informational marketplace capable of moving money and ideas to any place on this planet in minutes.”
“Believe me the secret of reaping the greatest fruitfulness and the greatest enjoyment from life is to live dangerously”
Friedrich Wilhelm Nietzsche
Financial Engineering
Computational finance, also called financial engineering, is a cross-disciplinary field which relies on computational intelligence, mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions. Utilizing various methods, practitioners of computational finance aim to precisely determine the financial risk that certain financial instruments create.
“To be alive at all involve some Risk” (Harold Macmillan)
Khurasan Institute of Higher Education Jalalabad, Afghanistan.
2 0 1 2 -1 3 What Is Risk?
Risk is the chance of financial loss, or more formally the variability of returns associated with a given asset. Risk provides the basis for opportunity. The terms risk and exposure have slight differences in their meaning. Risk refers to the probability of loss, while exposure (experience, contact) is the possibility of loss, although they are often used interchangeably. Risk arises as a result of exposure. Exposure to financial markets affects most organizations, either directly or indirectly. When an organization has financial market exposure, there is a possibility of loss but also an opportunity for gain or profit. Financial market exposure may provide strategic or competitive benefits.
Risk is the likelihood of losses resulting from events such as changes in market prices. Events with a low probability of occurring, but that may result in a high loss, are particularly troublesome because they are often not anticipated. Put another way, risk is the probable variability of returns.
Potential Size of Loss Probability of Loss Potential for Large Loss High Probability of Occurrence Potential for Small Loss Low Probability of Occurrence
Since it is not always possible or desirable to eliminate risk, understanding it is an important step in determining how to manage it. Identifying exposures and risks forms the basis for an appropriate financial risk management strategy.
Investment
A commitment of funds made in the expectation of the positive rate of returns. Returns: investment is made with the aim of returns.
Returns= yield +capital appreciations. Risk
Its inherent
May be capital loss
Or not receiving the interest payments or dividends. Longer maturity higher risk
Credit worthiness of the firm
2 0 1 2 -1 3 Return
Return can be defined as the total gain or loss experienced on an investment over a given period of time.
2 0 1 2 -1 3 Risk in Investment
Investors like return and dislike risk
Risk in holding securities is generally associated with the possibility that realized returns will be less than the returns that were expected.
Risk is the variability of the in returns of a security How Does Financial Risk Arise?
Financial risk arises through countless transactions of a financial nature, including sales and purchases, investments and loans, and various other business activities. It can arise as a result of legal transactions, new projects, mergers and acquisitions, debt financing, the energy component of costs, or through the activities of management, stakeholders, competitors, foreign governments, or weather. When financial prices change dramatically, it can increase costs, reduce revenues, or otherwise adversely impact the profitability of an organization. Financial fluctuations may make it more difficult to plan and budget, price goods and services, and allocate capital.
There are three main sources of financial risk:
1. Financial risks arising from an organization’s exposure to changes in market prices, such as interest rates, exchange rates, and commodity prices.
2. Financial risks arising from the actions of, and transactions with, other organizations such as vendors, customers, and counterparties in derivatives transactions
3. Financial risks resulting from internal actions or failures of the organization, particularly people, processes, and systems. These are discussed in more detail in subsequent chapters.
What Is Financial Risk Management?
Financial risk management is a process to deal with the uncertainties resulting from financial markets. It involves assessing the financial risks facing an organization and developing management strategies consistent with internal priorities and policies. Addressing financial risks proactively may provide an organization with a competitive advantage. It also ensures that management, operational staff, stakeholders, and the board of directors are in agreement on key issues of risk. Managing financial risk necessitates making organizational decisions about risks that are acceptable versus those that are not. The passive strategy of taking no action is the acceptance of all risks by default.
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Organizations manage financial risk using a variety of strategies and products. It is important to understand how these products and strategies work to reduce risk within the context of the organization’s risk tolerance (acceptance) and objectives.
Strategies for risk management often involve derivatives. Derivatives are traded widely among financial institutions and on organized exchanges. The value of derivatives contracts, such as futures, forwards, options, and swaps, is derived from the price of the underlying asset. Derivatives trade on interest rates, exchange rates, commodities, equity and fixed income securities, credit, and even weather. The products and strategies used by market participants to manage financial risk are the same ones used by speculators to increase leverage and risk. Although it can be argued that widespread use of derivatives increases risk, the existence of derivatives enables those who wish to reduce risk to pass it along to those who seek risk and its associated opportunities.
The ability to estimate the possibility of a financial loss is highly desirable. However, standard theories of probability often fail in the analysis of financial markets. Risks usually do not exist in isolation, and the interactions of several exposures may have to be considered in developing an understanding of how financial risk arises. Sometimes, these interactions are difficult to forecast, since they ultimately depend on human behavior.
The process of financial risk management is an ongoing one. Strategies need to be implemented and refined as the market and requirements change. Refinements may reflect changing expectations about market rates, changes to the business environment, or changing international political conditions, for example. In general, the process can be summarized as follows:
• Identify and prioritize key financial risks.
• Determine an appropriate level of risk tolerance.
• Implement risk management strategy in accordance with policy.
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Risk Classification
TYPES OF RISK:Thus far, our discussion has concerned the total risk of an asset, which is one important consideration in investment analysis. However, modern investment analysis categorizes the traditional sources of risk identified previously as .causing variability in returns into two
General types: those that are pervasive in nature, such as market risk or interest rate risk, and those that are specific to a particular security issue, such as business or financial risk. Therefore, we must consider these two categories of total risk.
Dividing total risk into its two components, a general (market) component and a specific (issuer) component, we have systematic risk and nonsystematic risk, which are additive:
Total risk = General risk + Specific risk = Market risk + Issuer risk
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Risk Classification
Total Risk
Systematic RiskMarket Risk Interest Rate Risk Purchasing Power Risk
Unsystematic Risk
Business
Risk Financial Risk
A. Systematic Risk
Systematic (Market) Risk, (Non-diversifiable Risk):
Risk attributable to broad macro factors affecting all securities. Acting according to a fixed plan or system
Systematic risk is caused by system wide factors that affect the entire community.
• Change in economic conditions
• Change in political system
• Change in social system
The effect of such system wide factors which are beyond the control of individual, business establishments and which affect all the business establishments in the system called “Systematic Risk”.
