VICOBA

February 5, 2024August 10, 2022 by Louise PIZON

VICOBA

In this article, Louise PIZON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2020-2022) explains the concept of Village Community Bank (VICOBA) which is a type of micro funding used in non-governmental organizations (NGOs).

Village Community Bank (VICOBA)

Village Community Bank (VICOBA) is a savings and loan fund for members who have joined together and formed a group for economic improvement purposes. The system started in Tanzania twenty years ago and has shown great success for its members in being able to lend to each other, helping each other to solve various problems as well set up joint economic projects.

What is micro funding? It is the funding of projects that are too small to gain support from mainstream venture capital firms. Through micro funding, such projects can be linked to a group of investors willing to take a chance on the project. Micro funding allows entrepreneur to network with investors and managers to grow your business to the next level.

Purpose of VICOBA group and activities

A VICOBA group is a group of people who have agreed to gather their strengths and resources together to eradicate poverty and bring development in their household. Group members will participate to all group activities as weekly meetings and general meetings, elect a steering committee and establish group rules to guide them.

It is better for groups to meet weekly to increase intimacy and help the loan’ fund to grow faster. Previous experiences have shown that the growth of a group that meet weekly is faster from the growth of a group that meet once a month. Weekly meeting helps people to repay their loans on time and keep the cash flow within the group stable.

All VICOBA group activities are run by the group members themselves through volunteerism. By experience, group members can effectively carry out their activities after receiving leadership training and management teamwork from VICOBA experts, which are AJISO members.

AJISO is a legal aid provision organization in Tanzania who help women to empowered themselves economically, in pushing them to be part of a VICOBA group and giving them some entrepreneurship trainings to allows them to be engage in economic activities and improve their livelihood.

Steps to create a VICOBA group

A VICOBA group is created following the steps:

Persons with the idea of starting a group to meet (not less than fifteen and not more than thirty)
Members collect admission fees usually 10,000 TZS per member. The money is used to buy equipment such as ledgers, passbooks, etc.; Admission fees are also used for group registration costs.
Members start the training supervised by an AJISO trainer.
Members formulate a constitution and rules that will include the level of shares, the social fund, and the date of the meeting.

Details rules of VICOBA

VICOBA groups are made up of 15 to 30 members who are self-selected. These groups come from small groups of five people whose members select and assemble themselves. Members begin to buy shares in the group and after a delay of twelve weeks the share fund begins to be lent to its members.

Membership of VICOBA groups is open to women and men and at least two of the five members of the steering committee must be women. A person who is heavily indebted to other such groups will not be allowed to join the scheme until he has paid off his debts. Religious and government leaders will be allowed to join the program but will not be allowed to lead the group, these leaders are not allowed to be leaders due to their positions and responsibilities they have in society, instead they will be group advisors.

VICOBA groups elect their leaders who are a chairperson, a secretary, a treasurer and two accountants. The members of the steering committee are elected annually and may be removed at any time if 2/3 of the members of the general assembly decide so. VICOBA groups formulate their own rules of governance, and these groups are self-reliant. Each group has its own rules, and these rules give authority to the group leadership to show direction for the conduct of group activities as well as the resolution of group conflicts.

Each participant needs to know all the group rules and to follow them accordingly. VICOBA groups met in a specific order: group members determine the best time to meet. This system emphasizes the group meeting weekly but may consider meeting monthly but will depend on the activities carried out by the members themselves. The group will agree on the date of the meeting, the time of the meeting and the place of meeting. However, the group is important to consider what this program suggests to going further strengthen collaboration and communication to be closer among members. Meeting weekly will allow some members who want to take out loans to make it easier and those who want to take out emergency loans as well.

Fundraising process

The fundraising process involves banking transactions and group deposits using a share system. Shares are funds that are injected by a group member into the group for the purpose of making profit and becoming the owner of the group. Group members contribute financially each week in buying one to five shares. The value of one share will be based on the agreement of the members of the group and it is recommended that the rate take into account the economic potential of its members.

This system requires that each group members buy shares in loudly stating the number of shares that they are buying and the amount of social fund they are investing. The member will submit the money to the accountants and the book is handed over to the treasurer for replenishing the shares and social fund in which the member has invested.

