Question

The S&P 500 Index is currently at 1,800. You manage a $9m indexed equity portfolio. The S&P 500 futures contract has a multiplier of $250.

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?

If T-bills pay 2% per six months and the semiannual dividend yield is 1%, what is the parity value of the futures price?

Show that if the contract is fairly priced, the total risk-free proceeds on the hedged strategy in the first part of this question provide a return equal to the T-bill rate.

Answer 1

Value of Portfolio- $9 Millions or $ 90 Lacs

S&P Future contract Multiplier- $250

1. Number of contracts to be sold to completely eliminate downside risk- (90 Lacs/250)= 36000 contracts.

2. Parity Value of Future Price= Spot price*(1+ Risk Free Interest Rate-Income Yield)

Spot price= $1800

Risk Free rate for 6 month= 2%

Dividend yield for 6 month is 1% (semi annual)

Thus, Parity value= 1800*(1+.02-.01)= $1818

PS- This can be calculated by following formula as well

F= S*e^{(r-y)t where,}

^{e= 2.71828}

^{r= Risk Free rate}

^{y- Income yield}

^{t= time (in this case assume time to be 1 as both rates are given for 6 months and future rate is to be calculated for 6 month}