Solutions to chapter 4

Solutions to chapter 4 - Chapter 4 Why Do Interest Rates...

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Chapter 4 Why Do Interest Rates Change? ± Quantitative Problems 1. You own a $1,000-par zero-coupon bond that has 5 years of remaining maturity. You plan on selling the bond in one year, and believe that the required yield next year will have the following probability distribution: Probability Required Yield 0.1 6.60% 0.2 6.75% 0.4 7.00% 0.2 7.20% 0.1 7.45% a. What is your expected price when you sell the bond? b. What is the standard deviation?
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Chapter 4 Why Do Interest Rates Change? 17 Solution: Probability Required Yield Price Prob × Price Prob × (Price Exp. Price) 2 0.1 6.60% $774.41 $ 77.44 12.84776241 0.2 6.75% $770.07 $154.01 9.775668131 0.4 7.00% $762.90 $305.16 0.013017512 0.2 7.20% $757.22 $151.44 6.862609541 0.1 7.45% $750.02 $ 75.02 16.5903224 $763.07 46.08937999 The expected price is $763.07. The variance is $46.09, or a standard deviation of $6.79. 2. Consider a $1,000-par junk bond paying a 12% annual coupon. The issuing company has 20% chance of defaulting this year; in which case, the bond would not pay anything. If the company survives the first year, paying the annual coupon payment, it then has a 25% chance of defaulting in the second year. If the company defaults in the second year, neither the final coupon payment nor par value of the bond will be paid. What price must investors pay for this bond to expect a 10% yield to maturity?
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This note was uploaded on 10/12/2011 for the course BIEMF 30006 taught by Professor Ippolito during the Fall '10 term at Università Bocconi.

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Solutions to chapter 4 - Chapter 4 Why Do Interest Rates...

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