Chapter 4. Pricing futures. 4.1 The cost of carry model

Transcription

1 Chapter 4 Pricing futures Stock index futures began trading on NSE on the 12th June Stock futures were launched on 9th November The volumes and open interest on this market has been steadily growing. Looking at the futures prices on NSE s market, have you ever felt the need to know whether the quoted prices are a true reflection of the price of the underlying index/stock? Have you wondered whether you could make risk-less profits by arbitraging between the underlying and futures markets? If so, you need to know the cost-of-carry to understand the dynamics of pricing that constitute the estimation of fair value of futures. 4.1 The cost of carry model We use fair value calculation of futures to decide the no-arbitrage limits on the price of a futures contract. This is the basis for the cost-of-carry model where the price of the contract is defined as: F S C where: F Futures price S Spot price C Holding costs or carry costs This can also be expressed as: F S where: r Cost of fi nancing

2 " 50 Pricing futures T Time till expiration If or, arbitrage opportunities would exist i.e. whenever the futures price moves away from the fair value, there would be chances for arbitrage. We know what the spot and futures prices are, but what are the components of holding cost? The components of holding cost vary with contracts on different assets. At times the holding cost may even be negative. In the case of commodity futures, the holding cost is the cost of financing plus cost of storage and insurance purchased etc. In the case of equity futures, the holding cost is the cost of financing minus the dividends returns. Note: In the futures pricing examples worked out in this book, we are using the concept of discrete compounding, where interest rates are compounded at discrete intervals, for example, annually or semiannually. Pricing of options and other complex derivative securities requires the use of continuously compounded interest rates. Most books on derivatives use continuous compounding for pricing futures too. However, we have used discrete compounding as it is more intuitive and simpler to work with. Had we to use the concept of continuous compounding, the above equation would have been expressed as: where: F S r Cost of fi nancing(using continuously compounded interest rate) T Time till expiration e Pricing futures contracts on commodities Let us take an example of a futures contract on a commodity and work out the price of the contract. The spot price of silver is Rs.7000/kg. If the cost of financing is 15% annually, what should be the futures price of 100 gms of silver one month down the line? Let us assume that we re on 1st January How would we compute the price of a silver futures contract expiring on 30th January? From the discussion above we know that the futures price is nothing but the spot price plus the cost-of-carry. Let us first try to work out the components of the cost-of-carry model. 1. What is the spot price of silver? The spot price of silver, S= Rs.7000/kg. 2. What is the cost of financing for a month?. 3. What are the holding costs? Let us assume that the storage cost = 0. In this case the fair value of the futures price, works out to be = Rs.708. F " " $

3 " " 4.2 Pricing equity index futures 51 Under normal market conditions, F, the futures price is very close to. However, on October 19,1987, the US market saw a breakdown in this classic relationship between spot and futures prices. It was the day the markets fell by over 20% and the volume of shares traded on the New York Stock Exchange far exceeded all previous records. For most of the day, futures traded at signifi cant discount to the underlying index. This was largely because delays in processing orders to sell equity made index arbitrage too risky. On the next day, October 20,1987, the New York Stock Exchange placed temporary restrictions on the way in which program trading could be done. The result was that the breakdown of the traditional linkages between stock indexes and stock futures continued. At one point, the futures price for the December contract was 18% less than the S&P 500 index which was the underlying index for these futures contracts! However, the highlight of the whole episode was the fact that inspite of huge losses, there were no defaults by futures traders. It was the ultimate test of the effi ciency of the margining system in the futures market. Box 4.8: The market crash of October 19, 1987 If the contract was for a three-month period i.e. expiring on 30th March, the cost of financing " would increase the futures price. Therefore, the futures price would be $ ". On the other hand, if the one-month contract was for 10,000 kg. of silver instead of 100 gms, then it would involve a non-zero storage cost, and the price of the futures contract would be Rs.708 plus the cost of storage. 4.2 Pricing equity index futures A futures contract on the stock market index gives its owner the right and obligation to buy or sell the portfolio of stocks characterized by the index. Stock index futures are cash settled; there is no delivery of the underlying stocks. In their short history of trading, index futures have had a great impact on the world s securities markets. Indeed, index futures trading has been accused of making the world s stock markets more volatile than ever before. The critics claim that individual investors have been driven out to the equity markets because the actions of institutional traders in both the spot and futures markets cause stock values to gyrate with no links to their fundamental values. Whether stock index futures trading is a blessing or a curse is debatable. It is certainly true, however, that its existence has revolutionized the art and science of institutional equity portfolio management. The main differences between commodity and equity index futures are that: There are no costs of storage involved in holding equity. Equity comes with a dividend stream, which is a negative cost if you are long the stock and a positive cost if you are short the stock. Therefore, Cost of carry = Financing cost - Dividends. Thus, a crucial aspect of dealing with equity futures as opposed to commodity futures is an accurate forecasting of dividends. The better the forecast of dividend offered by a security, the better is the estimate of the futures price.

