# Suppose that: S&P 500 index is

Suppose that: S&P 500 index is trading at 2000; index stocksdo not pay any dividends; and you can borrow and lend at 5% perannum. You have an index portfolio worth \$20 million. An indexfutures contract with a multiplier of 100 matures in a year – thismeans one futures contract represents an index basket of stockswith a market value of 100 times the index value. How will youfully hedge your portfolio for a one year horizon? What’s yourreturn if futures are trading at 2100? 2150? 2050? Suppose, youwant to hedge only for one month. Do you know what your return willbe if index futures are trading at 2100? 2150? 2050? Suppose yourportfolio is only \$300,000. Can you hedge perfectly? Suppose yourportfolio is different from the index basket of stocks – what isthe quality of your hedge?

1. Value of the future contract for 1 year horizon:

2000*e0.05*1=2102.54

Therefore, number of future contracts you require to sell to hedgeyour portfolio:

=20,000,000/(2102.54*100)

=95.12= 95 contracts

2) Return earned if index at:

2100

Portfolio:(20,000,000*(2100/2000))-20,000,000= 1,000,000

Future Contract(Short)=(2102.54-2100)*100*95= 24,130

Therefore, total profit=\$ 1,024,130

Therefore, total return=1,024,130/20,000,000= 5.12%

2150

Portfolio: (20,000,000*(2150/2000))-20,000,000= 1,500,000.00

Future Contract (Short)=(2102.54-2150)*100*95= -450,870.00

Therefore, total profit=\$ 1,049,130

Therefore, total return=1,049,130/20,000,000=5.24%

2050

Portfolio: (20,000,000*(2050/2000))-20,000,000= 500,000.00

Future Contract (Short)=(2102.54-2050)*100*95= 499,130.00

Therefore, total profit=\$ 999,130

Therefore, total return=999,130/20,000,000=4.99%

Suppose your portfolio is differentfrom the index basket of stocks – what is the quality of yourhedge?

If your portfolio is different fromindex and you wish to hedge your portfolio with index future thequality of hedge will be poor. There is a high basis risk (riskthat arises if your hedging instrument and portfolio are not highlycorrelated and different). Hence, gains and losses in the portfoliowill not be offset perfectly by the hedging instrument.

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