14

Risk Management and Trading with Derivatives

RISK

Risk is explained theoretically as the fluctuation in returns from a security. A security that yields consistent returns over a period of time is termed as “riskless security” or “risk free security”. Risk is inherent in all walks of life. An investor cannot foresee the future definitely, hence, risk will always exist for an investor. Risk is in fact the watchword for all investors who enter capital markets.

Investment risk can be an extraordinary stress for many investors. When the secondary market does not respond to rational expectations, the risk component of such markets are relatively high and most investors fail to recognise the real risk involved in the investment process. Risk aversion is the criteria commonly associated with many small investors in the secondary market. Many small investors look upon the market for a definite return and when their expectations are not met, the effect on the small investors’ morale is negative. Hence, these investors prefer to lock up their funds in securities that would rather give them back their investment with small returns than those securities that yield high returns on an average but are subject to wild fluctuations.

The investment environment also has risk seeking investors. Speculators are risk seekers and would rather invest in securities that yield high returns though the certainty around such returns is very minimal. They are also termed as risk takers in the market. Both risk takers and risk averting investors are essential for a secondary market. In between these two categories of investors, a market also nurtures moderate risk takers, ie, those who would not avoid totally risky securities but have a tendency to select securities that are risk free as well as securities that carry a certain element of tolerable risk. These are the moderators in the market. Conventionally, when the market players talk of risk, risk is loosely defined as the perception of change in a security’s prices/returns in future. The perceptual interpretation of risk, thus, defines it qualitatively rather than with a definite, quantitative measure. However, research in the risk behaviour of investors in the secondary market has tried to quantify the risk involved with securities in the market.

An investor given the following investment opportunities would definitely choose investment B to investment A in both Figure 14.1 (a) and (b). Investment A gives a definite flow of income, whereas, investment B is definite in the first figure while it varies in the second figure. The variation in the flow of income to investors is defined as the risk inherent in the security. Though there is risk in the second instance, the investor’s preference would still be for investment B because it offers a higher return in almost all instances. This is also inferred as the compensatory higher return for the higher risk borne by the investor.

Two investment opportunities given in Figures 14.2(a) and (b) are not so very simple for the investor to choose between. Some investors who are willing to bear an extra risk for a higher yield could prefer a security promising higher return to a security that gives fluctuating returns. Hence, a risk seeking investor may prefer investment A in the first figure and go for investment B in the second figure.

More complicated return patterns occur in the secondary market, as in Figures 14.3(a) and (b). All the available securities pose some amount of risk and, hence, the investor has to know the specific risk-return pattern that is preferred at any point of time. The difference in the pattern of risk-return that is offered by securities in the market poses a choice for the investor. If the choice were to be the same among all investors, then only a few securities that are preferred by all investors would be traded in the market. However, in practice, the preferred choice of investors need not necessarily be the same since perceptual inference of risk varies from person to person. Economic theory assumes an indifference curve exists among individuals, in which they are indifferent among different combinations of risk-return. This indifference line is the preferred set of risk-return outcomes.

The Indifference Curve

Indifference curves are also termed as utility curves. Figure 14.4 gives the indifference lines of an investor in the market. Assuming a government security is available for investment with zero deviation in return (riskless), the investor would prefer to gain higher than this return for each unit of additional risk. The line I₁ gives these indifference points. Assuming the riskless rate increases in the market, the specific individual’s preferences will also proportionately increase from line I₁. The line I₂, and I₃ show the shift in the market structure and hence the proportionate shift in the indifference pattern of the investor.

An investor who does not prefer any risk would expect larger returns for a small increase in risk. This makes the indifference curve look more steep, as shown in Figure 14.5(b). The risk seeker, on the other hand, is willing to stake a higher risk in the market for a relatively low level of increase in return [Figures 14.5 (a)]. The slope of the indifference curve suggests the risk preference level of an investor.

MEASURING RISK

Stock market returns can be described as random distributions. Over a long period of time, returns in a market or a particular part of a market may remain constant. Based on this assumption, the securities’ return over a period of time can be forced to fit into a linear line over time. This fit is called the regression line and is the average return that a security is expected to yield over time.

Statistically, actual returns fall as distributions around the average line in a rather predictable bell-shaped curve. This is the normal distribution of share return data. The measure of deviation based on this assumption is the statistical tool of standard deviation that is computed as follows:

Standard deviation, in other words, is the square root of variance. The formula computes the deviation of a share return from its mean over a period of time ‘n’.

Table 14.2 computes the standard deviation of returns of ITC’s shares. The share price over a one month period have been put in the first column. The daily returns, by comparing the current day’s prices with the previous traded day’s prices, are then computed. The third column gives the formulae that have been inserted in the cells. The fourth column gives the computed results. The standard deviation of these returns is then computed.

 

Investment managers describe investment risk as deviation around the expected rate of return. They measure it with standard deviation. One standard deviation will contain about 68 per cent of the expected future returns. A small standard deviation will indicate a closer grouping around the average, and less risk.

A larger deviation indicates that the shares’ returns fluctuate widely and hence can be viewed as more risky investments. The normal distribution that measures one standard deviation distance from the mean is given in Figure 14.6.

A security that yields a 10 per cent return on an average and has a standard deviation of 20 per cent could be expressed through Figure 14.7. The 20 per cent deviation could imply that about 68.26 per cent of the times, the returns from that security could be within -10 per cent and +30 per cent around the computed 10 per cent average returns. The probability measure of 68 per cent also implies that about 32 per cent of the times the security’s return might also fall outside this range of +30 per cent and -10 per cent from the average return of 10 per cent.

Under the normal distribution assumptions, the plot may be widened to an area of two or three standard deviations from the mean. To cover the area of 95.45%, an addition and subtraction of two standard deviations will be made. Assume from the example that the mean return is 10 per cent and standard deviation is 20%. By subtracting two standard deviations the lower limit value will be ( 10 per cent - (2 * 20 per cent) ) -30 per cent. The upper limit will be (10 per cent + (2 * 20 per cent)) 50 per cent. For an area of 99.97 per cent, the upper and lower limits would include a range of plus or minus three standard deviations. The respective measures are (10 per cent - (3*20 per cent)) and (10 per cent + (3*20 per cent)), ie, (-50 per cent) and 70 per cent. The actual data plotted over this area in a time period will show that there can be returns to the extent of around 0.2 per cent, which still fall beyond the marked area. Figure 14.8 shows a 99.97 per cent area within which the actual returns fall over a time period..

