2.) A stock index currently stands at 500. The risk-free interest rate is 5 perc

Question

2.) A stock index currently stands at 500. The risk-free interest rate is 5 percent per annum (with continuous compounding) and the dividend yield is 3 percent per annum.   What should the futures price for a 3-month contract be?

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

2.) Curretn Stock Index =500

Time =3 months =0.25 years

Risk Free Rate =5%

Dividend Yield=3%

Price of Index in 3-Months =500 x e(0.05-0.03)x0.25

                                       = 500 x 1.00501

                                       = 502.5063

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