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Systematic Risk is an investor can construct a diversified portfolio and eliminate pan of the total risk, the diversifiable or non-market part. What is left is the non-diversifiable portion or the market risk. Variability in a security's total returns that is directly associated with overall movements in the general market or economy is called systematic (market) risk.
Virtually all securities have some systematic risk, whether bonds or stocks, because systematic risk directly encompasses the interest rate, market, and inflation risks. The investor cannot escape this part of the risk, because no matter how well he or she diversifies, the risk of the overall market cannot be avoided. If the stock market declines sharply, most stocks will be adversely affected; if it rises strongly, as in the last few months of 1982, most stocks will appreciate in value. These movements occur regardless of what any single investor does. Clearly, market risk is critical to all investors.
1. Market Risk
This arises out of changes in demand and supply pressures in the markets, following the changing flow of information or expectations.
The totality of investor perception and subjective factors influence the events in the market which are unpredictable and give rise to risk, which is not controllable.
The basis for the reaction is a set of real, tangible events –political, social or economic Intangible events are related to market psychology
2. Interest Rate Risk
The return on an investment depends on the interest rate promised on it and changes in market rates of interest from time to time.
The cost of funds borrowed by companies or stockbrokers depends on interest rates. The market activity and investor perception change with the changes in interest rates.
Lower interest rates make it easier for people to borrow in order to buy cars and homes. Purchases of homes, in turn, increase the demand for other items, such as furniture and appliances, thus providing an additional boost to the economy.
Lower interest rates mean that consumers spend less on interest costs, leaving them with more of their income to spend on goods and services.
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3. Purchasing Power Risk It is also known as inflation risk
This risk is arises out of change in the prices of goods and services and technically it covers both inflation and deflation periods
Inflation: Rising prices on goods and services Deflation: Falling prices on goods and services Purchasing power risk= Inflation + Deflation
B. Unsystematic Risk
Nonsystematic (Non-market) Risk, (Diversifiable Risk): Risk attributable to factors unique to the security
Nonsystematic Risk is the variability in a security's total returns not related to overall market variability is called the nonsystematic (non-market) risk. This risk 1s unique to a particular security and is associated with such factors as business and financial risk as well as liquidity risk. Although all securities tend to have some nonsystematic risk, it is generally connected with common stocks.
Unsystematic risk emerges out of the known and controllable factors, internal to issuer of the securities or companies.
Factors such as management capability, consumer preferences and labor strikes can cause unsystematic variability of returns for a company’s stock.
The uncertainty surrounding the ability of the issuer to make payments on securities stops from two sources:
1. The operating environment of the business- Business Risk 2. The financing of the firm- Financial risk
1 Business Risk
This relates to the variability of the business, sales, income, profits etc. which in turn depend on the market conditions for the product mix, input supplies, strength of competitors, etc.
This Business risk is sometimes external to the company due to changes in govt. policy or strategies of competitors or unforeseen market conditions
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supply of electricity etc.
The internal business risk leads to fall in revenues and in profit of the company, but can be corrected by certain changes in the company’s policies.
2. Financial Risk
This relates to the method of financing, adopted by the company, high leverage leading to larger debt servicing problems or short-term liquidity problems due to bad debts, delayed receivables and fall in current assets or rise in current liabilities.
These problems could no doubt be solved, but they may lead to fluctuations in earnings, profits and dividends to shareholders.
Sometimes, if the company runs into losses or reduced profits, these may lead to fall in returns to investors or negative returns.
Proper financial planning and other financial adjustments can be used to correct this risk and as such it is controllable.
Risk management: Nature & Importance
Risk Management – The entire process of identifying, evaluating, controlling and reviewing risks, to
make sure that the organization is exposed to only those risks that it needs to take to achieve its primary objectives.
Risk management is Proactive (practical) process, As different markets, different types of risks so, the risk management procedures and techniques vary in their application ways but target is same; putting the risks under control and accomplishing the mission as expected.
Ways to Conduct Risk Management
There can be three approaches or sets of actions and within them the various instruments that are available to firms for risk management.
• Eliminate/Avoid
A firm can decide to eliminate certain risks that are not consistent with its desired financial characteristics or not essential to a financial asset created.
Moreover, the firm like a bank can use portfolio diversification in order to eliminate specific risk. Additionally, it can decide to buy insurance, for event risks. Furthermore, the firm can choose to avoid certain risk types up front by setting certain business practices/policies (e.g., underwriting standards,
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process control) to reduce the chances of certain losses and/or to eliminate certain risks ex ante. If the firm has no comparative advantage in managing a specific kind of risk, there is no reason to absorb and/or manage such a risk.
• Absorb/Manage
Some risks must or should be absorbed and managed at the firm level, because they have one or more of the following characteristics:
• They cannot be traded or hedged easily
• They have a complex, illiquid, or proprietary structure that is difficult, expensive, or impossible to reveal to others
• They are a business necessity. Some risks play a central role in the bank’s business purpose and should therefore not be eliminated or transferred
• Transfer
The transfer of risks to other market participants is decided on the basis of whether or not the firm has a competitive advantage in a specific (risk) segment. Any element of the systematic risk that is not required or desired can be either shed;
• by selling it in the spot market or
• hedged by using derivative instruments such as futures, forwards, or swaps
In all such circumstances, the bank needs to actively manage these risks by using one of the following instruments:
• Diversification: The bank is supposed to have superior skills (competitive advantages), because it can provide diversification more efficiently/at a lower cost than individual investors could do on their own. This might be the case in illiquid areas where shareholders cannot hedge on their own. Management of their credit portfolio is necessary, because the performance of a credit portfolio is determined not only by exogenous factors but also by endogenous factors such as superior ex ante screening capabilities and ex post monitoring skills. Diversification, typically, reduces the frequency of both worst-case and best-case outcomes, which generally reduces the bank’s probability of failure.
Holding capital:
For all other risks that cannot be diversified away or insured internally and which the bank decides to absorb, it has to make sure that it holds a sufficient amount of capital in order to ensure that its probability of default is kept at a sufficiently low level.
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• Note that equity finance is costly
• The cost of economic capital and the decision of not eliminating risk provide a trade-off • Both risk and return need to be monitored
In dealing with the challenge of risk management, the following interrelated guidelines should be considered;
Understanding the firm’s strategic exposure Employing a mix of real and financial tools Proactively managing uncertainty
Aligning risk management with corporate strategy Learning when it is worth reducing risk
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Risk Management Process
The process of financial risk management comprises strategies that enable an organization to manage the risks associated with financial markets. Risk management is a dynamic process that should evolve with an organization and its business. It involves and impacts many parts of an organization including treasury, sales, marketing, legal, tax, commodity, and corporate finance.
