1. Suppose the (cash) spot price of a 10% coupon Treasury bond is $115 (per $100 par). The bond matures on February 15, 2021; it therefore pays coupons of $5 (per $100 par) every February 15 and August 15. Suppose today is January 15. Find the forward price (per $100 par) for delivery of the bond on May 15 (4 months from now). Assume a continuously compounded repo rate of 2%.
2. A stock is trading for $50 per share, and is expected to pay a $0.20 dividend in 1 month. A futures contract with delivery in 3 months is priced at $49.80. Assume a continuously compounded riskless rate of 1%.
a) What is the arbitrage trading strategy and cash flows?
b) What would happen if, instead of paying a $0.20 dividend, the firm surprises the market and pays a $0.40 dividend instead? Will your strategy still make money?
3. Suppose the 2-month riskless interest rates are 2% in Switzerland and 5% in the U.S.; both rates are per annum with continuous compounding. The Swiss franc spot price is $0.8000, and the futures price for delivery in 2 months is $0.8100. What is arbitrage trade and cash flows?
4. Suppose you borrow at 3% and lend at 1% (both continuously compounded). To buy a stock you would pay $51 (the ask price), and if you sold the stock you will get only $50 (the bid price). Assume maturity is 1 year.
a) Find the no-arbitrage lower and upper bounds on the market forward price.
b) What is the arbitrage trading strategy and cash flows if the market forward price is $1 above the upper bound?
c) What is the arbitrage trading strategy and cash flows if the market forward price is $1 below the lower bound?
5. These were 1/30/14 UK spot and forward exchange rates from wsj.com (prices in dollars per pound):
|
UK pound
|
1.6485
|
|
1-mos forward
|
1.6481
|
|
3-mos forward
|
1.6473
|
|
6-mos forward
|
1.6461
|
The three-month U.S. LIBOR rate was 0.2376% (actual/360 day-count convention). What was the no-arbitrage three-month U.K. LIBOR rate (continuous compounding)? One approach is to convert the LIBOR rate to continuous compounding and use the formula from class. The easiest way to convert the rate is to match 90-day future value factors (both the loan and the forward contract are for a 90 day period) for the actual/360 day-count convention and the continuous- compounding convention.
6. Assume the value of a stock index is 400, the riskless interest rate is 1% APR with continuous compounding and the dividend yield on the index is 2% c.c. Delivery of the futures contract is in 4 months. What is the no-arbitrage futures price.
7. (old exam) On Jan 1 you short 3 forward contracts on XYZ stock. Delivery is on July 1 (in 6 months) and the forward price is $30.92. The stock is trading at $32 and will pay a $2 dividend on Feb 1 and no other dividends within the next year. The riskless interest rate is 6% c.c. Find the value of your forward position on May 1 assuming a stock price of $34 on that date.
8. 60 futures contracts are used to hedge an exposure to the price of silver. Each futures contract has a unit size of 5,000 ounces. At the time the hedge is closed out, the basis is $0.20 per ounce. What is the effect of the basis on the hedger's financial position if (a) the trader is hedging the purchase of silver, and (b) the trader is hedging the sale of silver.