forecasting, and strategic resource allocation. These financial management skills are directly applicable to finance roles, where expertise in budgeting and strategic financial planning is highly sought after.

Application of Financial Concepts: If one is interested in applying financial concepts learned at ESSEC or another top Business School, directly into business related challenges, while being the sole responsible to the results. Then you need to consider starting you own minor company.

Versatile Skill Development: Operating a consultancy necessitates a diverse skill set, including financial management, client engagement, and legal understanding. The development and application of such skills is crucial to survive against competitors.
Remember that when being a business owner, you cannot hide behind an excel sheet. You are the sole responsible for the survival and growth of your company and your wealth.

Useful resources

Denmark Tops List Of Best Countries For Business

Business demography statistics

About the author

The article was written in December 2023 by Magnus NIELSEN (ESSEC Business School, European Management Track, 2023-2024).

My experience as a student assistant at KMD

April 4, 2024December 2, 2023 by Magnus NIELSEN

My experience as a student assistant at KMD

In this article, Magnus NIELSEN (ESSEC Business School, European Management Track, 2023-2024) shares his professional experience as a student assistant at KMD. A company located in Denmark, mainly focusing on software solutions for the public sector in Denmark.

About the company

KMD A/S, is a Danish IT company, within development and delivery of software and service solutions tailored for municipalities, government entities, and businesses in Denmark, alongside selected segments in Scandinavia. The company, with branches in all major cities in Denmark, operates as a subsidiary of the NEC Corporation (Japanese multinational corporation). The KMD group works primarily in Denmark, but has recently expanded to Norway, Sweden, Finland, and Poland, boasting an annual turnover of approximately DKK 4.8 billion and a workforce exceeding 3,000 employees.

A significant player in the Danish IT landscape, KMD traces its roots back to 1972 when it was established as “Kommunedata” (translated to; “municipality data”), a merger of all Danish municipal IT centers. Until March 2009, the company was owned by Kommune Holding A/S, giving it close relations to the government. After 2009 it was privatized in a large selloff by the municipalities.

KMD’s systems play a crucial role in administering various Danish income transfers, including welfare, child benefits, maternity benefits, unemployment benefits, disability pensions, and old-age pensions. With a clientele exceeding 1,500 from both the public and private sectors, KMD serves around 800 Danish and international companies. Main competition comes from NNIT, Netcompany, TDC Group and SimCorp. Representing the forefront of the Danish IT industry.

In the evolution of its ownership structure, KMD transitioned from municipal ownership to becoming part of “EQT Partners and Arbejdsmarkedets Tillægspension” (a special pension fund system in Denmark) in 2009. Subsequently, in 2012, EQT Partners sold its stake to the private equity firm Advent International. Notably, KMD expanded its portfolio in 2015 through the acquisition of Banqsoft, a Nordic software company specializing in financial services.

The year 2019 marked a significant milestone for KMD as Japanese company NEC acquired the company for 8 billion DKK, solidifying KMD’s position in the ever-evolving landscape of IT solutions.

Logo of the company.
Logo of
Source: the company.

My internship and the department

Being a part of KMD in the role of a student employee within the Finance department is an enriching and dynamic experience. The company’s role in developing and managing over 400 IT systems that support the welfare of Denmark adds a sense of purpose to the work environment.

The focus of my position is primarily on maintaining and enhancing financial reporting for the business. The responsibilities extend to supporting the monthly closing process in collaboration with experienced controllers. This hands-on experience allows for a deep dive into the intricacies of financial operations, providing valuable insights into the core of KMD’s activities.

The role involves working with a substantial amount of data, requiring proficiency in tools such as Excel, PowerPoint, SAP, and Power BI. This emphasis on data analysis and modeling adds a layer of complexity to the tasks, making it an intellectually experience.

The position was for 15-hour per workweek which is normal in Denmark to do besides studies. Instead of internships, students often work in between 15-25 hours a week whil also keeping track of their academic

My missions

Strengthening Financial Reporting: Playing a key role in maintaining and enhancing financial reporting for the business.

Monthly Closing Support: Collaborating with senior controllers to facilitate the monthly closing process, involving the analysis of statistics from the previous month. This includes identifying areas where company performance may have fallen short and investigating the underlying reasons. Additionally, overseeing the tracking of consultants’ work hours and assessing their productivity.

Data Analysis and Modeling: Participating in data-related tasks, encompassing analysis and model development. Leveraging tools such as Excel, PowerPoint, SAP, and Power BI for efficient data management. SAP serves as the primary system for obtaining accountable data, subsequently analyzed using Excel and Power BI.

Required skills and knowledge

My position in KMD’s Finance department demanded a blend of both soft and hard skills essential for the dynamic responsibilities associated with financial reporting and analysis. On the soft skills front, effective communication was paramount, as conveying complex financial insights to diverse stakeholders required clarity and precision. Including the elaboration and communication of complex financials to non-financial employees.

Additionally, a high degree of analytical thinking was indispensable for interpreting data and contributing meaningfully to the monthly closing process. Being detail-oriented was crucial, ensuring accuracy in financial reporting and tracking of consultants’ work hours.

On the hard skills side, proficiency in tools like Excel, PowerPoint, SAP, and Power BI was fundamental. The ability to navigate and extract actionable insights from SAP, the primary system for accountable data, was essential for comprehensive financial analysis. Moreover, a solid foundation in data analysis and modeling techniques facilitated the creation of meaningful reports that contributed to the strategic decision-making processes within the department. The use of PivotTables thus exemplifies how technical skills, in this case, mastery of Excel functionalities, played a crucial role in the success of tasks within the dynamic environment of financial analysis at KMD.

What I learned

Financial Analysis and Communication

Analyzed corporate information and financial statements
Prepared pitch-books and presentations for effective communication with stakeholders
Utilized evidence-based conclusions and strategic thinking to propose innovative initiatives aligned with industry innovations and key success factors
Enhanced collaboration skills through engaging with diverse stakeholders.

Global Industry Understanding

Understanding value creation within the IT industry, drawing parallels with academic studies in competitor theory
Explored potential channels for international expansion, broadening perspectives on global finance dynamics
Applied financial modeling and analysis skills in a real-world context.

Financial concepts related my internship

DuPont Analysis

A powerful and simple financial tool, holds particular relevance in the financial reporting function at KMD. Rooted in financial ratio analysis, DuPont Analysis breaks down Return on Equity (ROE) into three key components, providing an understanding of the drivers behind financial performance.

The theoretical foundation of DuPont Analysis lies in the decomposition of ROE using the formula:

Return on Equity (ROE)

Net Profit Margin (NPM): The first component assesses profitability, reflecting the proportion of each revenue dollar that translates into net income. The formula for Net Profit Margin is:

Net Profit Margin (NPM)

Asset Turnover (ATO): The second component, Asset Turnover, evaluates the efficiency of asset utilization in generating sales. The formula is:

Asset Turnover (ATO)

Equity Multiplier (EM): The third component, Equity Multiplier, gauges the financial leverage used to magnify returns. It is calculated as the ratio of total assets to shareholders’ equity:

Equity Multiplier (EM)

By breaking down ROE into these components, DuPont Analysis enables a more structured assessment of financial performance. The application of DuPont Analysis enhances the finance department’s ability to interpret and communicate the multifaceted nature of financial performance within the context of KMD’s operations. Likewise, it provided an opportunity to pinpoint areas where improvement actions could be initiated.

Real options valuation

The application of real options valuation (ROV) methods in the context of KMD’s IT projects involves adapting and selecting appropriate models to capture the dynamic and uncertain nature of these projects. Considering that KMD’s projects may span various stages and encounter multiple uncertainties, the valuation method addresses American-styled exercises and incorporate flexibility throughout the project lifecycle.

When large uncertainties surround costs and revenues of a complex IT project, where development costs already is initiated before the actual contract is won, the traditional Black-Scholes approach can be used to estimate the value. When multiple uncertainties exist Monte Carlo simulation can also be a way to estimate the value of a project.

One must understand the concepts of IT projects, as these are put out to tender. And development cost almost always arise before the company even know if they have won the tender offer. Thus, there is a chance that the option will never get exercised, and the value is lost.
In the context of an IT project, the real option is often more analogous to a call option than a put option.

Call Option Characteristics:

A call option provides the holder with the right, but not the obligation, to buy an asset at a predetermined price (strike price) within a specified period (expiration date).

Similarly, in an IT project, the company holds the real option to proceed with the project but is not obligated to do so. The company has the flexibility to exercise the option if the conditions (such as winning a tender) are favorable.

With a call option, the holder’s downside is limited to the premium paid for the option.
In the case of an IT project, the development costs incurred before knowing the tender outcome represent a limited downside. If the tender is not won, the company may choose not to exercise the option, limiting the financial exposure.

This is a simple case. And the real option of KMD’s IT projects are often much more complex.

Monte Carlo simulation can be a powerful tool instead of the Black and Scholes formula.

In the context of an IT project’s real options valuation, Monte Carlo simulation involves modeling the project’s uncertainties using stochastic variables and running numerous simulations to estimate the project’s value. Here’s how it can be applied:

1. Identify Stochastic Variables

Project Success Probability: The likelihood of winning the tender or securing the project
Development cost: The cost associated with developing the IT project
Exogenous factors: External factors impacting the project, such as changes in technology, regulatory environment, or market demand.

2. Define Probability Distributions

Assign probability distributions to the identified stochastic variables. For example:

Probability of success: Following a beta distribution representing high degree of uncertainty/
Cost of development: Triangular distribution based on optimistic, most likely, and pessimistic estimates
Market conditions: Following a gaussian distribution

Denote that one can assign any distribution to the stochastic variables, depending on what is assumed to fit best.

3. Run the Monte Carlo Simulation

Generate random values for the stochastic variables based on their probability distributions. For each set of randomly generated values, calculate the project’s Net Present Value (NPV) or other relevant financial metrics. Repeat the process for thousands of iterations to create a distribution of possible outcomes.

Finally one may analyze the result, and present the obtained results for a managing director, who will take the final decision together with the executives. Depending on NPV of the project and the degree of uncertainty, the executives may agree to bid for the tender offer, or not to engage.

Why should I be interested in this post?

For an ESSEC student aspiring to build a career in finance, this post offers an opportunity to explore the intersection of finance and information technology. The practical application of financial concepts, such as DuPont Analysis and Real Options Valuation, within the IT industry at KMD provides a valuable insight in the daily life of a Danish software firm.

The position requires a holistic understanding of financial operations within the company. Working with technologies like SAP and Power BI enhances your skill set, making you more versatile and competitive, particularly in a digitalized financial landscape.

The exposure to real-world scenarios involving strategic decision-making under uncertainty, as emphasized by Real Options Valuation, equips you with a strategic mindset—vital in finance roles where decision-making is critical.

Understanding the inner workings of a major IT company operating in Denmark and other Nordic countries, like KMD, provides insights into the challenges and opportunities in the competitive IT market. If you ever aspire to work in Denmark, this post offers international experience, giving you a taste of the Danish business environment and company culture.

Useful resources

About KMD

Goran Avlijaš (2019) Examining the Value of Monte Carlo Simulation for Project Time Management Management Journal of Sustainable Business and Management Solutions in Emerging Economies

Black F. and M. Scholes (1973) The Pricing of Options and Corporate Liabilities The Journal of Political Economy, 81(3) : 637-654.

About the author

The article was written in December 2023 by Magnus NIELSEN (ESSEC Business School, European Management Track, 2023-2024).

Extreme returns and tail modelling of the CSI 300 index for the Chinese equity market

January 27, 2024November 23, 2023 by Shengyu ZHENG

Extreme returns and tail modelling of the CSI 300 index for the Chinese equity market

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) describes the statistical behavior of extreme returns of the CSI 300 index for the Chinese equity market and explains how extreme value theory can be used to model the tails of its distribution.

The CSI 300 index for the Chinese equity market

The CSI 300 Index, or China Securities Index 300, is a comprehensive stock market benchmark that tracks the performance of the top 300 A-share stocks listed on the Shanghai and Shenzhen stock exchanges. Introduced in 2005, the index is designed to represent a broad and diverse spectrum of China’s leading companies across various sectors, including finance, technology, consumer goods, and manufacturing. The CSI 300 is a crucial indicator of the overall health and direction of the Chinese stock market, reflecting the dynamic growth and evolution of China’s economy.

The CSI 300 employs a free-float market capitalization-weighted methodology. This means that the index’s composition and movements are influenced by the market value of the freely tradable shares, providing a more accurate representation of the companies’ actual impact on the market. As China continues to play a significant role in the global economy, the CSI 300 has become a key reference point for investors seeking exposure to the Chinese market and monitoring economic trends in the dynamic economy. With its emphasis on the country’s most influential and traded stocks, the CSI 300 serves as an essential tool for both domestic and international investors navigating the complexities of the Chinese financial landscape.

In this article, we focus on the CSI 300 index of the timeframe from March 11th, 2021, to April 1st, 2023. Here we have a line chart depicting the evolution of the index level of this period.

Figure 1 below gives the evolution of the CSI 300 index from March 11th, 2021, to April 1st, 2023 on a daily basis.

Figure 1. Evolution of the CSI 300 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the logarithmic returns of CSI 300 index from March 11th, 2021, to April 1st, 2023 on a daily basis. We observe concentration of volatility reflecting large price fluctuations in both directions (up and down movements). This alternation of periods of low and high volatility is well modeled by ARCH models.

Figure 2. Evolution of the CSI 300 index logarithmic returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the CSI 300 index

Table 1 below presents the summary statistics estimated for the CSI 300 index:

Table 1. Summary statistics for the CSI 300 index.
summary statistics of the CSI 300 index returns
Source: computation by the author (data: Yahoo! Finance website).

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively. We can conclude that during this timeframe, the CSI 300 index takes on a downward trend, with relatively important daily deviation, negative skewness and excess of kurtosis.

Tables 2 and 3 below present the top 10 negative daily returns and top 10 positive daily returns for the index over the period from March 11th, 2021, to April 1st, 2023.

Table 2. Top 10 negative daily returns for the CSI 300 index.
Top 10 negative returns of the CSI 300 index
Source: computation by the author (data: Yahoo! Finance website).

Table 3. Top 10 positive daily returns for the CSI 300 index.
Top 10 positive returns of the CSI 300 index
Source: computation by the author (data: Yahoo! Finance website).

Modelling of the tails

Here the tail modelling is conducted based on the Peak-over-Threshold (POT) approach which corresponds to a Generalized Pareto Distribution (GPD). Let us recall the theoretical background of this approach.