Procedures for repaying loans

Loans given to VICOBA members should be repaid with a small interest which is used to fund the group. This supplement is distributed as a benefit to members based on the number of shares, they have each deposited. Initial loans that are usually smaller than subsequent loans are required to be repaid for a period of 3 to 6 months.

Benefits

VICOBA loans are small loans granted to the poor and low-income households for their microenterprises and small businesses to enable them to raise their income levels and improve their living standards.

This micro lending model has ensured women to be empowered and independent enough through loans taken from VICOBA, using this loan to develop their economic activities. This system promotes the integration of the poor into the process of economic growth, people who do not have access to the formal labor market can often benefit from pooling resources and working in these groups. VICOBA has cultivated the culture of saving, now members have some money to curter their daily expenses and savings. Most of them have changed from poor life to a better life.

Example of success story

Mary CHARLES (37 years old) lives in Usseri division tell her story :

“I am able to provide to my family all the necessities they need, including food, clothing, and medical treatment. I can educate my two children, one is in seventh grade and the other one in third grade, thanks to my dress hair salon business. I obtained the capital to start my business after joining a VICOBA group. I was able to borrow six hundred thousand shillings (600,000 TZS) and so far, I have been able to repay four and half thousand shillings (450,000 TZS) through the profit I get from my business. I aimed to have another salon in the Tara kea Division at the marketplace. Corona’s disease has pushed me back because the business was so volatile, customers were afraid of getting an infection.”

Mary Charles in her shop

Source: Mary Charles

Why should I be interested in this post?

If you are interesting to work for a NGO or helping low income people to going out of the poverty through micro funding this post is for you. In this post, I explain the principle of micro funding named VICOBA using by the association AJISO headquarter in Tanzania to help the population to live in better conditions and more particularly empowered women.
This system can be used in all countries, it only needs a good and devoted team to train future members to be autonomous and teach them some basic business knowledges.

Useful resources

VICOBA Micro funding (ICD)

About the author

The article was written in August 2022 by Louise PIZON (ESSEC Business School, Master in Strategy & Management of International Business (SMIB), 2020-2022).

My experience as an M&A Analyst Intern at Oaklins Atlas Capital

August 10, 2022 by Basma ISSADIK

My experience as an M&A Analyst Intern at Oaklins Atlas Capital

In this article, Basma ISSADIK (ESSEC Business School, Global Bachelor of Business Administration, 2019-2023) shares her experience as an M&A Analyst intern at Oaklins Atlas Capital.

In May-June 2021, I was able to intern at Oaklins Atlas Capital, which is the Moroccan branch of Oaklins, a leader of M&A advising in mid-market operations. Oaklins group has advisory teams in 45 countries around the world. The Oaklins team provides mergers and acquisitions, growth equity and equity capital markets, debt advisory and corporate finance advisory services.

Oaklins Atlas Capital

Founded in 1999, Atlas Capital is an independent investment bank in Morocco covering all businesses: investment banking, asset management, stock market intermediation and private management. Offering a range of financial services with high added value, it targets a diversified clientele, whether companies and public offices, financial institutions, private companies or individual investors. It then was included in the Oaklins group and network which has presence across the globe through its 45 teams from Stockholm to Shanghai, from New York to São Paulo. The bank benefits from cross-border collaboration which helps the teams find the best suitable deals for its clients with a track record of more than 1900 deals being closed in the past five years.

Logo Oaklins Atlas Capital

Source: Oaklins Atlas Capital.

My internship at Oaklins Atlas Capital

During May-June 2021, I worked as an M&A Analyst intern at Oaklins Atlas Capital. During my time at the bank, my main responsibilities were writing fact sheets about new clients (through communication with the Oaklins Network) and target companies / projects in Morocco. I was also responsible for drafting presentations (teaser, pitch, kick off meetings), for valuations (DCF, transactions) of the target companies once our clients confirmed their interest with it, and for assisting senior management in day-to-day tasks in relation to the transactions.

