3.) S&P 500 futures contracts give buyers the right to a basket of the stocks in

Question

3.)

S&P 500 futures contracts give buyers the right to a basket of the stocks in the S&P 500 on expiration date. Priced at 250 times the index, they're used mostly by institutional investors.

One mutual fund company has a $100 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                        (a)                                           (b)
(ii) A 25% stock dividend                   (a)                                           (b)
(iii) A $5 cash dividend                       (a)                                           (b)

Explanation / Answer

1

conversion factor=250

Portfolio=100000000

Number of contracts to be shorted=Beta*Portfolio/(conversion factor*current index level)=1.4*100000000/(250*2000)=280

Now if manager wants to halve the beta to 0.7, number of contracts will halve to 280/2=140

2.

a

Strike price=20/5=4 Number of shares=100*5=500

b

Strike price=20/1.25=16 Number of shares=100*1.25=125

c

Cash dividend no effect on strike price and number of shares. Since it is a ordinary dividend. Had it been special or extra dividend, the share price would have affected and thus the number of shares. So, strike price=20 Number of shares=100

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