The POT approach takes into account all data entries above a designated high threshold u. The threshold exceedances could be fitted into a generalized Pareto distribution:

Illustration of the POT approach

An important issue for the POT-GPD approach is the threshold selection. An optimal threshold level can be derived by calibrating the tradeoff between bias and inefficiency. There exist several approaches to address this problematic, including a Monte Carlo simulation method inspired by the work of Jansen and de Vries (1991). In this article, to fit the GPD, we use the 2.5% quantile for the modelling of the negative tail and the 97.5% quantile for that of the positive tail.

Based on the POT-GPD approach with a fixed threshold selection, we arrive at the following modelling results for the GPD for negative extreme returns (Table 4) and positive extreme returns (Table 5) for the CSI 300 index:

Table 4. Estimate of the parameters of the GPD for negative daily returns for the CSI 300 index.
Modelling of negative extreme returns of the CSI 300 index
Source: computation by the author (data: Yahoo! Finance website).

Table 5. Estimate of the parameters of the GPD for positive daily returns for the CSI 300 index.
Modelling of positive extreme returns of the CSI 300 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 3 represents the historical distribution of negative return exceedances and the estimated GPD for the left tail.

Figure 3. GPD for the left tail of the CSI 300 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Figures 4 represents the historical distribution of positive return exceedances and the estimated GPD for the right tail.

Figure 4. GPD for the right tail of the CSI 300 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Applications in risk management

Extreme Value Theory (EVT) as a statistical approach is used to analyze the tails of a distribution, focusing on extreme events or rare occurrences. EVT can be applied to various risk management techniques, including Value at Risk (VaR), Expected Shortfall (ES), and stress testing, to provide a more comprehensive understanding of extreme risks in financial markets.

Why should I be interested in this post?

Extreme Value Theory is a useful tool to model the tails of the evolution of a financial instrument. In the ever-evolving landscape of financial markets, being able to grasp the concept of EVT presents a unique edge to students who aspire to become an investment or risk manager. It not only provides a deeper insight into the dynamics of equity markets but also equips them with a practical skill set essential for risk analysis. By exploring how EVT refines risk measures like Value at Risk (VaR) and Expected Shortfall (ES) and its role in stress testing, students gain a valuable perspective on how financial institutions navigate during extreme events. In a world where financial crises and market volatility are recurrent, this post opens the door to a powerful analytical framework that contributes to informed decisions and financial stability.

Download R file to model extreme behavior of the index

You can find below an R file (file with txt format) to study extreme returns and model the distribution tails for the CSI 300 index.

Useful resources

Academic resources

Embrechts P., C. Klüppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance Springer-Verlag.

Embrechts P., R. Frey, McNeil A.J. (2022) Quantitative Risk Management Princeton University Press.

Gumbel, E. J. (1958) Statistics of extremes New York: Columbia University Press.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Other resources

Extreme Events in Finance

Chan S. Statistical tools for extreme value analysis

Rieder H. E. (2014) Extreme Value Theory: A primer (slides).

About the author

The article was written in November 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Extreme returns and tail modelling of the Nikkei 225 index for the Japanese equity market

November 23, 2023 by Shengyu ZHENG

Extreme returns and tail modelling of the Nikkei 225 index for the Japanese equity market

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) describes the statistical behavior of extreme returns of the Nikkei 225 index for the Japanese equity market and explains how extreme value theory can be used to model the tails of its distribution.

The Nikkei 225 index for the Japanese equity market

The Nikkei 225, often simply referred to as the Nikkei, is a stock market index representing the performance of 225 major companies listed on the Tokyo Stock Exchange (TSE). Originating in 1950, this index has become a symbol of Japan’s economic prowess and serves as a crucial benchmark in the Asian financial markets. Comprising companies across diverse sectors such as technology, automotive, finance, and manufacturing, the Nikkei 225 offers a comprehensive snapshot of the Japanese economic landscape, reflecting the nation’s technological innovation, industrial strength, and global economic influence.

Utilizing a price-weighted methodology, the Nikkei 225 calculates its value based on stock prices rather than market capitalization, distinguishing it from many other indices. This approach means that higher-priced stocks have a more significant impact on the index’s movements. Investors and financial analysts worldwide closely monitor the Nikkei 225 for insights into Japan’s economic trends, market sentiment, and investment opportunities. As a vital indicator of the direction of the Japanese stock market, the Nikkei 225 continues to be a key reference point for making informed investment decisions and navigating the complexities of the global financial landscape.

In this article, we focus on the Nikkei 225 index of the timeframe from April 1st, 2015, to April 1st, 2023. Here we have a line chart depicting the evolution of the index level of this period.

Figure 1 below gives the evolution of the Nikkei 225 index from April 1, 2015 to April 1, 2023 on a daily basis.

Figure 1. Evolution of the Nikkei 225 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the daily logarithmic returns of Nikkei 225 index from April 1, 2015 to April 1, 2023 on a daily basis. We observe concentration of volatility reflecting large price fluctuations in both directions (up and down movements). This alternation of periods of low and high volatility is well modeled by ARCH models.

Figure 2. Evolution of the Nikkei 225 index logarithmic returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Nikkei index

Table 1 below presents the summary statistics estimated for the Nikkei 225 index:

Table 1. Summary statistics for the Nikkei 225 index.
summary statistics of the Nikkei 225 index returns
Source: computation by the author (data: Yahoo! Finance website).

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively. We can conclude that during this timeframe, the Nikkei 225 index takes on a slight upward trend, with relatively important daily deviation, negative skewness and excess of kurtosis.

Tables 2 and 3 below present the top 10 negative daily returns and top 10 positive daily returns for the index over the period from April 1, 2015 to April 1, 2023.

Table 2. Top 10 negative daily returns for the Nikkei 225 index.
Top 10 negative returns of the Nikkei 225 index
Source: computation by the author (data: Yahoo! Finance website).

Table 3. Top 10 positive daily returns for the Nikkei 225 index.
Top 10 positive returns of the Nikkei 225 index
Source: computation by the author (data: Yahoo! Finance website).

Modelling of the tails

Here the tail modelling is conducted based on the Peak-over-Threshold (POT) approach which corresponds to a Generalized Pareto Distribution (GPD). Let’s recall the theoretical background of this approach.

The POT approach takes into account all data entries above a designated high threshold u. The threshold exceedances could be fitted into a generalized Pareto distribution:

Illustration of the POT approach

Table 4. Estimate of the parameters of the GPD for negative daily returns for the Nikkei 225 index.
Modelling of negative extreme returns of the Nikkei 225 index
Source: computation by the author (data: Yahoo! Finance website).

Table 5. Estimate of the parameters of the GPD for positive daily returns for the Nikkei 225 index.
Modelling of positive extreme returns of the Nikkei 225 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 3. GPD for the left tail of the Nikkei 225 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Figure 4. GPD for the right tail of the Nikkei 225 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Applications in risk management

Why should I be interested in this post?

Download R file to model extreme behavior of the index

You can find below an R file (file with txt format) to study extreme returns and model the distribution tails for the Nikkei 225 index.

Useful resources

Academic resources

Embrechts P., C. Klüppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance Springer-Verlag.

Embrechts P., R. Frey, McNeil A.J. (2022) Quantitative Risk Management Princeton University Press.

Gumbel, E. J. (1958) Statistics of extremes New York: Columbia University Press.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Other resources

Extreme Events in Finance

Chan S. Statistical tools for extreme value analysis

Rieder H. E. (2014) Extreme Value Theory: A primer (slides).

About the author

The article was written in November 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Extreme returns and tail modelling of the FTSE 100 index for the UK equity market

November 23, 2023 by Shengyu ZHENG

Extreme returns and tail modelling of the FTSE 100 index for the UK equity market

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) describes the statistical behavior of extreme returns of the FTSE 100 index for the UK equity market and explains how extreme value theory can be used to model the tails of its distribution.

The FTSE 100 index for the UK equity market

The FTSE 100 index, an acronym for the Financial Times Stock Exchange 100 Index, stands as a cornerstone of the UK financial landscape. Comprising the largest and most robust companies listed on the London Stock Exchange (LSE), this index is a barometer for the overall health and trajectory of the British stock market. Spanning diverse sectors such as finance, energy, healthcare, and consumer goods, the FTSE 100 encapsulates the economic pulse of the nation. The 100 companies in the index are chosen based on their market capitalization, with larger entities carrying more weight in the index’s calculation, making it a valuable tool for investors seeking a comprehensive snapshot of the UK’s economic performance.

Investors and analysts globally turn to the FTSE 100 for insights into market trends and economic stability in the UK. The index’s movements provide a useful reference point for decision-making, enabling investors to gauge the relative strength and weaknesses of different industries and the economy at large. Moreover, the FTSE 100 serves as a powerful benchmark for numerous financial instruments, including mutual funds, exchange-traded funds (ETFs), and other investment products. As a result, the index plays a pivotal role in shaping investment strategies and fostering a deeper understanding of the intricate dynamics that drive the British financial markets.

In this article, we focus on the FTSE 100 index of the timeframe from April 1st, 2015, to April 1st, 2023. Here we have a line chart depicting the evolution of the index level of this period.

Figure 1 below gives the evolution of the FTSE 100 index from April 1, 2015 to April 1, 2023 on a daily basis.

Figure 1. Evolution of the FTSE 100 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the daily logarithmic returns of FTSE 100 index from April 1, 2015 to April 1, 2023. We observe concentration of volatility reflecting large price fluctuations in both directions (up and down movements). This alternation of periods of low and high volatility is well modeled by ARCH models.

Figure 2. Evolution of the FTSE 100 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the FTSE 100 index

Table 1 below presents the summary statistics estimated for the FTSE 100 index:

Table 1. Summary statistics for the FTSE 100 index returns.
Summary statistics of the FTSE 100 index returns
Source: computation by the author (data: Yahoo! Finance website).

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively. We can conclude that during this timeframe, the FTSE 100 index takes on a slight upward trend, with relatively important daily deviation, negative skewness and excess of kurtosis.

Tables 2 and 3 below present the top 10 negative daily returns and top 10 positive daily returns for the index over the period from April 1, 2015 to April 1, 2023.

Table 2. Top 10 negative daily returns for the FTSE 100 index.
Top 10 negative returns of the FTSE 100 index
Source: computation by the author (data: Yahoo! Finance website).

Table 3. Top 10 positive daily returns for the FTSE 100 index.
Top 10 positive returns of the FTSE 100 index
Source: computation by the author (data: Yahoo! Finance website).

Modelling of the tails

The POT approach takes into account all data entries above a designated high threshold u. The threshold exceedances could be fitted into a generalized Pareto distribution:

Illustration of the POT approach

Table 4. Estimate of the parameters of the GPD for negative daily returns for the FTSE 100 index.

Source: computation by the author (data: Yahoo! Finance website).

Table 5. Estimate of the parameters of the GPD for positive daily returns for the FTSE 100 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 3. GPD for the left tail of the FTSE 100 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Figure 4. GPD for the right tail of the FTSE 100 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Applications in risk management

Why should I be interested in this post?

Download R file to model extreme behavior of the index

You can find below an R file (file with txt format) to study extreme returns and model the distribution tails for the FTSE 100 index.

Useful resources

Academic resources

Embrechts P., C. Klüppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance Springer-Verlag.

Embrechts P., R. Frey, McNeil A.J. (2022) Quantitative Risk Management Princeton University Press.

Gumbel, E. J. (1958) Statistics of extremes New York: Columbia University Press.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Other resources

Extreme Events in Finance

Chan S. Statistical tools for extreme value analysis

A copula, denoted typically as C∶[0,1]^d→[0,1] , is a multivariate distribution function whose marginals are uniformly distributed on the unit interval. The parameter d is the number of variables. For a set of random variables U₁, …, U_d with cumulative distribution functions F₁, …, F_d, the copula function C satisfies:

C(F₁(u₁),…,F_d(u_d)) = ℙ(U₁≤u₁,…,U_d≤u_d)

Fréchet-Hoeffding bounds

The Fréchet–Hoeffding theorem states that copulas follow the bounds:

max{1 – d + ∑^d_i=1u_i} ≤ C(u) ≤ min{u₁, …, u_d}

In a bivariate case (dimension equals 2), the Fréchet–Hoeffding bounds are

max{u+v-1,0} ≤ C(u,v) ≤ min{u,v}

The upper bound corresponds to the case of comonotonicity (perfect positive dependence) and the lower bound corresponds to the case of countermonotonicity (perfect negative dependence).

Sklar’s theorem

Sklar’s theorem states that every multivariate cumulative distribution function of a random vector X can be expressed in terms of its marginals and a copula. The copula is unique if the marginal distributions are continuous. The theorem states also that the converse is true.

Sklar’s theorem shows how a unique copula C fully describes the dependence of X. The theorem provides a way to decompose a multivariate joint distribution function into its marginal distributions and a copula function.

Examples of copulas

Many types of dependence structures exist, and new copulas are being introduced by researchers. There are three standard classes of copulas that are commonly in use among practitioners: elliptical or normal copulas, Archimedean copulas, and extreme value copulas.

Elliptical or normal copulas

The Gaussian copula and the Student-t copula are among this category. Be reminded that the Gaussian copula played a notable role in the 2008 financial crisis, particularly in the context of mortgage-backed securities and collateralized debt obligations (CDOs). The assumption of normality and underestimation of systemic risk based on the Gaussian copula failed to account for the extreme risks in face of crisis.

Here is an example of a simulated normal copula with the parameter being 0.8.

Figure 1. Simulation of normal copula.

Source: computation by the author.

Archimedean copulas

Archimedean copulas are a class of copulas that have a particular mathematical structure based on Archimedean copula families. These copulas have a connection with certain mathematical functions known as Archimedean generators.

Here is an example of a simulated Clayton copula with the parameter being 3, which is from the category of Archimedean copulas

Figure 2. Simulation of Clayton copula.

Source: computation by the author.

Extreme value copulas

Extreme value copulas could overlap with the two other classes. They are a specialized class of copulas designed to model the tail dependence structure of multivariate extreme events. These copulas are particularly useful in situations where the focus is on capturing dependencies in the extreme upper or lower tails of the distribution.

Here is an example of a simulated Tawn copula with the parameter being 0.8, which is from the category of extreme value copulas

Figure 3. Simulation of Tawn copula.
Simulation of Clayton copula
Source: computation by the author.

Download R file to simulate copulas

You can find below an R file (file with txt format) to simulate the 3 copulas mentioned above.

Why should I be interested in this post?

Copulas are pivotal in risk management, offering a sophisticated approach to model the dependence among various risk factors. They play a crucial role in portfolio risk assessment, providing insights into how different assets behave together and enhancing the robustness of risk measures, especially in capturing tail dependencies. Copulas are also valuable in credit risk management, aiding in the assessment of joint default probabilities and contributing to an understanding of credit risks associated with diverse financial instruments. Their applications extend to insurance, operational risk management, and stress testing scenarios, providing a toolset for comprehensive risk evaluation and informed decision-making in dynamic financial environments.