The risk management process involves both internal and external analysis. The first part of the process involves identifying and prioritizing the financial risks facing an organization and understanding their relevance. It may be necessary to examine the organization and its products, management, customers, suppliers, competitors, pricing, industry trends, balance sheet structure, and position in the industry. It is also necessary to consider stakeholders and their objectives and tolerance for risk.
Once a clear understanding of the risks emerges, appropriate strategies can be implemented in conjunction with risk management policy. For example, it might be possible to change where and how business is done, thereby reducing the organization’s exposure and risk. Alternatively, existing exposures may be managed with derivatives. Another strategy for managing risk is to accept all risks and the possibility of losses.
There are three broad alternatives for managing risk:
• Do nothing and actively, or passively by default, accept all risks.
• Hedge a portion of exposures by determining which exposures can and should be hedged.
• Hedge all exposures possible.
Measurement and reporting of risks provides decision makers with information to execute decisions and monitor outcomes, both before and after strategies are taken to mitigate them. Since the risk management process is ongoing, reporting and feedback can be used to refine the system by modifying or improving strategies.
An active decision-making process is an important component of risk management. Decisions about potential loss and risk reduction provide a forum for discussion of important issues and the varying perspectives of stakeholders.
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Factors that Impact Financial Rates and Prices
Financial rates and prices are affected by a number of factors. It is essential to understand the factors that impact markets because those factors, in turn, impact the potential risk of an organization.
A Factors that Affect Interest Rates
Interest rates are a key component in many market prices and an important economic barometer. They are comprised of the real rate plus a component for expected inflation, since inflation reduces the purchasing power of a lender’s assets. The greater the term to maturity, the greater the uncertainty. Interest rates are also reflective of supply and demand for funds and credit risk.
Interest rates are particularly important to companies and governments because they are the key ingredient in the cost of capital. Most companies and governments require debt financing for expansion and capital projects. When interest rates increase, the impact can be significant on borrowers. Interest rates also affect prices in other financial markets, so their impact is far-reaching.
Other components to the interest rate may include a risk premium to reflect the creditworthiness of a borrower. For example, the threat of political or sovereign risk can cause interest rates to rise, sometimes substantially, as investors demand additional compensation for the increased risk of default. Factors that influence the level of market interest rates include:
• Expected levels of inflation
• General economic conditions
• Monetary policy and the stance of the central bank
• Foreign investor demand for debt securities
• Levels of sovereign debt outstanding
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B Factors that Affect Foreign Exchange Rates
Foreign exchange rates are determined by supply and demand for currencies. Supply and demand, in turn, are influenced by factors in the economy, foreign trade, and the activities of international investors. Capital flows, given their size and mobility, are of great importance in determining exchange rates.
Factors that influence the level of interest rates also influence exchange rates among floating or market-determined currencies. Currencies are very sensitive to changes or anticipated changes in interest rates and to sovereign risk factors. Some of the key drivers that affect exchange rates include:
• Interest rate differentials net of expected inflation • Trading activity in other currencies
• International capital and trade flows
• International institutional investor sentiment • Financial and political stability
• Monetary policy and the central bank
• Domestic debt levels (e.g., debt-to-GDP ratio) • Economic fundamentals
C Factors that Affect Commodity Prices
Physical commodity prices are influenced by supply and demand. Unlike financial assets, the value of commodities is also affected by attributes such as physical quality and location.
Commodity supply is a function of production. Supply may be reduced if problems with production or delivery occur, such as crop failures or labor disputes. In some commodities, seasonal variations of supply and demand are usual and shortages are not uncommon.
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Demand for commodities may be affected if final consumers are able to obtain substitutes at a lower cost. There may also be major shifts in consumer taste over the long term if there are supply or cost issues.
Commodity traders are sensitive to the inclination of certain commodity prices to vary according to the stage of the economic cycle. For example, base metals prices may rise late in the economic cycle as a result of increased economic demand and expansion. Prices of these commodities are monitored as a form of leading indicator.
Commodity prices may be affected by a number of factors, including: • Expected levels of inflation, particularly for precious metals • Interest rates
• Exchange rates, depending on how prices are determined • General economic conditions
• Costs of production and ability to deliver to buyers
• Availability of substitutes and shifts in taste and consumption patterns • Weather, particularly for agricultural commodities and energy
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Calculation of Return
We are going to assess risk on the basis of variability of return, we need to be certain we know what return is and how to measure it. The return is the total gain or loss experienced on an investment over a given period of time. It is commonly measure as cash distributions during the period plus the change in value expressed as a percentage of the beginning of period investment value. The expression for calculating the rate of return earned on any asset over period, commonly defined as:
i = C + PC - PB PB
where:
i = rate of return
C = cash flow received from the investment PB = price (value) of asset at beginning PC = price (value) of asset after changes
Example: Mr. Moody wishes to determine the return of two video machines, C and D. C was purchased 1 year ago for $ 20,000 and currently has a market value of $ 21,500. During the year it generated $ 800 of after tax cash receipts. D was purchased 4 years ago, its value in the year just completed declined from m$ 12,000 to $ 11,800. During the year it generated $ 1,700 of after tax cash receipts.
We can calculate the annual rate of return i for each video machine. For video machine C
2 0 1 2 -1 3 PB i = 800 + 21,500 - 20,000 20,000 i = 2,300 20,000 i = 11.5%
For video machine D
i = C + PC - PB PB i = 1,700 + 11,800 - 12,000 12,000 i = 1,500 12,000 i = 12.5%
Although the market value of D declined during the year, its cash flow caused it to earn higher rate of return than C earned during the same period. Clearly the combined impact of cash flow changes in value as measured by the rate of return is important.
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Risk Preferences
Feelings about risk differ among managers and firms. Thus it is important to specify a generally acceptable level of risk. The three basic risk preference behaviors risk averse, risk indifferent and risk seeking are explained below:
A Risk Indifferent
Risk Indifferent is the attitude toward risk in which no change in return would be required for an increase risk. For the risk indifferent manager the required return does not change as risk goes from x1 to x2. In essence no change in return would be required for the increase in risk.
