Stress Testing used by Financial Institutions

Stress Testing used by Financial Institutions

Jayati WALIA

In this article, Jayati WALIA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) introduces the concept of Stress testing used by financial institutions to estimate the impact of extraordinary market conditions characterized by a high level of volatility like stock market crashes.

Introduction

Asset price movements in financial markets are based on several local or global factors which can include economic developments, risk aversion, asset-specific financial information amongst others. These movements may lead to adverse situations which can cause unpredicted losses to financial institutions. Since the financial crisis of 2008, the need for resilience of financial institutions against market shocks has been exemplified, and regulators around the world have implemented strict measures to ensure financial stability and stress testing has become an imperative part of those measures.

Stress testing techniques were applied in the 1990s by most large international banks. In 1996, the need for stress testing by financial institutions was highlighted by the Basel Committee on Banking Supervision (BCBS) in its regulation recommendations (Basel Capital Accord). Following the 2008 financial crisis, focus on stress testing to ensure adequate capital requirements was further enhanced under the Dodd-Frank Wall Street reform Act (2010) in the United States.

Financial institutions use stress testing as a tool to assess the susceptibility of their portfolios to potential adverse market conditions and protect the capital thus ensuring stability. Institutions create extreme scenarios based on historical, hypothetical, or simulated macro-economic and financial information to measure the potential losses on their investments. These scenarios can incorporate single market variable (such as asset prices or interest rates) or a group of risk factors (such as asset correlations and volatilities).

Thus, stress tests are done using statistical models to simulate returns based on portfolio behavior under exceptional circumstances that help in gauging the asset quality and different risks including market risk, credit risk and liquidity risk. By using the results of the stress tests, the institutions evaluate the quality of their processes and implement further controls or measures required to strengthen them. They can also be prepared to use different hedging strategies to mitigate the potential losses in case of an adverse event.

Types of Stress testing

Stress testing can be based on different sets of information incorporated in the tests. These sets of information can be of two types: historical stress testing and hypothetical stress testing.

Historical stress testing

In this approach, market risk factors are analyzed using historical information to run the stress tests which can include incorporating information from previous crisis episodes in order to measure potential losses the portfolio may incur in case a similar situation reoccurs. For example, the downfall in S&P500 (approximately 30% during February 2020-March 2020) due to the Covid pandemic could be used to gauge future downsides if any such event occurs again. A drawback of this approach is that historical returns alone may not provide sufficient information about the likelihood of abnormal but plausible market events.

The extreme value theory can be used for calculation of VaR especially for stress testing. considers the distribution of extreme returns instead of all returns i.e., extreme price movements observed during usual periods (which correspond to the normal functioning of markets) and during highly volatile periods (which correspond to financial crises). Thus, these extreme values cover almost all market conditions ranging from the usual environments to periods of financial crises which are the focus of stress testing.

Hypothetical stress testing

In this method, hypothetical scenarios are constructed in order to measure the vulnerability of portfolios to different risk factors. Simulation techniques are implemented to anticipate scenarios that may incur extreme losses for the portfolios. For example, institutions may run a stress test to determine the impact of a decline of 3% in the GDP (Gross Domestic Product) of a country on their fixed income portfolio based in that country. However, a drawback of this approach is estimating the likelihood of the generated hypothetical scenario since there is no evidence to back the possibility of it ever happening.

EBA Regulations

In order to ensure the disciplined functioning and stability of the financial system in the EU, the European Banking Authority (EBA) facilitates the EU-wide stress tests in cooperation with European Central Bank (ECB), the European Systemic Risk Board (ESRB), the European Commission (EC) and the Competent Authorities (CAs) from all relevant national jurisdictions. These stress tests are conducted every 2 years and include the largest banks supervised directly by the ECB. The scenarios, key assumptions and guidelines implemented in the stress tests are jointly developed by EBA, ESRB, ECB and the European Commission and the individual and aggregated results are published by the EBA.

The purpose of this EU-wide stress testing is to assess how well banks are able to cope with potentially adverse economic and financial shocks. The stress test results help to identify banks’ vulnerabilities and address them through informed supervisory decisions.