Another quantitative measure of risk is the systematic risk measure. This is a component of the total risk measured earlier. The total risk (variance) can be divided into the component that is unique to the security and the one that is associated with the market. The unique risk to the security is due to certain internal factors that are borne only by that company, for example risk due to poor management, risk due to labour unrest, poor product quality, and so on. The unique risk can be reduced by diversification and hence it is called diversifiable risk or unsystematic risk.

The market risk relates to the risk that is inherent in the market and hence cannot be diversified. This is called the undiversifiable risk or systematic risk.

Statistically the total risk subdivision into systematic and unsystematic components can be stated as follows:

Total risk (variance) = Systematic risk + Unsystematic risk

Total risk (variance) = Undiversifiable risk (Systematic) + Diversifiable (Unsystematic)

Market movement can be represented through the market index and all securities that are traded in the market are expected to have a certain relationship with market movements. Beta measures this relative change in security prices with respect to the change in the market movements. Hence, beta can also be used as a measure of comparative risk between securities.

Beta is the slope of the regression line drawn between market returns and security returns.

Statistically, beta can be computed using the following formula:

β_s is the slope of the regression line (Security Beta) [y = α + β^x_s]

Where y = γ_s and x = γ_m ; γ_s = Security Return ; γ_m = Market Return.

Beta can also be computed using the statistical measures of co-variance and market variance. The formula will be:

Again this can be rewritten as

Security Beta = [Correlation between security and market return x security standard deviation x market standard deviation]/Market variance.

Table 14.3 and Table 14.4 show the computation of beta. The price and index values are the input variables for the computation of beta or slope of the regression line. The function slope requires independent and dependent variables. The dependent variable is the return from the security while the independent variable will be the return from the index. Graphically, this can be shown as in Figure 14.9.

Using beta coefficient as an index of systematic risk helps in the ranking of systematic risk of shares. A share with a beta value of more than 1 is said to be an aggressive share. When the beta is 1, it implies that when the market moves up by 10 per cent, the share returns also move up by 10 per cent. The movement of the share is in tandem with the market. In the case of an aggressive share, since it has a beta of more than one, for every 1 per cent movement of the market return the share return moves up by beta times the market return. For example, when the market moves up by 10 per cent and the beta of the share is 1.5, then the share return moves up by 15 per cent.

A beta value less than one indicates a defensive share, as the return from the share will be less than that of the market return. For example, when the market moves up by 10 per cent and the beta of the share is 0.50, the share return will move up by only 5 per cent.

The explanation of total risk in terms of beta can be stated as follows:

Total risk (variance) = Systematic risk + Unsystematic risk

                                 = [(beta)^² * market variance] + [Security error variance]

Sources of Risk

Risk comes from several sources and they can be listed as follows:

• Business Risk: The ability of a company to earn operational revenue is represented by the business risk. When a company fails to earn through its operations, it finally leads to the erosion of capital contributed and there is a risk of business failure. In this situation, the investor will not get any value for the share of the company.
• Market Risk: The company may have the ability to earn business profits but the overall economic situation may force the market to value the share at a lesser figure. This risk of going down with the market movements is known as market risk.
• Interest Rate Risk: The value of debt securities varies inversely with interest rates. When interest rates are higher, the value of debt will be lower; while lower interest rates will push up the value of debt securities. The value of other types of securities may also be affected due to the general rise or fall in interest rates.
• Inflation Risk: Inflation in the economy also influences the risk inherent in investments. It may also result in the return from investments not matching the rate of increase in general price level (inflation). The change in the inflation rate also changes the consumption pattern and hence investment returns carry an additional risk.
• Currency Risk: Foreign holdings and international trade movements cause a change in the value of currency exchange rates. The currency risk is applicable mainly to companies that operate overseas.
• Political Risk: The possibility that the government may change and hence the policies of the government may affect the business prospects constitute political risk. Policy changes in the tax structure, concessions and levy of duties to products, relaxation or tightening of foreign trade relations etc, carry a risk component that will change the return pattern of businesses.

An Investor’s View of Risk

In the capital market, investors define risk in a variety of ways. Risk is commonly associated with the loss of the initial investment. It is referred to as the erosion of capital. Investors tend to look at the market price of the share as what their capital is worth. Fluctuations in the market price do not necessarily result in an erosion of capital, since the market continues to value the share even after a slump. However, when a company goes into liquidation, the share value may come to a halt as on that date. Unless the liquidation value of the share is zero, the investor receives a certain amount for the investment. Hence, in the capital market, capital need not necessarily be lost fully unless the investor gets out of the market in a slump or the company goes into liquidation.

While many of the risks have to be borne by the investor, the investor has the possibility of managing market risk through derivative instruments.

Investors in the capital market can manage market risk by investing in financial instruments like futures and options. These derivative instruments help in the management of risk and they are also called hedge instruments since a hedger uses such derivative instruments to reduce the overall risk inherent in underlying instruments.

INTERNATIONAL DERIVATIVES MARKETS

The first derivative market was the Chicago Board of Trade (CBOT), which was established in 1848 to bring farmers and merchants together. The need for futures markets was felt since it was necessary to look at the needs of both the farmers and middlemen/merchants. Initially, the CBOT’s main task was to standardise the quantities and qualities of the grains that were traded, to enable futures trade.

The CBOT now offers futures contracts on many different underlying assets in both the commodities and financial markets. Many other exchanges in the world now offer futures contracts. A few international derivative markets are given in Appendix I.

DERIVATIVES MARKETS IN INDIA

Derivatives markets in India can broadly be classified into two categories, those that are traded on the exchange and those traded one to one or ‘over-the-counter’.

