Question

4. An investor has a portfolio of stocks worth $9.45 million. The portfolio beta is 0.85. The investor plans to use the CME September futures contract on the S&P 500 to change the market risk of the portfolio. The index futures price is currently 2674.90. (The payoff on of each futures contract is based on $250 times the S&P 500 index.)

a. What position should the company take to minimize the portfolio’s risk relative to the market?

b. What position should the company take to reduce the beta of the portfolio from 0.85 to 0.425 (i.e., half the current level of market risk)?

c. What position should the company take to increase the beta of the portfolio from 0.85 to 1.35?

Answer 1

We need to short the future contract to minimise the portfolio risk Portfolio value Portfolio beta to be reduced by Index price 9450000 0.85 2674.9 No of contracts to be sold 12 9 b) 10 We need to short the future contract to minimise the portfolio risk 12 13 Portfolio value Portfolio beta to be reduced by Index price 9450000 0.425 2674.9 15 16 17 c 18 19 20 21 No of contracts to be sold We need to long the future contract to minimise the portfolio risk Portfolio value Portfolio beta to be reduced by Index price 9450000 2674.9 23 No of contracts to be bought

e need to short the future contract to minimise the portfolio risk Portfolio value Portfolio beta to be reduced by Index price -9.45 1000000 0.85 2674.9 No of contracts to be sold ROUND(C4 C3 (C5*250),0) 9 b) 10 We need to short the future contract to minimise the portfolio risk 12 13 Portfolio value Portfolio beta to be reduced by Index price #9.45*1000000 -0.85-0.425 2674.9 15 16 17/с) 18 19 20 No of contracts to be sold ROUND (C12 C11/(C13*250),0) We need to long the future contract to minimise the portfolio risk Portfolio value Portfolio beta to be reduced by Index price -9.45 1000000 -1.35-0.85 2674.9 23 No of contracts to be bought ROUND(C20 C19/(C21 250),0)