4 52 Pricing futures Pricing index futures given expected dividend amount The pricing of index futures is also based on the cost-of-carry model, where the carrying cost is the cost of financing the purchase of the portfolio underlying the index, minus the present value of dividends obtained from the stocks in the index portfolio. Example Nifty futures trade on NSE as one,two and three-month contracts. Money can be borrowed at a rate of 15% per annum. What will be the price of a new two-month futures contract on Nifty? 1. Let us assume that M & M will be declaring a dividend of Rs. 10 per share after 15 days of purchasing the contract. 2. Current value of Nifty is 1200 and Nifty trades with a multiplier of Since Nifty is traded in multiples of 200, value of the contract is 200*1200 = Rs.240, If M & M has a weight of 7% in Nifty, its value in Nifty is Rs.16,800 i.e.(240,000 * 0.07). 5. If the market price of M & M is Rs.140, then a traded unit of Nifty involves 120 shares of M & M i.e.(16,800/140). 6. To calculate the futures price, we need to reduce the cost-of-carry to the extent of dividend received. The amount of dividend received is Rs.1200 i.e.(120 * 10). The dividend is received 15 days later and hence compounded only for the remainder of 45 days. To calculate the futures price we need to compute the amount of dividend received per unit of Nifty. Hence we divide the compounded dividend fi gure by Thus, futures price F Rs Pricing index futures given expected dividend yield If the dividend flow throughout the year is generally uniform, i.e. if there are few historical cases of clustering of dividends in any particular month, it is useful to calculate the annual dividend yield. where: F futures price S spot index value r cost of fi nancing q expected dividend yield T holding period

5 4.2 Pricing equity index futures 53 Figure 4.1 Variation of basis over time The fi gure shows how basis changes over time. As the time to expiration of a contract reduces, the basis reduces. Towards the close of trading on the day of settlement, the futures price and the spot price converge. The closing price for the June 28 futures contract is the closing value of Nifty on that day. Price Futures price Spot price t1 t2 Time T Example A two-month futures contract trades on the NSE. The cost of financing is 15% and the dividend yield on Nifty is 2% annualized. The spot value of Nifty What is the fair value of the $ " " $ futures contract? Fair value Rs. $ $ " The cost-of-carry model explicitly defines the relationship between the futures price and the related spot price. As we know, the difference between the spot price and the futures price is called the basis. Nuances As the date of expiration comes near, the basis reduces - there is a convergence of the futures price towards the spot price. On the date of expiration, the basis is zero. If it is not, then there is an arbitrage opportunity. Arbitrage opportunities can also arise when the basis (difference between spot and futures price) or the spreads (difference between prices of two futures contracts) during the life of a contract are incorrect. At a later stage we shall look at how these arbitrage opportunities can be exploited. There is nothing but cost-of-carry related arbitrage that drives the behavior of the futures price. Transactions costs are very important in the business of arbitrage. Note: The pricing models discussed in this chapter give an approximate idea about the true future price. However the price observed in the market is the outcome of the price discovery mechanism (demand supply principle) and may differ from the so-called true price.

6 54 Pricing futures 4.3 Pricing stock futures A futures contract on a stock gives its owner the right and obligation to buy or sell the stocks. Like index futures, stock futures are also cash settled; there is no delivery of the underlying stocks. Just as in the case of index futures, the main differences between commodity and stock futures are that: There are no costs of storage involved in holding stock. Stocks come with a dividend stream, which is a negative cost if you are long the stock and a positive cost if you are short the stock. Therefore, Cost of carry = Financing cost - Dividends. Thus, a crucial aspect of dealing with stock futures as opposed to commodity futures is an accurate forecasting of dividends. The better the forecast of dividend offered by a security, the better is the estimate of the futures price Pricing stock futures when no dividend expected The pricing of stock futures is also based on the cost-of-carry model, where the carrying cost is the cost of financing the purchase of the stock, minus the present value of dividends obtained from the stock. If no dividends are expected during the life of the contract, pricing futures on that stock is very simple. It simply involves multiplying the spot price by the cost of carry. Example SBI futures trade on NSE as one,two and three-month contracts. Money can be borrowed at 15% per annum. What will be the price of a unit of new two-month futures contract on SBI if no dividends are expected during the two-month period? 1. Assume that the spot price of SBI is Rs Thus, futures price F Rs Pricing stock futures when dividends are expected When dividends are expected during the life of the futures contract, pricing involves reducing the cost of carry to the extent of the dividends. The net carrying cost is the cost of financing the purchase of the stock, minus the present value of dividends obtained from the stock. Example M & M futures trade on NSE as one,two and three month contracts. What will be the price of a unit of new two month futures contract on M & M if dividends are expected during the two month period?

7 4.3 Pricing stock futures Let us assume that M & M will be declaring a dividend of Rs. 10 per share after 15 days of purchasing the contract. 2. Assume that the market price of M & M is Rs To calculate the futures price, we need to reduce the cost-of-carry to the extent of dividend received. The amount of dividend received is Rs.10. The dividend is received 15 days later and hence compounded only for the remainder of 45 days. 4. Thus, futures price F Rs. Solved problems Q: The model is used for pricing futures contracts. 1. Black & Scholes 2. Cost of carry 3. Miller 4. Time value A: The correct answer is number 2. Q: Suppose the Nifty spot is at 1000 and two-month futures trade at Suppose the transaction costs involved in placing an index trade are 0.25% and the Nifty index dividends over two months are 0.10%. What is the net rate of return? % per month % per month % per month % per month A: The return on the futures is 1040/1000, i.e. 4%. After adding 0.1% dividends and deducting 0.25% transactions cost, the total return over 2 months works out to be 3.85%. Therefore the net return per month works out to be 1.92%. The correct answer is number 4. Q: What is the riskless profi t that can be earned over two months if the Nifty spot is at 1000 and the two month futures are at Suppose cash can be risklessly invested at 12% p.a. and there are no transaction costs % % % % A: At a riskfree rate of 12%, futures are underpriced. One can make an arbitrage profi t by buying Nifty futures at 1010, selling Nifty spot and investing the 1000 risklessly for two months. At the end of two months this money would grow to be about i.e. a return of ( )/1000. The correct answer is number 3.

