Econ%2B310%2Bw10%2BHW3%2BAnswers

Econ%2B310%2Bw10%2BHW3%2BAnswers - Econ 310 Homework...

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Econ 310 Homework Assignment 3 Answer Key Question Seven (a) A coupon bond matures in five years, has face value of $1000, a coupon rate of 10% and sells today for a price of $1216.50. The inflation rate over the following five years is expected to be around 5% per annum. A 5 year indexed bond has a face value of $1000, a coupon rate of 1% and a current price of $1000. Which of these bonds would you prefer? The price of the nominal bond equals its present value: 1216.50 = 100/(1+r) + 100/(1+r) 2 + 100/(1+r) 3 + 100/(1+r) 4 + 100/(1+r) 5 + 1000/(1+r) 5 . Clearly, the nominal yield to maturity is less than 10%, as the price of the bond is above its face value. In fact, the nominal yield to maturity is 5%. This is easily verified by plugging r=0.05 into the expression. Notice, though, that this is a nominal yield to maturity. We can use the Fisher equation to generate the real yield: r = i - ∏ e where r is the real rate, i is the nominal rate and ∏ e is the expected inflation rate. Therefore, r = 0.05 – 0.05 = 0 (i.e. 0%). The nominal bond, therefore, generates no real return. But the indexed bond generates a 1% real return. I would prefer the indexed bond. (b) Do you think the prices of the nominal coupon bond and the indexed bond could be equilibrium prices? If yes, explain why. If not, predict what would happen to the relative prices of the two bonds. These are unlikely to be equilibrium prices of the two bonds. If they were, all agents would prefer to hold the indexed bond. This would force the relative price of the nominal bond down, implying an increase in the real rate on the nominal bond. (c) In the first year, changes in operating procedures at the central bank give their monetary policies new credibility. Inflation ran at 3% over the year, and is expected now to remain at that rate for the next four years. Suppose the price of the indexed bond has risen to $1030. What would the price of the nominal coupon bond have to be to leave
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you indifferent between the two bonds? (To answer this, presume that you don’t care about inflation risk inherent in holding the nominal bond; you care only about expected real returns). First, think about the indexed bond. In current dollars, the price of the bond is $1030. But in last year’s dollars, its price is $1000 (deflating $1030 by the inflation rate over the past year). Therefore, the price of this bond in real terms is still equal to its face value. That means that the real yield to maturity of the indexed bond is still equal to its coupon rate (1%). Now, the real rate on the nominal bond will also have to be 1% to leave the market indifferent between them. And as the expected inflation rate is now 3%, this means that the nominal yield to maturity would have to be 4%. Therefore, we can use this to discount the next four years’ payments to the bond holder to calculate the price of the bond: P = 100/(1+r) + 100/(1+r) 2 + 100/(1+r) 3 + 100/(1+r) 4 + 1000/(1+r) 4 where r=0.04. P=1082.53
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This note was uploaded on 09/28/2010 for the course ECON 310 taught by Professor Hogan during the Winter '08 term at University of Michigan.

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Econ%2B310%2Bw10%2BHW3%2BAnswers - Econ 310 Homework...

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