This experience was my very first in investment banking and it helped me understand the M&A process and how important negotiation and customer relationships were to this field. This internship introduced me to the very basics of Mergers and Acquisitions through a high-level of personal attention and monitoring as I was in a team of five in total including two partners and three interns. I had the opportunity to learn directly from professionals who have been in the field for 20+ years. Moreover, through this internship, I have been exposed to many industries: textile, technology, agriculture, food processing industry, electrical equipment, infrastructure, renewable energy and to clients from all over the world.

Skills needed

Strong interpersonal skills
Financial analysis skills
Customer service (if you are to interact with clients)
To be familiar with finance and be able to analysis financial data
To be familiar with digital tools such as pptx and excel

What I have learnt from the internship

This internship has helped me learn so much about cross-border operations and how to approach potential acquirers with target companies and discuss the acquisition with them. It has also enabled me to have a solid understanding of many industries as I was in charge of sectoral research.

Key concepts related to my work

Mergers and acquisitions

Why do companies merge with and acquire other companies? Mergers and acquisitions are the act of consolidating companies or assets with an eye toward stimulating growth (it can expand a company’s market shares without it having to do significant heavy lifting), gaining competitive advantages (maybe eliminating competition and gaining market share), increasing market share, or influencing supply chains (eliminating a tier of costs).

A merger describes two companies uniting into a single company, where one of the two companies ceases to exist after being absorbed by the other company. The boards of directors of both companies must first secure approval from their respective shareholder bases. In 2006, Disney and Pixar completed a successful merger.

An acquisition occurs when one company (the acquirer) obtains a majority stake in the target firm, which incidentally retains its name and legal structure. For example, after Amazon acquired Whole Foods in 2017, the latter company maintained its name and continued executing its business model, as usual.

Tender Offer

A tender offer is a bid to purchase some or all of shareholders’ stock in a corporation. Tender offers are typically made publicly and invite shareholders to sell their shares for a specified price and within a particular window of time.

The price offered is usually at a premium to the market price and is often contingent upon a minimum or a maximum number of shares sold. To tender is to invite bids for a project or accept a formal offer such as a takeover bid. An exchange offer is a specialized type of tender offer in which securities or other non-cash alternatives are offered in exchange for shares. For example, Elon Musk has recently announced making a tender offer to acquire Twitter.

Proxy fight

A proxy fight refers to the act of a group of shareholders joining forces and attempting to gather enough shareholder proxy votes to win a corporate vote. Sometimes referred to as a “proxy battle,” this action is mainly used in corporate takeovers. For example, Microsoft Corporation made an unsolicited offer to buy Yahoo for $31 per share. The board of directors at Yahoo believed the offer by Microsoft under-valued the company, and, consequently, the board stalled any negotiations between Microsoft and Yahoo executives.

Why should I be interested in this post

This post is interesting for everyone who would like to work in investment banking and who would like to kick start their career by doing a summer internship.

Useful resources

Oaklins Atlas Capital

About the author

The article was written in August 2022 by Basma ISSADIK (ESSEC Business School, Global Bachelor of Business Administration, 2019-2023).

My experience as an M&A/TS intern at Deloitte

August 10, 2022 by Basma ISSADIK

My experience as an M&A/TS intern at Deloitte

In this article, Basma ISSADIK (ESSEC Business School, Global Bachelor of Business Administration, 2019-2023) shares her experience as an M&A/TS (Mergers and Acquisitions / Transaction Services) Intern at Deloitte.

Summer 2021, I was able to intern at Deloitte Casablanca for a couple of months. I was in the Transaction Services team which was in charge of advisory in deal and IPO readiness, target screening, sell-side and buy-side due diligence, transaction accounting and reporting, and business integration or separation. Transaction services typically refers to the services provided when a business transaction takes place. An example of a business transaction would be a merger or acquisition of a company.

Deloitte

Founded in 1845, Deloitte is one of the biggest professional service providers in the world. Being one of the “Big Four” accounting firms, it provides services in audit and assurance, consulting, financial advisory, risk advisory, tax and legal advisory. Deloitte was founded by William Welch Deloitte in London in 1845 and expanded into the United States in 1890. It merged with Haskins & Sells to form Deloitte Haskins & Sells in 1972 and with Touche Ross in the US to form Deloitte & Touche in 1989. As of 2020, Deloitte is the third-largest privately-owned company in the United States, according to Forbes. The firm has sponsored a number of activities and events including the 2012 Summer Olympics.

