Question

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

Answer 1

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

                  2000*e^0.05*1=2102.54

             Therefore, number of future contracts you require to sell to hedge your 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 different from the index basket of stocks – what is the quality of your hedge?

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