• Exchange Traded Derivatives
• OTC Derivatives (Over-the-Counter)

Equity Derivative Exchanges in India

In the equity markets both the National Stock Exchange of India Limited (NSE) and The Stock Exchange, Mumbai (BSE) have, with the consent of the SEBI, started derivatives segments.

OTC Equity Derivatives

Traditionally, equity derivatives have a long history in India in the OTC market. Options of various kinds (called Teji, Mandi, and Fatak) were traded in unorganised markets as early as 1900 in Mumbai. The SCRA (Security Control Regulatory Authority) however banned all kind of options in 1956.

The prohibition on options by the SCRA was removed in 1995. Foreign currency options in currency pairs other than the Rupee were the first options permitted by the RBI. The Reserve Bank of India has permitted options, interest rate swaps, currency swaps, and other risk reduction OTC derivative products. Besides, the Forward market in currencies has been a vibrant market in India for several decades. In addition, the Forward Markets Commission has allowed the setting up of commodities futures exchanges. Today we have 18 commodities exchanges, most of which trade futures. Examples are The Indian Pepper and Spice Traders Association (IPSTA) and the Coffee Owners Futures Exchange of India (COFEI).

In 2000 an amendment to the SCRA expanded the definition of securities to include derivatives, thereby enabling stock exchanges to trade equity based derivative products.

BSE’s and NSE’s Derivative Trading

Both the exchanges have set up an in-house segment instead of setting up a separate exchange for derivatives. BSE’s derivatives segment, started with Sensex futures as its first product. NSE’s futures and options segment was launched with Nifty futures as the first product.

 

Table 14.5 Product Specifications of BSE and NSE Index Derivatives

Criteria	BSE-30 Sensex Futures	S&P CNX Nifty Futures
Contract Size	Rs 50 times the Index	Rs 200 times the Index
Tick Size	0.1 points or Rs 5	0.05 points or Rs 10
Expiry Day	Last Thursday of the month	Last Thursday of the month
Settlement Basis	Cash settlement	Cash settlement
Contract Cycle	3 months	3 months
Active contracts	3 nearest months	3 nearest months

 

Trading Systems NSE’s trading system for its futures and options segment is called NEAT F&O. It is based on the NEAT system for the cash segment. BSE’s trading system for its derivatives segment is called DTSS. It is built on a platform different from the BOLT system, though most of their features are similar. The product specifications on index futures is given in Table 14.5. Table 14.6 gives the contract specifications for Nifty index options.

 

Table 14.6

Specifications	S&PCNX Nifty
Contract size	Permitted lot size 200 or multiples thereof
Price steps	Re 0.05
Style	European/Americ an
Trading cycle	The options contracts will have a maximum of three month trading cycle: the near month (one), the next month (two), and the far month (three). New contracts will be introduced on the next trading day follo wing the expiry of near month contract.
Expiry day	The last Thursday of the expiry month or the previous trading day if the last Thursday is a trading holiday.
Settlement basis	Cash settlement on a T + 1 basis
Settlement prices	B ased on expiration price, as may be decided by the Exchange

 

Futures Trading

Closing Out

The majority of futures contracts are closed out before they mature. Since there are typically only 4 maturity dates each year it is unlikely that the needs of futures users will coincide with one of these 4 dates (for most futures contracts there are maturity dates in March, June, September and December). Closing out involves taking a futures position opposite to the original position. If the position was opened by buying a contract with a March maturity date, it would be closed out by selling a March futures contract; likewise, a short position (futures sold) would be closed out by buying futures with the same maturity date. When futures contracts are closed out, the transactor is left with no futures position; the purchases and sales are deemed to cancel each other.

Ticks A tick is the smallest futures price movement permitted by the exchange on which the futures are traded. In the case of London stock market, the size of a futures contract is £25 per index point. In the Bombay Stock Exchange, for BSE futures, the tick is 0.1 point; the contract size is Rs 50 per index point. Hence, the monetary value is Rs 5. The profit or losses from futures contracts are therefore computed by multiplying Rs 5 by the number of ticks by which the futures price has changed.

Option Trading

Options, since they give the buyer of the instrument a right but not an obligation to exercise the contract, have an advantage of limiting losses while providing scope for unlimited profits from share price movements. Option contracts are entered into when investors foresee a trend in share prices. Many option trading strategies have been formulated for investors to take desired price positions in the market.

Derivative trading strategies are based on the direction and the quantum of movement in the expected share prices. Trading strategies are formulated by a combination of derivative instruments that are available in the market. The buyer of a derivative contract usually gets the benefit of risk reduction of the investment while the seller of a option contract takes a risk for which the premium is paid by the buyer at the time the contract is entered into. The premium, which is paid at the beginning, assumes the form of a financial charge for the writer (or seller) of the option contract, for bearing the inherent risk in the derivative instrument.

Basic option contracts that are available to investors are the call and put options. When an investor expects the share price to increase in the near future, a trading position could be entered into to assure the investor a minimum return from the expected rise. The strategy that the investor would enter into will be to go for a long call or a short put.

A long call gives the buyer the right to buy the share at a predetermined price in the future. Since a bullish market expectation is there, the investor can protect against increased price, when prices go beyond the expectation, by buying now at a predetermined price. When the market becomes bullish in the future as anticipated, and share prices rise above the option strike price, the buyer can exercise the option and benefit from the long call trading strategy. However, even if the market prices do not rise beyond expectation, the investor who had entered into the derivative contract benefits since there is no obligation to buy the share.

A short put is the position taken by the writer of a option contract to sell the shares in the future. In a bullish market, the market prices are expected to go up and when the expected prices are higher than the strike price, the writer of the put option gains by the amount of premium that has been received in the beginning. Without trading in the market the writer of the put contract makes a profit from the willingness to take the risk.

The profit/loss position of these basic option contracts are given in Figure 14.10. When the quantum of rise in prices is anticipated to be vary large then the long call will be the best trading instrument since the profits from the contract will be very high. On the other hand, when the quantum of increase is not expected to be very high, but just moderate, the short put will benefit the investor. However, an investor opting for a short put would have a risk element since the potential loss is unlimited if share prices moves in a contrary direction.