Useful resources

Course notes from Quantitative Risk Management of Prof. Marie Kratz, ESSEC Business School.

About the author

The article was written in November 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Extreme returns and tail modelling of the EURO STOXX 50 index for the European equity market

November 12, 2023 by Shengyu ZHENG

Extreme returns and tail modelling of the EURO STOXX 50 index for the European equity market

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) describes the statistical behavior of extreme returns of the EURO STOXX 50 index for the European equity market and explains how extreme value theory can be used to model the tails of its distribution.

The EURO STOXX 50 index for the European equity market

The EURO STOXX 50 index stands as a benchmark of the European equity market, comprising 50 blue-chip stocks that collectively reflect the performance and market capitalization of leading companies across the Eurozone. Methodically constructed to represent diverse sectors, the index encapsulates the economic dynamics of 11 Eurozone nations. Established by STOXX Ltd., a subsidiary of Deutsche Börse Group, the selection of constituent stocks is governed by stringent criteria, including liquidity, free-float market capitalization, and sector representation. The objective is to provide investors with a comprehensive and representative gauge of the Eurozone’s equity markets.

The construction of the EURO STOXX 50 is rooted in a transparent and rules-based methodology. Component weights are determined by free-float market capitalization, a methodology designed to consider only the tradable shares of each company. This ensures that the index accurately reflects the economic significance of each constituent while preventing undue influence from large, non-tradable share blocks. Furthermore, the index is regularly reviewed and adjusted to accommodate changes in the market landscape, such as corporate actions, ensuring its relevance and accuracy in reflecting the dynamics of the Eurozone equities.

From an application standpoint, the EURO STOXX 50 serves as a valuable tool for market participants seeking exposure to the broader European equity markets. Investors and fund managers often utilize the index as a benchmark against which to measure the performance of their portfolios, assess market trends, and make informed investment decisions. Its widespread use as an underlying asset for financial products, such as exchange-traded funds (ETFs) and derivatives, underscores its significance as a reliable barometer of the Eurozone’s economic health and a foundational element in the global financial landscape.

In this article, we focus on the EURO STOXX 50 index of the timeframe from April 1st, 2015, to April 1st, 2023. Here we have a line chart depicting the evolution of the index level of this period.

Figure 1 below gives the evolution of the EURO STOXX 50 index from April 1, 2015 to April 1, 2023 on a daily basis.

Figure 1. Evolution of the EURO STOXX 50 index.
Evolution of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the daily logarithmic returns of EURO STOXX 50 index from April 1, 2015 to April 1, 2023 on a daily basis. We observe concentration of volatility reflecting large price fluctuations in both directions (up and down movements). This alternation of periods of low and high volatility is well modeled by ARCH models.

Figure 2. Evolution of the EURO STOXX 50 index logarithmic returns.
Evolution of the S&P 500 index return
Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the EURO STOXX 50 index

Table 1 below presents the summary statistics estimated for the EURO STOXX 50 index:

Table 1. Summary statistics for the EURO STOXX 50 index.
summary statistics of the EURO STOXX 50 index returns
Source: computation by the author (data: Yahoo! Finance website).

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively. We can conclude that during this timeframe, the EURO STOXX 50 index takes on a slight upward trend, with relatively important daily deviation, negative skewness and excess of kurtosis.

Tables 2 and 3 below present the top 10 negative daily returns and top 10 positive daily returns for the index over the period from April 1, 2015 to April 1, 2023.

Table 2. Top 10 negative daily returns for the EURO STOXX 50 index.
Top 10 negative returns of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Table 3. Top 10 positive daily returns for the EURO STOXX 50 index.
Top 10 positive returns of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Modelling of the tails

The POT approach takes into account all data entries above a designated high threshold u. The threshold exceedances could be fitted into a generalized Pareto distribution:

Illustration of the POT approach

Table 4. Estimate of the parameters of the GPD for negative daily returns for the EURO STOXX 50 index.
Modelling of Top 10 negative returns of the SX5E index
Source: computation by the author (data: Yahoo! Finance website).

Table 5. Estimate of the parameters of the GPD for positive daily returns for the EURO STOXX 50 index.
Modelling of Top 10 positive returns of the EURO STOXX 50 index
Source: computation by the author (data: Yahoo! Finance website).

Figure 3. GPD for the left tail of the EURO STOXX 50 index returns.
GPD for the left tail of the SX5E index returns
Source: computation by the author (data: Yahoo! Finance website).

Figure 4. GPD for the right tail of the EURO STOXX 50 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Applications in risk management

EVT as a statistical approach is used to analyze the tails of a distribution, focusing on extreme events or rare occurrences. EVT can be applied to various risk management techniques, including Value at Risk (VaR), Expected Shortfall (ES), and stress testing, to provide a more comprehensive understanding of extreme risks in financial markets.

Why should I be interested in this post?

The Extreme Value Theory is a useful tool to model the tails of the evolution of a financial instrument. In the ever-evolving landscape of financial markets, being able to grasp the concept of EVT presents a unique edge to students who aspire to become an investment or risk manager. It not only provides a deeper insight into the dynamics of equity markets but also equips them with a practical skill set essential for risk analysis. By exploring how EVT refines risk measures like Value at Risk (VaR) and Expected Shortfall (ES) and its role in stress testing, students gain a valuable perspective on how financial institutions navigate during extreme events. In a world where financial crises and market volatility are recurrent, this post opens the door to a powerful analytical framework that contributes to informed decisions and financial stability.

Download R file to model extreme behavior of the index

You can find below an R file (file with txt format) to study extreme returns and model the distribution tails for the EURO STOXX 50 index.

Useful resources

Academic resources

Embrechts P., C. Klüppelberg and T Mikosch (1997) Modelling Extremal Events for Insurance and Finance.

Embrechts P., R. Frey, McNeil A. J. (2022) Quantitative Risk Management, Princeton University Press.

Gumbel, E. J. (1958) Statistics of extremes. New York: Columbia University Press.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Other resources

Extreme Events in Finance

Chan S. Statistical tools for extreme value analysis

Rieder H. E. (2014) Extreme Value Theory: A primer (slides).

About the author

The article was written in October 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Bitcoin: the mother of all cryptocurrencies

October 26, 2023 by Snehasish CHINARA

Bitcoin: the mother of all cryptocurrencies

In this article, Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024) explains Bitcoin which is considered as the mother of all cryptocurrencies.

Historical context and background

The genesis of Bitcoin can be traced back to the aftermath of the Financial Crisis of 2008, when a growing desire emerged for a currency immune to central authority control. Traditional banks had faltered, leading to the devaluation of money through government-sanctioned printing. The absence of a definitive limit on money creation fostered uncertainty. Bitcoin ingeniously addressed this quandary by establishing a fixed supply of coins and a controlled production rate through transparent coding. This code’s openness ensured that no entity, including governments, could manipulate the currency’s value. Consequently, Bitcoin’s worth became solely determined by market dynamics, evading the arbitrary alterations typical of government-managed currencies.

Furthermore, Bitcoin revolutionized financial transactions by eliminating reliance on third-party intermediaries, exemplified by banks. Users can now engage in direct peer-to-peer transactions, circumventing the potential for intermediaries to engage in risky financial ventures akin to the 2008 Financial Crisis. The process of safeguarding one’s Bitcoins is equally innovative, as users manage their funds through a Bitcoin Wallet. Unlike traditional banks, these wallets operate as personal assets, with users as their own bankers. While various companies offer wallet services, the underlying code remains accessible for review, ensuring customers’ trust and the safety of their deposits.

Bitcoin Logo

Source: internet.

Figure 1. Key Dates in Bitcoin History

Source: author of this post.

Key features and use cases

Examples of areas where Bitcoin is currently being used:

Digital Currency: Bitcoin serves as a digital currency for everyday transactions, allowing users to buy goods and services online and in physical stores.
Crypto Banking: Bitcoin is used in decentralized finance (DeFi) applications, where users can lend, borrow, and earn interest on their Bitcoin holdings.
Asset Tokenization: Bitcoin is used to tokenize real-world assets like real estate and art, making them more accessible and divisible among investors.
Onchain Governance: Some blockchain projects utilize Bitcoin for on-chain governance, enabling token holders to vote on protocol upgrades and changes.
Smart Contracts: While Ethereum is more widely associated with smart contracts, Bitcoin’s second layer solutions like RSK (Rootstock) allow for the execution of smart contracts on the Bitcoin blockchain.
Corporate Treasuries: Large corporations, such as Tesla, have invested in Bitcoin as a store of value and an asset to diversify their corporate treasuries.
State Treasuries: Some countries, like El Salvador, have adopted Bitcoin as legal tender and added it to their national treasuries to facilitate cross-border remittances and financial inclusion.
Store of Value During Times of Conflict: In regions with economic instability or conflict, Bitcoin is used as a hedge against currency devaluation and asset confiscation.
Online Gambling: Bitcoin is widely accepted in online gambling platforms, providing users with a secure and pseudonymous way to wager on games and sports.
Salary Payments for Freelancers in Emerging Markets: Freelancers in countries with limited access to traditional banking use Bitcoin to receive payments from international clients, circumventing costly and slow remittance services.
Cross-Border Transactions with Bitcoin Gold: Cross-border transactions can often be complex, time-consuming, and costly due to the involvement of multiple intermediaries and the varying regulations of different countries. However, Bitcoin Gold offers a streamlined solution for facilitating global payments, making cross-border transactions more efficient and accessible.

These examples highlight the diverse utility of Bitcoin, ranging from everyday transactions to more complex financial applications and as a tool for economic empowerment in various contexts.

Technology and underlying blockchain

Blockchain technology is the foundational innovation that underpins Bitcoin, the world’s first and most well-known cryptocurrency. At its core, blockchain is a decentralized and distributed ledger system that records transactions across a network of computers in a secure and transparent manner. In the context of Bitcoin, this blockchain serves as a public ledger that tracks every transaction ever made with the cryptocurrency. What sets blockchain apart is its ability to ensure trust and security without the need for a central authority, such as a bank or government. Each block in the chain contains a set of transactions, and these blocks are linked together in a chronological and immutable fashion. This means that once a transaction is recorded on the blockchain, it cannot be altered or deleted. This transparency, immutability, and decentralization make blockchain technology a revolutionary tool not only for digital currencies like Bitcoin but also for a wide range of applications in various industries, from finance and supply chain management to healthcare and beyond.

Moreover, Bitcoin operates on a decentralized network of computers (nodes) worldwide. These nodes validate and confirm transactions, ensuring that the network remains secure, censorship-resistant, and immune to central control. The absence of a central authority is a fundamental characteristic of Bitcoin and a key differentiator from traditional financial systems. Bitcoin relies on a PoW consensus mechanism for securing its network. Miners compete to solve complex mathematical puzzles, and the first one to solve it gets the right to add a new block of transactions to the blockchain. This process ensures the security of the network, prevents double-spending, and maintains the integrity of the ledger. Bitcoin has a fixed supply of 21 million coins, a feature hard-coded into its protocol. The rate at which new Bitcoins are created is reduced by half approximately every four years through a process known as a “halving.” This limited supply is in stark contrast to fiat currencies, which can be printed without restriction.

These technological aspects collectively make Bitcoin a groundbreaking innovation that has disrupted traditional finance and is increasingly studied and integrated into the field of finance. It offers unique opportunities and challenges for finance students to explore, including its impact on monetary policy, investment, and the broader financial ecosystem.

Supply of coins

Looking at the supply side of bitcoins, the number of bitcoins in circulation is given by the following mathematical formula:

Formula for the number of bitcoins in circulation

This calculation hinges upon the fundamental concept of the Bitcoin supply schedule, which employs a diminishing issuance rate through a process known as “halving”.

Figure 2 represents the evolution of the number of bitcoins in circulation overt time based on the above formula.

Figure 2. Number of bitcoins in circulation

Source: computation by the author.

You can download below the Excel file for the data and the figure of the number of bitcoins in circulation.

Historical data for Bitcoin

How to get the data?

The Bitcoin is the most popular cryptocurrency on the market, and historical data for the Bitcoin such as prices and volume traded can be easily downloaded from the internet sources such as Yahoo! Finance, Blockchain.com & CoinMarketCap. For example, you can download data for Bitcoin on Yahoo! Finance (the Yahoo! code for Bitcoin is BTC-USD).

Figure 4. Bitcoin data

Source: Yahoo! Finance.

Historical data for the Bitcoin market prices

The market price of Bitcoin is a dynamic and intricate element that reflects a multitude of factors, both intrinsic and extrinsic. The gradual rise in market value over time indicates a willingness among investors and traders to offer higher prices for the cryptocurrency. This signifies a rising interest and strong belief in the project’s potential for the future. The market price reflects the collective sentiment of investors and traders. Comparing the market price of Bitcoin to other similar cryptocurrencies or benchmark assets can provide insights into its relative strength and performance within the market.

The value of Bitcoin in the market is influenced by a variety of elements, with each factor contributing uniquely to their pricing. One of the most significant influences is market sentiment and investor psychology. These factors can cause prices to shift based on positive news, regulatory changes, or reactive selling due to fear. Furthermore, the real-world implementations and usages of Bitcoin are crucial for its prosperity. Concrete use cases such as Decentralized Finance (DeFi), Non-Fungible Tokens (NFTs), and international transactions play a vital role in creating demand and propelling price appreciation. Meanwhile, adherence to basic economic principles is evident in the supply-demand dynamics, where scarcity due to limited issuance, halving events, and token burns interact with the balance between supply and demand.

With the number of coins in circulation, the information on the price of coins for a given currency is also important to compute Bitcoin’s market capitalization.

Figure 5 below represents the evolution of the price of Bitcoin in US dollar over the period October 2014 – August 2023. The price corresponds to the “closing” price (observed at 10:00 PM CET at the end of the month).

Figure 5. Evolution of the Bitcoin price

Source: computation by the author (data source: Yahoo! Finance).

Python code

Python script to download Bitcoin historical data and save it to an Excel sheet::

import yfinance as yf
import pandas as pd

# Define the ticker symbol and date range
ticker_symbol = “BTC-USD”
start_date = “2020-01-01”
end_date = “2023-01-01”

# Download historical data using yfinance
data = yf.download(ticker_symbol, start=start_date, end=end_date)

# Create a Pandas DataFrame
df = pd.DataFrame(data)

# Create a Pandas Excel writer object
excel_writer = pd.ExcelWriter(‘bitcoin_historical_data.xlsx’, engine=’openpyxl’)

# Write the DataFrame to an Excel sheet
df.to_excel(excel_writer, sheet_name=’Bitcoin Historical Data’)

# Save the Excel file
excel_writer.save()

print(“Data has been saved to bitcoin_historical_data.xlsx”)

# Make sure you have the required libraries installed and adjust the “start_date” and “end_date” variables to the desired date range for the historical data you want to download.