B Risk Averse
It is the attitude toward risk in which increased return would be required for an increase in risk. For the risk averse manager the required return increases for an increase in risk. Because they shy away from risk, these managers require expected returns to compensate them for taking greater risk. C Risk Seeking
Risk seeking is the attitude toward risk in which a decreased return would be accepted for an increase in risk. For the risk seeking manager, the required return decreases for an increase in risk. Theoretically because they enjoy risk these managers are willing to give up some return to take more risk. However such behavior would not be likely to benefit the firm.
Most managers are risk averse; for a given increase in risk they require an increase in return. They generally tend to be conservative rather than aggressive hen accepting risk for their firm. Accordingly a risk averse financial manager requiring higher returns for greater risk is assumed throughout this text.
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Risk of a single asset
The concept of risk can be developed by first considering a single asset held in isolation. We can look at expected return behaviors to assess risk, and statistics can be used to measure it.
Risk Assessment
Sensitivity analysis and probability distributions can be used to assess the general level of risk embodied in a given asset.
Sensitivity analysis
An approach for assessing risk that uses several possible return estimates to obtain a sense of the variability among outcomes. Sensitivity analysis uses several possible return estimates to obtain a sense of the variability among outcomes. One common method involve s making pessimistic worst, most likely expected and optimistic best estimates of the returns associated with a given asset. In this case the assets risk can be measured by the range of returns. The range is found by subtracting the pessimistic outcome from the optimistic outcome. The greater the range the more variability or risk the asset is said to have.
Example
Norman company a golf equipment manufacturer, wants to choose the better two investments, A and B. each requires an initial outlay of Rs. 10,000 and each has a most likely annual rate of return of 15%. Management has made pessimistic an optimistic estimates of the returns associated with each. The three estimates for each asset along with its range are given below:
Assets A and B
Asset A Asset B
Initial Investment Rs 100,000 Rs 100,000
Annual rate of return
Pessimistic 13% 7%
Most likely 15% 15%
Optimistic 17% 23%
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Asset A appears to be less risky than asset B, its range of 4 percent (17% - 13%) is less than the range of 16% (23% - 7%) for asset B. the risk averse decision maker would prefer asset A over asset B, because A offers the same most likely return as B 15% with lower risk smaller range.
Although the use of sensitivity analysis and the range is rather crude, it does give the decision maker a feel for the behavior of returns, which can be used to estimate the risk involved.
Probability Distributions
Probability means the chance that a given outcome will occur. Probability distributions provide a more quantitative insight into an assets risk. The probability of a given outcome is its chance of occurring. An outcome with an 80% probability of occurrence would be expected to occur 8 out of 10 times. An outcome with a probability of 100 percent is certain to occur. Outcomes with a probability of zero will never occur.
A probability distribution is a model that relates probabilities to the associated outcomes. The simplest type of probability distribution is the bar chart, which shows only a limited number of outcome probability coordinates. The bar charts for Norman company’s assets A and B are show in the following figure. Although both assets have the same most likely return, the range of return is much greater or more dispersed for asset B than for asset A- 16 percent versus 4 percent.
Bar charts for asset A’s and B’s returns Continuous probability distribution
A probability distribution showing all the possible outcomes and associated probabilities for a given event. If we knew all the possible outcomes and associated probabilities, we could develop a continuous probability distribution. This type of distribution can be thought of as a bar chart for a very large number of outcomes. Following figure represents continuous probability distributions for assets A and B. note that although assets A and B have the same most likely return 15%, the distribution of returns for asset B has much greater dispersion than the distribution for asset A. clearly asset B is more risky than asset A.
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In real world situations, the risk of any single investment would not be viewed independently of other assets. We did so for teaching purposes. New investments must be considered in light of their impact on the risk and return of the portfolio of assets. The financial manager’s goal is to create an efficient portfolio, one that maximizes return for a given level of risk or minimizes risk for a given level of return. We therefore need a way to measure the return and the standard deviation of a portfolio of assets. Once we can do that we will look at the statistical concept of correlation, which underlies the process of diversification that is used to develop an efficient portfolio.
Efficient portfolio
A portfolio that maximizes return for a given level of risk or minimizes risk for a given level of return.
Correlation
A statistical measure of the relationship between any two series of numbers representing data of any kind. The numbers may represent data of any kind from returns to test scores.
Positively correlated
If two series move in the same direction they are positively correlated. Or describes two series that move in the same direction.
Negatively correlated
If the series move in opposite directions they are negatively correlated. Or describes two series that move in opposite directions.
Hedging and Correlation
Hedging is the business of seeking assets or events that offset, or have weak or negative correlation to, an organization’s financial exposures.
Correlation measures the tendency of two assets to move, or not move, together. This tendency is quantified by a coefficient between -1 and +1. Correlation of +1.0 signifies perfect positive correlation and means that two assets can be expected to move together. Correlation of -1.0 signifies perfect negative correlation, which means that two assets can be expected to move together but in opposite directions.
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The concept of negative correlation is central to hedging and risk management. Risk management involves pairing a financial exposure with an instrument or strategy that is negatively correlated to the exposure.
A long futures contract used to hedge a short underlying exposure employs the concept of negative correlation. If the price of the underlying (short) exposure begins to rise, the value of the (long) futures contract will also increase, offsetting some or all of the losses that occur. The extent of the protection offered by the hedge depends on the degree of negative correlation between the two.
Derivatives
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One of the most significant events in the securities markets has been the development and expansion of financial derivatives. The term “derivatives” is used to refer to financial instruments which derive their value from some underlying assets. The underlying assets could be equities (shares), debt (bonds, T-bills, and notes), currencies, and even indices of these various assets, such as the Nifty 50 Index. Derivatives derive their names from their respective underlying asset. Thus if a derivative’s underlying asset is equity, it is called equity derivative and so on. Derivatives can be traded either on a regulated exchange, such as the NSE or off the exchanges, i.e., directly between the different parties, which is called “over-the-counter” (OTC) trading. The basic purpose of derivatives is to transfer the price risk (inherent in fluctuations of the asset prices) from one party to another; they facilitate the allocation of risk to those who are willing to take it. In so doing, derivatives help mitigate the risk arising from the future uncertainty of prices. For example, on November 1, 2009 a rice farmer may wish to sell his harvest at a future date (say January 1, 2010) for a pre-determined fixed price to eliminate the risk of change in prices by that date. Such a transaction is an example of a derivatives contract. The price of this derivative is driven by the spot price of rice which is the "underlying".
