One mutual fund company has a S100 million portfolio with a beta of 1.4. It woul

Question

One mutual fund company has a S100 million portfolio with a beta of 1.4. It would like to use futures contracts on the S&P; 500 Index to hedge its risk. The relevant future index is currently standing at 2,000 and each contract is for delivery of $250 times the index (a) What is the hedge ratio that minimizes risk? (b) What should the company do if it wants to reduce the beta of the portfolio to 0.7? 4 Consider an exchange traded put option to sell 100 shares for $20.Give (a) the new strike price and (b) the number of shares that can be sold after (i) A 5 for 1 stock split (ii) A 25% stock dividend (iii) A S5 cash dividend

Explanation / Answer

1.

Number of contracts to be shorted=Portfolio*Beta/(Futures price*delivery factor)

=100000000*1.4/(2000*250)

=280

To reduce the beta to 0.7, exactly half would be required as 0.7/1.4=0.5..So number of contracts=280/2=140

2.

In case of stock split, the share price would go down hence the strike price is also adjusted. The new strike price=20/5=4

Number of shares=100*5=500

In case of stock dividend, the share price goes down by 1/(1+x%) where x is the stock dividend. The new strike price=20/1.25=16

Number of shares=100*1.25=125

Cash dividend would not impact the sahre price unless it is extra or special. hence, strike price would also be unaffected. New strike price=20

Number of shares=100

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