The code above allows you to download the data from Yahoo! Finance.

R code

The R program below written by Shengyu ZHENG allows you to download the data from Yahoo! Finance website and to compute summary statistics and risk measures about the Bitcoin.

Data file

The R program that you can download above allows you to download the data for the Bitcoin from the Yahoo! Finance website. The database starts on September 17, 2014.

Table 3 below represents the top of the data file for the Bitcoin downloaded from the Yahoo! Finance website with the R program.

Table 3. Top of the data file for the Bitcoin.
Top of the file for the Bitcoin data
Source: computation by the author (data: Yahoo! Finance website).

Evolution of the Bitcoin

Figure 6 below gives the evolution of the Bitcoin from September 17, 2014 to December 31, 2022 on a daily basis.

Figure 6. Evolution of the Bitcoin.

Source: computation by the author (data: Yahoo! Finance website).

Figure 7 below gives the evolution of the Bitcoin returns from September 17, 2014 to December 31, 2022 on a daily basis.

Figure 7. Evolution of the Bitcoin returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the Bitcoin

The R program that you can download above also allows you to compute summary statistics about the returns of the Bitcoin.

Table 4 below presents the following summary statistics estimated for the Bitcoin:

The mean
The standard deviation (the squared root of the variance)
The skewness
The kurtosis.

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively.

Table 4. Summary statistics for the Bitcoin.

Source: computation by the author (data: Yahoo! Finance website).

Statistical distribution of the Bitcoin returns

Historical distribution

Figure 8 represents the historical distribution of the Bitcoin daily returns for the period from September 17, 2014 to December 31, 2022.

Figure 8. Historical distribution of the Bitcoin returns.

Source: computation by the author (data: Yahoo! Finance website).

Gaussian distribution

The Gaussian distribution (also called the normal distribution) is a parametric distribution with two parameters: the mean and the standard deviation of returns. We estimated these two parameters over the period from September 17, 2014 to December 31, 2022. The annualized mean of daily returns is equal to 30.81% and the annualized standard deviation of daily returns is equal to 62.33%.

Figure 9 below represents the Gaussian distribution of the Bitcoin daily returns with parameters estimated over the period from September 17, 2014 to December 31, 2022.

Figure 9. Gaussian distribution of the Bitcoin returns.
Gaussian distribution of the daily Bitcoin returns
Source: computation by the author (data: Yahoo! Finance website).

Risk measures of the Bitcoin returns

The R program that you can download above also allows you to compute risk measures about the returns of the Bitcoin.

Table 5 below presents the following risk measures estimated for the Bitcoin:

The long-term volatility (the unconditional standard deviation estimated over the entire period)
The short-term volatility (the standard deviation estimated over the last three months)
The Value at Risk (VaR) for the left tail (the 5% quantile of the historical distribution)
The Value at Risk (VaR) for the right tail (the 95% quantile of the historical distribution)
The Expected Shortfall (ES) for the left tail (the average loss over the 5% quantile of the historical distribution)
The Expected Shortfall (ES) for the right tail (the average loss over the 95% quantile of the historical distribution)
The Stress Value (SV) for the left tail (the 1% quantile of the tail distribution estimated with a Generalized Pareto distribution)
The Stress Value (SV) for the right tail (the 99% quantile of the tail distribution estimated with a Generalized Pareto distribution)

Table 5. Risk measures for the Bitcoin.

Source: computation by the author (data: Yahoo! Finance website).

The volatility is a global measure of risk as it considers all the returns. The Value at Risk (VaR), Expected Shortfall (ES) and Stress Value (SV) are local measures of risk as they focus on the tails of the distribution. The study of the left tail is relevant for an investor holding a long position in the Bitcoin while the study of the right tail is relevant for an investor holding a short position in the Bitcoin.

Why should I be interested in this post?

Students would be keenly interested in this article discussing Bitcoin’s history and trends due to its profound influence on the financial landscape. Bitcoin, as a novel and dynamic asset class, presents a unique opportunity for students to explore the evolving world of finance. By delving into Bitcoin’s past, understanding its market trends, and assessing its impact on global economies, students can equip themselves with the knowledge and skills needed to navigate a financial landscape that is increasingly intertwined with cryptocurrencies and blockchain technology. Moreover, this knowledge can enhance their career prospects in an industry undergoing significant transformation and innovation.

Useful resources

Academic research about risk

Longin F. (2000) From VaR to stress testing: the extreme value approach Journal of Banking and Finance, N°24, pp 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Data

Yahoo! Finance

Yahoo! Finance Historical data for Bitcoin

CoinMarketCap Historical data for Bitcoin

About the author

The article was written in September 2023 by Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024).

Extreme returns and tail modelling of the S&P 500 index for the US equity market

October 20, 2023 by Shengyu ZHENG

Extreme returns and tail modelling of the S&P 500 index for the US equity market

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) describes the statistical behavior of extreme returns of the S&P 500 index for the US equity market and explains how extreme value theory can be used to model the tails of its distribution.

The S&P 500 index for the US equity market

The S&P 500, or the Standard & Poor’s 500, is a renowned stock market index encompassing 500 of the largest publicly traded companies in the United States. These companies are selected based on factors like market capitalization and sector representation, making the index a diversified and reliable reflection of the U.S. stock market. It is a market capitalization-weighted index, where companies with larger market capitalization represent a greater influence on their performance. The S&P 500 is widely used as a benchmark to assess the health and trends of the U.S. economy and as a performance reference for individual stocks and investment products, including exchange-traded funds (ETF) and index funds. Its historical significance, economic indicator status, and global impact contribute to its status as a critical barometer of market conditions and overall economic health.

Characterized by its diversification and broad sector representation, the S&P 500 remains an essential tool for investors, policymakers, and economists to analyze market dynamics. This index’s performance, affected by economic data, geopolitical events, corporate earnings, and market sentiment, can provide valuable insights into the state of the U.S. stock market and the broader economy. Its rebalancing ensures that it remains current and representative of the ever-evolving landscape of American corporations. Overall, the S&P 500 plays a central role in shaping investment decisions and assessing the performance of the U.S. economy.

In this article, we focus on the S&P 500 index of the timeframe from April 1st, 2015, to April 1st, 2023. Here we have a line chart depicting the evolution of the index level of this period. We can observe the overall increase with remarkable drops during the covid crisis (2020) and the Russian invasion in Ukraine (2022).

Figure 1 below gives the evolution of the S&P 500 index from April 1, 2015 to April 1, 2023 on a daily basis.

Figure 1. Evolution of the S&P 500 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 2 below gives the evolution of the daily logarithmic returns of S&P 500 index from April 1, 2015 to April 1, 2023 on a daily basis. We observe concentration of volatility reflecting large price fluctuations in both directions (up and down movements). This alternation of periods of low and high volatility is well modeled by ARCH models.

Figure 2. Evolution of the S&P 500 index logarithmic returns.

Source: computation by the author (data: Yahoo! Finance website).

Summary statistics for the S&P 500 index

Table 1 below presents the summary statistics estimated for the S&P 500 index:

Table 1. Summary statistics for the S&P 500 index.
summary statistics of the S&P 500 index returns
Source: computation by the author (data: Yahoo! Finance website).

The mean, the standard deviation / variance, the skewness, and the kurtosis refer to the first, second, third and fourth moments of statistical distribution of returns respectively. We can conclude that during this timeframe, the S&P 500 index takes on a slight upward trend, with relatively important daily deviation, negative skewness and excess of kurtosis.

Tables 2 and 3 below present the top 10 negative daily returns and top 10 positive daily returns for the S&P 500 index over the period from April 1, 2015 to April 1, 2023.

Table 2. Top 10 negative daily returns for the S&P 500 index.
Top 10 negative returns of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Table 3. Top 10 positive daily returns for the S&P 500 index.
Top 10 positive returns of the S&P 500 index
Source: computation by the author (data: Yahoo! Finance website).

Modelling of the tails

The POT approach takes into account all data entries above a designated high threshold u. The threshold exceedances could be fitted into a generalized Pareto distribution:

Illustration of the POT approach

Table 4. Estimate of the parameters of the GPD for negative daily returns for the S&P 500 index.

Source: computation by the author (data: Yahoo! Finance website).

Table 5. Estimate of the parameters of the GPD for positive daily returns for the S&P 500 index.

Source: computation by the author (data: Yahoo! Finance website).

Figure 3. GPD for the left tail of the S&P 500 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Figure 4. GPD for the right tail of the S&P 500 index returns.

Source: computation by the author (data: Yahoo! Finance website).

Applications in risk management

Why should I be interested in this post?

Download R file to model extreme behavior of the index

You can find below an R file (file with txt format) to study extreme returns and model the distribution tails for the S&P 500 index.

Useful resources

Academic resources

Embrechts P., C. Klüppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance Springer-Verlag.

Embrechts P., R. Frey, McNeil A.J. (2022) Quantitative Risk Management Princeton University Press.

Gumbel, E. J. (1958) Statistics of extremes New York: Columbia University Press.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Other resources

Extreme Events in Finance

Chan S. Statistical tools for extreme value analysis

Rieder H. E. (2014) Extreme Value Theory: A primer (slides).

About the author

The article was written in October 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Les distributions statistiques

October 16, 2023 by Shengyu ZHENG

Distributions statistiques : variable discrète vs variable continue

Dans cet article, Shengyu ZHENG (ESSEC Business School, Grande Ecole – Master in Management, 2020-2024) explique les distributions statistiques pour des variables aléatoires discrètes et continues.

Variables aléatoires discrète et continue

Une variable aléatoire est une variable dont la valeur est déterminée d’après la réalisation d’un événement aléatoire. Plus précisément, la variable (X) est une fonction mesurable depuis un ensemble de résultats (Ω) à un espace mesurable (E).

X : Ω → E

On distingue principalement deux types de variables aléatoires : discrètes et continues.

Une variable aléatoire discrète prend des valeurs dans un ensemble dénombrable comme l’ensemble des entiers naturels. Par exemple, le nombre de points marqués lors d’un match de basket est une variable aléatoire discrète, car elle ne peut prendre que des valeurs entières telles que 0, 1, 2, 3, etc. Les probabilités associées à chaque valeur possible de la variable aléatoire discrète sont appelées probabilités de masse.

En revanche, une variable aléatoire continue prend des valeurs dans un ensemble non dénombrable comme l’ensemble des nombres réels. Par exemple, la taille ou le poids d’une personne sont des variables aléatoires continues, car elles peuvent prendre n’importe quelle valeur réelle positive. Les probabilités associées à une variable aléatoire continue sont déterminées par une fonction de densité de probabilité. Cette fonction permet de mesurer la probabilité que la variable aléatoire se situe dans un intervalle donné de valeurs.

Méthodes pour décrire des distributions statistiques

Afin de mieux comprendre une variable aléatoire, il y a plusieurs moyens pour décrire la distribution de la variable.

Calcul des statistiques

Une statistique est le résultat d’une suite d’opérations appliquées à un ensemble d’observations appelé échantillon et une mesure numérique qui résume une caractéristique de cet ensemble. Par exemple, la moyenne est un exemple de statistiques.
Les statistiques peuvent être divisées en deux types principaux : les statistiques descriptives et les statistiques inférentielles.

Les statistiques descriptives sont utilisées pour résumer et décrire les caractéristiques de base d’un ensemble de données. Elles comprennent des mesures telles que les moments d’une distribution (la moyenne, la variance, le skewness, le kurtosis, …). Une explication plus détaillée est disponible dans l’article Moments de la distribution.

Les statistiques inférentielles, quant à elles, sont utilisées pour faire des inférences sur une population à partir d’un échantillon de données. Elles incluent des tests d’hypothèses, des intervalles de confiance, des analyses de régression, des modèles prédictifs, etc.

Histogramme

Un histogramme est un type de graphique qui permet de représenter la distribution des données d’un échantillon. Il est constitué d’une série de rectangles verticaux, où chaque rectangle représente une plage de valeurs de la variable étudiée (appelée classe), et dont la hauteur correspond à la fréquence des observations de cette classe.

L’histogramme est un outil très utilisé pour visualiser la distribution des données et pour identifier les tendances et les formes dans les données pour les variables discrètes ainsi que continues discrétisées.

Fonction de masse et fonction de densité

Une fonction de masse de probabilité est une fonction mathématique qui permet de décrire la distribution de probabilité d’une variable aléatoire discrète.

La fonction de masse de probabilité associe à chaque valeur possible de la variable aléatoire discrète une probabilité. Par exemple, si X est une variable aléatoire discrète prenant les valeurs 1, 2, 3 et 4 avec des probabilités respectives de 0,2, 0,3, 0,4 et 0,1, alors la fonction de masse de probabilité de X (loi multinomiale) est donnée par :
P(X=1) = 0,2
P(X=2) = 0,3
P(X=3) = 0,4
P(X=4) = 0,1

Il est important de noter que la somme des probabilités pour toutes les valeurs possibles de la variable aléatoire doit être égale à 1, c’est-à-dire, pour toute variable aléatoire discrète X :
∑ P(X=x) = 1

Figure 1. Fonction de masse d’une loi multinomiale (pour une variable discrète).

Source : calcul par l’auteur

Par contre, une fonction de densité représente la distribution de probabilité d’une variable aléatoire continue. La fonction de densité permet de calculer la probabilité que la variable aléatoire prenne une valeur dans un intervalle donné.
Graphiquement, l’aire sous la courbe de la fonction de densité entre deux valeurs a et b correspond à la probabilité que la variable aléatoire prenne une valeur dans l’intervalle [a, b].

Il est important de noter que la fonction de densité est une fonction continue, positive et intégrable sur tout son domaine. L’intégrale de la fonction de densité sur l’ensemble des valeurs possibles de la variable aléatoire est égale à 1.

Figure 2. Fonction de densité d’une loi normale (pour une variable continue).

Source : calcul par l’auteur

Fonction de répartition

La fonction de répartition (ou fonction de distribution cumulative) est une fonction mathématique qui décrit la probabilité qu’une variable aléatoire prenne une valeur inférieure ou égale à une certaine valeur donnée. Elle est définie pour toutes les variables aléatoires, qu’elles soient continues ou discrètes.
Pour une variable aléatoire discrète, la fonction de répartition F(x) est définie comme la somme des probabilités des valeurs inférieures ou égales à x :

F(x) = P(X ≤ x) = Σ P(X = xi) pour xi ≤ x

Pour une variable aléatoire continue, la fonction de répartition F(x) est définie comme l’intégrale de la densité de probabilité f(x) de -∞ à x :
F(x)=P(X≤x)= ∫_-∞^xf(t)dt

Exemples

Dans cette partie, nous allons prendre deux exemples d’analyse de distribution statistique, l’un d’une variable aléatoire discrète et l’autre d’une variable continue.

