4. 5 pts) Suppose we made a forward contract with delivery price K on a stock wh

Question

4. 5 pts) Suppose we made a forward contract with delivery price K on a stock whose current price is $100. The maturity date is one year from now, and the compounding factor for a year is 1.1. (4 pts) Construct a replicating portfolio of the stock and a risk-free asset for the long position of this forward contract. In other words, identify 1) the number of shares of the stock and 2) the amount of money to be invested in the risky-free asset so that the pay-off o this portfolio is identical to that of the forward contract. (a) (b) 1 pts) What is the fair delivery price K?

Explanation / Answer

The forward price can be arrived at using the formula = S0 * ert where S0 is the current price (given $ 100), e is the 2.7183, r is the applicable interest rate for the period and t is the time period (given 1 year). Now we are directly given the compounding factor as 1.1, hence forward price (K) = S0 * 1.1 or K = 100*1.1= 110

The pay off from a long forward contract at price K, S0 = 100 and time period 1 year, will be as below:

The price of forward contract is essentially the carrying cost of the position basis the current stock price and interest rates - as we can see from the Forward Price formula. To replicate the long forward contract pay off, we simply borrow the present value of price K and invest into the stock today. So we in effect short a risk free asset (borrow) present value of 110 (forward contract price) which will be (110/1.1) = 100. With this 100, we will buy 1 stock at current price.

Thus we see that a portfolio of short risk free asset (borrow present value of K) and stock purchased at S0 gives us same pay off as long forward contract.

Fair delivery price K is given by K = S0 * ert ; which we calculated above to be $ 110

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