The term structure for zero-coupon bonds is currently: Maturity (Years) YTM (%)

Question

The term structure for zero-coupon bonds is currently: Maturity (Years) YTM (%) 4.4% 5.4 6.4 Next year at thls time, you expect it to be Maturity (Years) YTM (%) 5. 4% 6.4 7.4 a. What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond? (Round your answer to 1 declmal place.) Rate of return 96 b-1. Under the expectations theory, what ylelds to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year? (Round your answers to 2 declmal places.) Maturity YTM 96 96 b-2. Is the market's expectation of the return on the 3-year bond greater or less than yours? O Greater O Less

Explanation / Answer

Part a)

The rate of return is deteremined as below:

Today the 3-Year zero coupon bond (having a face value of $100) will sell at 6.4% rate of interest with a price of $83.02 [100/(1+6.4%)^3].  

The bond will have a remaining maturity of 2 years in the following year. The yield will again be 6.4% (refer to second table) and will sell at a price of $88.33 [100/(1+6.4%)^2].

The holding period return will be calculated as below:

Holding Period Return (Rate of Return Over Coming Year) = (88.33 - 83.02)/83.02*100 = 6.40%

Answer for Part 1 is 6.40%.

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Part b-1)

Step 1: Calculate Forward Rates Based on Today's Yield Curve

The forward rates are calculated as below:

Year 2 = (1+5.4%)^2/(1+4.4%) - 1 = 6.41%

Year 3 = (1+6.4%)^3/(1+5.4%)^2 - 1 = 8.43%

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Step 2: Calculate Yield to Maturity on 1 and 2-Year Zeroes at the End of the Year

The yield to maturity is determined as below:

Yield to Maturity (1 Year Maturity) = 6.41%

Yield to Maturity (2 Year Maturity) = ((1+6.41%)*(1+8.43%))^(1/2) - 1 = 7.41%

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Tabular Representation

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Part b-2)

Greater.

____

Explanation:

The YTM on 2-year bonds as per market expectations turns out be higher than your forecast. Therefore, it can be concluded that the market expects a lower price and greater rate of return as there is an inverse relationship between return and bond price.

Maturity YTM 1 6.41% 2 7.41%

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