Origin of derivatives
While trading in derivatives products has grown tremendously in recent times, the earliest evidence of these types of instruments can be traced back to ancient Greece. Even though derivatives have been in existence in some form or the other since ancient times, the advent of modern day derivatives contracts is attributed to farmers’ need to protect themselves against a decline in crop prices due to various economic and environmental factors. Thus, derivatives contracts initially developed in commodities. The first “futures” contracts can be traced to the Yodoya rice market in Osaka, Japan around 1650. The farmers were afraid of rice prices falling in the future at the time of harvesting. To lock in a price (that is, to sell the rice at a predetermined fixed price in the future), the farmers entered into contracts with the buyers. These were evidently standardized contracts, much like today’s futures contracts. In 1848, the Chicago Board of Trade (CBOT) was established to facilitate trading of forward contracts on various commodities. From then on, futures contracts on commodities have remained more or less in the same form, as we know them today. While the basics of derivatives are the same for all assets
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such as equities, bonds, currencies, and commodities, we will focus on derivatives in the equity markets and all examples that we discuss will use stocks and index (basket of stocks).
Two important terms
Before discussing derivatives, it would be useful to be familiar with two terminologies relating to the underlying markets. These are as follows:
Spot Market
In the context of securities, the spot market or cash market is a securities market in which securities are sold for cash and delivered immediately. The delivery happens after the settlement period. Let us describe this in the context of India. The NSE’s cash market segment is known as the Capital Market (CM) Segment.
Index
Stock prices fluctuate continuously during any given period. Prices of some stocks might move up while that of others may move down. In such a situation, what can we say about the stock market as a whole? Has the market moved up or has it moved down during a given period? Similarly, have stocks of a particular sector moved up or down? To identify the general trend in the market (or any given sector of the market such as banking), it is important to have a reference barometer which can be monitored. Market participants use various indices for this purpose. An index is a basket of identified stocks, and its value is computed by taking the weighted average of the prices of the constituent stocks of the index. A market index for example consists of a group of top stocks traded in the market and its value changes as the prices of its constituent stocks change.
Definitions of Basic Derivatives
There are various types of derivatives traded on exchanges across the world. They range from the very simple to the most complex products. The following are the three basic forms of derivatives, which are the building blocks for many complex derivatives instruments (the latter are beyond the scope of this book):
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Knowledge of these instruments is necessary in order to understand the basics of derivatives. We shall now discuss each of them in detail.
A Forwards
A forward contract or simply a forward is a contract between two parties to buy or sell an asset at a certain future date for a certain price that is pre-decided on the date of the contract. The future date is referred to as expiry date and the pre-decided price is referred to as Forward Price. It may be noted that Forwards are private contracts and their terms are determined by the parties involved.
A forward contract is a particularly simple derivative. It is an agreement to buy or sell an asset at a certain future time at a certain price.
It can be contrasted with a spot contract, which is an agreement to buy or sell an asset today.
A forward contract is traded in the over-the-counter market, usually between two financial institutions or between a financial institution and one of its clients.
One of the parties to a forward contract assumes a long position and agrees to buy the underlying asset on a certain specified future date for a certain specified price. The other party assumes a short position and agrees to sell the underlying asset on the same for the same price.
The price in a forward contract is known as the delivery price.
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A forward is thus an agreement between two parties in which one party, the buyer, enters into an agreement with the other party, the seller that he would buy from the seller an underlying asset on the expiry date at the forward price. Therefore, it is a commitment by both the parties to engage in a transaction at a later date with the price set in advance. This is different from a spot market contract, which involves immediate payment and immediate transfer of asset. The party that agrees to buy the asset on a future date is referred to as a long investor and is said to have a long position. Similarly the party that agrees to sell the asset in a future date is referred to as a short investor and is said to have a short position. The price agreed upon is called the delivery price or the Forward Price. Forward contracts are traded only in Over the Counter (OTC) market and not in stock exchanges. OTC market is a private market where individuals/institutions can trade through negotiations on a one to one basis.
Example 1: (Hedging Currency Risk with a Forward Contract)
Suppose it is April 5 of a certain year and the treasurer of a U.S. Corporation knows that the corporation will receive 1 million EUROs in three months (on July 5th), and wants to hedge against the exchange rate moves. The treasurer could contact a bank, and find out that the exchange rate for a 3-month forward contract on EURO is $1.25, and agree to sell 1 million EUROs. In this case, the corporation takes a short forward position (agrees to sell), whereas the bank assumes a long forward position (agrees to buy). This forward contract eliminates all exchange rate risk, since the corporation will receive $1.25 million no matter what happens to the Euro currency rate in the course of the next three months.
Settlement of forward contracts
When a forward contract expires, there are two alternate arrangements possible to settle the obligation of the parties: physical settlement and cash settlement. Both types of settlements happen on the expiry date and are given below.
Physical Settlement
A forward contract can be settled by the physical delivery of the underlying asset by a short investor (i.e. the seller) to the long investor (i.e. the buyer) and the payment of the agreed
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forward price by the buyer to the seller on the agreed settlement date. The following example will help us understand the physical settlement process.
Example II
Consider two parties (A and B) enter into a forward contract on 1 August, 2009 where, A agrees to deliver 1000 stocks of Unitech to B, at a price of Rs. 100 per share, on 29 the August, 2009 (the expiry date). In this contract, A, who has committed to sell 1000 stocks of Unitech at Rs. 100 per share on 29 the August, 2009 has a short position and B, who has committed to buy 1000 stocks at Rs. 100 per share is said to have a long position.
In case of physical settlement, on 29th August, 2009 (expiry date), A has to actually deliver 1000 Unitech shares to B and B has to pay the price (1000 * Rs. 100 = Rs. 10,000) to A. Incase A does not have 1000 shares to deliver on 29th August, 2009, he has to purchase it from the spot market and then deliver the stocks to B.
On the expiry date the profit/loss for each party depends on the settlement price, that is, the closing price in the spot market on 29 August, 2009. The closing price on any given day is the weighted average price of the underlying during the last half an hour of trading in that day.
