The current yield curve for default-free zero-coupon bonds is as follows: Maturi

Question

The current yield curve for default-free zero-coupon bonds is as follows: Maturity (years) YTM 1 9.4 % 2 10.4 3 11.4 a. What are the implied one-year forward rates? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Maturity (years) YTM Forward Rate 1 9.4 % 2 10.4 % 11.50 % 3 11.4 % 13.65 % b. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the pure yield curve (that is, the yields to maturity on one- and two-year zero-coupon bonds) be next year? There will be a shift upwards in next year's curve. There will be a shift downwards in next year's curve. There will be no change in next year's curve. c-1. If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? (Hint: Compute the current and expected future prices.) Ignore taxes. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Expected total rate of return % c-2. If you purchase a three-year zero-coupon bond now, what is the expected total rate of return over the next year? (Hint: Compute the current and expected future prices.) Ignore taxes. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Expected total rate of return %

Explanation / Answer

a. Let us define zero rates for next years as follows:

s1 = 9.4% (1 year rate)

s2 = 10.4%

s3 = 11.4%

Also define 1-year implied forward rates as follows:

1-year fwd for 1 year = f11

1-year fwd for 2 years = f12

Using no arbitrage of interest rate returns:

(1+s1)*(1+f11) = (1+s2)^2

=> f11 = 11.41%

Also, (1+s1)*(1+f12)^2 = (1+s3)^3

=> f12 = 12.41%

b. Under the pure expectations theory, the 1-year fwd rates we just calcualted will become the 1-year and 2-yer zero coupon YTM 1 year from now. Since these rates are more than the current rates, the yield curve will have an upward shift.

c. Price of 2 year zero coupon bond can be calculated by this formula:

P = 100/(1+s2)^2

using current rate = 10.4% and next years rates = 12.41%, we can calculate the prices and then get the return

Return = -3.54%

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