The level of confidence in the expected direction of the share price will help the investor in choosing the strike price of the instrument. When the confidence is quite high and the investor is a risk seeker then a higher premium payment might be accepted by the investor. However, an investor who intends to avoid risk will look for out-of-the money options since premium payments will be low.

When the expected movement in the market is a downward trend, investors can enter into a short call or a long put trading strategy to protect investments against such decline. A long put gives the investor a right to sell shares at a predetermined price. Since the market is expected to move down, the investor assumes a minimum sale price for shares through the put contract. The investor can also enter into a writer’s position of a call option since there is a possibility of gaining the premium amount for taking the risk associated with the share price movement.

The bearish expectations of the market and the profit/loss position for investors from the associated trading strategies are given in Figure 14.11.

A long put assures the investor of large profits as prices decline in the market. The investor can sell securities to the writer at the strike price and buy it from the market at very low prices when the expectation matches actual bearish market movements. An option writer willing to take the risk may enter into a call contract to make a profit by just assuming the risk of a bearish trend in the market. Without making any trade the writer of the call stands to gain the premium amount received for the option contract.

Vertical Spreads

An investor can form spreads by entering into two simultaneous derivative contracts. Vertical spreads involve the simultaneous buying and selling of options on the same underlying instrument for the same expiry date, but with different exercise prices. An investor who estimates the market price movement between a low and a high figure can enter into a spread position to protect against further fluctuations in the market. At the same time, the spread position limits the profit earning opportunity of the investor between the two strike prices entered through the simultaneous contracts.

A spread is formed when

• A call option is bought at a lower price and a call option with same maturity date is sold at a higher price. This option trading is suitable when the investor estimates a bullish trend in the market and hence it is called a bull spread. Prices are expected to be on the rise, but the investor does not foresee a unlimited rise in the price trend.
• A put option is bought at a higher price and a put option with same maturity date is sold at a lower price. When the market expectations are supposed to lower share prices, but not beyond a certain level, an investor can enter into this spread position. This spread position is also termed as a bear spread or a bear-put spread.

Bull Call Spread

A bull spread is also termed as the bull call spread. Option contracts are available with the same expiry date for different strike prices at different premiums. The following call option contracts can be used to create a bull Call spread for BHEL shares.

A call option for BHEL at Rs 190, for a premium of Rs 13.25, with an expiry date of February 27,2003.

A call option for BHEL at Rs 220, for a premium of Rs 1.50, with an expiry date of February 27,2003.

 

Step 1: An investor can take two positions with these two contracts. A call option can be bought at Rs 190 for a payment of Rs 13.25 as premium.

Step 2: The investor can sell a call option contract at Rs 220 for receipt of a premium of Rs 1.50.

Step 3: The net cost for the investor from these two contracts of a payment of Rs 13.25 and a receipt of Rs 1.50 is a net expenditure of Rs 11.75.

 

The minimum loss out of these contracts will be Rs 11.75 when market prices behave unexpectedly and fall below Rs 190. When market prices are above Rs 220, the investor will have both the options that will come up for exercise. As a call writer the investor has to sell the BHEL shares at Rs 220. But since the investor also has bought a call option at Rs 190 for the same share, which also can be exercised and will result in buying the shares at Rs 190 and selling them at Rs 220 on the expiry date. The net amount of receipt for the investor will be the difference of Rs 30.

However, the two contracts had an initial net expenditure of Rs 11.75, when contracts were entered into. Hence, the maximum net profit from the spread position for the investor, when market prices rise above Rs 220, at the time of expiry will be Rs 18.25 per share.

When the market price at the time of expiry moves between these two strike prices (Rs 190-Rs 220), the profit/loss position will also be proportionately less, since the second contract, ie, the call option with a strike price of Rs 220, will not be exercised. The investor can buy the shares at Rs 190 and sell the shares at the market price to gain the difference. Assuming the market price at the expiry date is Rs 215, the call option at Rs 220 will not be exercised, but the investor can exercise the call option at Rs 190 and sell it in the market at Rs 215. The investor receives Rs 25 from the contract. The net expenditure in the beginning was Rs 11.75, hence, the net profit for the investor will be Rs 13.25 per share.

The break-even point for the investor will be when the market price reaches Rs 201.75 (Rs 190 + Rs 11.75). At this point, the investor neither makes a profit nor a loss. When the market price is below this level, but above Rs 190, the net loss position for the investor will be proportionately reduced from the maximum loss of Rs 11.75. Assume, for example, the market price falls to Rs 195, the net position for the investor will be (Rs 195-Rs 190-Rs 11.75) a loss of Rs 6.75.

Figure 14.12 illustrates the profit/loss position for the investor from a bull call spread option-trading strategy at the expiry date.

The time value of the options can be incorporated into the previous figure to provide for the value of options before the expiry date. The time value is the discount factor applied for exercising the option prior to the expiry date. The vertical distance between the prior-to-expiry and expiry date profit/loss position is the time value of the option strategy. The initial expenditure is the time value of the premium for the call option bought and the time value of the premium received for the call option written. Similarly, the profit/ loss position when the anticipated market price moves can also be worked out. This is incorporated in Figure 14.13.

The net time value is positive when the purchased (ie, long) option is at-the-money, but negative when the written (ie, short) option is at-the-money.

Example The SBI call options are available at the following strike prices.

Buys call option with a strike price of Rs 280 at a premium of Rs 18.10, with the expiry date: Februray 27,2003.

Writes call option with a strike price of Rs 340 at a premium of Rs 0.40, with the expiry date: Februray 27,2003

Show the profit/loss position for the investor from a bull call spread.

Buying a call option at the strike price of Rs 280 and selling the call option at the strike price of Rs 340 will give the bull call spread strategy.

The maximum loss from the strategy is when the two contracts cannot be exercised, ie, the market price is below Rs 280. The cost to the investor is (Rs 18.10-Rs 0.40) Rs 17.70.

