Problem 1: Total Return Swap

The spot price of MSFT is $150. The CCIR is 5%. MSFT pays a continuously compounded dividend of 4%. (All rates are yearly).

a. Compute the forward price of MSFT for delivery t=6/12.

b. What is the effect of an increase in volatility on the forward price of MSFT?

Lee expects to receive 20 shares of MSFT at t=6/12 and 25 shares of MSFT at t=12/12.

c. If Lee wants to hedge the risk from the uncertain price of MSFT, how can Lee hedge today using forwards? (Specify quantities, time of delivery, forward price and whether is a short or long).

Instead of using forwards, Lee wants to enter a swap. In the deal, Lee will give the 20 shares of MSFT at t=6/12 and receive an amount of money $K and at t=12/12, Lee will give the 25 shares of MSFT at t=12/12 and receive an amount of money $K.

d. What is the PV of the Swap (as a function of K and spot prices)?

e. What is the swap price $K?

f. Assume that Lee entered the contract in e). At t=4/12, the price of MSFT is $160. If the CCIR and the dividend yield remain the same, what is the value of the swap at t=4/12?

Instead of selling the shares of MSFT, Lee now wants to swap the returns. In that swap, at t=6/12, Lee will give the returns accrued from t=0 to t=6/12 and receive an amount $K, and at t=12/12, Lee will give the returns accrued from t=0 to t=12/12 and receive an amount $K.

g. What is the PV of the Swap payoff?

h. What is the swap price?