Useful resources

Wikipedia: Stress testing

EBA Guidelines: EU-wide stress testing

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

Related Posts

   ▶ Walia J. Quantitative Risk Management

   ▶ Walia J. Value at Risk

   ▶ Walia J. The historical method for VaR calculation

   ▶ Walia J. The variance-covariance method for VaR calculation

About the author

Article written in January 2022 by Jayati Walia (ESSEC Business School, Master in Management, 2019-2022).

Protective Put

Protective Put

Akshit Gupta

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) presents the concept of protective put using option contracts.

Introduction

Hedging is a strategy implemented by investors to reduce the risk in an existing investment. In financial markets, hedging is an effective tool used by investors to minimize the risk exposure and change the risk profile for any investment in securities. While hedging does not necessarily eliminate the entire risk for any investment, it does limit the potential losses that the investor can incur.

Option contracts are commonly used by market participants (traders, investors, asset managers, etc.) as hedging mechanisms due to their great flexibility (in terms of expiration date, moneyness, liquidity, etc.) and availability. Positions in options are used to offset the risk exposure in the underlying security, another option contract or in any other derivative contract. There are various popular strategies that can be implemented through option contracts to minimize risk and maximize returns, one of which is a protective put.

Buying a protective put

A put option gives the buyer of the option, the right but not the obligation, to sell a security at a predefined date and price.

A protective put also called as a synthetic long option, is a hedging strategy that limits the downside of an investment. In a protective put, the investor buys a put option on the stock he/she holds in its portfolio. The protective put option acts as a price floor since the investor can sell the security at the strike price of the put option if the price of the underlying asset moves below the strike price. Thus, the investor caps its losses in case the underlying asset price moves downwards. The investor has to pay an option premium to buy the put option.

The maximum payoff potential from using this strategy is unlimited and the potential downside/losses is limited to the strike price of the put option.

Market scenario

A put option is generally bought to safeguard the investment when the investor is bullish about the market in the long run but fears a temporary fall in the prices of the asset in the short term.

For example, an investor owns the shares of Apple and is bullish about the stock in the long run. However, the earnings report for Apple is due to be released by the end of the month. The earnings report can have a positive or a negative impact on the prices of the Apple stock. In this situation, the protective put saves the investor from a steep decline in the prices of the Apple stock if the report is unfavorable.

Let us consider a protective position with buying at-the money puts. One of following three scenarios may happen:

Scenario 1: the stock price does not change, and the puts expire at the money.

In this scenario, the market viewpoint of the investor does not hold correct and the loss from the strategy is the premium paid on buying the put options. In this case, the option holder does not exercise its put options, and the investor gets to keep the underlying stocks.

Scenario 2: the stock price rises, and the puts expire in the money.

In this scenario, since the price of the stock was locked in through the put option, the investor enjoys a short-term unrealized profit on the underlying position. However, the put option will not be exercised by the investor and it will expire worthless. The investor will lose the premium paid on buying the puts.

Scenario 3: the stock price falls, and the puts expire out of the money.

In this scenario, since the price of the stock was locked in through the put option, the investor will execute the option and sell the stocks at the strike price. There is protection from the losses since the investor holds the put option.

Risk profile

In a protective put, the total cost of the investment is equal to the price of the underlying asset plus the put price. However, the profit potential for the investment is unlimited and the maximum losses are capped to the put option price. The risk profile of the position is represented in Figure 1.

Figure 1. Profit or Loss (P&L) function of the underlying position and protective put position.

Protective put

Source: computation by the author.

You can download below the Excel file for the computation of the Profit or Loss (P&L) function of the underlying position and protective put position.

Download the Excel file to compute the protective put value

The delta of the position is equal to the sum of the delta of the long position in the underlying asset (+1) and the long position in the put option (Δ). The delta of a long put option is negative which implies that a fall in the asset price will result in an increase in the put price and vice versa. However, the delta of a protective put strategy is positive. This implies that in a protective put strategy, the value of the position tends to rise when the underlying asset price increases and falls when the underlying asset prices decreases.

