# Chapter 6 Single Stock Futures and Stock Index

• Slides: 35

Chapter 6 Single Stock Futures and Stock Index Futures © 2011 Dorling Kindersley (India) Pvt. Ltd

Objectives of the Chapter Understanding what a single stock future is What the uses of single stock futures are How such futures are priced What stock indexes and index futures are What the uses of stock index futures are How stock index futures are priced The concept of index arbitrage and portfolio insurance © 2011 Dorling Kindersley (India) Pvt. Ltd

Single Stock Futures Single stock futures are those with the stock of a company as the underlying asset By taking short or long positions in single stock futures, the investor agrees to either sell or buy a specified number of stocks at the prevailing price in the futures market at the time of agreement, at the maturity date © 2011 Dorling Kindersley (India) Pvt. Ltd

Specifications of Single-Stock Futures Listed in the NSE/BSE Trading cycle of three months Expiry date is the last Thursday of the month Contract size is specified by the exchange Daily settlement price is the weighted average of prices in the last half-hour of trading Subject to marking-to-market on a daily basis Final settlement will be in cash, not delivery © 2011 Dorling Kindersley (India) Pvt. Ltd

Example to Calculate Margin and Final Settlement ICICI March Futures selling at INR 1230 on Feb 1 Contract size = 175 shares Margin = 5% of contract value ICICI share price on March 28, contract maturity is INR 1260 Calculate the settlement amount on March 28: Settlement amount = (1260 – 1230)*175 = INR 5, 250 © 2011 Dorling Kindersley (India) Pvt. Ltd

Hedging with Single Stock Futures I Single stock futures can be used to hedge the price risk of the shares of a company If an investor holds stock and expects the price to drop, he will go for a short hedge by selling futures If an investor plans to buy the shares at a future tme and expects the price to increase, he will go for a long hedge by buying futures © 2011 Dorling Kindersley (India) Pvt. Ltd

Hedging with Single Stock Futures II © 2011 Dorling Kindersley (India) Pvt. Ltd

Example of Short Hedge with Stock Futures On Jan 10, you own 2400 shares of Canara Bank, and are planning to sell them on February 25. The contract size is 800 shares. February futures expiring on February 25 are priced at INR 272 and you take short position in futures. On February 25, Canara Bank shares are selling at INR 265. What is the net price received per share if you sell them on February 25? Cash settlement received = (272 – 265)*800*3 = INR 16, 800 Sales receipt = 265*800*3 = INR 636, 000 Net receipt per share = 652, 800 © 2011 Dorling Kindersley (India) Pvt. Ltd

Example of Long Hedge with Stock Futures On January 10, Biocon Futures are selling at INR 245. 00, and you plan to buy 7, 200 shares on February 25 when Feb futures expire. Contract size for Biocon = 1800 shares On February 25, Biocon sells for INR 270. You would go for a long hedge buying 4 Biocon futures at INR 245 On February 25, you receive a cash settlement of 4*1800*(270 -245) = INR 180, 000 Payment for 7200 shares = 7200 * 270 = 1, 944, 000 Net payment = 1, 764, 000/7200 = INR 245 © 2011 Dorling Kindersley (India) Pvt. Ltd

Risks in Hedging Using Stock Futures Stock futures will protect against downside risk, but all upside potential will be lost If the price moves in favour of the hedger, hedging will result in a loss compared to not hedging at all The hedger should decide whether to hedge or not based on their expectations of future price movement Other risk is basis risk, which arises when Futures are not available on the shares you want to hedge The number of shares to be hedged is not an exact integer multiple of the future contract size The time to end-of-exposure is different from contract maturity © 2011 Dorling Kindersley (India) Pvt. Ltd

Speculation Using Stock Futures Speculators believe that the price will move in a particular direction over a short period of time Stock futures are cheap means of speculating on share price movement If price is expected to move higher or lower, a long or short position respectively will be taken in futures Speculation is risky, as losses can be high if the price moves in the opposite direction © 2011 Dorling Kindersley (India) Pvt. Ltd

Example of Speculation Using Stock Futures IOC shares are selling at INR 800 on March 1. April futures with a contract size of 600 shares are priced at INR 820. You believe that IOC share price will increase to INR 840 by March 5 and want to speculate You can take a long position in April futures If the IOC share price on March 5 is INR 840, and April futures are priced at INR 862, then the speculative gain by closing futures on March 5 = 600*(862 – 820) = INR 25, 200 If the IOC share price falls instead to INR 780 by March 5, causing the futures price to be at INR 792, the loss would be 600*(820 – 792) = INR 16, 800 © 2011 Dorling Kindersley (India) Pvt. Ltd