Logo Deloitte.

Source: Deloitte.

My internship at Deloitte

When I arrived at Deloitte in July 2021, the team was working on a specific project in cooperation with the Minister of the Industry. I was in charge of analyzing the eligibility of our clients to obtain financing from the Minister of the Industry. We already had set criteria for the companies that would later be presented to the Minister of the Industry. Our mission was to select the interesting project in accordance with the “banque de projet” which had already been established and advise the companies to meet the criteria as best as they can. These criteria were of different natures:

In financing for instance, there should be a portion of the project financed by the shareholders / founders.
The forecasted financial figures should be realistic.
The business plan should fit within the criteria and so on…

The junior analysts made sure I was closely supervised and assisted whenever I needed help with anything. I was communicating with them on a daily basis, and they all ensured I had a great experience at Deloitte which is what differentiates the firm from other competitive professional services companies. From the start I was given a lot of responsibilities which I was very happy about. I was able to participate in meetings and had the opportunity to lead one at the end of my internship. It was a really good experience in a way that enabled me to have direct contact with professionals and feel very useful to the team as well.

Skills needed

To have some experience in accounting
To be able to communicate and interact with the team
To possess analytical skills and problem-solving skills
To be familiar with financial reporting
To be familiar with digital tools such as pptx and excel
To have a strong learning ability
Be able to take responsibilities early on

What I have learnt from the internship

This internship has taught me a lot on the importance of meticulousness and how vital it is to be very rigorous with the data we are given and the analysis we do of it. I have also learned lots about the role of an auditing and consulting firm in advising clients to make the best decisions for their companies.

Key concepts related to my internship

Due diligence

Due diligence is an investigation, audit, or review performed to confirm facts or details of a matter under consideration. In the financial world, due diligence requires an examination of financial records before entering a proposed transaction with another party. Due diligence (DD) is an extensive process undertaken by an acquiring firm in order to thoroughly and completely assess the target company’s business, assets, capabilities, and financial performance. There may be as many as 20 or more angles of due diligence analysis.

The main types of due diligence inquiry are as follows:

Administrative DD: Is the aspect of due diligence that involves verifying admin-related items such as facilities, occupancy rate, number of workstations, etc.
Financial DD: Financial DD aims to provide a thorough understanding of all the company’s financials, including, but not restricted to, audited financial statements for the last three years, recent unaudited financial statements with comparable statements of the last year, the company’s projections and the basis of such projections, capital expenditure plan, schedule of inventory, debtors and creditors, etc.
Legal DD
Asset DD
Human Resources DD
Environmental DD
Taxes DD : Due diligence in regard to tax liability includes a review of all taxes the company is required to pay and ensuring their proper calculation with no intention of under-reporting of taxes.
Intellectual Property DD: Almost every company has intellectual property assets that they can use to monetize their business. These intangible assets are something that differentiates their products and services from their competitors.
Customer DD
Strategic Fit: Acquirers are generally also very careful about exercising due diligence in regard to evaluating how well the target company fits in with the overall strategic business plan of the buyer.

Why should I be interested in this post

You should be interested in this post if you are interested in working in finance in general because it might help you understand if you would like to work in the field or not, and maybe help you refine your professional project.

Useful resources

Deloitte

About the author

The article was written in August 2022 by Basma ISSADIK (ESSEC Business School, Global Bachelor in Business Administration, 2019-2023).

Moving averages

August 7, 2022 by Jayati WALIA

Moving averages

In this article, Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains the concept of moving averages and its implementation in financial markets as an indicator in technical analysis of stock price movements.

What is a moving average?

A moving average is a technique to analyze a time-series of data points by taking subsets of data and computing their averages. The subsets of data can explicitly be of a fixed size like simple moving averages or implicitly take into account all past points like exponential moving averages. These averages computed on rolling windows constitute a new time series. The aim of this exercise is essentially to filter noise and smoothen out the data in order to identify an overall trend in the data.

In financial markets, moving averages are one of the most popular indicators used in technical analysis. A moving average is used to interpret the current trend of a stock price (or any asset). It basically shows the price fluctuations in a stock as a single curve and is calculated using previous prices. Hence, a moving average is a lagging indicator.

