# Final Exam FIN 525 Fixed-Income Securities

Philip H. Dybvig
Washington University in Saint Louis
March, 2005

This is a closed-book examination. Answer all questions as directed. Mark your answers directly on the examination. There are no trick questions on the exam. There are some formulas from the course (including some you will not need) at the end of the exam. All cash flows and interest rates are annual. Good luck!

A. General Concepts Short Anwer: 20 points (Answer each question in no more than two sentences of ordinary length.)

1. When interest rates rise, what happens to most bond prices?
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2. If the spot interest rate rises 1% today, do we expect the 10-year forward rate to rise by more than 1%, by less than 1%, or by 1%?
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3. What is the usual reason to buy an interest cap?
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4. Does a coupon bond's duration rise, fall, or stay the same when interest rates rise? Explain.
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5. Is mortgage fallout higher or lower when rates rise? Explain why.
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B. Basic rates and arbitrage 30 points

Today we can buy or sell a riskless claim paying \$100 a year from now for \$75. Or, we can buy a self-amortizing claim paying \$100 one year out and \$100 two years out for \$140.

1. What are the discount factors for one year out and two years out?
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2. What are the implied one- and two-year par coupon yields?
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3. Suppose you can buy or sell a two-period par coupon bond yielding 30%. Construct an arb with the original two claims.
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C. Duration 20 points

A pension liability consists of three cash flows: \$625 million 5 years out, \$800 million 10 years out, and \$250 million 15 years out. The liability is funded by a single asset, a pure discount bond maturing in 10 years. The market value of the pension asset equals the market value of the liability, that is, the pension is fully funded in economic terms.

1. The discount factor is 0.8 for 5 years out, 0.5 for 10 years out, and 0.4 for 15 years out. What is the market value of the liability?
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2. What is the duration of the liability? What is the duration of the asset?
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3. According to the duration measure, will the reduction in market value be larger for the asset or for the liability if rates rise? Explain briefly.
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D. Binomial Option Pricing 30 points

Assume that the interest rate starts at 4% and in each period and either increases by 2% or decreases by 2% (from 4% up to 6% or down to 2% would be the first move). The risk-neutral probabilities of ups and downs are all 1/2.

1. What is the price now of a discount bond with face of \$100 maturing one year from now?
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2. What is the price now of a discount bond with face of \$100 maturing two years from now?
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3. What is the price today of a two-year collar with a cap price of 5% and a floor price of 3%? The underlying notional is \$1,000.
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