Pricing of Stock Futures Stock futures on stocks that do not pay dividends during futures are priced based on cost-of-carry model as: F 0 = S 0 * er. T where r = risk-free interest rate and T = maturity of futures in years If the stock pays dividends of D at time t, F 0 = S 0 * er. T – D * er(T – t) © 2011 Dorling Kindersley (India) Pvt. Ltd

Pricing of Stock Futures – Example ICICI Bank shares are selling at INR 1250 on January 1 Feb futures expiring on February 27 are available Risk-free rate = 6%/year Futures price = 1250 * e(0. 06)*(58/365) = INR 1261. 98 If ICICI pays a dividend of INR 10 on Jan 21, then Futures price = 1250* e(0. 06)*(58/365) – 10 * e(0. 06)(58 -21/365) = INR 1251. 91 © 2011 Dorling Kindersley (India) Pvt. Ltd

Stock Futures and Arbitrage Pricing relationship is theoretical value based on current share price If the actual futures price is different from theoretical value, arbitrage opportunity exists If futures are overvalued, sell them and buy shares If futures are undervalued, buy futures and short-sell shares Futures price may be based on expectations about futures and arbitrage may not be possible © 2011 Dorling Kindersley (India) Pvt. Ltd

Arbitrage Example IOC shares are selling at INR 800 on March 1 April IOC futures are priced at INR 820 with maturity on April 27 Theoretical futures value: 800 * e(0. 06)*(58/365) = INR 810. 23 Futures are overvalued and hence, one would sell futures and buy shares On March 2, IOC shares are selling at INR 810 and futures are selling at a theoretical value of INR 820. 18. One would close the position in futures and sell shares. Gain from shares: INR 10 Loss from futures: INR 0. 18 Net gain: INR 9. 82 © 2011 Dorling Kindersley (India) Pvt. Ltd

Stock Futures and Insurance Stock futures can be used to insure a minimum value for the share price in the future This can be accomplished by borrowing money at risk- free rate, selling futures and buying shares This strategy will provide a known value of shares at futures maturity © 2011 Dorling Kindersley (India) Pvt. Ltd

Stock Futures and Insurance -Example India Cements shares are priced at INR 135 on January 1. The contract size is 1450. January futures, with expiry on January 29, are priced at INR 135. 75. The risk-free rate is 7%. You sell the futures on January 1. Value of portfolio on January 29: Share price Value of Shares Gain from Futures Interest Paid Value of Portfolio 130 188500 8337. 50 1091. 73 19575. 77 135 195750 1087. 50 1091. 73 195745. 77 140 203000 -6162. 50 1091. 73 195745. 77 © 2011 Dorling Kindersley (India) Pvt. Ltd

Stock Futures and Investment Using stock futures and risk-free investment, one can get the same value as the value of investing in shares directly Using this principle, one can create synthetic positions as follows: Long futures long stock + Risk-Free Borrowing Short futures short stock + risk-free borrowing Long stock long futures + risk-free investment Short stock short futures + risk-free borrowing © 2011 Dorling Kindersley (India) Pvt. Ltd

Stock Indices Index captures the overall behaviour of a group of stocks Index is created by selecting a group of stocks that are representative of the whole market, or a specified sector Index backs the changes in the value of portfolio of stocks Based on index, index funds, index futures and options are created © 2011 Dorling Kindersley (India) Pvt. Ltd

Index Futures Index futures use a particular stock index as the underlying asset Index futures are used to hedge equity portfolio risk Index futures are also used for speculative purposes These can also be used for portfolio insurance © 2011 Dorling Kindersley (India) Pvt. Ltd

Contracts Traded in India Index Futures Contract Multiplier BSE 30 Sensex Futures 15 BSE Sensex Mini Futures 5 BSE Teck Futures 124 BSE Bankex Futures 25 BSE Oil and Gas Futures 38 NSE CNX Nifty Futures 50 NSE CNX Nifty Mini Futures 20 NSE CNX IT Futures 100 NSE Bank Nifty Futures 50 NSE Nifty Midcap 50 Futures 300 © 2011 Dorling Kindersley (India) Pvt. Ltd

Example of How Index Futures Work CNX Nifty Index is at 5200 on December 1 CNX Nifty Index futures with expiry on December 28 is at 5232 If CNX Nifty Index is at 5300 on December 28, the long hedger will gain, and the short hedger will lose Value of futures on December 1 = 5232 * 50 = INR 261, 600 Value of futures on December 28 = 5300 * 50 = INR 265, 000 Gain for long hedger = (265000 – 261600) = INR 3400 Loss for short hedger = (261600 – 265000) = INR 3400 The long hedger will bet that the index will increase, and the short hedger will bet that the index will decrease © 2011 Dorling Kindersley (India) Pvt. Ltd