Moving averages can be computed for different time periods such as 10 days, 20 days or 200 days. The greater the length of the time period (the lag in the trend), the greater the degree of smoothness in the moving average, however, the lower the price sensitivity of the moving average.

To measure the direction and strength of a trend, moving averages involve price averaging to establish a baseline. For instance, if the price moves above the average, the indicated trend is bullish and if it moves below the average, the trend is bearish. Moving average crossovers are also used commonly in trading strategies to identify trends. It then involves two moving averages: one computed on a short-term period and another one computed over a long-term period. When a shorter period moving average crosses above a longer period moving average, the trend is identified as bullish and indicates a buy signal. When a shorter period moving average crosses below a longer period moving average, the trend is identified as bearish and indicates a sell signal.

Moving averages are also used in development of other indicators such as Bollinger’s bands and Moving Average Convergence Divergence (MACD).

Types of moving averages

The moving average indicator can be of many types. Two basic types of moving averages and their interpretation are explained below: simple moving average and exponential-weighted moving average.

Simple moving average

Simple moving average (SMA) is the easiest type of moving average to compute. An n-period SMA is simply calculated by taking the sum of the closing prices of an asset for the past ‘n’ time-periods divided by ‘n’.

The formula to compute the SMA at time t is given by:

Simple moving average formula

Where P_i represents the asset price at time i (i indicating any time between the interval [t-n, t]).

If the current asset price is greater than the SMA value, the viewpoint for trend is established as bullish and similarly, if the current asset price is less than the SMA value, the viewpoint for trend is established as bearish.

Figure 1 below illustrates the 20-day and 50-day SMA for Amazon stock price.

Figure 1. 20-day and 50-day simple moving averages for Amazon stock price.
20-day and 50-day SMA for Amazon stock price Source: Computation by author.

We can observe from the above figure that when the price is going down, the SMA also is going downwards (as expected from the formula). It can also be seen that the movement of the SMA curve lags the change in price movements. The greater is the chosen time-period for SMA, the greater is the lag observed. Thus, while a 50-day SMA maybe smoother compared to a 20-day SMA, the lag observed will also be greater.

Exponential-weighted moving average

Exponential-weighted moving average (EWMA), also known as exponential moving average (EMA) is an improvisation of moving average over the SMA. It assigns weights to moving averages such that the recent data points are assigned greater weight factors than older data points. Thus, EWMA is more sensitive to recent price changes and the line is smoother than that of SMA.

The formula to compute the value of the EWMA at time t is given by:

Exponential-weighted moving average formula

Where P_t represents the stock price at time t, and α is a smoothing (or weighting) factor.

The series is initialized as: EWMA₀ = P₀.

The smoothing factor, α, is a constant value which lies between 0 and 1. The higher the value of α, the greater the weight assigned to the recent data, and the less smooth the EWMA curve.

How to set alpha for an exponential-weighted moving average?

α can be varied by a trader using EWMA based on how heavily he or she wants the recent data to be weighted. If a single EWMA is being considered, an optimal value for alpha can be chosen by minimizing the mean-squared errors (MSE).

A rule of thumb sometimes by traders is specified as:
Alpha for EWMA

For instance, for a short-term EWMA with the lookback period, n = 20, and alpha is equal to 2/21 = 0.095. For a long-term EWMA with n = 50, and alpha is equal to 0.039. Note that n is not related to a meaningful number of days like for the SMA.

When α=2/(n+1), the weights of an SMA and EWMA have the same center of mass.

A more sophisticated method is to relate alpha to the ‘half-life’ concept, meaning how long it takes for the weight to become half of the weight of the most recent data.

If the formula of EWMA is expanded for k days, we get the following:

EWMA formula expanded

For α=2/(n+1), the idea is that for a sufficiently large value of n, the sum of weights assigned to last n days is around 86%.

Figure 2 below illustrates the weights of each day for a EWMA with α equal to 3.92% (corresponding to n equal to 50 with the rule of thumb used by traders). It can be observed that the weights are decreasing in an exponential fashion and lower values are assigned as weights to the least recent days. The sum of the weights assigned to the first 10 days is 35.60 %, the first 50 days 86.47%, and the first 100 days 98.24%.