The maximum profit from the strategy is when two contracts are exercised, ie, the market price is above Rs 340. The profit to the investor is (Rs 340-Rs 280-Rs 17.70) = Rs 42.30.

The break-even situation for the investor will occur when the market price is equal to Rs 297.70 (Rs 280 + Rs 17.70).

Figure 14.14 depicts the above profit/loss position for the investor from the bull call spread strategy.

Bear Put Spread

When prices are expected to decline in the market, a spread strategy will help investor to lock the share price between two prices for a specific time. The bear spread is formed by buying a put option at a higher price and selling a put option at a lower price simultaneously for a share with the same expiry date. The two contracts will have the same expiry date but different strike prices. The following put option contracts available for Digital Global can be used to create a bear put spread trading strategy.

Put option with a strike price of Rs 480, at a premium of Rs 2.00, with the expiry date 27/02/2003.

Put option with a strike price of Rs 660, at a premium of Rs 44.00, with the expiry date 27/02/2003.

 

Step 1: The investor buys a put option with a strike price of Rs 660 and pays a premium of Rs 44.

Step 2: The investor sells a put option with a strike price of Rs 480 and receives a premium of Rs 2.00.

Step 3: The net cost out of these trading is Rs 42.00 (Rs 44.00-Rs 2.00). The options will not be exercised when the market price at expiry date is greater than Rs 660. In that situation the net loss for the investor is the loss of entering into the option contracts ie, Rs 42.

 

When the market price at expiry date is below Rs 480 both the put option contracts will be exercised. The investor will exercise the right to sell the Digital Global shares at Rs 660. The other option buyer will also exercise the right to sell and hence the investor has to buy the Digital Global share at Rs 480. However, the maximum profit from this will be (Rs 660-Rs 480-Rs 42) = Rs 138.

The break-even point (BEP) for the investor will be reached when the market price touches Rs 618 (Rs 660-Rs 42). When the market price is above Rs 618 but below Rs 660, the investor will lose a proportionate amount since the Rs 480 contract will not be exercised but the investor has to buy it at the market price and sell the shares at Rs 660. For example, if the market price on the expiry date is Rs 620, only the put option contract at Rs 660 will be exercised. The difference in the price is Rs 40 (Rs 660-Rs 620); however, the investor had already paid a net amount of Rs 42 on the bear spread. Hence, the net loss for the investor will be Rs 2 (Rs 40-Rs 42). Assume the market price is Rs 640, then the net loss position to the investor will be Rs 22 (Rs 660-Rs 640-Rs 42).

Below the break-even point the investor will have a proportionate profit from the bear put spread trading strategy. Assume the market price is Rs 600, the net profit position for the investor will be (Rs 660-Rs 600-Rs 42) Rs 18. Assume the market price on expiry date had fallen further to Rs 500, the put option at Rs 480 will not be exercised but the option at Rs 660 will be exercised. The net profit position for the investor will be (Rs 660-Rs 500-Rs 42) = Rs 118. The net profit amount will be lesser than the maximum profit of Rs 138. Figure 14.15 presents the profit/loss position for the investor at expiry date for different market prices.

The position of the investor before expiry date will consider the time value of the option contract and hence the profit/loss position for the investor before expiry date will be as shown in Figure 14.16. The maximum loss will be the time value of premium paid minus the time value of premium received. Similarly, the maximum value before the expiry date for other market prices can be computed by applying a discount rate (risk-free rate).

Bull Put Spread

Writing a put option with a high exercise price and buying a put option with a low exercise price creates a bull put spread. A bull put spread is entered into when there is a bullish expectation in the market price of the share. The Infosys put options available can be used to take advantage of the premium difference.

Infosys put option strike price Rs 4,000, at a premium of Rs 29.05, with the expiry date February 27,2003.

Infosys put option strike price Rs 4,800, at a premium of Rs 505.00, with the expiry date February 27,2003.

 

Step 1: Sell a put option at the strike price of Rs 4,800 and receive a premium of Rs 505.

Step 2: Buy a put option at the strike price of Rs 4,000 and pay a premium of Rs 29.05.

Step 3: Since the market price of Infosys shares are expected to rise, the investor can benefit to the extent of the premium differential. For example, if the market price goes up beyond Rs 4,800, both the options will not be exercised and the investor will gain Rs 475.95 (Rs 505-Rs 29.05) per share.

 

On the other hand, if the market price is below the Rs 4,000 level, both the options can be exercised and the loss position of the investor will be (Rs 4,800-Rs 4,000 - Rs 475.95) Rs 324.05. Intermediate market prices will give a proportionate profit/loss to the investor between these two values. This is shown in Figure 14.17.

Bear Call Spread

When the expectations are bearish, an investor can also enter into a bear call spread trading strategy. A bear call spread involves selling a call option with a low exercise price and buying a call option with a high exercise price.

The following call option contracts can be utilised to build a bear call spread of Wipro.

The Wipro call options with a strike price of Rs 1,350 has a premium of Rs 90.00. The Wipro call option with a strike price of Rs 1,400 has a premium of Rs 50.50. Both call options have a 27/02/2003 expiry date. The investor can enter into a bear call spread when he expects a decline in the price of Wipro’s shares.

 

Step 1: Sell a call option at Rs 1,350 and receive a premium of Rs 90.00

Step 2: Buy a call option at Rs 1400 and pay a premium of Rs 50.50.

Step 3: The net profit out of the two simultaneous trades will be Rs 39.50 (Rs 90.00-Rs 50.50). When the market price, at expiry date, goes down below Rs 1350, both contracts are not exercised and the profit to the investor is Rs 39.50. When the market price goes above Rs 1,400, both options are exercised and the net loss to the investor will be (Rs 1350-Rs 1400 + Rs 39.50) Rs 10.50. In between these two market prices the profit/loss will be proportionately less. The break-even point for the investor will occur when the market price reaches Rs 1,389.50 At this price the call option with a strike price of Rs 1,400 will not be exercised, while the call option with a strike price of Rs 1,350 will be exercised. Since the investor has written the call option at Rs 1,350, the investor has to buy the shares at the market price of Rs 1,389.50 and sell it at Rs 1,350 (strike price). The loss from the transaction is Rs 39.50, which is equal to the profit from the premiums. Hence, the net profit/loss to the investor at the expiry date will be zero. Figure 14.18 illustrates the profit/loss position for the investor from the bear call spread trading strategy.