8 56 Pricing futures Q: What is the fair value of one month future if the spot value of Nifty is 1150? The money can be invested at 11% p.a. and Nifty gives a dividend yield of 1% per annum A: The fair value is The correct answer is number 2. Q: What is the fair value of one month future if the spot value of Nifty is 1150? The money can be invested at 14% p.a. and Nifty gives a dividend yield of 4% per annum A: The fair value is The correct answer is number 2. Q: The Nifty spot stands at 1260 and the cost of fi nancing is 12% per year. What is the fair value of one-month Nifty futures contracts? A: Using the cost-of-carry model, the price of the futures contract is computed as which is approximately The correct answer is number 2. Q: The Nifty spot stands at 1260 and the cost of fi nancing is 12% per year. The annual dividend yield on the Nifty works out to be 2%. What is the fair value of one-month Nifty futures contracts? A: Using the cost-of-carry model, the price of the futures contract is computed as which is approximately The correct answer is number 4.

9 4.3 Pricing stock futures 57 Q: Nifty futures trade on NSE as one, two and three-month contracts. Spot Nifty stands at BASF which currently trades at Rs.120 has a weight of 5% in Nifty. It is expected to declare a dividend of Rs.20 per share after 15 days of purchasing the contract. The cost of borrowing is 15% per annum. What will be the price of a new two-month futures contract on Nifty? A: Since Nifty stands at 1200, value of the contract is 200*1200 = Rs If BASF has a weight of 5% in Nifty, its value in Nifty is Rs If the market price of BASF is Rs.120, then a traded unit of Nifty involves 100 shares. Thus, the futures price F Rs. The correct answer is number 4. Q: The Tata Tea trades on the spot market at Rs.177. The cost of fi nancing is 12% per year. What is the fair value of one-month futures on Tata Tea? A: Using the cost-of-carry model, the price of the futures contract is computed as which is This could also be computed as which gives approximately the same answer.the correct answer is number 1. Q: The Tata Tea trades on the spot market at Rs.177. The cost of fi nancing is 12% per year. It is expected to pay a dividend of Rs.10, 45 days later. What is the fair value of three-month futures on Tata Tea? A: Using the cost-of-carry model, the price of the futures contract is computed as which is The correct answer is number 2. Q: The ITC trades on the spot market at Rs.720. The cost of fi nancing is 15% per year. What is the fair value of two-month futures on ITC? A: Using the cost-of-carry model, the price of the futures contract is computed as is The correct answer is number 1. which

10 58 Pricing futures Q: The Tata Tea trades on the spot market at Rs.177. The cost of fi nancing is 15% per year. It is expected to pay a dividend of Rs.10, 45 days later. What is the fair value of three-month futures on Tata Tea? A: Using the cost-of-carry model, the price of the futures contract is computed as which is The correct answer is number 1.

11 Chapter 5 Using index futures There are eight basic modes of trading on the index futures market: Hedging 1. Long security, short Nifty futures 2. Short security, long Nifty futures 3. Have portfolio, short Nifty futures 4. Have funds, long Nifty futures Speculation 1. Bullish index, long Nifty futures 2. Bearish index, short Nifty futures Arbitrage 1. Have funds, lend them to the market 2. Have securities, lend them to the market 5.1 Hedging: Long security, short Nifty futures Investors studying the market often come across a security which they believe is intrinsically undervalued. It may be the case that the profits and the quality of the company make it seem worth a lot more than what the market thinks. A stockpicker carefully purchases securities based on a sense that they are worth more than the market price. When doing so, he faces two kinds of risks: 1. His understanding can be wrong, and the company is really not worth more than the market price; or, 2. The entire market moves against him and generates losses even though the underlying idea was correct.

12 60 Using index futures The second outcome happens all the time. A person may buy Reliance at Rs.190 thinking that it would announce good results and the security price would rise. A few days later, Nifty drops, so he makes losses, even if his understanding of Reliance was correct. There is a peculiar problem here. Every buy position on a security is simultaneously a buy position on Nifty. This is because a LONG RELIANCE position generally gains if Nifty rises and generally loses if Nifty drops. In this sense, a LONG RELIANCE position is not a focused play on the valuation of Reliance. It carries a LONG NIFTY position along with it, as incidental baggage. The stockpicker may be thinking he wants to be LONG RELIANCE, but a long position on Reliance effectively forces him to be LONG RELIANCE + LONG NIFTY. Even if you think WIPRO is undervalued, the position LONG WIPRO is not purely about WIPRO; it is also partly about Nifty. Every trader who has a LONG WIPRO position is forced to be an index speculator, even though he may have no interest in the index. It is useful to ask: does the person feel bullish about WIPRO or about the index? Those who are bullish about the index should just buy Nifty futures; they need not trade individual securities. Those who are bullish about WIPRO do wrong by carrying along a long position on Nifty as well. There is a simple way out. Every time you adopt a long position on a security, you should sell some amount of Nifty futures. This offsets the hidden Nifty exposure that is inside every long security position. Once this is done, you will have a position which is purely about the performance of the security. The position LONG WIPRO + SHORT NIFTY is a pure play on the value of WIPRO, without any extra risk from fluctuations of the market index. When this is done, the stockpicker has hedged away his index exposure. The basic point of this hedging strategy is that the stockpicker proceeds with his core skill, i.e. picking securities, at the cost of lower risk. Warning: Hedging does not remove losses. The best that can be achieved using hedging is the removal of unwanted exposure, i.e. unnecessary risk. The hedged position will make less profits than the un-hedged position, half the time. One should not enter into a hedging strategy hoping to make excess profits for sure; all that can come out of hedging is reduced risk. How do we actually do this? 1. We need to know the beta of the security, i.e. the average impact of a 1% move in Nifty upon the security. If betas are not known, it is generally safe to assume the beta is 1. Suppose we take LUPINLAB, whose beta is 1.2, and suppose we have a LONG LUPINLAB position of Rs.200, The size of the position that we need on the index futures market, to completely remove the hidden Nifty exposure, is ,000, i.e. Rs.240, Suppose Nifty is at 1200, and the market lot on the futures market is 200. Hence each market lot of Nifty is Rs.240,000. To sell Rs.240,000 of Nifty we need to sell one market lot. 4. We sell one market lot of Nifty (200 nifties) to get the position: LONG LUPINLAB Rs.200,000 SHORT NIFTY Rs.240,000