Figure 2 represents the delta of the protective put position as a function of the price of the underlying asset. The delta of the put option is computed with the Black-Scholes-Merton model (BSM model).

Figure 2. Delta of a protective put position.
Delta Protective put
Source: computation by the author (based on the BSM model).

You can download below the Excel file for the computation of the delta of a protective put position.

Download the Excel file to compute the delta of the protective put position

Example

An investor holds 100 shares of Apple bought at the current price of $144 each. The total initial investment is equal to $14,400. He is skeptical about the effect of the upcoming earnings report of Apple by the end of the current month. In order to avoid losses from a possible downside in the price of the Apple stock, he decides to purchase at-the-money put options on the Apple stock (lot size is 100) with a maturity of one month, using the protective put strategy.

We use the following market data: the current price of Appel stock is $144, the implied volatility of Apple stock is 22.79% and the risk-free interest rate is equal to 1.59%.

Based on the Black-Scholes-Merton model, the price of the put option $3.68.

Let us consider three scenarios at the time of maturity of the put option:

Scenario 1: stability of the price of the underlying asset at $144

The market value of the investment $14,400. The total cost of the initial investment is the cost of acquiring the Apple stocks ($14,400) plus the cost of buying the put options ($368 = $3.68*100), which is equal to $14,768, (i.e. ($14,400 + $368)).

As the stock price is stable at $144, the investor will not execute the put option and the option will expire worthless.

By not executing the put option, the investor incurs a loss which is equal to the price of the put option which is $368.

Scenario 2: an increase in the price of the underlying asset to $155

The market value of the investment $15,500. The total cost of the initial investment is the cost of acquiring the Apple stocks ($14,400) plus the cost of buying the put options ($368 = $3.68*100), which is equal to $14,768, (i.e. ($14,400 + $368)).

As the stock price is at $155, the investor will not execute the put option and hold on the underlying stock.

By not executing the put option, the investor incurs a loss which is equal to the price of the put option which is $368.

Scenario 3: a decrease in the price of the underlying asset to $140

The market value of the investment $14,000. The total cost of the initial investment is the cost of acquiring the Apple stocks ($14,400) plus the cost of buying the put options ($368 = $3.68*100), which is equal to $14,768, (i.e. ($14,400 + $368)).

As the stock price has decreased to $140, the investor will execute the put option and sell the Apple stocks at $144. By executing the put option, the investor will protect himself from incurring a loss of $400 (i.e.($144-$140)*100) due to a decrease in the Apple stock prices.

Related Posts

   ▶ All posts about Options

   ▶ Akshit GUPTA Options

   ▶ Akshit GUPTA The Black-Scholes-Merton model

   ▶ Akshit GUPTA Option Greeks – Delta

   ▶ Akshit GUPTA Covered call

   ▶ Akshit GUPTA Option Trader – Job description

Useful Resources

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

Hull J.C. (2015) Options, Futures, and Other Derivatives, Ninth Edition, Chapter 10 – Trading strategies involving Options, 276-295.

Merton R.C. (1973) “Theory of Rational Option Pricing” Bell Journal of Economics, 4(1): 141–183.

Wilmott P. (2007) Paul Wilmott Introduces Quantitative Finance, Second Edition, Chapter 8 – The Black Scholes Formula and The Greeks, 182-184.

About the author

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

Straddle and strangle strategy

Straddle and Strangle

Akshit Gupta

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) presents the strategies of straddle and strangle based on options.

Introduction

In financial markets, hedging is implemented by investors to minimize the risk exposure and maximize the returns for any investment in securities. While hedging does not necessarily eliminate the entire risk for an investment, it does limit or offset any potential losses that the investor can incur.

Option contracts are commonly used by investors / traders as hedging mechanisms due to their great flexibility (in terms of expiration date, moneyness, liquidity, etc.) and availability. Positions in options are used to offset the risk exposure in the underlying security, another option contract or in any other derivative contract. Option strategies can be directional or non-directional.