Calendar Spread

The investor can consider the time value of option contracts and enter into two options with different expiry dates. A trader using the calendar spread will sell a near expiry option contract and buy a far expiry contract. In a calendar spread, the trader goes for two call options with the same strike price or two put options with the same strike price. The time value of an option that is very near the expiry date will be almost zero, whereas the time value of the far expiry contract will be more. See Figure 14.19. The investor makes a gain from the difference in time values. The investor can use out-of-the money near expiry options so that the probability of early exercise of these options will be very less, if there is still time for expiry.

The profit/loss position of the investor when the calendar call spread is traded by an investor is given in the Figure 14.19. In a calendar call spread, the investor buys a call option with a far expiry contract and sells a call option with a nearby expiry date. The profit/loss position of the investor for the written call option will be similar to the expiry date profit/loss profile, while the far expiry contract will have the time value as the profit/loss position for the investor. The combination of these profit/loss profiles will be given as the time value of the far expiry dated option (at the time of the nearby expiry contract final day) minus the net premium cost from both the trades.

A calendar spread can also be created with put options. With put options the investor buys a long maturity put option and sells a short maturity put option. The profit pattern is similar to the calendar call option. Towards the first expiry date the value of the short maturity option costs very little for the investor while the long maturity option is valuable and the investor makes a net profit at the time of expiry of the short put option. Figure 14.20 explains the profit/loss position for the investor entering into a put calendar spread.

Butterfly Spread

A butterfly spread takes three call prices all having the same expiry date into consideration. A butterfly call spread is created by buying a call option with a low strike price, another call option with a high strike price, and selling two call options with a strike price in between the high and low strike prices. Usually the call options that are sold are near the current market price. When the share price in the market moves between the low and high prices, the investor makes a profit from the butterfly spread position. When the share price moves nearer to the low and high prices and goes beyond these points the investor incurs a loss, ie, cost of entering into the butterfly strategy. The following example uses a butterfly spread.

The following Sterlite Opticals call options are available to the investor. The current market price of the underlying instrument is Rs 60.

Strike Price	Premium	Expiry Date
55	6.70	28/11/2002
60	3.85	28/11/2002
65	1.95	28/11/2002

The investor buys one call option with a strike price of Rs 55 and Rs 65 and pays a premium of Rs 8.65 (Rs 6.70 + Rs 1.95). The investor also sells two call options at the strike price of Rs 60, receiving Rs 7.70 (Rs 3.85 * 2). The net cost of the strategy is Rs 0.95 (Rs 8.65-Rs 7.70).

When the market price falls below Rs 55, none of the call options are exercised, hence the investor incurs a net loss on the option strategy cost, ie, Rs 0.95. When the market price is above Rs 65, all the option contracts are exercised. The investor buys a call option at Rs 55 and sells one of the call options at Rs 60 and incurs a profit of Rs 5. However, from the other buy option at Rs 65 and sell option at Rs 60, the investor loses Rs 5. Thus, the gross profit/loss from the three options is 0. Here also, the net loss from the strategy, including the premium cost, will be Rs 0.95.

The maximum profit for the investor is when the market price is Rs 60. Only the call option with the strike price of Rs 55 is exercised. Hence, the profit for the investor is Rs 5 less the option strategy cost of Rs 0.95, ie, Rs 4.05.

When the market price is between Rs 55 and Rs 60, the investor’s profit is proportionately reduced since the value yield from the difference in market prices will be lesser than the maximum difference of Rs 5. Similarly when the market price is between Rs 60 and Rs 65, the buy option at Rs 55 is exercised and the two call options at Rs 60 will also be exercised. Hence, the maximum value difference from one buy and sell will be reduced by the loss from the sale of the other call option at Rs 60. For this the investor has to buy the security at market value.

The break-even point for the investor will be two market prices, one between Rs 55 and Rs 60 and the other between Rs 60 and Rs 65. Here the profit/loss situation for the investor will be zero, ie, the price differences are equal to the option strategy cost of Rs 0.95. The break-even points are hence Rs 55.95 and Rs 64.05. Figure 14.21 shows the profit/loss from a butterfly spread using call options.

A butterfly spread created using put options is illustrated below. For the same Sterlite Opticals, with the current market price of Rs 60 the following put options are available.

Strike Price	Premium	Expiry Date
55	1.75	28/11/2002
60	3.05	28/11/2002
65	7.55	28/11/2002

In a butterfly put option spread, the investor buys one put option each with a minimum strike price and a maximum strike price. Here the premium paid by the investor will be Rs 9.30 (Rs 1.75 + Rs 7.55). Again, the investor sells two put options with a strike price of Rs 60 (near market price). This gives the investor a receipt from the put option buyer of Rs 6.10 (3.05 * 2). The net cost from the trading strategy will be (Rs 9.30-Rs 6.10) Rs 3.20.

When the market price is above Rs 65 none of the options will be exercised. The net profit/loss from the strategy will be the loss on premium, ie, Rs 3.20. When the market price is below Rs 55, all the options will be exercised. The investor sells one share at Rs 65 and buys another at Rs 60, resulting in a profit of Rs 5. Similarly, from selling one share at Rs 55 and buying another at Rs 60, the investor loses Rs 5. The net result is the nil value from market price differences and the net loss to the investor is the premium paid, ie, Rs 3.20.

The maximum profit accures to the investor when the market price is Rs 60. At this price, only one put contract is exercised. Hence, the investor sells the put contract at Rs 65 and buys it at the market price of Rs 60, resulting in a value of Rs 5 from price differential. When the cost of option contracts is considered, the net profit to the investor is Rs 1.80.