13 5.1 Hedging: Long security, short Nifty futures 61 This position will be essentially immune to fluctuations of Nifty. The profi ts/losses position will fully reflect price changes intrinsic to LUPINLAB, hence only successful forecasts about LUPINLAB will benefi t from this position. Returns on the position will be roughly neutral to movements of Nifty. Example 1. Shyam adopts a position of Rs.1 million LONG MTNL on date 5th June He plans to hold the position till the 25th. 2. Suppose the beta of MTNL happens to be Hence he needs a short position of Rs.1.2 million on the index futures market to totally remove his Nifty exposure. 4. On date 5th June 2001, Nifty is 980 and the nearest futures contract (with expiration 28th June 2001) is trading at about Hence, each market lot of the futures (200 nifties) is worth Rs.200,000. To sell Rs.1.2 million of Nifty, we need to sell 6 lots (by rounding off to the nearest market lot). 5. He sells 6 market lots of Nifty (1200 nifties) to get the position: LONG MTNL Rs.1,000,000 SHORT NIFTY Rs.1,200, days later, Nifty crashed because of instability in the government. 7. On Thursday, Shyam unwound both positions. His position on MTNL lost Rs.120,000 since MTNL had dropped to 880,000. His short position on Nifty June futures earned Rs.141,600. Overall, he earned Rs.21,600. Nuances 1. HowdoIfindoutthebetaofasecurity? The betas of major securities are available in the NSE Newsletter or over the Internet on Note that the security prices and betas used in this workbook are only illustrative in nature. 2. What if I am still stuck without a beta estimate? If a beta is not known, it is generally useful to guess that the beta of an unknown security is near 1. In other words, a speculative long position of Rs.500,000 on any security should be accompanied by selling Rs.500,000 of Nifty in order to obtain a complete hedge. This (slightly wrong) hedged position is always much better than a totally un-hedged position (i.e. not selling any Nifty). Of course, knowing the true beta gives the most accurate hedge. 3. Does this only work for index securities? No, this works for any securities in the country. Some index securities have a weak link to the index, and some non index securities have a very tight link with the index. 4. How much risk reduction do I gain? It varies from security to security. The naked LONG SILVERLINE position is around twice the risk of the hedged position LONG SILVERLINE + SHORT NIFTY. The risk reductions obtained range of 25% to 60%. Suppose the daily returns of a security has a variance of. Then the variance of the fully hedged position is where is the standard deviation of daily returns on Nifty. Typically, is around 1.6 percent/day. For example, if SILVERLINE has a variance of 9 and a beta of 1.2, then the fully hedged position has a variance of Through this formula, we can precisely quantify the magnitude of the risk reduction that complete hedging delivers. 5. Will hedging always help if my forecast about the security is wrong? It depends. If the forecast about the security itself is wrong, then hedging is no help. If the forecast goes wrong because Nifty crashes, thena complete hedge will reimburse these losses.

14 62 Using index futures 6. Nifty futures with several different expirations are available at the same time. Which one should I use? There are three criteria: liquidity, expiration date, and potential mispricings: Liquidity Using the most liquid of them (i.e. the one with the tightest bid ask spread) saves money on impact cost. Expiration date If the speculative position is a two week view, then it s convenient if the index futures that is used also has at least two weeks to go. Potential mispricings Finally, it never hurts to be clever and sell a futures contract which is somewhat overpriced. This will not only do the job of hedging, but it could also yield some profi ts out of the mispriced futures. Hence it helps to check the market price of all available futures contracts against their fair values, and try to use the most overpriced contract as part of the hedging. Solved problems Q: The beta of ORIENTBANK is 0.8. A person has a long position of Rs.200,000 of ORIENTBANK. Which of the following gives a complete hedge? 1. SELL 200,000 of Nifty 2. BUY 200,000 of Nifty 3. BUY 160,000 of Nifty 4. SELL 160,000 of Nifty A: A long position in ORIENTBANK of Rs.200,000 is as vulnerable to the index as a long position of Rs.160,000 of Nifty. To neutralize this, the hedger would need to sell Rs.160,000 of Nifty. The correct answer is number 4. Q: The beta of SBI is 0.8. A person has a LONG SBI position of Rs.200,000 coupled with a SHORT NIFTY position of Rs.100,000. Which of the following is true? 1. He has a partial hedge against fluctuations of Nifty 2. He has a complete hedge against fluctuations of Nifty 3. He is bearish on Nifty as well as on SBI 4. He is bullish on Nifty and bearish on SBI 5. This is not a hedge; it is just speculation 6. He is overhedged A: A long position in SBI of Rs.200,000 is as vulnerable to the index as a long position of Rs.160,000 of Nifty. To completely neutralize this, the hedger would need to sell Rs.160,000 of Nifty. He has actually sold Nifty to the extent of only Rs.100,000. Hence he is partially hedged. The correct answer is number 1.

