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2009-Quiz 4-1

# 2009-Quiz 4-1 - What is the net loss or gain on your...

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Fin 3144: Investments Quiz 4 Name: _KEY___________ 1. You are managing a portfolio with a current value of \$1 million. Your target duration is 10 years, and you can choose from three zero-coupon bonds, with maturities of 5 years, 7 years, and 15 years. The yield curve is flat and the YTM for each bond is 5%. (a) How much should you invest in each of the three bonds to achieve the target duration of 10 years? (b) If the face value of each bond is \$1,000, how many bonds of each maturity will you buy? 2. Today (day 0), you take a short position of one contract in a June crude oil futures contract at a price of \$51.50 per barrel. Today’s spot price is \$50.50, the collateral is \$7,500, and each contract is worth 1,000 barrels. The next day (day 1), the futures price rises to \$52, on day 2 the futures price falls to \$51. Unnerved by the volatility, you decide to close your position on day 3 at a futures price of \$50.75. At the same time on day 3, the spot price is \$49.85.

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Unformatted text preview: What is the net loss or gain on your futures position? Show your work. Key 1a. To get an average duration of 10 years, you must choose the 15-year bond and at least one of the other two bonds. For simplicity, I will choose the 5-year and 15-year bonds. 50% in each bond will give me a target duration of 10 years. Other fractions are also possible. 1b. Price of the 5-year bond = 1000/(1.05)^5 = \$783.53 Price of the 7-year bond = 1000/(1.05)^7 = \$710.68 Price of the 15-year bond = 1000/(1.05)^10 = \$481.02 \$500,000 each must be invested in the 5-year and 15-year bonds because 50% in each bond has to be invested. Thus we need 638 5-year bonds and 1039 15-year bonds. 2. Short one contract at \$51.50 today. Futures price when you close the contract = \$50.75. Difference = \$0.75. Since you were short, you gain \$0.75 per barrel, for a total profit of \$750. The spot prices are irrelevant....
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2009-Quiz 4-1 - What is the net loss or gain on your...

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