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Homework 2_solution

Homework 2_solution - Homework 2 E305 Money and Banking...

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Homework 2 E305: Money and Banking Spring 2010 1. Problem 6.6 A 10-year zero-coupon bond has a yield of 6 percent. Through a series of unfortunate circumstances, expected inflation rises from 2 percent to 3 percent. a. Compute the change in the price of the bond. b. Suppose that expected inflation is still 2 percent, but the probability that it will move to 3 percent has risen. Describe the consequences for the price of the bond. Answer: a. Price (with 2% expected inflation) = 100/(1.06) 10 = $55.84 Price (with 3% expected inflation) = 100/(1.07) 10 = $50.83 The price has fallen by $5.01 b. There is increased inflation risk. Investors will require compensation for taking on additional risk, so the price will fall and the yield will rise. 2. Problem 6.8 As you read the business news, you come across an advertisement for a bond mutual fund – a fund that pools the investments from a large number of people and then purchases bonds, giving the individuals “shares” in the fund. The company claims their fund has had a return of 13½ percent over the last year. But you remember that interest rates have been pretty low – 5 percent at most. A quick check of the numbers in the business section you’re holding tells you that your recollection is correct. Explain the logic behind the mutual fund’s claim in the advertisement. Answer: There are two possible explanations for the high return. The first is that the mutual fund is investing in relatively risky bonds and is being compensated for taking on this risk with higher returns. The second is that the fund was holding bonds during a period when interest rates were falling, so the holding period return far exceeded the interest rate. 3. Problem 7.6 According to the liquidity premium theory, if the yield on both one-and two-year bonds are the same, would you expect the one-year yield in one-year’s time to be higher, lower or the same? Explain your answer.
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Answer: According to the liquidity premium theory, the two-year yield (i 2,t ) is an average of this year’s and next year’s one-year yields (i 1,t +i e 1, t+1 ) plus a risk premium (rp) to compensate for the inflation and interest-rate risk associated with the longer maturity. i 2,t = (i 1,t +i e 1, t+1 )/2 +rp We can see from the formula, if the current one-and two-year yields are the same and there is a risk premium included in the two-year yield, then next year’s one-year yield must be lower than this year’s. 4. Problem 7.7 You have $1000 to invest over an investment horizon of 3 years. The bond market offers various options. You can buy (i) a sequence of three one-year bonds; (ii) a three-year bond; or (iii) a two-year bond followed by a one-year bond. The current yield curve tells you that the one-year, two-year, and three-year yields to maturity are 3.5 percent, 4.0 percent, and 4.5 percent respectively. You expect that one-year interest rates will be 4 percent next year and 5 percent the year after that. Assuming annual compounding, compute the return on each of the three investments, and discuss which one you would choose.
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