Directional strategy is when the investor has a specific viewpoint about the movement of an asset price and aims to earn profit if the viewpoint holds true. For instance, if an investor has a bullish viewpoint about an asset and speculates that its price will rise, she/he can buy a call option on the asset, and this can be referred as a directional trade with a bullish bias. Similarly, if an investor has a bearish viewpoint about an asset and speculates that its price will fall, she/he can buy a put option on the asset, and this can be referred as a directional trade with a bearish bias.

On the other hand, non-directional strategies can be used by investors when they anticipate a major market movement and want to gain profit irrespective of whether the asset price rises or falls, i.e., their payoff is independent of the direction of the price movement of the asset but instead depends on the magnitude of the price movement. There are various popular non-directional strategies that can be implemented through a combination of option contracts to minimize risk and maximize returns. In this post, we are interested in straddle and strangle.

Straddle

In a straddle, the investor buys a European call and a European put option, both at the same expiration date and at the same strike price. This strategy works in a similar manner like a strangle (see below). However, the potential losses are a bit higher than incurred in a strangle if the stock price remains near the central value at expiration date.

A long straddle is when the investor buys the call and put options, whereas a short straddle is when the investor sells the call and put options. Thus, whether a straddle is long or short depends on whether the options are long or short.

Market Scenario

When the price of underlying is expected to move up or down sharply, investors chose to go for a long straddle and the expiration date is chosen such that it occurs after the expected price movement. Scenarios when a long straddle might be used can include budget or company earnings declaration, war announcements, election results, policy changes etc.
Conversely, a short straddle can be implemented when investors do not expect a significant movement in the asset prices.

Example

In Figure 1 below, we represent the profit and loss function of a straddle strategy using a long call and a long put option. K1 is the strike price of the long call i.e., €98 and K2 is the strike price of the long put position i.e., €98. The premium of the long call is equal to €5.33, and the premium of the long put is equal to €3.26 computed using the Black-Scholes-Merton model. The time to maturity (T) is of 18 days (i.e., 0.071 years). At the time of valuation, the price of the underlying asset (S0) is €100, the volatility (σ) of the underlying asset is 40% and the risk-free rate (r) is 1% (market data).

Figure 1. Profit and loss (P&L) function of a straddle position.
 Profit and loss (P&L) function of a straddle
Source: computation by the author.

You can download below the Excel file for the computation of the straddle value using the Black-Scholes-Merton model.

Download the Excel file to compute the straddle value

Strangle

In a strangle, the investor buys a European call and a European put option, both at the same expiration date but different strike prices. To benefit from this strategy, the price of the underlying asset must move further away from the central value in either direction i.e., increase or decrease. If the stock prices stay at a level closer to the central value, the investor will incur losses.

Like a straddle, a long strangle is when the investor buys the call and put options, whereas a short strangle is when the investor sells (issues) the call and put options. The only difference is the strike price, as in a strangle, the call option has a higher strike price than the price of the underlying asset, while the put option has a lower strike price than the price of the underlying asset.

Strangles are generally cheaper than straddles because investors require relatively less price movement in the asset to ‘break even’.

Market Scenario

The long strangle strategy can be used when the trader expects that the underlying asset is likely to experience significant volatility in the near term. It is a limited risk and unlimited profit strategy because the maximum loss is limited to the net option premiums while the profits depend on the underlying price movements.

Similarly, short strangle can be implemented when the investor holds a neutral market view and expects very little volatility in the underlying asset price in the near term. It is a limited profit and unlimited risk strategy since the payoff is limited to the premiums received for the options, while the risk can amount to a great loss if the underlying price moves significantly.

Example

In Figure 2 below, we represent the profit and loss function of a strangle strategy using a long call and a long put option. K1 is the strike price of the long call i.e., €98 and K2 is the strike price of the long put position i.e., €108. The premium of the long call is equal to €5.33, and the premium of the long put is equal to €9.47 computed using the Black-Scholes-Merton model. The time to maturity (T) is of 18 days (i.e., 0.071 years). At the time of valuation, the price of the underlying asset (S0) is €100, the volatility (σ) of the underlying asset is 40% and the risk-free rate (r) is 1% (market data).