Variable discrète : résultat du lancer d’un dé à six faces

Le jeu de lancer de dé à six faces consiste à lancer un dé pour obtenir un résultat aléatoire entre 1 et 6, correspondant aux six faces du dé. Les résultats ne prennent que les valeurs entières (1, 2, 3, 4, 5 et 6) et ils ont tous une probabilité identique de 1/6.

Dans cet exemple, le code R permet de simuler N lancers de dé et de visualiser la distribution des N résultats à l’aide d’un histogramme. En utilisant ce code, il est possible de simuler des parties de lancer de dé et d’analyser les résultats pour mieux comprendre la distribution des probabilités.

Si cette expérience aléatoire est répétée 1 000 fois, nous arrivons à un résultat dont l’histogramme est comme :

Figure 3. Histogramme des résultats de lancers d’un dé à six faces.

Source : calcul par l’auteur

Nous constatons que les résultats sont distribués d’une manière équilibrée et ont la tendance de converger vers la probabilité théorique 1/6.

Variable continue : rendments de l’indice CAC40

Le rendement d’un indice d’actions comme le CAC 40 pour le marché français est une variable aléatoire continue parce qu’elle peut prendre toutes les valeurs réelles.

Nous utilisons un historique de l’indice boursier journalier pour des cours de clôture de l’indice CAC 40 du 1^er avril 2021 au 1^er avril 2023 pour calculer des rendements journalières (rendements logarithmiques).

En finance, la distribution des rendements journalières de l’indice CAC 40 est souvent modélisée par une loi normale, même si la loi normale ne modélise pas forcément bien la distribution observée, surtout les queues de distributions observées. Dans le graphique ci-dessous, nous voyons que la distribution normale ne décrit pas bien la distribution réelle.

Figure 4. Fonction de densité des rendements journalières de l’indice CAC 40 (variable continue).

Source : calcul par l’auteur

Pour des observations issues pour une variable continue, il est toujours possible de regrouper les observations dans des intervalles et de représenter dans un histogramme.

La table 1 ci-dessous donne les statistiques descriptives pour les rendements journalières de l’indice CAC 40.

Table 1. Statistiques descriptives pour les rendements journalières de l’indice CAC 40.

Statistiques descriptives	Valeur
Moyenne	0.035
Médiane	0.116
Écart-type	1.200
Skewness	-0.137
Kurtosis	6.557

Les résultats du calcul des statistiques descriptives correspondent bien à ce que nous pouvons remarquer du graphique. La distribution des rendements a une moyenne légèrement positive. La queue de la distribution empirique est plus épaisse que celle de la distribution normale vu les survenances des rendements (positives ou négatives) extrêmes.

Fichier R pour cet article

A propos de l’auteur

Cet article a été écrit en octobre 2023 par Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

My experience as Actuarial Apprentice at La Mutuelle Générale

October 9, 2023 by Shengyu ZHENG

My experience as Actuarial Apprentice at La Mutuelle Générale

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024) shares his professional experience as Actuarial Apprentice at La Mutuelle Générale .

About the company

La Mutuelle Générale is a major French mutual insurance company that has established itself as a trusted provider of health and social protection solutions. With a history dating back to its foundation in 1945 as the mutual health insurance provider for La Poste et France Télécom, La Mutuelle Générale has grown to become a key player in the mutual health insurance sector in France.

Unlike private insurance companies, mutual insurance companies are based on the concept of solidarity and not for lucrative purposes. As a mutual insurance company, La Mutuelle Générale has no shareholders but only member clients who also contribute to the decision making of the company.

Specializing in health insurance and complementary health coverage, La Mutuelle Générale offers a comprehensive range of insurance products and services designed to meet the diverse needs of both individual and collective clients. On top of the coverage offered by the French social security system, la Mutuelle Générale’s health insurance offerings encompass a wide array of guarantees, including medication reimbursement, hospitalization coverage, dental care, optical care, and so forth. The company strives to provide flexible and tailored solutions to suit the specific requirements of the member clients.

The core business of the mutual insurance company is composed of health insurance and social protection (short-term incapacity, long-term invalidity, dependency and death). For the purpose of providing a more comprehensive healthcare service, in 2020, the company launched its Flex service platform, which enables partner companies to access services such as home care or personal assistance.

Overall, La Mutuelle Générale stands as a reliable and reputable insurance company, driven by the mission to provide quality healthcare coverage and social protection to individuals and businesses across France. They combine their extensive expertise, expansive coverage, and a dedicated workforce to promote well-being, financial security in face of healthcare needs, and peace of mind for their members.

Logo of La Mutuelle Générale

Source: website of La Mutuelle Générale

My position

Since September 2022, I have been engaged in a one-year apprenticeship contract for the position of Actuarial Analyst in the Technical Department that englobes all the actuarial missions. Specifically, I was in the team of Studies and Products Collective Health Insurance and Social Protection. This team takes charge of the actuarial studies of social protections and collective health insurance contracts.

My missions

Within the team, I had the chance to assist my colleagues to conduct actuarial studies in various subjects:

Monitor the profitability and risk of different insurance portfolios

We continually evaluate the financial performance and risk exposure associated with individual and group Health Insurance and Life Insurance policies. We assess factors such as claims experience, investment returns, and expenses to gauge the profitability and financial health of the portfolios. By closely monitoring these aspects, the management can make informed decisions to ensure the sustainability and growth of the company.

Calculate and provide rates for group Health Insurance and Life Insurance products

We are responsible for developing the pricing structure and tools for group Health Insurance and Life Insurance products. According to the size of the clients, we deploy different pricing strategies.

We model factors such as the demographics and health profiles of the insured individuals, expected claims frequency and severity, and desired profit margins. Through mathematical models and statistical analysis, we determine appropriate premia for corresponding products.

Here I introduce brief the key idea of insurance pricing. The mechanism of insurance is that the insured person pays for a premium beforehand to get guarantee against a certain risk for a period in the future. Insurance works on the basis of mutualisation, explained by the Law of Large Numbers. For example, for automobile insurance against the risk of theft. The risk does not befall everyone (the probability of occurrence is relatively low). Whereas, when it happens, the owner has to endure a loss amount that is relatively high and it is in this case that insurance companies accompany the car owner to cover part or all of the loss if the owner is insured.

Let’s denote X_i as the loss amount for insured person i (X_i equals 0 if the risk does not take place). If an insurance company has n insured persons, and we assume all X_i are independent and identically distributed. According to the Law of Large Numbers, we have:

1/n ∑ ⁿ_{i =1} X_i → 𝔼[ X_i]

If n is large enough, the total claim amount will converge to 𝔼[ X₁]. Therefore, if every insured person pays individually a premium of 𝔼[ X₁], the insurance company as a whole would be able to pay off all the possible claims.

Ensure the implementation of the underwriting policy:

The Underwriting Department relies on a tool to assess and price group insurance contracts. Actuaries play a crucial role in guaranteeing the consistency and accuracy of the pricing scales used within this tool. We review and validate the formulas and algorithms used to calculate premia, to make sure that they are aligned with the company’s underwriting guidelines and principles and with our calculations.

We work closely with the underwriting team to enforce the company’s underwriting policy. This involves establishing guidelines and criteria for accepting or rejecting insurance applications, determining coverage limits, and setting appropriate pricing. We provide insights and recommendations based on their analyses to ensure the underwriting policy is effectively implemented, balancing risk management and business objectives.

Conduct studies related to the current political and economic conditions

Given the dynamic nature of the insurance sector, we conduct studies to assess the impact of external factors, such as economic conditions, on insurance products. For example, we analyze the effects of the 100% Santé reform on insurance premia and claim payouts. We also conduct theoretical research of the impact of the 2023 retirement reform on our social protection portfolio.

By understanding these impacts, actuaries can adapt pricing strategies, adjust risk models, and make informed decisions to address emerging challenges and provide appropriate coverage to policyholders in conformity with the framework of regulations.

Required skills and knowledge

First and foremost, the position pivoted on actuarial studies requires solid understanding of actuarial and insurance concepts and theories. For example, it is indispensable to understand the contractual aspects of insurance policies, pricing theories and accounting rules of insurance products. Actuary is a profession that requires high-level specified expertise, and the title of Actuary is recognized by actuarial associations in respective countries after passing the credentialing process.

Besides, statistical and information techniques are highly needed. The professions of Actuary could be in a way considered as a combination of Statistician, Informatician and Marketer. Making use of statistical and information techniques, actuaries delve deep into data to uncover useful information that would aid the pricing of insurance policies and the decision-making process.

Last but not least, since the insurance sector is highly regulated and insurance offerings are mostly homogeneous, a solid and comprehensive knowledge of the local regulatory environment and business landscape is a must to make sure efficient development and management of the product portfolio. In my case, a thorough understanding of the French social security system and product specificities is crucial.

What I have learned

This apprenticeship experience takes place in parallel with my double curriculum in Actuarial Science at Institut de Statistique de Sorbonne Université (ISUP). I had the opportunities to apply the theoretical aspects in actual projects and work on various subjects with the guidance of experienced professionals. I had the chance to deepen my understanding in insurance pricing, health insurance & social protection and risk management for insurers.

Financial concepts related my internship

Insurance pricing

Health insurance pricing involves the application of theoretical concepts and statistical analysis to assess risk, project future claims, and determine suitable premiums. Insurers utilize statistical models to evaluate factors such as age, gender, pre-existing conditions, and healthcare utilization patterns to estimate the likelihood and cost of potential claims. By considering risk pooling, loss ratios, and health economic studies, insurers strive to set premiums that balance financial sustainability while providing adequate coverage to policyholders. Regulatory guidelines and statistical modeling further contribute to the development of pricing strategies in health insurance.

Solvency II

Solvency II is a regulatory framework for insurance companies in the European Union (EU) that aims to ensure financial stability and solvency. It establishes risk-based capital requirements, governance standards, and disclosure obligations for insurers. Under Solvency II, insurers are required to assess and manage their risks, maintain sufficient capital to withstand potential losses, and regularly report their financial and risk positions to regulatory authorities. The framework promotes a comprehensive approach to risk management, aligning capital requirements with the underlying risks of insurance activities and enhancing transparency and accountability in the insurance sector.

Useful resources

La Mutuelle Générale

Institut des Actuaires

Pricing Insurance #1: Pure Premium Method

About the author

The article was written in October 2023 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2024).

Application de la théorie des valeurs extrêmes en finance de marchés

February 4, 2024October 6, 2023 by Gabriel FILJA

Dans cet article, Gabriel FILJA (ESSEC Business School, Executive Master in Senior Bank Management, 2022-2023 & Head of Hedging à Convera) présente des applications de la théorie des valeurs extrêmes en finance de marchés et notamment en gestion des risques de marchés.

Principe

La théorie des valeurs extrêmes (TVE), appelé théorème de Fisher-Tippet-Gnedenko tente de fournir une caractérisation complète du comportement de la queue pour tous les types de distributions de probabilités.

La théorie des valeurs extrêmes montre que la loi asymptotique des rentabilités minimale et maximale a une forme bien déterminée qui est largement indépendante du processus de rentabilités lui-même (le lien entre les deux distributions apparaît en particulier dans la valeur de l’indice de queue qui reflète le poids des queues de distribution). L’intérêt de la TVE dans la gestion du risque c’est de pouvoir calculer le quantile au-delà de 99% du seuil de confiance dans le cadre des stress tests ou de la publication des exigences réglementaires.

Gnedenko a démontré en 1943 par la Théorie des valeurs extrêmes la propriété qui s’applique à des nombreuses distributions de probabilités. Soit F(x) la fonction de répartition d’une variable x. u est une valeur de x située dans la partie droite de la queue de distribution.

La probabilité que x soit compris entre u et u+y est de F(y+u) – F(u) et la probabilité que x soit supérieur à u est 1-F(u). Soit F_u(y) la probabilité conditionnelle que x soit compris entre u et u+y sachant que x>u∶

Probabilité conditionnelle

Estimation des paramètres

Selon les résultats de Gnedenko, pour un grand nombre de distribution, cela converge vers une distribution généralisée de Pareto au fur et à mesure que u augmente :

Distribution_généralisée_Pareto

β est le paramètre d’échelle représente la dispersion de la loi des extrêmes
ξ est l’indice de queue qui mesure l’épaisseur de la queue et la forme

Selon la valeur de l’indice de queue, on distingue trois formes dedistribiution d’extrêmes :

Frechet ξ > 0
Weibull ξ < 0
Gumbel ξ = 0

L’indice de queue ξ reflète le poids des extrêmes dans la distribution des rentabilités. Une valeur positive de l’indice de queue signifie que les extrêmes n’ont pas de rôle important puisque la variable est bornée. Une valeur nulle donne relativement peu d’extrêmes alors qu’une valeur négative implique un grand nombre d’extrêmes (c’est le cas de la loi normale).

Figure 1 : Densité des lois des valeurs extrêmes

Source : auteur.

Tableau 1 : Fonctions de distribution des valeurs extrêmes pour un ξ > 0, loi de Frechet, ξ < 0 loi de Weibull et ξ = 0, loi de Gumbel.
Source : auteur.

Les paramètres β et ξ sont estimés par la méthode de maximum de vraisemblance. D’abord il faut définir u (valeur proche du 95e centile par exemple). Une des méthodes pour déterminer ce seuil, c’est la technique appelée Peak Over Threshold (POT), ou méthode des excès au-delà d’un seuil qui se focalise sur les observations qui dépassent un certain seuil donné. Au lieu de considérer les valeurs maximales ou les plus grandes valeurs, cette méthode consiste à examiner toutes les observations qui franchissent un seuil élevé préalablement fixé.
L’objectif est de sélectionner un seuil adéquat et d’analyser les excès qui en découlent. Ensuite nous trions les résultats par ordre décroissant pour obtenir les observations telles que x>u et leur nombre total.

Nous étudions maintenant les rentabilités extrêmes pour l’action Société Générale sur la période 2011-2021. La Figure 2 représentes rentabilités journalières de l’action et les rentabilités extrêmes négatives obtenues avec l’approche des dépassements de seuil (Peak Over Threshold ou POT). Avec le seuil retenu de -7%, on obtient 33 dépassements sur 2 595 rentabilités journalières de la période 2011 à 2021.

Figure 2 : Sélection des rentabilités extrêmes négatives pour l’action Société Générale selon l’approche Peak Over Threshold (POT)

Source : auteur.