Pricing of Index Futures Index futures are priced using the cost of a carry model, as Or, Where D* = present value of dividends from all stocks, and d = dividend yield on the index © 2011 Dorling Kindersley (India) Pvt. Ltd

Example of Pricing on Index Futures On December 1, CNX Nifty Index is at 5200. CNX Nifty futures with maturity on December 28 and January 25 are available. The risk-free rate is 8% The dividend yield on the index is 2% December futures price = 5200*exp [(8%–%)28/365 ] = 5224 January Futures Price = 5200*exp [(8%– 2%)56/365] = 5248 © 2011 Dorling Kindersley (India) Pvt. Ltd

Speculation Using Index Futures Speculators who believe that the market as a whole will perform better in the future will buy index futures, and will gain if the index value increases beyond the contracted futures price Speculators who believe that the market as a whole will perform poorly in the future will sell index futures, and will gain if the index value decreases © 2011 Dorling Kindersley (India) Pvt. Ltd

Portfolio Insurance Using Index Futures Index futures can be used to provide a minimum futures value Portfolio insurance strategy calls for going short in futures so that gain in futures will exactly offset the loss, and vice versa such that the loss in futures will exactly offset the gain © 2011 Dorling Kindersley (India) Pvt. Ltd

Index Arbitrage Theoretical price = Ft = St e–(r – d)(T – t) If the market value of futures is different from theoretical value, arbitrage opportunity arises If market value exceeds theoretical value, one should sell futures and buy underlying shares of the index using risk-free borrowing On the other hand if the market value is less than theoretical value, one should buy futures, short-sell underlying shares of the index, and invest in risk-free securities © 2011 Dorling Kindersley (India) Pvt. Ltd

Program Trading Program trading refers to automatic trading triggered by computers whenever there is an index arbitrage opportunity © 2011 Dorling Kindersley (India) Pvt. Ltd

Hedging Portfolio Value Using Index Futures One would hedge portfolio value by selling index futures This strategy provides gains from futures if the market index goes down Optimal number of futures = Where b = beat of the portfolio, S = portfolio value, and F = value of futures contract = futures price x multiplier © 2011 Dorling Kindersley (India) Pvt. Ltd

Example of Hedging Portfolio Value On January 1, portfolio value = INR 500, 000 Nifty Index = 5250 Risk-free rate = 8%; dividend yield = 2% March futures at 5325. 62, expiry on March 28 Value of futures = 5325. 62 * 50 = INR 266281 Beta of portfolio = 1. 2 Number of contracts to sell = (1. 2 * 500, 000) /266281 = 2253 On Feb 28, Nifty is at 5100 Futures price would be 5107. 83 © 2011 Dorling Kindersley (India) Pvt. Ltd

Example of Hedging Portfolio Value: Value of Portfolio Change in index = (5250 – 5100)/5250 = -2. 857% Dividend yield = 2% per year = 2 (59/365) = 0. 32% Return on index = -2. 857% + 0. 32% = -2. 527% Expected return on portfolio = 8% (59/365) + 1. 2 [-2. 527 – (8% (59/365) ) = -3. 3% Portfolio value = 500, 00 (1 – 3. 3%) = 483, 503, 718 Gain from futures = 2253*50 (5325. 62 – 5107. 83) = 24, 534, 044 Hedged portfolio value = 483, 503, 718 + 24, 534, 044 Hedged portfolio value = 508, 031, 762 © 2011 Dorling Kindersley (India) Pvt. Ltd

Adjusting Equity Beta measures the sensitivity of a portfolio return to market return If the market is likely to do well, the appropriate strategy is to increase the beta of the portfolio If the market is likely to fall, one should decrease the portfolio beta Adjusting beta by buying or selling shares is costly Can be accomplished using futures © 2011 Dorling Kindersley (India) Pvt. Ltd

Adjusting Equity Beta Using Futures If the beta is to be increased, NF will be positive, and futures must be bought If the beta is to be decreased, NF will be negative, and futures must be sold © 2011 Dorling Kindersley (India) Pvt. Ltd

Issues in Index Futures Index underlying futures may not match with a portfolio Futures may not be valued correctly The number of contracts will be rounded Beta may be inaccurate Hedge may have to be lifted before maturity Borrowing and lending rates might differ © 2011 Dorling Kindersley (India) Pvt. Ltd