Figure 2. Profit and loss (P&L) function of a strangle position.
 Profit and loss (P&L) function of a Strangle
Source: computation by the author..

You can download below the Excel file for the computation of the strangle value using the Black-Scholes-Merton model.

Download the Excel file to compute the Strangle value

Related Posts

   ▶ All posts about Options

   ▶ Akshit GUPTA Options

   ▶ Akshit GUPTA The Black-Scholes-Merton model

   ▶ Akshit GUPTA Option Spreads

   ▶ Akshit GUPTA Option Trader – Job description

Useful resources

Academic research articles

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

Merton R.C. (1973) “Theory of Rational Option Pricing” Bell Journal of Economics, 4, 141–183.

Books

Hull J.C. (2015) Options, Futures, and Other Derivatives, Ninth Edition, Chapter 10 – Trading strategies involving Options, 276-295.

Wilmott P. (2007) Paul Wilmott Introduces Quantitative Finance, Second Edition, Chapter 8 – The Black Scholes Formula and The Greeks, 182-184.

About the author

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

Analysis of synergy-based theories for M&A

Analysis of synergy-based theories for M&A

Suyue MA

In this article, Suyue MA (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021) analyzes the synergy-based theories for M&As.

This article is structured as follows: I will first share with my professional experience. I will introduce the concepts of M&A and a brief analysis of past M&A market activity. We then expose the different theories based on synergies emphasized by companies in M&A deals.

About myself

I have been interested in finance ever since I started my study at ESSEC Business School in 2017. By acknowledging more about finance, during my 2nd year of study, I decided to build up my career in corporate finance, focusing on the primary market. By sending around 400 resumes to different companies and banks, I finally worked in the field of M&A. Until now, I have finished four internships in the field of corporate finance, private equity, capital-raising advisory, and mergers and acquisitions (M&A).

In this article, I would like to share with you about some very important M&A theories based on synergies that most of companies decided to execute as effective corporate strategies.

Introduction

M&As are defined as consolidation of companies, and it refers to corporate finance, corporate strategy, and corporate management, dealing with selling, buying, or combination of different firms, which can create resources, financing, and business development to a firm to grow its business without the need of creating a new business entity. Normally, a merger occurs between companies that have related interests with a similar company size or market cap. In addition, a merger is commonly understood as a fusion of two companies, which the bigger and better company will remain its name and status while the other one will disappear and not exist as a unique business entity. Nevertheless, acquisition means that a company is going to pay a certain price (in cash or stocks) to buyout or acquire the target company’s part of or full of stock right, achieving the controlling right or assets of the company that is being acquired, but the legal person’s status will remain.

To put in a nutshell, based on the historical M&A transactions, the primary objectives behind a merger or acquisition are to create long-term shareholder value, achieve larger market share, and improve the company’s efficiency. However, obviously, there are also a great number of M&A activities failed to reach such goals or even ruined companies. According to the collated research and a recent Harvard Business Review report in 2021, the M&A’s failure rate sites between 70% to 90%, which is an extremely high figure even though the report takes all rage of business, culture factors, and objectives factors into considerations. Thus, it remains doubtful whether a M&A transaction can help company’s development and create shareholder’s value.

Nowadays, companies use M&A for various reasons because companies are always facing the issues of dealing with global competition, market globalization, and constant technology innovation. It is now a fact that M&A has become the most popular corporate strategy around the world. We may ask why the management and shareholder boards are using merger and acquisition to promote the company’s advancement and shareholders’ return instead of other strategies, such as doing investments and innovations. According to the aforementioned report, some finance professionals believe that such transactions create short-cut for companies’ growth and market share, since the companies do not need to start a business sector over again, in which the risk of running a successful business is high and the cost of capital is high as well. On the contrary if both buy-side and sell-side companies can find synergies that benefit each other, ideally, they will gain more revenues due to the positive reaction, and therefore create value for their shareholders. Thus, here I will dig deeper in the following theories and synergies to better understand the aim and purpose of M&A.

Figure 1. Number and value of merger and acquisition deals worldwide from 1985 to 2020.

