A portfolio manager expects to purchase a portfolio of stocks in 90 days. In order to hedge against the potential price increase over the next 90 days, she decides to take a long position on a 90-day forward contract on the S&P 500 stock index. The index is currently 2200. The continuously compounded dividend yield is 6.50%. The discrete risk free rate is 2.50%.
A. What is the “no-arbitrage” forward price on this forward contract?
B. 30 days into the forward contract, the S&P 500 index is 2150. What is the value of the forward contract position 30 days into the contract (Vt), assuming forward price agreed was the “no-arbitrage” forward price and the discrete risk free rate does not change?
C. At expiration, the S&P 500 index value is 2250. What is the value of the forward contract position at expiration (VT)?