15 5.1 Hedging: Long security, short Nifty futures 63 Q: The beta of STERLITE is 1.3 and the total risk of STERLITE is 9. The daily of Nifty is 1.6. Once complete hedging is done, how much risk are we left with? A: A fully hedged position has total risk (variance) of, which evaluates to 4.6. Hence the risk suffered by the person with a view that STERLITE is undervalued drops from 9 to 4.6. This illustrates the sharp reduction in risk that a stockpicker obtains using the futures. A naked LONG STERLITE position has a variance of 9. The position LONG STERLITE + SHORT NIFTY fully captures the extent to which STERLITE is undervalued, but suffers a total risk of only 4.6. The correct answer is number 2. Q: Hari buys 1000 shares of HPCL at Rs.190 and obtains a complete hedge by shorting 300 nifties at Rs.972 each. He closes out his position at the closing price of the next day; at this point HPCL has dropped 5% and the Nifty futures have dropped 4%. What is the overall profi t/loss of this set of transactions? 1. Profi t of Rs.2, Profi t of Rs.9, Profi t of Rs.9, Profi t of Rs.11,664 A: The HPCL position loses Rs.9,500 and the short position on Nifty earns Rs.11,664. The net profi t on the position is Rs.2,164. The correct answer is number 1. Q: A speculator hopes that ROLTA is going to rise sharply. He has a long position on the cash market of Rs.1 crore on ROLTA. The beta of ROLTA is 1.2. Which of the following positions on the index futures gives him a complete hedge: 1. Long Nifty Rs.1 crore 2. Short Nifty Rs.1 crore 3. Long Nifty Rs.1.2 crore 4. Short Nifty Rs.1.2 crore 5. Do nothing. A: The correct answer is number 4.

16 64 Using index futures Q: A speculator expects that the rupee will depreciate, and hence profi ts of INFOSYSTCH will rise. Hence he does LONG INFOSYSTCH to the tune of Rs.2 lakh. The beta of INFOSYSTCH is How can this speculator completely remove his Nifty exposure? 1. Short Nifty Rs.2.06 lakh 2. Short Nifty Rs.2 lakh 3. Long Nifty Rs.2.06 lakh 4. Long Nifty Rs.2 lakh 5. Do nothing. A: The correct answer is number 1. Q: A speculator expects that the rupee will depreciate, and hence profi ts of PENTSFWARE will rise. Hence he does LONG PENTSFWARE to the tune of Rs.2 lakh. The beta of PENTSFWARE is In order to remove his Nifty exposure, he does SHORT NIFTY to the tune of Rs.2.5 lakh. Which is true: 1. He is overhedged 2. He is underhedged 3. He is completely hedged 4. None of the above A: The correct answer is number 1. Q: The beta of VIKASWSP is 1.2 and the total risk of VIKASWSP is 9. The daily of Nifty is 1.3. One complete hedging is done, how much risk are we left with? A: The correct answer is number 1. Q: Hari buys 1000 shares of HLL at Rs.210 and obtains a complete hedge by shorting 200 Nifties at Rs.1,078 each. He closes out his position at the closing price of the next day; at this point HLL has dropped 2% and the Nifty futures have risen 1%. What is the overall profi t/loss of this set of transactions? 1. Profi t of Rs.6, Loss of Rs.6, Profi t of Rs.4, Profi t of Rs.2,156 A: The correct answer is number 2.

17 5.2 Hedging: Short security, long Nifty futures Hedging: Short security, long Nifty futures Investors studying the market often come across a security which they believe is intrinsically over-valued. It may be the case that the profits and the quality of the company make it worth a lot less than what the market thinks. A stockpicker carefully sells securities based on a sense that they are worth less than the market price. In doing so he faces two kinds of risks: 1. His understanding can be wrong, and the company is really worth more than the market price; or, 2. The entire market moves against him and generates losses even though the underlying idea was correct. The second outcome happens all the time. A person may sell Reliance at Rs.190 thinking that Reliance would announce poor results and the security price would fall. A few days later, Nifty rises, so he makes losses, even if his intrinsic understanding of Reliance was correct. There is a peculiar problem here. Every sell position on a security is simultaneously a sell position on Nifty. This is because a SHORT RELIANCE position generally gains if Nifty falls and generally loses if Nifty rises. In this sense, a SHORT RELIANCE position is not a focused play on the valuation of Reliance. It carries a SHORT NIFTY position along with it, as incidental baggage. The stockpicker may be thinking he wants to be SHORT RELIANCE, but a short position on Reliance on the market effectively forces him to be SHORT RELIANCE + SHORT NIFTY. Even if you think WIPRO is over-valued, the position SHORT WIPRO is not purely about WIPRO; it is also partly about Nifty. Every trader who has a SHORT WIPRO position is forced to be an index speculator, even though he may have no interest in the index. It is useful to ask: does the person feel bearish about WIPRO or about the index? Those who are bearish about the index should just sell nifty futures; they need not trade individual securities. Those who are bearish about WIPRO do wrong by carrying along a short position on Nifty as well. There is a simple way out. Every time you adopt a short position on a security, you should buy some amount of Nifty futures. This offsets the hidden Nifty exposure that is inside every short security position. Once this is done, you will have a position which is purely about the performance of the security. The position SHORT WIPRO + LONG NIFTY is a pure play on the value of WIPRO, without any extra risk from fluctuations of the market index. When this is done, the stockpicker has hedged away his index exposure. The basic point of this hedging strategy is that the stockpicker proceeds with his core skill, i.e. picking securities, at the cost of lower risk. Warning: Hedging does not remove losses. The best that can be achieved using hedging is the removal of unwanted exposure, i.e. unnecessary risk. The hedged position will make less profits than the unhedged position, half the time. One should not enter into a hedging strategy hoping to make excess profits for sure; all that can come out of hedging is reduced risk. How do we actually do this? 1. We need to know the beta of the security, i.e. the average impact of a 1% move in Nifty upon the security. If betas are not known, it is generally safe to assume the beta is 1. Suppose we take LUPINLAB, where the beta is 1.2, and suppose we have a SHORT LUPINLAB position of Rs.200,000.