Similar to the call options, the put contracts also result in reduced profits when the market price moves between Rs 55 and Rs 60 or between Rs 60 and Rs 65. The break-even points for the investor in this case will be the no-profit no-loss situations of Rs 58.20 and Rs 61.80. The profit/loss diagram for these put butterfly spreads is given in Figure 14.22.

The time value of the butterfly spread can be plotted as shown in Figure 14.23.

When the market is expected to move beyond these estimated strike prices the volatility is said to be very high. Such highly volatile situations call for butterfly strategies with reverse buy and sell situations. In highly volatile situations, the investor can sell a call/put option at the low and high prices and buy two call/ put options, at the middle price. In these situations, the profit/loss profile of the investor will show constant profit when the prices are beyond the strike price range and maximum loss when the market price is equal to the middle price. The typical profit/loss profile is given in Figure 14.24.

The time value incorporated into the reverse butterfly spread is shown in Figure 14.25.

When the options with the current price as the middle strike price is entered into the time value of the strategy is highest. The other reason for using options close to being at-the-money (current market price) as the middle options in butterfly spreads is the achievement of a delta that is as close as possible to zero.

Delta is the ratio of the change in the price of a derivative instrument/strategy to the change in the price of the underlying share. The delta of a single call option is positive, while the delta of a put option is negative. In the butterfly strategy the delta, being near zero, gives us delta neutrality.

Example The February 2003 option contracts for Mastek, with the current market price of Rs 571.40, is given in the following table.

Strike Price	Call Premium	Put Premium
510	—	3.55
540	43.60	9.20
570	23.55	21.15
600	12.00	39.25
630	5.85	—

Design a strategy that would give an investor gain from a narrow price range in the security while limiting the maximum possible loss. Indicate the maximum profit, maximum loss, and break-even point(s).

The investor can devise a butterfly spread to gain from a narrow price range. For example, buying a Rs 540 call and buying another Rs 600 call while writing two Rs 570 calls will give the investor scope for making profit from a narrow price range.

The maximum loss is Rs 8.60, the net premium paid. [- Rs 43.60 - Rs 12.00 + (2*Rs 23.50)]

The maximum profit from this trading strategy will be (Rs 570 - Rs 540 - Rs 8.60) Rs 21.40.

The break-even points occur at 570 +/- 21.40, ie, Rs 591.40 and Rs 548.60.

Combinations of Call and Put Options

Market expectations might vary widely and an investor can combine call options with put options to protect against the high volatility in share prices. The popular strategies for trading volatility are devised by combining calls and puts such as straddles, and strangles.

Straddles

Combining a long call and a long put creates a long straddle. The simultaneous purchase of a call and a put on the same security, with the same exercise price, and for the same expiry month results in a long straddle. A short straddle, on the other hand, is the simultaneous sale of a call and put option with the same exercise price and with the same expiry time. An investor going for a long straddle will foresee a high volatility of the underlying share in the future while the investor preferring a short straddle has the opinion that the future volatility will be low. See Figure 14.26 and Figure 14.27.

Suppose that shares in Mahindra and Mahindra are at Rs 99 and that on December 12, January Rs 100 call options carry a premium of Rs 4, while January Rs 100 put options carry a premium of Rs 3. A long straddle could be constructed by simultaneously buying a January Rs 100 call and a January Rs 100 put so as to produce the profit/loss profile illustrated in Figure 14.28. The holder of the long straddle would make net profits if the share price moved outside the range Rs 93-Rs 107 (break-even points). The maximum loss would be Rs 7, the sum of the premiums paid. This loss would be incurred if the share price moved to and stayed at Rs 100.

A short straddle could be produced by means of writing a January Rs 100 call and simultaneously writing a January Rs 100 put. The resulting profit/loss profile is illustrated in Figure 14.29. The seller of the short straddle will make a profit if the share price remains within the range Rs 93-Rs 107 (break-even points). The maximum profit of Rs 5 is the sum of the premiums received.

Thus, the holder of a long straddle hopes for high volatility, whereas the holder of a short straddle desires low volatility. When the investor looks at closing the contract before expiry, this requires consideration of profit/loss profiles that take account of time value.

The time value of the profit/loss profile of the investor entering into the straddle position can be computed. The intrinsic value of the option is the difference in the market price and the strike price. This is the profit/loss profile to the investor, without considering the premium cost. The intrinsic value of an option, hence, is the profit (without consideration of premium) to be obtained from immediate exercise of the option. Option premiums consist of time value as well as intrinsic value. Time value can be looked upon as a payment for the possibility that the intrinsic value might change prior to the expiry date. When an option is closed, rather than exercised, time value is received in addition to the intrinsic value. Figure 14.30 represents the expiry date and prior expiry date profile for a long straddle position. The vertical distance between the two profiles represents the time value.

One of the factors that determine time value is the market expectation of volatility. If it is expected that the price of the share will be highly volatile in the period up to the expiry date of the option, the time value will be relatively high, reflecting the strong possibility of a substantial increase in intrinsic value.

Since call options have positive deltas and put options have negative deltas, combining a call and a put option cancels each other out. This offset results in a situation in which the option premiums, when considered together, show little response to movements in the underlying share price.

Example The Shipping Corporation’s share market price in February is Rs 71.25. The option contracts available for this security are given in the following table.

Strike Price	Calls	Puts
65	7.50	0.85
70	4.00	2.30
75	2.00	5.10

Describe a strategy using options that will result in a profit from a movement of the share price, irrespective of direction, when market expectations of volatility remains high. What might cause a loss to be incurred?

Answer Buy one Rs 70 call at Rs 4.00 and one Rs 70 put for a premium of Rs 2.30. Both these will cost the investor Rs 6.30.

A fall in the security price would cause the investor to exercise the put option. A rise in the security price would make the investor exercise the call option. When market price exceeds Rs 76.30, the investor exercises the call option and makes a profit. When the market price falls below the Rs 63.70 level, the investor exercises the put option and makes a profit.

Losses could be incurred if market expectations of volatility were to decline and thereby make the market price hover between the break-even points of Rs 63.70 and Rs 76.30. The maximum loss of Rs 6.30 will be incurred when the market price touches Rs 70 on expiry of the option.

