1. A stock is expected to pay a dividend of $2 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock. (a) What are the forward price and the initial value of the forward contract? (b) Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract? 2. The current price of oil is $32.00 per barrel. Forward prices for 3, 6, 9, and 12 months are $31.37, $30.75, $30.14, and $29.54. Assuming a 2% continuously compounded annual risk-free rate, what is the annu- alized lease rate for each maturity? Is this an example of contango or backwardation? 3. Suppose the gold spot price $300/oz, the 1-year forward price is 310.686, and the continuously compounded risk-free rate is 5%. What is the lease rate? What is the return on a cash-and-cash ( / ) in which gold is not loaned? What is the return on a cash-and-carry in which gold is loaned, earning the lease rate? 4. Assume that the continuously compound interest rate is 6% and the storage cost of widgets is $0.03 quarterly (payable at the end of the quarter). Here is the forward price curve for widgets: Yr0 Yr1 Yr1 Yr1 Yr1 Yr2 Yr2 Dec Mar June Sept Dec Mar June 3.000 3.075 3.152 2.750 2.822 2.894 2.968 (a) What annualized rate of return do you earn on a cash-and-carry entered into December of Year 0 and closed in March of Year 1? Is your answer sensible? (b) What annualized rate of return do you earn on a cash-and-carry entered into in December of Year 0 and closed in September of Year 1? Is your answer sensible? (c) Suppose that you want to borrow a widget beginning in December of Year 0 and ending in March of Year 1. What payment will be required to make the transaction fair to both parties? (d) Suppose that you want to