Depending on the closing price, three different scenarios of profit/loss are possible for each party. They are as follows:
Scenario I Closing spot price on 29 August, 2009 (S T) is greater than the Forward price (FT) Assume that the closing price of Unitech on the settlement date 29 August, 2009 is Rs. 105. Since the short investor has sold Unitech at Rs. 100 in the Forward market on 1 August, 2009, he can buy 1000 Unitech shares at Rs. 105 from the market and deliver them to the long investor. Therefore the person who has a short position makes a loss of (100 – 105) X 1000 = Rs. 5000. If the long investor sells the shares in the spot market immediately after receiving them, he would make an equivalent profit of (105 – 100) X 1000 = Rs. 5000.
Scenario II Closing Spot price on 29 August (S T), 2009 is the same as the Forward price (FT) The short seller will buy the stock from the market at Rs. 100 and give it to the long investor. As the settlement price is same as the Forward price, neither party will gain or lose anything.
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Scenario III Closing Spot price (S T) on 29 August is less than t he futures price (F T) Assume that the closing price of Unitech on 29 August, 2009 is Rs. 95. The short investor, who has sold Unitech at Rs. 100 in the Forward market on 1 August, 2009, will buy the stock from the market at Rs. 95 and deliver it to the long investor. Therefore the person who has a short position would make a profit of (100 – 95) X 1000 = Rs. 5000 and the person who has long position in the contract will lose an equivalent amount (Rs. 5000), if he sells the shares in the spot market immediately after receiving them.
The main disadvantage of physical settlement is that it results in huge transaction costs in terms of actual purchase of securities by the party holding a short position (in this case A) and transfer of the security to the party in the long position (in this case B). Further, if the party in the long position is actually not interested in holding the security, then she will have to incur further transaction cost in disposing off the security. An alternative way of settlement, which helps in minimizing this cost, is through cash settlement.
Cash Settlement
Cash settlement does not involve actual delivery or receipt of the security. Each party either pays (receives) cash equal to the net loss (profit) arising out of their respective position in the contract. So, in case of Scenario I mentioned above, where the spot price at the expiry date (ST) was greater than the forward price (FT), the party with the short position will have to pay an amount equivalent to the net loss to the part y at the long position. In our example, A will simply pay Rs. 5000 to B on the expiry date. The opposite is the case in Scenario (III), when ST < FT. The long party will be at a loss and have to pay an amount equivalent to the net loss to the short party. In our example, B will have to pay Rs. 5000 to A on the expiry date. In case of Scenario (II) where S T = FT, there is no need for any party to pay anything to the other party. Please note that the profit and loss position in case of physical settlement and cash settlement is the same except for the transaction costs which is involved in the physical settlement.
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Default risk in forward contracts
A drawback of forward contracts is that they are subject to default risk. Regardless of whether the contract is for physical or cash settlement, there exists a potential for one party to default, i.e. not honor the contract. It could be either the buyer or the seller. This results in the other party suffering a loss.
This risk of making losses due to any of the two parties defaulting is known as counter party risk. The main reason behind such risk is the absence of any mediator between the parties, who could have undertaken the task of ensuring that both the parties fulfill their obligations arising out of the contract. Default risk is also referred to as counter party risk or credit risk.
Forward Prices and Arbitrage
Arbitrage involves locking in a profit by simultaneously entering into transactions in two or more markets to exploit a pricing anomaly. Such opportunities to make riskless profits are quite rare, since when the traders start moving to exploit them the prices adjust accordingly so that the arbitrage opportunity disappears.
Example III (Arbitrage with a Forward Contract on Gold).
This example illustrates the possibility of arbitrage when the delivery price on a forward contract is too high or too low. Consider a trader who owns one ounce of gold today. Suppose the spot prices for gold is such that in the spot market traders can buy an ounce of gold at PB = $100 and sell at PS = $95. Furthermore, suppose that the 1-year borrowing and lending rates are such that traders can borrow at RB = 5% and lend at RL = 4% a year.
Suppose first that the delivery price for a one year forward contract on gold is F = $107. In this case, the following arbitrage strategy yields a riskless profit.
Borrow $100 at 5%, buy one ounce of gold in the spot market and take a short position in the forward contract.
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To see why, note that at time of delivery for the forward, the trader will sell the gold she bought for $107, whereas she has to pay back the loan at $100(1+0.05) = $105, which leaves her with $107 − $105 = $2 profits.
Note that once traders start exploiting this arbitrage opportunity by taking short forward positions, there will be an excess supply to deliver gold at $107, which will drive the 1-year gold forward delivery price down.
For the arbitrage opportunity to disappear, the delivery price F should be less than F < PB (1 + RB) = $100(1 + 0.05) = $105
⇒ F < $105.
Example III (continued)
Suppose now that the delivery price for a one year forward contract on gold is F = $96. In this case, the following arbitrage strategy yields a riskless profit (recall that our trader own one ounce of gold to begin with).
Sell the gold today at PS = $95, lend the proceeds at RL = 4%, and take a LONG position in the forward contract.
To see why, note that at time of delivery for the forward contract, the trader will BUY the gold at F = $96, whereas she will receive $95(1 + 0.04) = $98.8 (for the funds she invested at 4%), which leaves her with $98.8 − $96 = $2.8 profits.
Note that once traders start exploiting this arbitrage opportunity by taking long forward positions, there will be an excess demand to be delivered gold at $96, which will drive the 1-year gold forward delivery price up. For the arbitrage opportunity to disappear, the delivery price F should be more than
F > PS (1 + RL) = $95(1 + 0.04) = $98.8 ⇒ F > $98.8
2 0 1 2 -1 3 Practice Problems
Problem 1 A U.S. Company expects to pay 1 million Euros in six months. How can they use forward contracts to hedge against the exchange rate risk?
Problem 2 The price of gold is currently $500 per ounce. The forward price for delivery in one year is $700. An arbitrage trader can borrow money at 10% per annum. Identify an arbitrage strategy.
Problem 3 A traders owns one unit of gold. The trader can buy gold at $50 per ounce and sell it at $40 per ounce in the spot market. She can borrow money at 6% per year and can invest money at 5% per year. For what range of one-year gold forward price F does this trader have no arbitrage opportunities?