Number and value of merger and acquisition deals worldwide from 1985 to 2020

Source: Institute of Mergers, Acquisitions and Alliances (IMAA)

Figure 2. Number and value of merger and acquisition deals in the United States from 1985 to 2020.

Number and value of merger and acquisition deals in the United States from 1985 to 2020

Source: Institute of Mergers, Acquisitions and Alliances (IMAA)

The figures above are about the number and value of M&A transactions in both U.S. and worldwide in the last two and half decades (1985-2020). The reason why I choose these geographic locations is because the global M&A transactions’ number and value can provide us the activity level of the market; secondly, the U.S. market has the most active level from all time, and therefore, by viewing such figures, it can provide us a very clear overview of the market. According to both figures above, both M&A’s value and transactions are increasing stably except three serious drops in year of 2000, 2008, and 2020. The first drop is because of 2000’s financial crisis that happened in most of developed countries; the second drop happened right after the U.S. subprime crisis, and the last drop just happened from years of 2019 to 2021, in which the whole world was shut down because of COVID-19 virus. A great number of big companies went bankrupt and most of financial institutions had to stop their operations. What is more, we can find that after each recession, the value and number of M&A transactions rebounded rapid to the average level and kept increasing the volume within the following years. As I mentioned previously, although M&As have a super rate of failure, the success rate of successful company’s transactions must surpass the risks involved. Consequently, it is not difficult to explain why companies are keeping entering M&A transactions.

M&A’s main theories

The history of mergers and acquisitions exists for more than a hundred years, and financial professionals and scholars came forward with a great number of merger and acquisition theories. Most of these theories are based on the motives and benefits of merger and acquisition, and several major models have been developed. The following part is a brief introduction of these theories.

Efficiency theory assumes that both the acquiring company and the target company are interested in maximizing shareholder value, that the merger is a value-adding investment for both the acquiring company and the target company; the total benefits of the merger (the sum of the values of target and acquiring companies after vs before the deal) are positive. Efficiency theories are powerful in explaining the motivation of mergers, but the exact motivation of mergers in terms of synergies and efficiency improvements requires further examination and analysis and is beyond the scope of this dissertation. The different sources of efficiency theory based on value addition can be divided into the following areas: management synergy, operating synergy, diversification and strategic synergy, financial synergy, and undervaluation theory.

Management synergy

Since there are differences between the management capabilities of any two firms, the merger and acquisition activity may enable the more efficient management capabilities to diffuse in the new post-acquisition firm, bringing about efficiency improvements. For example, a relatively efficient firm may improve the management and operations of the acquired firm by acquiring a relatively inefficient firm to improve efficiency, thus increasing the value of the acquired firm; or a firm with relatively poor management efficiency may acquire a firm with higher management efficiency to improve its own efficiency, thus acquiring the organizational capital unique to the acquired firm.

Operating synergy

Operating synergies assume that there are economies of scale and economies of scope, which are cost advantages reaped by companies when production becomes efficient, in an industry, and that through merger and acquisition, companies can improve their original operating efficiency. In this theory, merger and acquisition can create great value.

The scale of the enterprise before the merger is far from the economies of scale, and the enterprise entity (consortium) formed after the merger can minimize the cost or maximize the profit in production, personnel, equipment, management, and sales. On the other hand, through vertical mergers, enterprises at different stages of development in the industry can be combined to reduce transaction costs and obtain effective synergies. Economies of scope mean that companies can use their existing product manufacturing and sales experience to produce related add-on products at a lower cost. For example, in the automotive industry, additional production of small cars and various vans would benefit from the existing automotive technology and manufacturing experience.

Diversification and strategic synergy

Companies can diversify their operations through M&A activities, which can diversify risks and stabilize revenue streams and provide employees with greater security and advancement opportunities; ensure continuity of the corporate team and organization; secure the company’s reputation. For strategic synergy, the company can acquire new management skills and organizational costs through M&A to increase the ability to enter new growth areas or overcome new competitive threats.

