1. The six-month zero rate is 8% with semiannual compounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate? Answer as a percent with two decimal place accuracy
2. The yield curve is flat at 6% per annum with semiannual compounding. What (to the nearest cent) is the value of an FRA where the holder receives interest at the rate of 8% per annum for a six-month period on a principal of $1,000 starting in two years?
3. A trader enters into a one-year short forward contract to sell an asset for $60 when the spot price is $58. The spot price in one year proves to be $63. What is the trader’s gain or loss? Show a dollar amount and indicate whether it is a gain or a loss.
4. A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on the S&P index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to achieve the following. (Indicate the number of contracts that should be traded and whether the position is long or short.)
Eliminate all systematic risk in the portfolio
Reduce the beta to 0.9
Increase beta to 1.8
5. The spot price of an investment asset that provides no income is $30 and the risk-free rate for all maturities (with continuous compounding) is 10%.
What, to the nearest cent, is the three-year forward price?
Assume that the asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price?
6. A portfolio is worth $24,000,000. The futures price for a Treasury note futures contract is 110 and each contract is for the delivery of bonds with a face value of $100,000. On the delivery date the duration of the bond that is expected to be cheapest to deliver is 6 years and the duration of the portfolio will be 5.5 years. How many contracts are necessary for hedging the portfolio?