S&P 500 index has a dividend yield of 3% today. The current index is trading at $1800 and the risk-free interest rate is 5% per annum with continuous compounding. An investor would like to enter into a short one-year forward contract on the index.
A. What would be the fair forward price for this contract?
B. Suppose that six months later, S&P 500 index trades at $2000, the risk-free interest rate is 6% per annum and the annualized dividend yield increased to 4%. What would be the current value of the investor’s short position?