Figure 2. Weights of each day for an EWMA
EWMA day weights
Source: Computation by author.

Crossovers

EWMA is typically used in crossovers, which is a common strategy used by traders wherein two or more moving averages can help determine a more long-term trend. Basically, if a short-term EWMA crosses above a long-term EWMA, the crossover indicates an uptrend and similarly, if a short-term EWMA crosses below a long-term EWMA, the crossover indicates a downtrend. Traders can utilize it to establish their position in the stock.

Figure 3. below illustrates short-term and long-term EWMA curves for Amazon stock prices.

Figure 3. Short-term and long-term EWMA for Amazon stock price.
img_SimTrade_EWMA_Amazon_stock
Source: Computation by author.

We can observe in the figure above that the short-term EWMA follows the price movements in Amazon stock more closely than the long-term EWMA does. We can also see that a crossover of the two EWMA curves is followed by a change in trend. For instance, in April 2022, the short-term EWMA crosses below the long-term EWMA and there is an evident downtrend observed post the crossover.

You can also download below the Excel file for computation of SMA and EWMA for Amazon stock price and visualize the above graphs.

Useful resources

Hunter, J. S. (1986). The exponentially weighted moving average. Journal of Quality Technology, 18:203–210.

Wikipedia Moving averages

National Institute of Standards and Technology (NIST) US Department of Commerce Single Exponential Smoothing

About the author

The article was written in August 2022 by Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022).

Pricing barrier options with simulations and sensitivity analysis with Greeks

July 10, 2022 by Shengyu ZHENG

Pricing barrier options with simulations and sensitivity analysis with Greeks

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains the pricing of barrier options with Monte-Carlo simulations and the sensitivity analysis of barrier options from the perspective of Greeks.

Pricing of discretely monitored barrier options with Monte-Carlo simulations

With the simulation method, only the pricing of discretely monitored barrier options can be handled since it is impossible to simulate continuous price trajectories with no intervals. Here the method is illustrated with a down-and-out put option. The general setup of economic details of the down-and-out put option and related market information are presented as follows:

General setup of simulation for barrier option pricing

Similar to the simulation method for pricing standard vanilla options, Monte Carlo simulations based on Geometric Brownian Motion could also be employed to analyze the pricing of barrier options.

Figure 1. Trajectories of 600 price simulations.

With the R script presented above, we can simulate 6,000 times with the simprice() function from the derivmkts package. Trajectories of 600 price simulations are presented above, with the black line representing the mean of the final prices, the green dashed lines 1x and 2x standard deviation above the mean, the red dashed lines 1x and 2x derivation below the mean, the blue dashed line the strike level and the brown line the knock-out level.

The simprice() function, according to the documentation, computes simulated lognormal price paths with the given parameters.

With this simulation of 6,000 price paths, we arrive at a price of 0.6720201, which is quite close to the one calculated from the formulaic approach from the previous post.

Analysis of Greeks

The Greeks are the measures representing the sensitivity of the price of derivative products including options to a change in parameters such as the price and the volatility of the underlying asset, the risk-free interest rate, the passage of time, etc. Greeks are important elements to look at for risk management and hedging purposes, especially for market makers (dealers) since they do not essentially take these risks for themselves.

In R, with the combination of the greeks() function and a barrier pricing function, putdownout() in this case, we can easily arrive at the Greeks for this option.

Barrier option R code Sensitivity Greeks

Table 1. Greeks of the Down-and-Out Put

Barrier Option Greeks Summary

We can also have a look at the evolutions of the Greeks with the change of one of the parameters. The following R script presents an example of the evolutions of the Greeks along with the changes in the strike price of the down-and-out put option.

Barrier option R code Sensitivity Greeks Evolution

Figure 2. Evolution of Greeks with the change of Strike Price of a Down-and-Out Put

Evolution Greeks Barrier Price

Download R file to price barrier options

You can find below an R file (file with txt format) to price barrier options.

Why should I be interested in this post?

As one of the most traded but the simplest exotic derivative products, barrier options open an avenue for different applications. They are also very often incorporated in structured products, such as reverse convertibles. It is, therefore, important to be equipped with knowledge of this product and to understand the pricing logics if one aspires to work in the domain of market finance.

