Part 1 - Multiple Choice Questions
Questions come from the Hull Test Bank
1. An investor sells a futures contract an asset when the futures price is $1,500. Each contract is on 100 units of the asset. The contract is closed out when the futures price is $1,540. Which of the following is true?
2. As the convenience yield increases, which of the following is true?
3. The time-to-maturity of a Eurodollar futures contract is 4 years and the time-to-maturity of the rate underlying the futures contract is 4.25 years. The standard deviation of the change in the short term interest rate = 0.011. What does the model in the text give as the difference between the futures and the forward interest rate?
4. The most recent settlement bond futures price is $103.5. Which of the following four bonds is the cheapest to deliver?
5. Which of the following is closest to the duration of a 2-year bond that pays a coupon of 8% per annum semi-annually? The yield on the bond is 10% per annum with continuous compounding.
6. Which of the following is true?
7. What should a trader do when the one-year forward price of an asset is too low? Assume that the asset provides no income.
8. The zero curve is upward sloping. Define X as the 1-year par yield, Y as the 1-year zero rate and Z as the forward rate for the period between 1 and 1.5 year. Which of the following is true?
9. The price of a stock on February 1 is $124. A trader sells 200 put options on the stock with a strike price of $120 when the option price is $5. The options are exercised when the stock price is $110. The trader’s net profit or loss is
Hint: Calculate the profit from the holder’s perspective. Then reverse it for the issuer.
10. A trader buys a call and sells a put with the same strike price and maturity date. What is the position equivalent to?
11. Company X and Company Y have been offered the following rates
Suppose that Company X borrows fixed and company Y borrows floating. If they enter into a swap with each other where the apparent benefits are shared equally, what is company X’s effective borrowing rate?
Part 2 - Essay Questions
1. Please answer all three parts.
2. The Japanese (Yen) interest rate equals 4% per annum while the Australian dollar (AUD) rate equals 6% per annum. The spot rate is 1 AUD equals 85.62 Yen. In a SWAP agreement, an Australian company pays 5% per annum in Yen and receives 7% per annum in AUD. The principals of the two currencies are 127.5 million Yen and $1.5 million AUD. Payments are exchange every year with one exchange that the parties completed. The SWAP will last two more years.
3. A one-year gold futures contract is selling for $1780. Spot gold prices are $1767 and the one-year risk-free rate is 4%. What arbitrage opportunity is available to investors? What strategy should they use and what will be the profits on the strategy?
4. Suppose that the yield curve is flat at 5% per annum with continuous compounding. A swap with a notional principal of $100 million in which 6% is received and six-month LIBOR is paid will last another 15 months. Payments are exchanged every six months. The six-month LIBOR rate at the last payment date (three months ago) was 7%.
5. A trader wants to pay the fixed rate in a $20 million FRA for a six month period starting in three years. The three-year LIBOR zero rate is 6% p.a. continuously compounded, and the 3.5 year LIBOR zero rate is 6.5% p.a. continuously compounded.
6. Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum.
7. Explain the role of short put option holder. Under what circumstances will the seller of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.
8. Assume zero rates are 5%, 5.3%, 5.6%, and 6% are the 6-month, 12-month, 18-month, and 24-month respectively with quarterly annual compounding.
Short Answer Essay
1. a. Convert to continuous rates. F = 6% and applies to payment between 2 and 3 years.
2. The bond discounted cash flows and forward rate methods yield the same answer, which is $6,569.459 AU
3. F = $1,839.11
4. PV(receive) = 102.61 million
5. FRA = $20 million (6 / 12)[ x - 0.0972 ]
6. a. Portfolio A
b. The percent change for both portfolios = -0.59%
7. The answer is a plain short put option. Just choose an exercise price, k, and premium, p, and explain it. Then draw a diagram for the profit. Note: profit = p + ST - k
8. a. Interest rates in order 0.0497, 0.0527, 0.0556,, and 0.0596