2 0 1 2 -1 3 B Futures
Like a forward contract, a futures contract is an agreement between two parties in which the buyer agrees to buy an underlying asset from the seller, at a future date at a price that is agreed upon today. However, unlike a forward contract, a futures contract is not a private transaction but gets traded on a recognized stock exchange. In addition, a futures contract is standardized by the exchange. All the terms, other than the price, are set by the stock exchange (rather than by individual parties as in the case of a forward contract). Also, both buyer and seller of the futures contracts are protected against the counter party risk by an entity called the Clearing Corporation. The Clearing Corporation provides this guarantee to ensure that the buyer or the seller of a futures contract does not suffer as a result of the counter party defaulting on its obligation. In case one of the parties defaults, the Clearing Corporation steps in to fulfill the obligation of this party, so that the other party does not suffer due to non-fulfillment of the contract. To be able to guarantee the fulfillment of the obligations under the contract, the Clearing Corporation holds an amount as a security from both the parties. This amount is called the Margin money and can be in the form of cash or other financial assets. Also, since the futures contracts are traded on the stock exchanges, the parties have the flexibility of closing out the contract prior to the maturity by squaring off the transactions in the market. The basic flow of a transaction between three parties, namely Buyer, Seller and Clearing Corporation is depicted in the diagram below:
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What is the difference between forward and futures contracts?
Fundamentally, forward and futures contracts have the same function: both types of contracts allow people to buy or sell a specific type of asset at a specific time at a given price.
Forwards Futures
Privately negotiated contracts Traded on an exchange
Not standardized Standardized contracts
Settlement dates can be set by the parties Fixed settlement dates as declared by the exchange
2 0 1 2 -1 3 C Options
Like forwards and futures, options are derivative instruments that provide the opportunity to buy or sell an underlying asset on a future date. An option is a derivative contract between a buyer and a seller, where one party (say First Party) gives to the other (say Second Party) the right, but not the obligation, to buy from (or sell to) the First Party the underlying asset on or before a specific day at an agreed -upon price. In return for granting the option, the party granting the option collects a payment from the other party. This payment collected is called the “premium” or price of the option. The right to buy or sell is held by the “option buyer” (also called the option holder); the party granting the right is t he “option seller” or “option writer”. Unlike forwards and futures contracts, options require a cash payment (called the premium) upfront from the option buyer to the option seller. This payment is called option premium or option price. Options can be traded either on the stock exchange or in over the counter (OTC) markets. Options traded on the exchanges are backed by the Clearing Corporation thereby minimizing the risk arising due to default by the counter parties involved.
There are two types of options, call options and put options, which are explained below: Call option
A call option is an option granting the right to the buyer of the option to buy the underlying asset on a specific day at an agreed upon price, but not the obligation to do so. It is the seller who grants this right to the buyer of the option. It may be noted that the person who has the right to buy the underlying asset is known as the “buyer of the call option”. The price at which the buyer has the right to buy the asset is agreed upon at the time of entering the contract. This price is known as the strike price of the contract (call option strike price in this case). Since the buyer of the call option has the right (but no obligation) to buy the underlying asset, he will exercise his right to buy the underlying asset if and only if the price of the underlying asset in the market is more than the strike price on or before the expiry date of the contract. The buyer of the call option does not have an obligation to buy if he does not want to.
2 0 1 2 -1 3 Put option
A put option is a contract granting the right to the buyer of the option to sell the underlying asset on or before a specific day at an agreed upon price, but not the obligation to do so. It is the seller who grants this right to the buyer of the option. The person who has the right to sell the underlying asset is known as the “buyer of the put option”. The price at which the buyer has the right to sell the asset is agreed upon at the time of entering the contract. This price is known as the strike price of the contract (put option strike price in this case). Since the buyer of the put option has the right (but not the obligation) to sell the underlying asset, he will exercise his right to sell the underlying asset if and only if the price of the underlying asset in the market is less than the strike price on or before the expiry date of the contract. The buyer of the put option does not have the obligation to sell if he does not want to.
Illustration
Suppose A has “bought a call option” of 2000 shares of Unilever at a strike price of Rs 260 per share at a premium of Rs 10. This option gives A, the buyer of the option, the right to buy 2000 shares of Unilever from the seller of the option, on or before August 27, 2009 (expiry date of the option). The seller of the option has the obligation to sell 2000 shares of Unilever at Rs 260 per share on or before August 27, 2009 (i.e. whenever asked by the buyer of the option).
Suppose instead of buying a call, A has “sold a put option” on 100 Reliance Industries (RIL) shares at a strike price of Rs 2000 at a premium of Rs 8. This option is an obligation to A to buy 100 shares of Reliance Industries (RIL) at a price of Rs 2000 per share on or before August 27 (expiry date of the option) i.e., as and when asked by the buyer of the put option. It depends on the option buyer as to when he exercises the option. As stated earlier, the buyer does not have the obligation to exercise the option.
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Differences between futures and options:
Terminology of Derivatives
In this section we explain the general terms and concepts related to derivatives. Spot price (ST)
Spot price of an underlying asset is the price that is quoted for immediate delivery of the asset. For example, at the National Stock Exchange of India (NSE), the spot price of Reliance Ltd. at any given time is the price at which Reliance Ltd. shares are being traded at that time in the Cash Market Segment of the NSE. Spot price is also referred to as cash price sometimes.
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Forward price or futures price is the price that is agreed upon at the date of the contract for the delivery of an asset at a specific future date. These prices are dependent on the spot price, the prevailing interest rate and the expiry date of the contract.
Strike price (K)
The price at which the buyer of an option can buy the stock (in the case of a call option) or sell the stock (in the case of a put option) on or before the expiry date of option contracts is called strike price. It is the price at which the stock will be bought or sold when the option is exercised. Strike price is used in the case of options only; it is not used for futures or forwards.
Expiration date (T)
In the case of Futures, Forwards and Index Options, Expiration Date is the only date on which settlement takes place. In case of stock options, on the other hand, Expiration date (or simply expiry), is the last date on which the option can be exercised. It is also called the final settlement date.
Contract size
As futures and options are standardized contracts traded on an exchange, they have a fixed contract size. One contract of a derivatives instrument represents a certain number of shares of the underlying asset. For example, if one contract of BHEL consists of 300 shares of BHEL, then if one buys one futures contract of BHEL, then for every Re 1 increase in BHEL’s futures price, the buyer will make a profit of 300 X 1 = Rs 300 and for every Re 1 fall in BHEL’s futures price, he will lose Rs 300.