Strangles

Strangles are similar to straddles but they differ since the two options will have different exercise prices, though the date of expiry is the same. A strangle would typically be constructed using an out-of-the-money call and an out-of-the-money put. It can also be constructed with an in-the-money call and an in-the-money put, or with one option being in-the-money and the other out-of- the-money. However, in the case of a short strangle it must be borne in mind that strategies involving in-the-money options run a relatively high risk of early exercise ie, the short option position could be closed out by an option holder who chooses to exercise the option. The buyer of the strangle is of the opinion that volatility is going to be huge, while the seller of strangle is expecting low volatility. See Figures 14.31 and 14.32.

If shares in M&M are Rs 99, a long strangle on December 10 can be made by buying a January Rs 95 put option for a premium of Rs 1.40 and a January Rs 110 call option for a premium of Rs 3.80. The profit/loss profile of the investor is as follows. The holder of strangle would make a profit if the stock price moved outside the range of Rs 89.80-Rs 115.20. The maximum loss of Rs 5.20, the sum of the premiums paid, would be incurred in the event of the stock price remaining in the range Rs 95-Rs 110. A short strangle can also be created by writing a January Rs 95 put and writing a January Rs 110 call, resulting in an inverse profit/loss profile for the investor. Both these strangles are illustrated Figure 14.33 and Figure 14.34.

Although long and short strangles are suitable for taking positions on volatility, they are more likely to be used for taking positions on changes in market expectations of volatility, with the combining of calls and puts being for the purpose of achieving delta neutrality. The Figure 14.35 illustrates the profit/loss profile of short strangle, with time value due to market expectations of volatility. The intrinsic value is the money immediately lost in the event of the buyer of the option exercising it. The time value reflects the possibility that this potential loss might increase prior to expiry. Expectation of a lower volatility suggests a diminished possibility of intrinsic value rising substantially. Hence, if the market expectation of volatility falls, the time value paid and received when options change hands will also face a similar fall. The vertical distance between prior to expiry and at expiry represents time value.

The buyer of a strangle hopes for an increase in market expectations of share price volatility, which will cause time value to rise and the profit/loss profile to move away from the profile that excludes time value.

Comparison of Volatility Trading Strategies

A comparison of profit/loss profiles for straddles, strangles, and butterflies can be made to identify the subtle differences between the strategies. Figure 14.36 shows the position of an investor from different trading strategies in the market.

Example It is October 18,2002, TISCO shares are quoted at Rs 160 and the option prices are as follows.

Strike Price	Calls	Puts
150	7.25	1.85
160	2.40	6.65
170	0.70	6.00

An investor holds TISCO share and is bullish about its price. Suggest two distinct trading strategies based on the view that the volatility is too high.

A week later the share price is Rs 156 and the option prices are as follows.

Strike Price	Calls	Puts
150	5.85	1.70
160	1.55	7.00
170	0.50	15.00

Calculate the profit/loss on the two strategies and comment on the reasons for the outcomes.

When volatility is high and the market is expected to be bullish, a long straddle position is one trading strategy that can be held by the investor. The investor can buy a call and put at Rs 160 (current market price), creating a long straddle. The cost incurred by the investor in this strategy will be Rs 9.05 (2.40 + 6.65).

Another strategy could be the reverse butterfly strategy. The investor can write a Rs 150 call option and write another call option at Rs 170. In addition, to create the reverse butterfly the investor can buy two call options at Rs 160. The income, to the investor, from this trading strategy will be Rs 3.15 [7.25 + 0.70 -(2 * 2.40)].

One week hence the market price falls to Rs 156. From the holding of the long straddle strategy, the investor Rs 8.55 (1.55 + 7.00). The notional loss to the investor from holding this strategy is (Rs 9.05 -Rs 8.55) Re 0.50.

The reverse butterfly strategy results in a notional cost of Rs 3.25 [-5.85–0.50 + (2 * 1.55)]. The net loss to the investor will be (Rs 3.15 - Rs 3.25) Re 0.10. The investor loses Re 0.10 by closing the strategic position.

When bullish strategies are entered into, but, in reality the market prices behave oppositely by going down, there is a resultant loss to the investor. The volatility of the security is also not very high during that week. This also adds to the loss of the investor. If the price movement had been highly volatile, ie, moved down to Rs 140 (even though bearish) instead of Rs 156, the investor would have had a better trading position.

Derivative trading strategies, to a large extent, depend on the price movement expectations of the investor. Derivative trading strategies will be successful only to the extent that the investor’s forecasts are realistic.

SUMMARY

Risk is inherent in markets. An investor can hedge the prevalent market risk by entering into suitable positions in the derivative markets.

Derivatives, being instruments that help in fixing the traded price for the future, can be combined in different ways to reduce the risk inherent in security trading. The most common and easily understood derivative trading strategies are spreads. The bull and the bear spread help in reducing risk when the investor foresees an increase/decrease in the price within a specific range.

Other strategies are butterflies, straddles, and strangles. These are also referred to as volatile trading strategies. Suitable trading strategies limit the losses and/or profit profile of the investors, thus, helping the investor to reduce the market risk inherent in share prices.

CONCEPTS

• Straddles	• Strangles
• Butterflies	• Vertical Spreads
• Calendar Spreads	• Delta

SHORT QUESTIONS

1. What are the types of derivative contracts?
2. What are the measures of market risk?
3. What are butterfly strategies?
4. What are straddles?
5. What are strangles?

ESSAY QUESTIONS

1. Explain how derivatives help in risk management.
2. Discuss the volatile trading strategies that help an investor to protect his position in the market.

PROBLEMS

1. From the following scenario build an investment strategy for an investor when the market is expected to be bullish.
   
2. From the following scenario build an investment strategy for an investor when the market is expected to be bearish.
   
3. When the market expectations of volatility are very high, what should the trading option be for an investor with put and call options as quoted below:
   
4. Devise the strategy for an investor whose expectations of market volatility are low.
   
5. An investor wishes to take a position to neutralise the delta. Advise.