Question

The S&P 500 Index is currently at 2,000. You manage a $15 million indexed equity portfolio. The S&P 500 futures contract has a multiplier of $50.

a. If you are temporarily bearish on the stock market, how many contracts should you sell to fully eliminate your exposure over the next six months?

b. If T-bills pay 1.8% per six months and the semiannual dividend yield is 1.6%, what is the parity value of the futures price? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a) No. of contracts of S&P futures to be shorted

= Value of S&P linked portfolio / current value of one contract

= $15 million / (2000*$50) = 150

So, 150 contracts need to be shorted

NOTE: The value of one contract should be calculated at Futures price, However, since the futures price is not available, we have to use the current index level.)

b) The Futures price is given as

F =S * (1+r)/(1+i)

where r is the semiannual risk free rate

i is the semiannual dividend yield

and S is the spot price of the Index

So, F = 2000* 1.018/1.016 = 2003.94

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