Méthode d’estimation statistique

Nous allons maintenant voir comment déterminer les β et ξ en utilisant la fonction de maximum de vraisemblance qui s’écrit :

Fonction de vraisemblance

Pour un échantillon de n observations, l’estimation de 1-F(u) est n_u/n. Dans ce cas, la probabilité inconditionnelle de x>u+y vaut :

Fonction de vraisemblance

Et l’estimateur de la queue de distribution de probabilité cumulée de x (pour un grand) est :

Estimateur queue distribution

Mon travail personnel a consisté à estimer le paramètre d’échelle β et le paramètre de queue ξ à partir de la formule par le maximum de vraisemblance en utilisant le solveur Excel. Nous avons précédemment déterminé n=0,07 par la méthode de POT en Figure 2, et n_u= 2595

Ainsi nous obtenons β=0,0378 et ξ=0,0393 ce qui maximise par la méthode du maximum de vraisemblance la somme du logarithme des valeurs extrêmes à un total de 73,77.

Estimation de la VaR TVE

Pour calculer le VaR au seuil q, nous obtenons F(VaR) = q

VaR TVE

Mon travail personnel a consisté à estimer la VaR du titre de la Société Générale de la période de 2011 à 2021 sur un total de 2595 cotations avec 33 dépassements de seuil (-7%). En appliquant les données obtenues à la formule nous obtenons :

VaR 99% Société Générale

Puis nous estimons la VaR à 99,90% et 99,95% :

VaR 99,90% Société Générale

Il n’est pas surprenant que l’extrapolation à la queue d’une distribution de probabilité soit difficile, pas parce qu’il est difficile d’identifier des distributions de probabilité possibles qui pourraient correspondre aux données observées (il est relativement facile de trouver de nombreuses distributions possibles différentes), mais parce que l’éventail des réponses qui peuvent vraisemblablement être obtenues peut être très large, en particulier si nous voulons extrapoler dans la queue lointaine où il peut y avoir peu ou pas de points d’observation directement applicables.

La théorie des valeurs extrêmes, si elle est utilisée pour modéliser le comportement de la queue au-delà de la portée de l’ensemble de données observées, est une forme d’extrapolation. Une partie de la cause du comportement à queue épaisse (fat tail) est l’impact que le comportement humain (y compris le sentiment des investisseurs) a sur le comportement du marché.

En quoi ça peut m’intéresser ?

Nous pouvons ainsi mener des stress tests en utilisant la théorie des valeurs extrêmes et évaluer les impacts sur le bilan de la banque ou encore déterminer les limites de risques pour le trading et obtenir ainsi une meilleure estimation du worst case scenario.

Autres articles sur le blog SimTrade

▶ Shengyu ZHENG Catégories de mesures de risques

▶ Shengyu ZHENG Moments de la distribution

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

Ressources

Articles académiques

Falk M., J. Hüsler, et R.-D. Reiss, Laws of Small Numbers: Extremes and Rare Events. Basel: Springer Basel, 2011. doi: 10.1007/978-3-0348-0009-9.

Gilli M. et E. Këllezi, « An Application of Extreme Value Theory for Measuring Financial Risk », Comput Econ, vol. 27, no 2, p. 207‑228, mai 2006, doi: 10.1007/s10614-006-9025-7.

Gkillas K. and F. Longin (2018) Financial market activity under capital controls: lessons from extreme events Economics Letters, 171, 10-13.

Gnedenko B., « Sur La Distribution Limite Du Terme Maximum D’Une Serie Aleatoire », Annals of Mathematics, vol. 44, no 3, p. 423‑453, 1943, doi: 10.2307/1968974.

Hull J.et A. White, « Optimal delta hedging for options », Journal of Banking & Finance, vol. 82, p. 180‑190, sept. 2017, doi: 10.1016/j.jbankfin.2017.05.006.

Longin F. (1996) The asymptotic distribution of extreme stock market returns Journal of Business, 63, 383-408.

Longin F. (2000) From VaR to stress testing : the extreme value approach Journal of Banking and Finance, 24, 1097-1130.

Longin F. (2016) Extreme events in finance: a handbook of extreme value theory and its applications Wiley Editions.

Longin F. and B. Solnik (2001) Extreme Correlation of International Equity Markets, The Journal of Finance, 56, 649-676.

Roncalli T. et G. Riboulet, « Stress testing et théorie des valeurs extrêmes : une vision quantitée du risque extrême ».

Sites internet

Extreme Events in Finance

A propos de l’auteur

Cet article a été écrit en juillet 2023 par Gabriel FILJA (ESSEC Business School, Executive Master in Senior Bank Management, 2022-2023 & Head of Hedging à Convera).

How to get crypto data

March 25, 2024October 4, 2023 by Snehasish CHINARA

How to get crypto data

In this article, Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024) explains how to get crypto data.

Types of data

Number of coins

The information on the number of coins in circulation for a given currency is important to compute its market capitalization. Market capitalization is calculated by multiplying the current price of the cryptocurrency by its circulating number of coins (supply). This metric gives a rough estimate of the cryptocurrency’s total value within the market and its relative size compared to other cryptocurrencies. A lower circulating supply often implies a greater level of scarcity and rarity.

For cryptocurrencies (unlike fiat money), the number of coins in circulation is given by a mathematical formula. The number of coins may be limited (like the Bitcoin) or unlimited (like Ethereum and Dogecoin) over time.

Cryptocurrencies with limited supplies, such as Bitcoin’s maximum supply of 21 million coins, can be perceived as more valuable due to their finite nature. Scarcity can contribute to investor interest and potential price appreciation over time. A lower circulating supply might indicate the potential for future adoption and value appreciation, as the limited supply can create scarcity-driven demand, especially if the cryptocurrency gains more utility and usage.

Bitcoin’s blockchain also relies on a key equation to steadily allow new BTC to be introduced. The equation below gives the total supply of bitcoins:

Total supply of bitcoins

Figure 1 below represents the evolution of the supply of Bitcoins.

Figure 1. Evolution of the supply of Bitcoins

Source: computation by the author.

Market price of a coin

The market price of a cryptocurrency in the market holds crucial insights into how well the cryptocurrency is faring. Although not the sole factor, the market price significantly contributes to evaluating the cryptocurrency’s performance and its prospects. The market price of a cryptocurrency is a dynamic and intricate element that reflects a multitude of factors, both intrinsic and extrinsic. The gradual rise in market value over time indicates a willingness among investors and traders to offer higher prices for the cryptocurrency. This signifies a rising interest and strong belief in the project’s potential for the future. The market price reflects the collective sentiment of investors and traders. Comparing the market price of a cryptocurrency to other similar cryptocurrencies or benchmark assets like Bitcoin can provide insights into its relative strength and performance within the market. A rising market price can indicate increasing adoption of the cryptocurrency for various use cases. Successful projects tend to attract more users and real-world applications, which can drive up the price.

The value of cryptocurrencies in the market is influenced by a variety of elements, with each factor contributing uniquely to their pricing. One of the most significant influences is market sentiment and investor psychology. These factors can cause prices to shift based on positive news, regulatory changes, or reactive selling due to fear. Furthermore, the real-world implementation and usage of a cryptocurrency are crucial for its prosperity. Concrete use cases such as Decentralized Finance (DeFi), Non-Fungible Tokens (NFTs), and international transactions play a vital role in creating demand and propelling price appreciation. Meanwhile, adherence to basic economic principles is evident in the supply-demand dynamics, where scarcity due to limited issuance, halving events, and token burns interact with the balance between supply and demand.

With the number of coins in circulation, the information on the price of coins for a given currency is also important to compute its market capitalization.

Figure 2 below represents the evolution of the price of Bitcoin in US dollar over the period October 2014 – August 2023. The price corresponds to the “closing” price (observed at 10:00 PM CET at the end of the month).

Figure 2. Evolution of the Bitcoin price

Source: computation by the author (data source: Yahoo! Finance).

Trading volume

Trading volume is crucial when assessing the health, reliability, and potential price movements of a cryptocurrency. Trading volume refers to the total amount of a cryptocurrency that is bought and sold within a specific time frame, typically measured in units of the cryptocurrency (e.g., BTC) or in terms of its equivalent value in another currency (e.g., USD).

Trading volume directly mirrors market liquidity, with higher volumes indicative of more liquid markets. This liquidity safeguards against drastic price fluctuations when trading, contrasting with low-volume scenarios that can breed volatility, where even a single substantial trade may disproportionately shift prices. Price alterations are most reliable and meaningful when accompanied by substantial trading volume. Price movements upheld by heightened volume often hold greater validity, potentially pointing to more pronounced market sentiment. When price surges parallel rising trading volume, it suggests a sustainable upward trajectory. Conversely, low trading volume amid rising prices may hint at a forthcoming correction or reversal. Scrutinizing the correlation between price oscillations and trading volume can uncover potential divergences. For instance, ascending prices coupled with dwindling trading volume may suggest a weakening trend.

Figure 3 below represents the evolution of the monthly trading volume of Bitcoin over the period October 2014 – July 2023.

Figure 3. Evolution of the trading volume of Bitcoin

Source: computation by the author (data source: Yahoo! Finance).

Bitcoin data

You can download the Excel file with Bitcoin data used in this post as an illsutration.

Python code

You can download the Python code used to download the data from Yahoo! Finance.

Python script to download Bitcoin historical data and save it to an Excel sheet:

import yfinance as yf
import pandas as pd

# Define the ticker symbol and date range
ticker_symbol = “BTC-USD”
start_date = “2020-01-01”
end_date = “2023-01-01”

# Download historical data using yfinance
data = yf.download(ticker_symbol, start=start_date, end=end_date)

# Create a Pandas DataFrame
df = pd.DataFrame(data)

# Create a Pandas Excel writer object
excel_writer = pd.ExcelWriter(‘bitcoin_historical_data.xlsx’, engine=’openpyxl’)

# Write the DataFrame to an Excel sheet
df.to_excel(excel_writer, sheet_name=’Bitcoin Historical Data’)

# Save the Excel file
excel_writer.save()

print(“Data has been saved to bitcoin_historical_data.xlsx”)

# Make sure you have the required libraries installed and adjust the “start_date” and “end_date” variables to the desired date range for the historical data you want to download.

APIs

Calculating the total number of Bitcoins in circulation over time
Access – Bitcoin Blockchain data
By running a Bitcoin node or by using blockchain data providers like Blockchain.info, Blockchair, or a similar service.

Extract Block Data: Once you have access to the blockchain data, you would need to extract information from each block. Each block contains a record of the transactions that have occurred, including the creation (mining) of new Bitcoins in the form of a “Coinbase” transaction.

Calculate Cumulative Supply: You can calculate the cumulative supply of Bitcoins by adding up the rewards from each block’s Coinbase transaction. Initially, the block reward was 50 Bitcoins, but it halves approximately every four years due to the Bitcoin halving events. So, you’ll need to account for these halving in your calculations.

Code – python

import requests

# Replace ‘YOUR_API_KEY’ with your CoinMarketCap API key
api_key = ‘YOUR_API_KEY’

# Define the endpoint URL for CoinMarketCap’s API
url = ‘https://pro-api.coinmarketcap.com/v1/cryptocurrency/quotes/latest’

# Define the parameters for the request
params = {
‘symbol’: ‘BTC’,
‘convert’: ‘USD’,
‘CMC_PRO_API_KEY’: api_key
}

# Send the request to CoinMarketCap
response = requests.get(url, params=params)

# Parse the response JSON
data = response.json()

# Extract the circulating supply from the response
circulating_supply = data[‘data’][‘BTC’][‘circulating_supply’]

print(f”Current circulating supply of Bitcoin: {circulating_supply} BTC”)

## Replace ‘YOUR_API_KEY’ with your actual CoinMarketCap API key.

Why should I be interested in this post?

Cryptocurrency data is becoming increasingly relevant in these fields, offering opportunities for research, data analysis skill development, and even career prospects. Whether you’re aiming to conduct research, stay informed about the evolving financial landscape, or simply enhance your data analysis abilities, understanding how to access and work with crypto data is an asset. Plus, as the cryptocurrency industry continues to grow, this knowledge can open new career paths and improve your personal finance decision-making. In a rapidly changing world, diversifying your knowledge with cryptocurrency data acquisition skills can be a wise investment in your future.

Useful resources

APIs

CoinMarketCap Source of API keys and program

CoinGecko Source of API keys and Programs

CryptoNews Source of API keys and Programs

Data sources

Yahoo! Finance Historical data for Bitcoin

Coinmarketcap Historical data for Bitcoin

Blockchain.com Market Data and charts on Bitcoin history

About the author

The article was written in October 2023 by Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, (2022-2024).

My Experience as an External Junior Consultant with Eurogroup Consulting

August 2, 2023 by Snehasish CHINARA

My Experience as an External Junior Consultant with Eurogroup Consulting

In this article, Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024) shares his experience as an External Junior Consultant with Eurogroup Consulting, which is a consulting company specialized in organization and operations (supply chain).

About Eurogroup Consulting

Eurogroup Consulting, founded in 1982, is a French consulting firm with a European approach to management, strategy and organization. With a focus on freedom to take risks, requirements of the clients and the projects, and solidarity to the success of their entrepreneurial partners, Eurogroup consulting has been able to expand its network to 16 countries and clientele to all sectors of activity. They have grown significantly in the areas of banking and finance, business, insurance and welfare, logistics and transportation, retail, energy and the environment, and public sector, including healthcare. Today, Eurogroup Consulting stands out as a highly reputable and able partner for companies seeking all-encompassing solutions and knowledgeable advisory in the areas of Digital, Operational Excellence, and Transitions.

Eurogroup Consulting Logo

Source: Eurogroup Consulting.

Junior Consultant Experience

As a part of my Master in Management program at ESSEC Business School, I and a few other students a ESSEC (my team) collaborated as an External Junior Consultant with Eurogroup Consulting for a consulting project in the aviation sector based in Singapore. With my team, I closely worked with the managing partner of Eurogroup Consulting in Singapore to offer strategic recommendations to one of the firm’s clients in the aviation sector dealing with logistics (for the maintenance, repair and overhaul (MRO) of airplanes). Our focus was on addressing the real-world challenges faced by the aviation industry in the post-Covid era in the Asia-Pacific region.

My project with Eurogroup Consulting dealt with logistics and supply chain within the aviation sector. Efficient logistics and supply chain management are vital for businesses to remain competitive in today’s globalized marketplace as they ensure the efficient flow of goods, services and information from the point of origin to the point of consumption.

Our focus was on Contract Logistics in the aviation sector, which is a type of third-party logistics (3PL) service where a company delegates certain aspects of its supply chain operations to a specialized provider. This provider, known as the contract logistics provider, oversees a portion or all the company’s supply chain, which includes transportation, distribution, and related activities, as per the contractual agreement. The primary objective of contract logistics is to enhance the efficiency of the customer’s supply chain, reduce expenses, and optimize overall performance. By leveraging expertise, resources, and technology, contract logistics providers enable clients to concentrate on core business activities while entrusting the management of their logistics operations to the specialized service. Contract logistics providers provide services such as warehouse management, inventory management, order fulfillment, distribution and transportation management. In the aviation sector, contract logistics play an important role in offering services like space part logistics. Airlines face challenges with “Inoperable parts” (INOPs), which necessitate costly replacements or risk grounding the aircraft indefinitely. Major companies provide essential services to address this spare parts availability issue, such as Order Tracking & Tracing, spare parts storage management, advanced stock organization, and repair logistics management.

