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

2. 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

3. 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
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4. 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
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5. 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
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6. 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
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7. Hedging with Single Stock Futures II
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8. 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
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9. Example of Long Hedge with Stock Futures
On January 10, Biocon Futures are selling at INR , 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*( ) = INR 180,000
Payment for 7200 shares = 7200 * 270 = 1,944,000
Net payment = 1,764,000/7200 = INR 245
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10. 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
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11. 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
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12. 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
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13. Pricing of Stock Futures
Stock futures on stocks that do not pay dividends during futures are priced based on cost-of-carry model as:
F0 = S0 * erT
where r = risk-free interest rate and T = maturity of futures in years
If the stock pays dividends of D at time t,
F0 = S0 * erT – D * er(T – t)
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14. 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
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
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15. Stock Futures and Arbitrage
Pricing relationship is theoretical value based on current share price
If the actual futures price is different from the 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
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16. 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
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 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
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17. 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
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18. Stock Futures and Insurance -- Example
India Cements shares are priced at INR 135 on January 1. The contract size is January futures, with expiry on January 29, are priced at INR 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
135
195750
140
203000
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19. 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
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20. 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
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21. 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
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22. 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
NSE Nifty Midcap 50 Futures
300
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23. 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 = INR265,000
Gain for long hedger = ( – ) = INR 3400
Loss for short hedger = ( – ) = INR 3400
The long hedger will bet that the index will increase, and the short hedger will bet that the index will decrease
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24. 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
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25. Example of Pricing on Index Futures
On December 1, CNX Nifty Index is at 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
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26. 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
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27. 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
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28. Theoretical price = Ft = St e–(r – d)(T – t)
Index Arbitrage
Theoretical price = Ft = St e–(r – d)(T – t)
If the market value of futures is different from the 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 the theoretical value, one should buy futures, short-sell underlying shares of the index, and invest in risk-free securities
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29. Program Trading
Program trading refers to automatic trading triggered by computers whenever there is an index arbitrage opportunity
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30. 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
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31. Example of Hedging Portfolio Value
On January 1, portfolio value = INR 500,000,000 Nifty Index = 5250 Risk-free rate = 8%; dividend yield = 2% March futures at , expiry on March 28 Value of futures = * 50 = INR Beta of portfolio = 1.2 Number of contracts to sell = (1.2 * 500,000,000) / = 2253 On Feb 28, Nifty is at 5100 Futures price would be
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32. Example of Hedging Portfolio Value: Value of Portfolio
Change in index = (5250 – 5100)/5250 = % Dividend yield = 2% per year = 2 (59/365) = 0.32% Return on index = % % = % Expected return on portfolio = 8% (59/365) [ – (8% (59/365) ) = -3.3% Portfolio value = 500,000,00 (1 – 3.3%) = 483,503,718 Gain from futures = 2253*50 ( – ) = 24,534,044 Hedged portfolio value = 483,503, ,534,044 Hedged portfolio value = 508,031,762
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33. Adjusting Equity Beta
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
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34. 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
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35. 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
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