Contract Value
Contract value is notional value of the transaction in case one contract is bought or sold. It is the contract size multiplied but the price of the futures. Contract value is used to calculate margins etc. for contracts. In the example above if BHEL futures are trading at Rs. 2000 the contract value would be Rs. 2000 x 300 = Rs. 6 lacs.
2 0 1 2 -1 3 Margins
In the spot market, the buyer of a stock has to pay the entire transaction amount (for purchasing the stock) to the seller. For example, if Infosys is trading at Rs. 2000 a share and an investor wants to buy 100 Infosys shares, then he has to pay Rs. 2000 X 100 = Rs. 2,00,000 to the seller. The settlement will take place on T+2 basis; that is, two days after the transaction date.
In a derivatives contract, a person enters into a trade today (buy or sell) but the settlement happens on a future date. Because of this, there is a high possibility of default by any of the parties. Futures and option contracts are traded through exchanges and the counter party risk is taken care of by the clearing corporation. In order to prevent any of the parties from defaulting on his trade commitment, the clearing corporation levies a margin on the buyer as well as seller of the futures and option contracts. This margin is a percentage (approximately 20%) of the total contract value. Thus, for the aforementioned example, if a person wants to buy 100 Infosys futures, then he will have to pay 20% of the contract value of Rs 2,00,000 = Rs 40,000 as a margin to the clearing corporation. This margin is applicable to both, the buyer and the seller of a futures contract.
Moneyness of an Option
“Moneyness” of an option indicates whether an option is worth exercising or not i.e. if the option is exercised by the buyer of the option whether he will receive money or not.
“Moneyness” of an option at any given time depends on where the spot price of the underlying is at that point of time relative to the strike price. The premium paid is not taken into consideration while calculating moneyness of an Option, since the premium once paid is a sunk cost and the profitability from exercising the option does not depend on the size of the premium. Therefore, the decision (of the buyer of the option) whether to exercise the option or not is not affected by the size of the premium. The following three terms are used to define the moneyness of an option.
2 0 1 2 -1 3 In-the-money option
An option is said to be in-the-money if on exercising the option, it would produce a cash inflow for the buyer. Thus, Call Options are in-the-money when the value of spot price of the underlying exceeds the strike price. On the other hand, Put Opt ions are in-the- money when the spot price of the underlying is lower than the strike price. Moneyness of an option should not be confused with the profit and loss arising from holding an option contract. It should be noted that while moneyness of an option does not depend on the premium paid, profit/loss do. Thus a holder of an in-the-money option need not always make profit as the profitability also depends on the premium paid.
Out-of- the-money option
An out-of-the-money option is an opposite of an in-the-money option. An option-holder will not exercise the option when it is out-of-the-money. A Call option is out-of-the-money when its strike price is greater than the spot price of the underlying and a Put option is out-of-the-money when the spot price of the underlying is greater than the option’s strike price.
At- the-money option
An at-the-money-option is one in which the spot price of the underlying is equal to the strike price. It is at the stage where with any movement in the spot price of the underlying, the option will either become in-the-money or out-of-the-money.
Illustration
Consider some Call and Put options on stock XYZ. As on 13 August, 2009, XYZ is trading at Rs 116.25. The table below gives the information on closing prices of four options, expiring in September and December, and with strike prices of Rs. 115 and Rs. 117.50.
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Moneyness of call and put options
Suppose the spot price of the underlying (closing share price) as at end of September is Rs. 116 and at end of December is Rs. 118. On the basis of the rules stated above, which options is in-the-money and which ones is out-of-in-the-money are given in the following table.
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It may be noted that an option which is in-the-money at a particular instance may turn into out-of-the– money (and vice versa) at another instance due to change in the price of the underlying asset.
Applications of Derivatives
We look at the participants in the derivatives markets and how they use derivatives contracts. Participants in the Derivatives Market
As equity markets developed, different categories of investors started participating in the market. Equity market participants currently include retail investors, corporate investors, mutual funds, banks, foreign institutional investors etc. Each of these investor categories uses the derivatives market to as a part of risk management, investment strategy or speculation. Based on the applications that derivatives are put to, these investors can be broadly classified into three groups:
Hedgers
Speculators, and Arbitrageurs
We shall now look at each of these categories in detail.
1 Hedgers
These investors have a position (i.e., have bought stocks) in the underlying market but are worried about a potential loss arising out of a change in the asset price in the future. Hedgers participate in the derivatives market to lock the prices at which they will be able to transact in the future. Thus, they try to avoid price risk through holding a position in the derivatives market. Different hedgers take different positions in the derivatives market based on their exposure in the underlying market. A hedger normally takes an opposite position in the derivatives market to what he has in the underlying market. Hedging in futures market can be done through two positions, viz. short hedge and long hedge.
2 0 1 2 -1 3 Short Hedge
A short hedge involves taking a short position in the futures market. Short hedge position is taken by someone who already owns the underlying asset or is expecting a future receipt of the underlying asset.
For example, an investor holding Reliance shares may be worried about adverse future price movements and may want to hedge the price risk. He can do so by holding a short position in the derivatives market. The investor can go short in Reliance futures at the NSE. This protects him from price movements in Reliance stock. In case the price of Reliance shares falls, the investor will lose money in the shares but will make up for this loss by the gain made in Reliance Futures. Note that a short position holder in a futures contract makes a profit if the price of the underlying asset falls in the future. In this way, futures contract allows an investor to manage his price risk. Similarly, a sugar manufacturing company could hedge against any probable loss in the future due to a fall in the prices of sugar by holding a short position i n the futures/ forwards market. If the prices of sugar fall, the company may lose on the sugar sale but the loss will be offset by profit made in the futures contract.
Long Hedge
A long hedge involves holding a long position in the futures market. A Long position holder agrees to buy the underlying asset at the expiry date by paying the agreed futures/ forward price. This strategy is used by those who will need to acquire the underlying asset in the future.
For example, a chocolate manufacturer who needs to acquire sugar in the future will be worried about any loss that may arise if the price of sugar increases in the future. To hedge against this risk, the chocolate manufacturer can hold a long position in the sugar futures. If the price of sugar rises, the chocolate manufacture may have to pay more to acquire sugar in the normal market, but he will be compensated against this loss through a profit that will arise in the futures market. Note that a long position holder in a futures contract makes a profit if the price of the underlying asset increases in the future. Long hedge strategy can also be used by those investors who desire to purchase the underlying asset at a future date (that is, when he acquires the cash to
