1. 1.1 Forward and Futures contracts Exercise* (Forward price) A stock pays a continuous dividend yield of 2% per annum. The stock price is $100, and the riskfree rate of interest is 1% per annum. An investor has just taken a long position in a 3-month forward contract on the stock. (a) What is the forward price? What is the initial value of the forward contract? (b) One month later, the price of the stock is $95 and the risk-free rate is still 1%. What would be the new forward price? What is the value of the long position in the forward contract? (c) At maturity of the forward contract, the stock price is $110. What is the investor's P&L? 1.2 Exercise (Forward price) A stock is expected to pay a dividend of $1 per share in 2 months and in 5 months. The stock price is $50, and the risk-free rate of interest is 8% per annum. An investor has just taken a short position in a 6- month forward contract on the stock. 1.3 (a) What is the forward price? What is the initial value of the forward contract? (b) Three months later, the price of the stock is $48 and the risk-free rate is still 8%. What would be the new forward price? What is the value of the short position in the forward contract? (c) At maturity of the forward contract, the stock price is $55. What is the investor's P&L? Exercise** (Hedging an equity portfolio) On July 1st, an investor holds 50,000 shares of a stock whose market price is $30. The investor is interested in hedging against movements in the market over the next month. She decides to use the September Mini S&P 500 futures contract. The index futures price is currently 1,500 points, and one contract is for delivery of $50 times the index. The stock's beta is 2.0 and the risk-free rate is 2%. (a) How many futures contracts should be shorted? (b) Under what circumstances will it be profitable? (c) Assuming that the CAPM holds, what is the stock's expected return if the stock index futures falls to 1,275 points? (d) In this case, what is the investor's P&L on the stock position and on the futures position? Is the hedging strategy followed by the investor performing adequately?