18 66 Using index futures 2. The size of the position that we need on the index futures market, to completely remove the hidden Nifty exposure, is ,000, i.e. Rs.240, Suppose Nifty is at 1200, and the market lot on the futures market is 200. Hence each market lot of Nifty is Rs.240,000. To long Rs.240,000 of Nifty we need to buy one market lot. 4. We buy one market lot of Nifty (200 nifties) to get the position: SHORT LUPINLAB Rs.200,000 LONG NIFTY Rs.240,000 This position will be essentially immune to fluctuations of Nifty. The profi ts/losses position will fully reflect price changes intrinsic to LUPINLAB, hence only successful forecasts about LUPINLAB will benefi t from this position. Returns on the position will be roughly neutral to movements of Nifty. Example 1. Shyam adopts a position of Rs.1 million SHORT MTNL on date 1st April He plans to hold the position till Thursday the 24th. 2. The beta of MTNL happens to be Hence he needs a long position of Rs.1.2 million on the index futures market to totally remove his Nifty exposure. 4. On date 1st April 97, Nifty is 980 and the nearest futures contract (with expiration 24th April) is trading at about Hence, each market lot of the futures (200 nifties) is worth Rs.200,000. To buy Rs.1.2 million of Nifty, we need to buy 6 lots (by rounding off to the nearest market lot). 5. He buys 6 market lots of Nifty (1200 nifties) to get the position: SHORT MTNL Rs.1,000,000 LONG NIFTY Rs.1,200, days later, Nifty rose because of stable political outlook. 7. On Thursday, Shyam unwound both positions. His position on MTNL lost Rs.120,000 since MTNL had gone up to 1,120,000. His short position on Nifty April futures earned Rs.93,600. Overall, he lost Rs.26,400. Solved problems Q: The beta of ORIENTBANK is 0.8. A person has a short position of Rs.200,000 of ORIENTBANK. Which of the following gives a complete hedge? 1. SELL 200,000 of Nifty 2. BUY 200,000 of Nifty 3. BUY 160,000 of Nifty 4. SELL 160,000 of Nifty 5. Do nothing A: A short position in ORIENTBANK of Rs.200,000 is as vulnerable to the index as a short position of Rs.160,000 of Nifty. To neutralize this, the hedger would need to buy Rs.160,000 of Nifty. The correct answer is number 3.

19 5.2 Hedging: Short security, long Nifty futures 67 Q: The beta of SBI is 0.8. A person has a SHORT SBI position of Rs.200,000 coupled with a LONG NIFTY position of Rs.100,000. Which of the following is true? 1. He has a partial hedge against fluctuations of Nifty 2. He has a complete hedge against fluctuations of Nifty 3. He is bearish on Nifty as well as on SBI 4. He is bullish on Nifty and bearish on SBI 5. This is not a hedge; it is just speculation 6. He is overhedged A: A short position in SBI of Rs.200,000 is as vulnerable to the index as a short position of Rs.160,000 of Nifty. To completely neutralize this, the hedger would need to buy Rs.160,000 of Nifty. He has actually bought Nifty to the extent of only Rs.100,000. Hence he is partially hedged. The correct answer is number 1. Q: The beta of STERLITE is 1.3 and the total risk of STERLITE is 9. The daily of Nifty is 1.6. One complete hedging is done, how much risk are we left with? A: A fully hedged position has total risk (variance) of, which evaluates to 4.6. Hence the risk suffered by the person with a view that STERLITE is undervalued drops from 9 to 4.6. This illustrates the sharp reduction in risk that a stockpicker obtains using the futures. A naked SHORT STERLITE position has a variance of 9. The position SHORT STERLITE + LONG NIFTY fully captures the extent to which STERLITE is undervalued, but suffers a total risk of only 4.6. The correct answer is number 2. Q: Gopal sells 1000 shares of HPCL at Rs.190 and obtains a complete hedge by buying 300 nifties at Rs.972 each. He closes out his position at the closing price of the next day; at this point HPCL has risen 5% and the Nifty futures have risen 4%. What is the overall profi t/loss of this set of transactions? 1. Profi t of Rs.2, Profi t of Rs.9, Profi t of Rs.9, Profi t of Rs.11,664 A: The HPCL position loses Rs.9,500 and the long position on Nifty earns Rs.11,664. The net profi t on the position is Rs.2,164. The correct answer is number 1.

