1. A 2-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $139 and the risk-free interest rate is 10.1% per annum with continuous compounding. 1 year later, the price of the stock is $146 and the risk-free rate is 9.7%. What is the value of the forward contract?
2. Calculate the present value of $100 in 9 years using 9.8% interest rate with continuous compounding.
3. Suppose that a bank has entered into an interest rate swap, where the bank pays six-month LIBOR and receives 7% per annum (with semiannual compounding) on a notional principal of $100. The swap has a remaining life of 1.25 years. The LIBOR rates with continuous compounding for 3-month, 9-month and 15-month maturities are 10%, 10.3%, and 11%, respectively. The 6-month LIBOR rate at the last payment date was 10.1% (with semiannual compounding). What is the current value of the swap?
4. On 6/1/2013, you entered into a semiannual interest rate swap contract, where you pay a fixed rate of 4.3% per annum and receive 6-m LIBOR on a principal amount of $1,000,000. Suppose the 6-m LIBOR rates were 3.6% on 6/1/2013 and 3.7% on 12/1/2013. What is the net cash flow of the swap contract on 12/1/2013?
5. Suppose the dividend yield on market index is 2% per annum and the risk-free rate is 8% per annum. The beta of your stock portfolio is 1.3. Assume the index level changes by 16% in 4 months. Calculate the expected return on your portfolio in 4 months.
6. The 12-month, 15-month, 18-month zero rates are 4.5%, 4.6%, 4.7% with continuous compounding. What is the value of an FRA that enables the holder to earn 5.6% (with semiannual compounding) for a 3-month period starting in 1 year on a principal of $1,000,000?