My missions

The objective my project was to achieve the following:

Identify the post-Covid supply chain strategies of major multinational corporations (MNCs) in the aviation sector, including the evolution of their supply chain footprints and their expectations from contract logistics providers (an intermediary between the different manufacturers and an airline company).
Evaluate the current positioning and services offered by prominent contract logistics providers and anticipate how their positioning and offerings might evolve in the future.
Recommend new potential offerings and analyze their suitability and key factors for success.

Required skills and knowledge

As a part of a cross-functional team of ESSEC students to achieve the shared project objectives through efficient cooperation, and decision-making, I gained an understanding of the aerospace Third Party Logistic (3PL) and Maintenance, Repair and Overhaul (MRO) industry in the Asia-Pacific region as we conducted comprehensive market research. We gathered and analysed large sets of data related to the aviation contract-logistics market, customers, competitors, and industry trends to identify growth opportunities. Following the analysis, we had weekly meetings with the managing partner of Eurogroup consulting, a professor-mentor of the team at ESSEC and the client to discuss our approach to the problem statement, challenges faced by the team to gather access to information, since aviation industry is well-known for its confidentiality norms, and the assessments produced after detailed analysis of the data. Attending the weekly team-mentor meetings was vital to our learning, providing us with first-hand exposure to the real-life operations within a consulting firm. In these meeting we decided upon the objective targets for the coming weeks and how to address the challenges faced this week.

As a junior consultant, I engaged with subject matter experts in the region in order to gain a holistic understanding of the impact of Covid-19 on the aviation contract-logistics industry. I conducted detailed financial statement analysis to understand how the larger players and competition were leveraging their cash flows, and debt to counter the crisis caused on the industry by the pandemic. In order to measure the risk of the competitors of the client, we conducted a fundamental calculation of Altman’s Z-Score and developed a credit rating model based on key financial indicators, both quantitative and qualitative, in Excel. This allowed us to scrutinize the key players in the current market and identify competitors to be focused on. Based on our discussions with experts, and analysis conducted, we identified the gap in the service offerings which allowed us to provide strategic recommendations for the client company. This 3-month long learning-by-doing experience gave me immense exposure to the operations of a consulting firm and the way they respect the needs of the stakeholders of the project.

What I learned

Key Learning Outcomes of this project :

To utilise evidence-based conclusions and strategic thinking to propose new strategic initiatives that aligned with industry innovations and key success factors.
To analyse corporate information and financial statements, preparing pitch-books and presentations while collaborating with stakeholders.
To define the value chain of aviation contract-logistics industry in Asia-Pacific region and observe potential channels to expand.
To develop custom credit rating tool based on key performance indicators.

Concepts related my internship

Third-Party Logistics in Aviation Sector

Third-Party Logistics (3PL) is a crucial aspect of Logistics and Supply Chain Management, that has transformed how businesses handle the transportation and storage of products and services. Through strategic outsourcing, companies delegate specific logistics tasks to external service providers, known as 3PL providers. These service providers streamline supply chain processes, resulting in increased efficiency, cost reduction, and improved overall performance. Within the aviation sector, 3PL is crucial for aiding airlines, aircraft manufacturers, and associated enterprises with intricate global logistics. Due to the complexity and time-sensitivity of aviation operations, 3PL providers offer customized solutions to address the unique demands and challenges of the industry. 3PL companies in the aviation industry offer a range of essential services to streamline operations. These include arranging the transportation of aviation-related cargo and goods, managing efficient warehousing and inventory systems for quick access to items, handling customs clearance for international shipments, ensuring prompt last-mile delivery to designated destinations, managing the distribution of critical spare parts for airlines’ maintenance facilities worldwide, and facilitating smooth transportation of large components and sub-assemblies for aircraft manufacturers. These services contribute significantly to the industry’s efficiency and help reduce aircraft downtime, making them indispensable partners for aviation businesses.

Aviation 3PL Services:

Freight Transportation: 3PL companies arrange timely transport of aviation cargo to airports, maintenance facilities, and aircraft assembly lines.
Efficient Warehousing: These providers manage aviation-related inventory in well-organized warehouses, reducing lead times.
Customs Compliance: 3PLs handle international shipments’ customs documentation, ensuring smooth clearance.
Last-Mile Delivery: They ensure prompt delivery of aviation components to their destinations.
Spare Parts Distribution: Airlines rely on 3PLs for critical spare parts distribution, minimizing aircraft downtime.
Aircraft Manufacturing Support: Specialized 3PLs facilitate smooth production by transporting large components for aircraft manufacturers.

Aviation companies benefit from the expertise of 3PL providers in handling complex logistics. Outsourcing these services saves on capital investments and allows them greater flexibility in scaling services based on demand. 3PL providers’ extensive network aids in smoother international operations for the customers.

Credit risk

The evaluation of credit risk holds significant importance in financial risk management, especially concerning lending and investment activities. It pertains to the potential financial loss that a lender or investor might encounter in the event of non-payment or failure of a borrower or counterparty to fulfil their financial commitments. Credit risk occurs when people, companies, or governmental entities take loans or offer credit with the possibility that they might be unable to repay the borrowed amount according to the agreed terms.

Several key concepts allow us to gauge the risk involved with an investment and make better decisions. The Probability of Default (PD) is a measure that evaluates the probability of a borrower being unable to fulfil their contractual obligations and defaulting. Although defaulting doesn’t always result in immediate losses, it can raise the risk of bankruptcy and eventual losses. PD is expressed as a percentage, with higher percentages indicating a higher risk of default. Loss Given Default (LGD) is a commonly used expression to describe the ‘loss severity’ of an investment. It calculates the proportion of an exposure (such as a bond or loan equivalent) that is expected to remain unrecovered if a default occurs. It is a percentage of the outstanding debt or investment that is not recoverable after a default occurs.

Credit agencies are responsible for assigning credit ratings to both corporations and governments based on their ability to fulfil financial obligations. These credit ratings serve as indicators for lenders regarding the entity’s capacity to repay loans. Each credit agency employs slightly varied approaches in determining credit ratings. On the other hand, credit scores pertain to individuals and reflect their creditworthiness, considering their credit history and financial conduct. Credit risk models play a vital role in the financial industry as they employ mathematical techniques to foresee the probability of default, evaluate potential losses, and handle credit risk. These sophisticated tools aid both financial institutions and investors in making well-informed choices concerning lending and investment matters. As the global economy continues to evolve, understanding and managing credit risk will remain paramount for safeguarding financial stability and ensuring sustainable growth in lending and investment sectors. By employing comprehensive credit risk analysis, stakeholders can navigate potential challenges, capitalize on opportunities, and foster a resilient financial landscape for the future.

The evaluation of credit risk had a vital role in the extensive market research conducted for the top players in the aviation contract logistics segment. Although credit risk analysis mainly concentrates on appraising the creditworthiness of potential collaborators or customers, it offered valuable insights that prove beneficial for competitive intelligence and market research objectives. Conducting credit risk analysis on companies within the industry allowed for the identification of major players and their market position. Assessing financial stability, including liquidity, profitability, and debt levels, helped evaluate potential investment opportunities and market disruptions. Additionally, studying competitors’ credit risk provided insights into their market share, customer base, and potential risks of default or bankruptcy. Understanding their financial strength aided in formulating effective strategies for competitive positioning in the aviation contract logistics niche.

Corporate Risk Management

In order to mitigate various types of financial risks, such as credit risk, market risk, liquidity risk, and operational risk, investors and management can use risk analysis to identify, measure, and mitigate these risks effectively. Instabilities and losses in financial markets generally caused by fluctuations in stock prices, currencies, interest rates and more lead to rise in financial risks. Market risk reflects the fluctuations of interest rates, currencies, and prices of raw materials. Probability of failing to pay creditors such as banks or lenders leads to credit risk. Liquidity risk is the inability of a company to meet its short-term financial obligations (to pay the salaries of its employees, to settle the invoices to its suppliers, to pay back the capital and interests to the bank, to pay the taxes to the State, etc.) and is generally signs of cashflow inefficiencies. Flawed policies, processes, events or systems disrupt business operations and are known to cause operational risks. Financial risks are measured by calculating specific ratios that indicate the overall health of a company, which are then compared against the industry benchmark.

The following table provides some of the important financial ratios used to estimate the risk of a company. High financial risk is implied by high or low measure according to the ratio.

Table 1. Financial ratios

Source: The author.

Ratios are most useful when compared between companies in similar sectors and over time. Multiple measurements may be necessary for each given firm to fully comprehend the financial risk.

Why should I be interested in this post?

Working closely with subject matter experts and engaging in financial statement analysis to assess the impact of Covid-19 on the various industries equipped us with valuable skills and knowledge in financial analysis and risk assessment. Additionally, learning to calculate Altman’s Z-Score and developing a credit score model allowed us to evaluate the financial health of companies, a crucial skill in the finance industry. The exposure to strategic decision-making, data analysis, and client interactions during this consulting project helped me develop problem-solving capabilities and communication skills, which are highly sought-after attributes in the finance job market. Overall, this hands-on experience provided me with practical experience for finance roles, especially in consulting firms.

Useful resources

Eurogroup Consulting

Financial Risk – Allianz Trade

Financial Risk – Deloitte

About the author

The article was written in August 2023 by Snehasish CHINARA (ESSEC Business School, Grande Ecole Program – Master in Management, 2022-2024).

Netflix 'Billions' Analysis of characters through CFA Code and Standards

July 24, 2023 by William LONGIN

Netflix ‘Billions’ Analysis of characters through CFA Code of Ethics and Standards of Professional Conduct

In this article, William LONGIN (EDHEC Business School, Global BBA 2020-2024) analyzes the show “Billions” through the lens of the Code of Ethics and Standards of Professional Conduct developed by the CFA Institute. I wrote this post while I prepared for the Level 1 of the CFA exam.

Overview of ‘Billions’ and ethics

The Netflix show “Billions,” set in New York City, portrays the intense story between three individuals: Bobby Axelrod, CEO of hedge fund ‘Axe Capital’, Chuck Rhoades, a tenacious US Attorney, and Wendy Rhoades, the wife of Chuck Rhoades and a talented performance coach working at Axe Capital. Bobby Axelrod and Chuck Rhoades fight for their honor and survival throughout the series with sometimes questionnable actions. Wendy Rhoades often plays the role of a middle person to find compromise and communication between Bobby Axelrod and Chuck Rhoades. The main characters insatiable greed has led them to indulge in misconduct, disregarding the ethical rules that govern investment and legal professionals in the real world.

Billions
Source: Showtime / Netflix.

CFA Institute’s Code of Ethics and Standards of Professional Conduct

The CFA Institute’s Code of Ethics and Professional Standards defines a comprehensive canvas for ethical and professional behavior. It states that it is for “investment professionals globally, regardless of job function, cultural differences, or local laws and regulations.” The Code places a strong emphasis on honesty to ensure that investment professionals operate in clients’ best interests. In “Billions”, the characters’ choices and actions often cross paths with these moral guidelines. In this article we will explore the three main characters Bobby Axelrod, Chuck and Wendy Rhoades through the lens of the CFA Code of Ethics and Standards of Professional Conduct.

“Billions” main characters: Bobby Axelrod, Chuck and Wendy Rhoades
Billions main characters: Bobby Axelrod, Chuck and Wendy Rhoades
Source: Netflix.

Bobby Axelrod: the hedge fund manager

Bobby Axelrod is the main character of the series “Billions”. He is the CEO of the hedge fund Axe Capital. Bobby Axelrod possesses exceptional financial acumen (the ability to make good judgements and take quick decisions) but his actions often push the boundaries of ethical behavior. These actions are driven by the drive to always beat the market at whatever cost.

Insider trading

By definition, insider trading is the illegal practice of trading on the stock exchange to one’s own advantage using material non-public information (confidential information).

One important ethical concern surrounding Bobby is his open willingness to engage in insider trading for himself and his firm. Despite having a legal department at Axe Capital, insider trading has been normalized throughout the series and undetected in most cases by the Securities and Exchange Commission (SEC) – the US authority in charge of regulating the financial markets. Bobby Axelrod gets his information through his extensive professional network and from his spies. Insider trading is forbidden by CFA standards of professional conduct as it violates point II.A. of CFA standards of professional conduct.

II.A. Material Nonpublic Information. Members and Candidates who possess material nonpublic information that could affect the value of an investment must not act or cause others to act on the information.

Insider trading is also forbidden by law in the United States. According to Cornell Law School “Courts impose liability for insider trading with Rule 10b-5 under the classical theory of insider trading and, since U.S. v. O’Hagan, 521 U.S. 642 (1997), under the misappropriation theory of insider trading”.

An example of insider trading is in the Episode 1 Season 1: “Pilot”. Bobby Axelrod approves a short-sell on Superior Automotive based on insider information. In this scene, Bobby Axelrod listens to two points of view: a deduction based on public information from one of his employees and another point of view based on confidential information from the character Dollar-Bill. When Axe asks Dollar-Bill “his level of certainty” about the excess supply that wasn’t disclosed by the company, there is a cut scene that shows the bribing with cash & watches of an employee of Superior Automotive and Dollar-Bill directly looking at the physical inventories of the company. To which Dollar-Bills answers famously “I am not uncertain”. When in possession of insider information, professionals cannot share, or influence action based on that information according to CFA Code of Professional Standards. Although Dollar-Bill is the one that actively tried to act on insider information, Axelrod is also in fault because of his lack of due diligence and supervision of his employee.

Independence and Objectivity

Bobby Axelrod has been found to use financial incentives to influence other people’s decisions in his favor. For example, Axelrod tipped the policeman that was going to arrest his employee. This tip avoided legal charges for his employee and bad image for the firm. Axelrod is found to disregard point I.B of the CFA standards of professional conduct.

I.B. Independence and Objectivity. (…) Members and Candidates must not offer, solicit, or accept any gift, benefit, compensation, or consideration that reasonably could be expected to compromise their own or another’s independence and objectivity.

In season 1 episode 7 “The Punch”, Bobby Axelrod pays a police officer named Lonnie Watley to prevent the arrest of one of his employees, Donnie Caan. Donnie Caan is a key member of Axe Capital, and Bobby Axelrod takes measures to protect him from legal troubles related to an insider trading investigation. In a later episode this incident was discovered by Raul Gomez, New York City Police and Fire Department Pension Fund Manager that asks him to not “greed” his colleagues in the future.