20 68 Using index futures Q: A speculator thinks that ROLTA is going to crash sharply. He has a short position on the cash market of Rs.1 crore on ROLTA. The beta of ROLTA is 1.2. Which of the following positions on the index futures gives him a complete hedge? 1. Long Nifty Rs.1 crore 2. Short Nifty Rs.1 crore 3. Long Nifty Rs.1.2 crore 4. Short Nifty Rs.1.2 crore 5. Do nothing. A: The correct answer is number 3. Q: A speculator expects that the rupee will appreciate, and hence profi ts of INFOSYSTCH will fall. Hence he does SHORT INFOSYSTCH to the tune of Rs.2 lakh. The beta of INFOSYSTCH is How can this speculator completely remove his Nifty exposure? 1. Short Nifty Rs.2.06 lakh 2. Short Nifty Rs.2 lakh 3. Long Nifty Rs.2.06 lakh 4. Long Nifty Rs.2 lakh 5. Do nothing. A: The correct answer is number 3. Q: A speculator expects that the rupee will appreciate, and hence profi ts of PENTSFWARE will fall. Hence he does SHORT PENTSFWARE to the tune of Rs.2 lakh. The beta of PENTSFWARE is In order to remove his Nifty exposure, he does LONG NIFTY to the tune of Rs.2.5 lakh. Which is true: 1. He is overhedged 2. He is underhedged 3. He is completely hedged 4. None of the above A: The correct answer is number 1. Q: The beta of ITC is 1.3 and the total risk of ITC is 9. The daily of Nifty is 1.3. One complete hedging is done, how much risk are we left with? A: The correct answer is number 3.

21 5.3 Hedging: Have portfolio, short Nifty futures 69 Q: Hari sells 1000 shares of HLL at Rs.210 and obtains a complete hedge by buying 200 Nifties at Rs.1078 each. He closes out his position at the closing price of the next day; at this point HLL has risen 2% and the Nifty futures have fallen 1%. What is the overall profi t/loss of this set of transactions? 1. Profi t of Rs.6, Loss of Rs.6, Profi t of Rs.4, Profi t of Rs.2,156 A: The correct answer is number Hedging: Have portfolio, short Nifty futures The only certainty about the capital market is that it fluctuates! A lot of investors who own portfolios experience the feeling of discomfort about overall market movements. Sometimes, they may have a view that security prices will fall in the near future. At other times, they may see that the market is in for a few days or weeks of massive volatility, and they do not have an appetite for this kind of volatility. The union budget is a common and reliable source of such volatility: market volatility is always enhanced for one week before and two weeks after a budget. Many investors simply do not want the fluctuations of these three weeks. This is particularly a problem if you need to sell shares in the near future, for example, in order to finance a purchase of a house. This planning can go wrong if by the time you sell shares, Nifty has dropped sharply. When you have such anxieties, there are two alternatives: 1 Sell shares immediately. This sentiment generates panic selling which is rarely optimal for the investor. 2 Do nothing, i.e. suffer the pain of the volatility. This leads to political pressures for government to do something when security prices fall. In addition, with the index futures market, a third and remarkable alternative becomes available: 3 Remove your exposure to index fluctuations temporarily using index futures. This allows rapid response to market conditions, without panic selling of shares. It allows an investor to be in control of his risk, instead of doing nothing and suffering the risk. The idea here is quite simple. Every portfolio contains a hidden index exposure. This statement is true for all portfolios, whether a portfolio is composed of index securities or not. In the case of portfolios, most of the portfolio risk is accounted for by index fluctuations (unlike individual securities, where only 30 60% of the securities risk is accounted for by index fluctuations). Hence a position LONG PORTFOLIO + SHORT NIFTY can often become one tenth as risky as the LONG PORTFOLIO position! Suppose we have a portfolio of Rs.1 million which has a beta of Then a complete hedge is obtained by selling Rs.1.25 million of Nifty futures. Warning: Hedging does not always make money. The best that can be achieved using hedging is the removal of unwanted exposure, i.e. unnecessary risk. The hedged position will make less profits than the unhedged position, half the time. One should not enter into a hedging strategy hoping to make excess profits for sure; all that can come out of hedging is reduced risk.