Financial synergy

One source of financial synergy is the lower cost of internal and external financing. For example, companies with high internal cash flow and low investment opportunities should have excess cash flow, while companies with lower internal capital production capacity and significant investment opportunities should require additional financing. Therefore, merger of these two firms may have the advantage of lower internal capital costs. On the other hand, the combined firm’s ability to leverage debt is greater than the sum of ability of the two firms before the merger, which provides a tax saving advantage.

Undervaluation theory

This theory suggests that the most direct basis for M&A comes from the difference in the value of the target company as judged by different investors and market players, since there is no purely efficient stock market in the world, it is possible that market value of the target company is lower than its true or potential value for some reason. The main reasons for undervaluation are: first, the inability of the target company’s management to realize the full potential of the company. The second reason could be insider information, because the M&A firm has information about the true value of the target company that is not known to the outside world. Thirdly, the Q-ratio. This is the ratio of the market value of the firm’s securities over the replacement cost of its assets. When inflation persists, as the Q ratio falls below one, it is cheaper to acquire an existing firm than to build a new one.

Useful resources

Institute of Mergers, Acquisitions and Alliances (IMAA) M&A Statistics.

Christensen, C.M., Alton, R., Rising, C., Waldeck, A., (March 2011) The Big Idea: The New M&A Playbook Harvard Business Review (89):48-57.

Dineros-De Guzman, C., (May 2019) Creating value through M&A PWC.

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

About the author

The article was written in January 2022 by Suyue MA (ESSEC Business School, Global Bachelor of Business Administration, 2017-2021).

Option Spreads

Option Spreads

Akshit Gupta

This article written by Akshit GUPTA (ESSEC Business School, Grande Ecole Program – Master in Management, 2019-2022) presents the different option spreads used to hedge a position in financial markets.

Introduction

In financial markets, hedging is implemented by investors to minimize the risk exposure for any investment in securities. While hedging does not necessarily eliminate the entire risk for an investment, it does limit or offset any potential losses that the investor can incur.

Option contracts are commonly used by traders and investors as hedging mechanisms due to their great flexibility (in terms of expiration date, moneyness, liquidity, etc.) and availability. Positions in options are used to offset the risk exposure in the underlying security, another option contract or in any other derivative contract. Option strategies can be directional or non-directional.

Spreads are hedging strategies used in trading in which traders buy and sell multiple option contracts on the same underlying asset. In a spread strategy, the option type used to create a spread has to be consistent, either call options or put options. These are used frequently by traders to minimize their risk exposure on the positions in the underlying assets.

Bull Spread

In a bull spread, the investor buys a European call option on the underlying asset with strike price K1 and sells a call option on the same underlying asset with strike price K2 (with K2 higher than K1) with the same expiration date. The investor expects the price of the underlying asset to go up and is bullish about the stock. Bull spread is a directional strategy where the investor is moderately bullish about the underlying asset, she is investing in.

When an investor buys a call option, there is a limited downside risk (the loss of the premium) and an unlimited upside risk (gains). The bull spread reduces the potential downside risk on buying the call option, but also limits the potential profit by capping the upside. It is used as an effective hedge to limit the losses.

Market Scenario

When the price of underlying asset is expected to moderately move up, investors chose to execute a bull spread and the expiration date is chosen such that it occurs after the expected price movement. If the price decreases significantly by the expiration of the call options, the investor loses money by using a bull spread.

Example

In Figure 1 below, we represent the profit and loss function of a bull spread strategy using a long and a short call option. K1 is the strike price of the long call i.e., €88 and K2 is the strike price of the short call position i.e., €110. The premium of the long call is equal to €12.62, and the premium of the short call is equal to €1.16 computed using the Black-Scholes-Merton model. The time to maturity (T) is of 18 days (i.e., 0.071 years). At the time of valuation, the price of the underlying asset (S0) is €100, the volatility (σ) of the underlying asset is 40% and the risk-free rate (r) is 1% (market data).

Figure 1. Profit and loss (P&L) function of a bull spread.

 Profit and loss (P&L) function of a bul spread

Source: computation by the author.

