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Q-10-40I

Expert-verified
Found in: Page 332

### Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

# Question: The current yield curve for default-free zero-coupon bonds is as follows:Maturity (Years)YTM110%211%312%a. What are the implied one-year forward rates?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? c. If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a three-year zero-coupon bond?(Hint: Compute the current and expected future prices.) Ignore taxes.

a. 12.01%, 14.03%

b. 13.02%

c. Two year zero coupon bond = 10.00% and three year zero coupon bond = 10.00%

See the step by step solution

## Step 1: Calculation of forward rates

Price for year 1 = 1000/ (1 + 10%) = $909.09 Price for year 2 = 1000/ (1 + 11%)2 =$811.62

Forward rate for year 2 = (1 + 11%)2 / (1 + 10%) – 1 = 0.1201 = 12.01%

Price for year 3 = 1000/ (1 + 12%)3 = $711.78 Forward rate for year 3 = (1 + 12%)3 / (1 + 11%)2 – 1 = 0.1403 = 14.03% Therefore,  Maturity Years YTM Forward rates Price 1 10.00%$909.09 2 11.00% 12.01% $811.62 3 12.00% 14.03%$711.78

## Step 2: Calculation of pure yield curve for the next year

For this, we discount each zero’s face value at the forward rates derived in the previous part, as below:

 Maturity Years Price Forward rates YTM 1 $892.78 1000/1.1201 12.01% 2$782.93 1000/1.1201x1.1403 13.02%

According to the expectation hypothesis, this year’s upward sloping curve implies a shift upward in next year’s curve

## Step 3: Calculation of total rate of return

Next year, the two-year zero will be a one-year zero, and it will therefore sell at: $1000/1.1201 =$892.78

Similarly, the current three-year zero will be a two-year zero, and it will sell for: $782.93 Expected total rate of return: Two year bond =$892.78/$811.62 – 1 = 0.1000 = 10.00% Three year bond =$782.93 / \$711.78 – 1 = 0.1000 = 10.00%