22 70 Using index futures How do we actually do this? 1. We need to know the beta of the portfolio, i.e. the average impact of a 1% move in Nifty upon the portfolio. It is easy to calculate the portfolio beta: it is the weighted average of securities betas. Suppose we have a portfolio composed of Rs.1 million of Hindalco, which has a beta of 1.4 and Rs.2 million of Hindustan Lever, which has a beta of 0.8, then the portfolio beta is ( )/3 or 1. If the beta of any securities is not known, it is safe to assume that it is The complete hedge is obtained by adopting a position on the index futures market which completely removes the hidden Nifty exposure. In the above case, the portfolio is Rs.3 million with a beta of 1, hence we would need a position of Rs.3 million on the Nifty futures. 3. Suppose Nifty is 1250, and the market lot on the futures market is 200. Each market lot of Nifty costs Rs.250,000. Hence we need to sell 12 market lots, i.e Nifties to get the position: LONG PORTFOLIO Rs.3,000,000 SHORT NIFTY Rs.3,000,000. This position will be essentially immune to fluctuations of Nifty. If Nifty goes up, the portfolio gains and the futures lose. If Nifty goes down, the futures gain and the portfolio loses. In either case, the investor has no risk from market fluctuations when he is completely hedged. The investor should adopt this strategy for the short periods of time where (a) the market volatility that he anticipates makes him uncomfortable, or (b) when his financial planning involves selling shares at a future date and would be affected if Nifty drops. It does not make sense to use this strategy for long periods of time if a two year hedging is desired, it is better to sell the shares, invest the proceeds, and buy back shares after two years. This strategy makes the most sense for rapid adjustments. Another important choice for the investor is the degree of hedging. Complete hedging eliminates all risk of gain or loss. Sometimes the investor may be willing to tolerate some risk of loss so as to hang on to some risk of gain. In that case, partial hedging is appropriate. The complete hedge may require selling Rs.3 million of the futures, but the investor may choose to only sell Rs.2 million of the futures. In this case, two thirds of his portfolio is hedged and one third of the portfolio is held unhedged. The exact degree of hedging chosen depends upon the appetite for risk that the investor has. Example 1. On 25 May 2001, Shyam has a portfolio composed of fi ve securities: ITCHOTEL (100 shares, value Rs ), ORIENTBANK (200 shares, value Rs.68.25), CIPLA (100 shares, value Rs ), LUPINLAB (200 shares, value Rs ), and SIEMENS (200 shares, value Rs ). The total portfolio value is 187,085 and the fi ve securities have weights (5.98%, 7.29%, 45.31%, 16.02%, 25.40%). Shyam does not want to worry about budget-related fluctuations from 26 May 2001 till 10 June The fi ve securities have the following betas: ITCHOTEL (beta 0.59), ORIENTBANK (beta 0.90), CIPLA (beta 0.75), LUPINLAB (beta 1.13), and SIEMENS (beta 1.10). Hence the portfolio beta works out to (0.0598* * * * *1.10) or For complete hedging he will need to sell futures worth 0.90 * 187,085, i.e. Rs.168, On 25 May 2001, Nifty is at 1, So he decides to sell 200 Nifties.

23 5.3 Hedging: Have portfolio, short Nifty futures 71 Table 5.1 Example of hedging a portfolio This example deliberately uses a small portfolio of small securities (each of the securities in this example has a market capitalization of below Rs.200 crore); in practice, the effectiveness of hedging would be greater with larger portfolios of larger securities. The hedging strategy is designed to dodge budget related volatility for the budget announcement of 1 June The hedging strategy is initiated on 25 May 2001 and ended on 10 June Over this period, the portfolio loses Rs or 17.63%. Security 25 May June 2001 Profi t/loss ITCHOTEL OREINTBANK CIPLA LUPINLAB SIEMENS Portfolio 187, (17.63%) Nifty (14.25%) 4. Hence Shyam supplements his portfolio with a short position on the Nifty futures with expiry on 25th JUNE worth Rs.224, On 10 June he buys back futures at a lower price and ends his hedge (see Table 5.1). His profi ts on the futures hedging was Rs.32,010 and his losses on the portfolio were Rs.32,990. Thus the net loss is Rs If he had not hedged, he would have lost 32,990. In this example, the budget announcement led to a drop in Nifty, so the short position on the futures market generated profits. If the budget announcement had led to a rise in Nifty, then the investor would have gained money on his securities portfolio, and lost money on the futures position. In either event, he would be hedged, i.e. he would neither gain nor lose from index fluctuations. Solved problems Q: A portfolio is composed of Rs.1000 invested in a securities with beta 1.1 and Rs.1000 invested in a securities with beta 0.8. What is the portfolio beta? A: The correct answer is number 3.

24 72 Using index futures Q: On 1 Jan 2001, an investor has a portfolio worth Rs.1 million which has a beta of 1.3. He will need money in middle March as there is a marriage in the family. So he wants to totally remove his equity market risk. The investor wants to be over cautious so he sells Rs.2 million of the Nifty futures. What has he achieved? 1. He is partially hedged. 2. He is completely hedged. 3. He is overhedged (he has effectively become a speculator betting that Nifty will drop). 4. None of the above A: To obtain a market neutral position requires selling 1.3 Rs.1 million or Rs.1.3 million of the Nifty futures. Over and above this, the remaining Rs.0.7 million is a bet that Nifty will drop. Even the most over cautious hedger does not benefi t by a larger sell position on the index futures market than the formula specifi es he just becomes a speculator. (Conversely, if a short position smaller than Rs.1.3 million is taken on the index futures market, the investor is speculating that Nifty will rise). The only way to not speculate is to completely hedge. The correct answer is number 3. Q: When the nuclear bombs go off, an investor with $1 billion invested in India becomes fundamentally gloomy about India and wants to embark a hedging program for the next three years. He will sell $1 billion of Nifty futures now, and constantly initiate new futures positions as old ones expire. What is the major problem with this strategy? 1. He suffers from rollover risk of getting into new positions on the futures positions. 2. He will have to recalculate his beta from time to time when adopting new futures positions. 3. He will suffer market impact cost selling $1 billion of the Nifty futures. 4. He would just be better off liquidating his portfolio, staying out for 3 years, and then getting back into equity. A: All the alternatives have a grain of truth in them. But the most powerful criticism is number 4. It is cheaper to implement long duration changes of position by trading in the equity cash market. The index futures is best suited for rapid, short term changes in position. The correct answer is number 4. Q: On 1 Jan 2001, an investor has a portfolio worth Rs.2 million which has a beta of 0.5. He needs money in middle February as there is a marriage in the family. So he wants to totally remove his equity market risk. What is the correct hedging strategy? 1. Short Nifty futures Rs.1 million, February expiration 2. Short Nifty futures Rs.1.3 million, March expiration 3. Buy Nifty futures Rs.1 million, February expiration 4. Buy Nifty futures Rs.1.3 million, March expiration A: The correct answer is number 1.