Question

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

Maturity (years) YTM
1 9.8 %
2 10.8
3 11.8

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 9.8 %
2 10.8 % %
3 11.8 % %

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.)

Answer 1

a. The implied one-year forward rates are 98.04% for year 1 and 92.59% for year 2. b. According to the pure expectations hypothesis, there will be no change in next year's curve. c-1. The expected total rate of return for a two-year zero-coupon bond is 111.65%. c-2. The expected total rate of return for a three-year zero-coupon bond is 122.57%.

Step-by-step explanation:

a. To calculate the implied one-year forward rates, we can use the formula:

Forward Rate = (1 + Yield to Maturity for the second year) / (1 + Yield to Maturity for the first year) - 1

Using the given data, we have:

Forward Rate for year 1 = (1 + 10.8%) / (1 + 9.8%) - 1 = 0.9804 or 98.04%
Forward Rate for year 2 = (1 + 11.8%) / (1 + 10.8%) - 1 = 0.9259 or 92.59%

b. According to the pure expectations hypothesis of the term structure, if market expectations are accurate, there will be no change in next year's curve. Therefore, the pure yield curve for one- and two-year zero-coupon bonds will remain the same.

c-1. The expected total rate of return for a two-year zero-coupon bond over the next year can be calculated using the formula:

Expected Total Rate of Return = (Expected Future Price - Current Price) / Current Price

Assuming the face value of the bond is $1,000, we have:

Current Price = $964 (1-year YTM)
Expected Future Price = $1,000 (1-year YTM + 1-year Forward Rate)

Using the given data:

Current Price = $964
Expected Future Price = $1,000 (1 + 9.8% + 0.9804) = $2,038.43

Expected Total Rate of Return = ($2,038.43 - $964) / $964 = 1.1165 or 111.65%

c-2. Similarly, the expected total rate of return for a three-year zero-coupon bond over the next year can be calculated using the same formula:

Expected Total Rate of Return = (Expected Future Price - Current Price) / Current Price

Assuming the face value of the bond is $1,000, we have:

Current Price = $964 (2-year YTM)
Expected Future Price = $1,000 (2-year YTM + 1-year Forward Rate)

Using the given data:

Current Price = $964
Expected Future Price = $1,000 (1 + 10.8% + 0.9259) = $2,144.43

Expected Total Rate of Return = ($2,144.43 - $964) / $964 = 1.2257 or 122.57%

Answer 2

A) the implied 1 year forward rates respectively 9,8 , 11,81 and 13,83 according to the formular

Step-by-step explanation:

b) pure expactations true then

1.108²/1.098 - 1 =11.81% for a two year bond

1.118²/1.108 - 1 = 12.81% for a three year bond

The answere: The will be a shift upwards in next years curve.

c) Assume a par of 1000

in the next year a two year zero coupon bond will be a year zero and sell at 1000/1.1181 = 894.37 to get the return we take divide selling prices at year zero the trading price according to ytm is 1000/1.108² =814.55

therefore expected return 894.37/814.55= 9.79%

c2 the zero coupon bond at three year zero is trading at 1000/1.1282 = 886.446 and according to the ytm the coupon is trading at 1000/13.83^3= 715.607

therefore the expected return is

785.711/715.607=9.79%