Unethical behavior

Axelrod frequently engages in aggressive tactics to push his personal agenda. A major example of unethical behavior is the Ice Juice Scheme from Season 2. In this case Bobby Axelrod sabotaged the initial public offering (IPO) of a company called “Ice Juice.” He used insider information to short the stock and profit immensely when the stock price immediate crash due to his scheme. His plan was to have some people get instantly sick after drinking Ice Juice and profit from media coverage. His scheme tampered with the public opinion and destabilised the fair consideration of Ice Juice on its IPO day. This also impacted his colleagues in the investment profession and their clients. According to point 1 of the CFA Code of Ethics this behaviour is unethical.

Act with integrity, competence, diligence, respect and in an ethical manner with the public, clients, prospective clients, employers, employees, colleagues in the investment profession, and other participants in the global capital markets.

Chuck Rhoades: the US Attorney for Southern district of New York

Chuck Rhoades is the United States Attorney for the Southern district of New York. During the first season Chuck attempts to take down Bobby Axelrod to protect fair competition in the markets. Bobby and Chuck both used their network to try and destabilize the other but ended in a stalemate in the 1rst season. It is important to note that Chuck Rhoades is not an investment professional, but the Code and Standards promotes ethical guidelines that can be interpreted in various professions.

Fraud

Chuck’s methods and ethical choices also raise concern. Chuck often bends the rules, manipulates evidence, and employs coercion to secure convictions and survive in his industry. Manipulating evidence goes against point II.D of the Code of standards of professional conduct regarding misconduct.

II.D. Misconduct. Members and Candidates must not engage in any professional conduct involving dishonesty, fraud, or deceit or commit any act that reflects adversely on their professional reputation, integrity, or competence.

Conflicts of interests

Additionally, Chuck’s relationship with Wendy Rhoades, who works as a performance coach for Axe Capital, raises ethical concerns regarding conflicts of interest and the appropriate boundaries between personal and professional relationships. While Chuck initially recuses himself from the Axe Capital case, he continued to work on the case behind the scene. This goes against the interest of the American people because he is biased in his work. Point VI.A. of CFA standards of professional conduct on conflicts of interests states the following.

VI.A. Disclosure of Conflicts. Members and Candidates must make full and fair disclosure of all matters that could reasonably be expected to impair their independence and objectivity or interfere with respective duties to their clients, prospective clients, and employer. Members and Candidates must ensure that such disclosures are prominent, are delivered in plain language, and communicate the relevant information effectively.

Wendy Rhoades: the middle woman

Wendy Rhoades is a performance coach at Axe Capital. She plays a key role in the series and is a powerful woman that often plays a role in resolving the fights between Axe and Chuck. Wendy tries to balance her professional responsibilities at Axe Capital while managing her personal relationship with Chuck Rhoades. Since Wendy Rhoades works in the finance industry she is therefore directly concerned by the Code of Ethics and Standards.

Whistleblowing

Wendy Rhoades is entrusted with confidential information, serving as a confidante to many within the organization. This fiduciary (involving trust) duty requires her to prioritize the interests and welfare of these individuals, acting with integrity and avoiding any conflicts that could compromise their trust. Across Season 2 we see that the information that Wendy has on the company is compromising and therefore we may ask ourselves if under national law she would be required to play a role of whistleblower. Indeed, Wendy has had knowledge of criminal activity and refused to whistle blow mostly due to her friendship with Bobby. This goes against point I.A of CFA standards of professional conduct.

I.A. Knowledge of the Law. Members and Candidates must understand and comply with all applicable laws, rules, and regulations (including the CFA Institute Code of Ethics and Standards of Professional Conduct) of any government, regulatory organization, licensing agency, or professional association governing their professional activities. (…) Members and Candidates must not knowingly participate or assist in and must dissociate from any violation of such laws, rules, or regulations.

Wendy’s loyalty to Bobby Axelrod adds another layer of complexity. Bobby relies heavily on Wendy’s expertise and guidance, seeking her advice on critical business decisions and relying on her insight into the minds of Axe Capital employees.

Wendy’s dual loyalties place her in a delicate position, as her duty to uphold the best interests of Axe Capital and with her personal relationship with her husband Chuck Rhoades.

Importance of ethics in the investment industry and popular media’s influence

Ethics play an important role in the investment industry as it gives it reputation and trust. A Code of Ethics and Professional Standards as proposed by the CFA Institute helps to work towards a stable financial system while reducing the likelihood of wrongdoings.

The Netflix series “Billions” that started in 2016, almost 10 years after the financial crisis of 2007 portrays traders as greedy and unethical in many cases. “Billions” stays nonetheless a fictional representation of the financial industry. However, this portrayal could badly influence and create false impressions, especially for future analysts and viewers who aspire to these positions.

Television shows and movies have the power to shape public opinion. “Billions” contributes to the overall perception of the financial sector along with other films like the Wolf of Wall Street and The Big Short. The financial sector is often a sector that is unknown or known very little by the average person. The portrayal of ethical dilemmas in popular media could raise awareness and generate important discussions about the role of ethics in finance. It encourages critical thinking and prompts viewers to question the ethical boundaries they would be willing to cross in pursuit of success.

Useful resources

U.S Securities Exchange Commission (SEC)

Cornell Law School Insider trading

CFA Code of Ethics and Professional Standards

About the author

Article written in July 2023 by William LONGIN (EDHEC Business School, Global BBA, 2020-2024).

Top 5 companies by market capitalization in India

January 29, 2024July 23, 2023 by Nithisha CHALLA

Top 5 companies by market capitalization in India

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the top 5 companies by market capitalization in India.

Introduction to market capitalization

Market capitalization is a crucial factor in investment analysis. Learning about the market capitalization of companies helps you evaluate their size, growth potential, and overall value in the market. This knowledge can assist you in making informed investment decisions and assessing the financial health of companies.

Top 5 companies by market capitalization in India

The top 5 companies in India according to market capitalization by 2023 are as follows:

Stock chart for Hindustan Unilever

Source: Yahoo! Finance.

The historical data for Hindustan Unileverstock prices can be downloaded from Yahoo! Finance website: Download the data for Hindustan Unilever

Why should I be interested in this post?

As a management student, understanding the top companies in different markets and their market capitalization holds significant value. It provides you with industry insights, allowing you to comprehend the competitive landscape and trends within specific sectors.

Analyzing market capitalization aids in investment analysis, enabling you to assess the size, growth potential, and financial health of companies. Moreover, studying successful companies (success being measured by their market capitalization) provides valuable lessons in competitive strategy, organizational management, and leadership practices.

Useful resources

Companies Market Cap Largest Indian companies by market capitalization

Yahoo! 15 Biggest Indian State-Owned Companies

Wikipedia List of largest companies in India

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

Top 5 companies by market capitalization in Europe

January 30, 2024July 23, 2023 by Nithisha CHALLA

Top 5 companies by market capitalization in the Europe

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the top 5 companies by market capitalization in Europe.

Introduction to market capitalization

Market capitalization, often referred to as “market cap,” is a key metric used in the financial world to assess the size and value of a publicly traded company. Market capitalization provides insights into a company’s position in the market and its relative size compared to other companies. It is a measure of a company’s total market value, calculated by multiplying its current stock price by the total number of outstanding shares. It is an important indicator for investors, analysts, and market participants as it reflects the perceived worth of a company by the investing public. Note that market capitalization assesses the size of the company in the equity market, but the total value of the company measured by its assets or the sum of its liabilities and shareholders’ equity may be larger if the company uses debt (financial leverage).

Top 5 companies by market capitalization in Europe

The top 5 companies in the European market according to market capitalization by 2023 are as follows:

Stock chart for SAP

Source: Yahoo! Finance.

The historical data for SAP stock prices can be downloaded from Yahoo! Finance website: Download the data for SAP

Why should I be interested in this post?

Useful resources

Companies Market Cap Largest European companies by market capitalization

Statista Market capitalization of leading companies on Euronext stock exchange as of February 2023

Yahoo! 10 Best European Companies To Invest In

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

Top 5 companies by market capitalization in China

January 30, 2024July 23, 2023 by Nithisha CHALLA

Top 5 companies by market capitalization in China

In this article, Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023) presents the top 5 companies by market capitalization in China.

Introduction to market capitalization

Top 5 companies by market capitalization in China

The top 5 companies in the Chinese market according to market capitalization by 2023 are as follows:

Stock chart for Ping An Insurance

Source: Yahoo! Finance.

The historical data for Ping An Insurance prices can be downloaded from Yahoo! Finance website: Download the data for Ping An Insurance

Why should I be interested in this post?

Useful resources

Companies Market Cap Largest Chinese companies by market capitalization

Yahoo! 15 Biggest Chinese State-Owned Companies

About the author

The article was written in June 2023 by Nithisha CHALLA (ESSEC Business School, Grande Ecole Program – Master in Management, 2021-2023).

Introduction to convertible bonds

December 31, 2023June 30, 2023 by Tanguy TONEL

Introduction to convertible bonds

In this article, Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023) explains about convertible bonds.

Introduction

In the ever-evolving financial landscape, investors are constantly seeking new opportunities to diversify their portfolios and maximize returns. One such investment vehicle that has gained traction in recent years is the convertible bond. As a hybrid security, convertible bonds offer a unique blend of debt and equity features, providing investors with the potential for capital appreciation and income generation. In this article, we will delve into the world of convertible bonds, exploring their characteristics, types, and the benefits they offer to both investors and issuers.

What are Convertible Bonds

A convertible bond is a type of corporate bond that can be converted into a predetermined number of shares of common stock in the issuing company upon or before its maturity.

Like traditional corporate bonds, convertible bonds entitle their holders to coupon (interest) payments at regular intervals and can usually be redeemed for their par value (original price) upon maturity, assuming they were not already converted into shares.

Technically, convertible bonds are considered debt instruments until they are converted into shares. However, due to their ability to be converted into equity, most investors consider them hybrid securities.

Types of Convertible Bonds

Vanilla Convertible Bonds

These are the most common type of convertible bonds, allowing investors the option to convert their bonds into shares at a predetermined conversion price and rate during the bond’s lifetime.

Mandatory Convertible Bonds

Unlike vanilla convertible bonds, mandatory convertible bonds require the bondholder to convert their bonds into shares at the maturity date. This feature makes them more equity-like in nature.

Reverse Convertible Bonds

These bonds give the issuer the option to either buy back the bond in cash or convert the bond into equity at a predetermined conversion price and rate at the maturity date.

Risks

Also known as Public Investment in Private Equity (PIPE), convertible bonds allow companies that have difficulties securing financing with a more traditional approach to get funding more easily.

Nevertheless, convertible bonds can lead to significant dilution for investors if the funds holding them decide, or are forced, to convert the debt into equity as they usually purchase the debt at a discount. Convertible bonds can be seen as debt combined to an already “in the money” option for newly emitted shares. Through “OCEANE” bonds in France, companies might refund the bondholders with existing shares, but it happens less often than a refund with newly emitted shares.

The Hull precises that “When these instruments are exercised, the company issues more shares of its own stock and sells them to the option holder for the strike price. The exercise of the instruments therefore leads to an increase in the number of shares of the company’s stock that are outstanding.”. Indeed, a major risk for the old shareholders is dilution and an important decrease in the value of their shares if the bond issuance is used as a form of credit line rather than funding growth.

As it is a common source of funding for companies in difficulties, that risk tends to be significative.

Indeed, according to Les Echos, the AMF (Autorité des marchés financiers) scrutinized a sample of 69 companies, and among them 57 companies, or 83% of the sample, saw their stock prices decline, with an average decrease of 72%. The stock price of 20 of them, or 29% of the sample, has even lost more than 90%.Only 12 companies, or 17% of the sample, saw their stock price rise.

Conditions of exercise

Convertible bonds come with specific conditions for exercise, offering investors the flexibility to convert their bonds into a predetermined number of common shares of the issuing company.

The conditions typically include a conversion ratio, which specifies the number of shares the bondholder will receive for each convertible bond converted.

Additionally, there is usually a conversion price, which is the predetermined price at which the conversion occurs. Investors can choose to exercise their convertible bonds if the market price of the company’s common stock exceeds the conversion price, enabling them to benefit from the appreciation in the stock value.

The issuing company may also impose restrictions on when and how the conversion can take place, such as waiting until a certain period has passed since the issuance of the bonds. These conditions are designed to balance the interests of both the bondholder and the issuing company and provide a mechanism for investors to participate in potential upside movements in the company’s stock.

Example

A convertible bond is issued at a value of €1,000 at a ratio of 1 bond to 5 shares.

Five years later, the number of shares associated to this bond are worth €3,000, the bondholder claims his five shares. His benefit is €2,000 plus the yield of the bond for the 5 years.

If, five years later, the 5 shares are worth €200, the bondholder claims a refund in cash and his benefit is the yield of the bond.

It is to be noted that the investor is granted no voting rights before claiming shares against his bond.

Also, in the case of mandatory convertible bonds, the investor will incur a loss of (1000-200) €800 and will get 5 shares now worth €200.

Why should I be interested in this post?

Small caps can offer larger returns than large caps which may attract the retail investor desiring to beat the market. Nevertheless, some companies abuse this financing method, generating unwanted risk that mainly hurts the investors. Therefore, it is important to be aware of the opportunities offered by those alternative investment vehicles while keeping in mind the associated risks.

Useful resources

Hull J.C. (2021) Options, Futures, and Other Derivatives Pearson, 11^th Edition.

Elbadraoui, Khalid & Lilti, Jean-Jacques & Mzali, Bouchra. (2008) La Performance Opérationnelle à Long Terme des Entreprises Françaises Émettrices d’Obligations Convertibles. Revue Finance Contrôle Stratégie 11, 125-154.

U.S. Securities and Exchange Commission (SEC) Private Investment in Public Equity (PIPE).

C.P. (18 octobre 2022) L’AMF met à nouveau en garde contre les OCABSA.

About the author

The article was written in June 2023 by Tanguy TONEL (ESSEC Business School, Global BBA, 2019-2023).

My Experience as a Communication Officer at La Française des Jeux (FDJ)

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Return on Investment (ROI )

Budget Management

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Financial concepts related my internship

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Real options valuation

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Options

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Extreme returns and tail modelling of the CSI 300 index for the Chinese equity market

The CSI 300 index for the Chinese equity market

Summary statistics for the CSI 300 index

Modelling of the tails

Applications in risk management

Why should I be interested in this post?

Download R file to model extreme behavior of the index

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Extreme returns and tail modelling of the Nikkei 225 index for the Japanese equity market

The Nikkei 225 index for the Japanese equity market

Summary statistics for the Nikkei index

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Why should I be interested in this post?

Download R file to model extreme behavior of the index

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Extreme returns and tail modelling of the FTSE 100 index for the UK equity market

The FTSE 100 index for the UK equity market

Summary statistics for the FTSE 100 index

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Why should I be interested in this post?

Download R file to model extreme behavior of the index