Simulation methods are very common in pricing derivative products, especially for those without closed-formed pricing formulas. This post only presents a simple example of pricing barrier options and much optimization is needed for pricing more complex products with more rounds of simulations.

Useful resources

Academic articles

Broadie, M., Glasserman P., Kou S. (1997) A Continuity Correction for Discrete Barrier Option. Mathematical Finance, 7:325-349.

Merton, R. (1973) Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science, 4:141-183.

Paixao, T. (2012) A Guide to Structured Products – Reverse Convertible on S&P500

Reiner, E.S., Rubinstein, M. (1991) Breaking down the barriers. Risk Magazine, 4(8), 28–35.

Rich, D. R. (1994) The Mathematical Foundations of Barrier Option-Pricing Theory. Advances in Futures and Options Research: A Research Annual, 7:267-311.

Wang, B., Wang, L. (2011) Pricing Barrier Options using Monte Carlo Methods, Working paper.

Books

Haug, E. (1997) The Complete Guide to Option Pricing. London/New York: McGraw-Hill.

Hull, J. (2006) Options, Futures, and Other Derivatives. Upper Saddle River, N.J: Pearson/Prentice Hall.

About the author

The article was written in June 2022 by Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023).

Asset Allocation

July 10, 2022 by Akshit GUPTA

Asset Allocation

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) explains asset allocation, a much-discussed topic in asset management.

Introduction

Asset allocation refers to the process of dividing an investment among different assets and, at a more integrated level, asset classes, sectors of the economy and geographical areas.

The allocation of an investor’s money across different assets can be analyzed according to different dimensions: investment objective, risk profile, and time horizon. The allocation process helps in finding a right balance between these dimensions and ultimately generates optimal returns in terms of expected return and risk. A key concept underlying asset allocation is diversification.

There are several assets in financial markets that the investor can use in his/her asset allocation. These asset classes include traditional assets like equities, bonds and cash, and alternative assets like real estates, commodities, and cryptocurrencies. Investors may also use combinations of such basic assets like mutual funds, exchange trade funds and more complex products like structured products.

Basics of asset allocation

Characteristics of investors

The characteristics of asset allocation for investors comes from its significant impact on the portfolio performance. Asset allocation decisions rely on input of the process: investment objective, risk profile, and time horizon.

Investment objective

The process of asset allocation impacts the financial objectives of the investor. If the investor has a low-risk appetite, he/she might be exposed to high degree of risk by investing in equities. Thus, such an investor should invest in safer assets such as bonds and fixed deposits to have a low-risk portfolio.

Risk Profile

The risk appetite of an investor determines the mix of different asset classes in a portfolio. Investors aiming for low risk should include a comparatively higher mix of risk less assets like bonds and real estate than equities.

Time horizon

The time horizon of an investment is also an important characteristic of the asset allocation process. Investors can either invest for a long-term time horizon or a short term depending on their investment objective.

Characteristics of assets

The characteristics of asset allocation comes from its significant impact on the portfolio performance. Asset allocation decisions can also rely on asset’s features such as: Expected returns, risk, and correlation.

Expected returns

The main focus of any investment in financial markets is to make maximum profits (returns) within a coherent risk level. Different asset classes have traditionally offered different returns, determined by their risk levels and market correlation. Generally, bonds have offered a lower long-term return as compared to the equity markets. Thus, investors aiming for higher returns should include an higher mix of these high return asset classes like equities than bonds.

Risk

Different asset classes have different characteristics and thus, different risk levels. The bonds market is generally considered less risky as compared to the equity markets. Thus, investment in bonds exposes the investor to a lower degree of risk than investing in equities.

Correlation

Different asset classes differ in their correlation which is also an important factor while deciding the optimal portfolio mix. It is possible that one asset class might be increasing in value whereas the other may be decreasing in value. For example, if the bonds markets are trending upwards, it is possible that the equity markets might be falling. Thus, by having an optimal mix of these asset, the investor can be compensated for the losses in equity markets with gains in the bond markets. Degree of correlation plays an important role in protecting the investor from downfalls in one asset class by compensating the losses with gains in other asset class.

Asset allocation processes

The asset allocation processes can be divided into two types: strategic asset allocation and tactical asset allocation.