You can download below the Excel file for the computation of the bull spread value using the Black-Scholes-Merton model.

Download the Excel file to compute the bull spread value

Bear Spread

In a bear spread, the investor expects the price of the underlying asset to moderately decline in the near future. In order to hedge against the downside, the investor buys a put option with strike price K1 and sells another put option with strike price K2, with K1 lower than < K2. Initially, this initial position leads to a cash outflow since the put option bought (with strike price K1) has a higher premium than put option sold (with strike price K2) as K1 is lower than < K2.

Market Scenario

When the price of underlying asset is expected to moderately move down, investors chose to execute a bear spread and the expiration date is chosen such that it occurs after the expected price movement. Bear spread is a directional strategy where the investor is moderately bearish about the stock he is investing in. If the price increases significantly by the expiration of the put options, the investor loses money by using a bear spread.

Example

In Figure 2 below, we represent the profit and loss function of a bear spread strategy using a long and a short put option. K1 is equal to the strike price of the short put i.e., €90 and K2 is equal to the strike price of the long put i.e., €105. The premium of the short put is equal to €0.86, and the premium long put is equal to €7.26 computed using the Black-Scholes-Merton model.

The time to maturity (T) is of 18 days (i.e., 0.071 years). At the time of valuation, the price of the underlying asset (S0) is €100, the volatility (σ) of stock is 40% and the risk-free rate (r) is 1% (market data).

Figure 2. Profit and loss (P&L) function of a bear spread.

 Profit and loss (P&L) function of a bear spread

Source: computation by the author.

You can download below the Excel file for the computation of the bear spread value using the Black-Scholes-Merton model.

Download the Excel file to compute the bear spread value

Butterfly Spread

In a butterfly spread, the investor expects the price of the underlying asset to remain close to its current market price in the near future. Just as a bull and bear spread, a butterfly spread can be created using call options. In order to profit from the expected market scenario, the investor buys a call option with strike price K1 and buys another call option with strike price K3, where K1 < K3, and sells two call options at price K2, where K1 < K2 < K3. Initially, this initial position leads to a net cash outflow.

Market Scenario

When the price of underlying asset is expected to stay stable, investors chose to execute a butterfly spread and the expiration date is chosen such that the expected price movement occurs before the expiration date. Butterfly spread is a non-directional strategy where the investor expects the price to remain stable and close to the current market price. If the price movement is significant (either downward or upward) by the expiration of the call options, the investor loses money by using a butterfly spread.

Example

In Figure 3 below, we represent the profit and loss function of a butterfly spread strategy using call options. K1 is equal to the strike price of the long call position i.e., €85 and K2 is equal the strike price of the two short call positions i.e., €98 and K3 is equal to the strike price of another long call position i.e., €111. The premium of the long call K1 is equal to €15.332, the premium of the long call K3 is equal to €0.993 and the premium of the short call K2 is equal to €5.334 computed using the Black-Scholes-Merton model. The premium of the butterfly spread is then equal to €5.657 (= 15.332 + 0.993 -2*5.334), which corresponds to an outflow for the investor.

The time to maturity (T) is of 18 days (i.e., 0.071 years). At the time of valuation, the price of the (S0) is €100, the volatility (σ) of stock is 40% and the risk-free rate (r) is 1% (market data).

Figure 3. Profit and loss (P&L) function of a butterfly spread.

 Profit and loss (P&L) function of a butterfly spread

Source: computation by the author.

You can download below the Excel file for the computation of the butterfly spread value using the Black-Scholes-Merton model.

Download the Excel file to compute the butterfly spread value

Note that bull, bear, and butterfly spreads can also be created from put options or a combination of call and put options.

Related posts

   ▶ All posts about options

   ▶ Gupta A. Options

   ▶ Gupta A. The Black-Scholes-Merton model

   ▶ Gupta A. Option Greeks – Delta

   ▶ Gupta A. Hedging Strategies – Equities

Useful resources

Hull J.C. (2018) Options, Futures, and Other Derivatives, Tenth Edition, Chapter 12 – Trading strategies involving Options, 282-301.

About the author

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