S&P 500 is now at 2,100. Ignore interest rate (assume everything is given in PV

Question

S&P 500 is now at 2,100. Ignore interest rate (assume everything is given in PV terms). Suppose you own a $20M portfolio with a beta of 0.9. S&P 500 is expected to drop by 3% (or by 33 points, 3% ·1,100 = 33). Futures on S&P500 have a multiplier 250.

A. Should you long or short futures on S&P500 to hedge your portfolio?

B. If S&P500 drops by 33 points, what is the dollar change in the portfolio value?

C. If S&P500 drops by 33 points, what is the dollar change in the value of one futures contract (with a multiplier 250)? [Note the sign of the delta depends on whether the contract is longed or shorted. Be careful.]

D. What is the delta of your portfolio?

E. What is the delta of one futures contract?

F. How many futures contracts should you take a position in to hedge away the risk of S&P500 dropping?

G. Your answer to “f” would change if the S&P500 index were expected to drop by 5%. (True / False)

Explanation / Answer

A. We are long the portfolio. Thus to hedge we need to go short on the S&P 500.

B. S&P 500 drops 3%. The portfolio has beta of 0.9. Which means if S&P increases by 1% portfolio increases by 0.9%. Thus if S&P 500 drops by 3% portfolio will drop by 2.7%.I.e. 2.7/100*20 MN. =-540,000

C.In order to hedge the portfolio No. Of future contracts =(0-0.9)/1*20...Value of futures=18 Million.If S&P drops by 3%...Futures will increase by 0.03*18 Million= +540,000

D.Delta of portfolio is 0.9

E. Delta of futures is generally 1 or close to 1.

F. As calculated in answer C..Value of futures contract is 18 Million. Moreover Multiplier is 250. So no. Of contracts=18 Million/250= 72,000 Contracts.

G.False. Since after shorting the futures beta is 0..hence despite increase or decrease in S&P return will remain unchanged

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