Strategic asset allocation

Strategic asset allocation is a long-term investment strategy driven by long term market outlook and fundamental trends in the market. The strategy follows a top-down approach, and the investor generally looks at the macro level trends followed by trends in different asset classes to take the investment decisions. The investor following this allocation type generally has a pre-defined return expectation and risk tolerance levels and practices diversification to lower the risk. These investments are made in traditional assets like equities, bonds and cash assets but can also include alternative assets.

The investor follows a fixed objective which remains unchanged throughout the investment horizon. This can include a policy mix of investing 40% of portfolio in equities, 30% in bonds, 10% in real estate and remaining 20% in cash. As opposed to the tactical asset allocation, strategic asset allocation involves periodical rebalancing of the portfolio to get higher returns. If the investor diverges from the fixed objective, he/she must rebalance the portfolio to unify it with the original mix.

This strategy is suited to new or irregular investors who seek to generate returns at par with the market returns. The standard asset class suited for this strategy includes mutual funds, ETFs, blue-chip equities, bonds, fixed deposits, and real estate.

Tactical asset allocation

Tactical asset allocation involves actively investing in asset and securities to enhance portfolio returns by constantly rebalancing the portfolio and exploiting market anomalies. Even though the investor is following strategic asset allocation, the financial markets often present attractive buying or selling opportunities which can be exploited by tactical asset allocation to attain even higher returns. These opportunities can involve cyclical deviations in businesses, momentum trends and exploiting under valuations. However, these deviations from strategic allocation are often done carefully so as not to hinder the long-term objective.

The investment horizon in this strategy can be short or long depending on the investor’s preferences. However, the investor tries to generate higher returns and constantly rebalances the portfolio to achieve these returns by exploiting the market inefficiencies. Tactical asset allocation requires good understanding of the financial markets and is generally practiced by experienced investors with moderate to high risk tolerance.

Asset allocation over time

The investors deciding on the asset allocation process over time can follow different approaches, which includes:

Passive management: the buy-and-hold approach

In a passive asset management, the aim of the investor is to replicate the performance of a benchmark index. These investors can have lower risk appetite; thus, replications help to reduce the risk exposure for them. The investors following a passive approach can buy the individual components of the index by applying similar weights and invest with a moderate to long term time horizon in mind. The suitable asset classes for such investors can include mutual funds, exchange traded funds, index funds, etc.

Active management: dynamic asset allocation

In active asset management, the aim of the investor is to maximize the returns on the portfolio by actively investing in asset classes. The portfolio mix is frequently adjusted to capitalize on the short-term trends across different asset classes. The rebalancing decisions are based on business and economic cycles, momentum trends, relative valuations across different asset classes and macro factors like inflation, GDP growth, etc. The investor tries to beat the benchmark indices by dynamically trading in different asset classes and exploiting the market inefficiencies. They generally have high risk appetite and good knowledge about different asset classes. The suitable asset classes for such investors can include equities, commodities, and bonds.

Useful resources

US Securities and Exchange Commission (SEC) Asset Allocation

▶ Youssef LOURAOUI Systematic risk and specific risk

▶ Youssef LOURAOUI Portfolio

About the author

Article written in July 2022 by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022).

Pricing barrier options with analytical formulas

February 5, 2024July 10, 2022 by Shengyu ZHENG

Pricing barrier options with analytical formulas

As is mentioned in the previous post, the frequency of monitoring is one of the determinants of the price of a barrier option. The higher the frequency, the more likely a barrier event would take place.

In this article, Shengyu ZHENG (ESSEC Business School, Grande Ecole Program – Master in Management, 2020-2023) explains the pricing of continuously and discretely monitored barrier options with analytical formulas.

Pricing of standard continuously monitored barrier options

For pricing standard barrier options, we cannot simply apply the Black-Sholes-Merton Formula for the particularity of the barrier conditions. There are, however, several models available developed on top of this theoretical basis. Among them, models developed by Merton (1973), Reiner and Rubinstein (1991) and Rich (1994) enabled the pricing of continuously monitored barrier options to be conducted in a formulaic fashion. They are concisely put together by Haug (1997) as follows:

Knock-in and knock-out barrier option pricing formula