Suppose that a 1-year zero coupon bond with face value $100 currently sells at $

Question

Suppose that a 1-year zero coupon bond with face value $100 currently sells at $95.11, while a 2-year zero sells at $79.52. You are considering the purchase of a 2-year maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 11% per year. What is the yield to maturity of the 2-year zero? The 2-year coupon bond? (Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the "%" sign in your response.) What is the forward rate for the second year? (Do not round intermediate calculations and rounded to whole number. Omit the "%" sign in your response.) Forward rate % If the expectations hypothesis is accepted, what are the expected price of the coupon bond at the end of the first year and the expected holding- period return on the coupon bond over the first year? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" & "%" signs in your response.)

Explanation / Answer

Part a)

The yield to maturity on 1-year zero coupon bond is calculated as follows:

Current Price of 1-Year Zero Coupon Bond = $100/(1+Yield to Maturity)

Substituting the values provided in the question, we get,

95.11 = 100/(1+YTM)

Rearranging Values, we get,

YTM = (100 - 95.11)/95.11 = 5.141%

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The yield to maturity on 2-year zero coupon bond is calculated as follows:

Current Price of 2-Year Zero Coupon Bond = $100/(1+Yield to Maturity)^2

Substituting the values provided in the question, we get,

79.52 = $100/(1+YTM)^2

Solving for YTM, we get

(1+YTM) = (100/79.52)^(1/2)

YTM on 2-Year Zero Coupon Bond = 12.140%

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The yield to maturity on 2-year coupon bond is calculated as follows:

Price of the 2-Year Coupon Bond = 11/(1+5.141%)^1 + (100+11)/(1+12.140%)^2 = $98.73

Now, we can calculate the YTM of 2-year coupon bond with the use of Rate Function/Formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Coupon Payment, PV = Current Price of Bond and FV = Face Value of Bond.

Here, Nper = 2, PMT = 100*11% = $11, PV = $98.73 and FV = $100

Using these values in the above function/formula for Rate, we get,

YTM on 2-Year Coupon Bond = Rate(2,11,-98.73,100) = 11.749% or 11.75%

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Part b)

The forward rate for the second year is calculated as follows:

Forward Rate for Second Year = (1+YTM of 2-Year Zero Coupon Bond)^2/(1+YTM of 1-Year Zero Coupon Bond) - 1 = (1+12.140%)^2/(1+5.141%) - 1 = 19.61% or 20%

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Part c)

The price of the coupon bond for the first year is calculated as follows:

Expected Price = (Face Value + Coupon Payment)/(1+Forward Rate) = (100 + 11)/(1+20%) = $92.81

The expected holding period return is calculated as follows:

Holding Period Return = [Coupon Payment + (Expected Price - Current Price)]/Current Price*100 = (11 + (92.81 - 98.73))/98.73*100 = 5.14% (same as yield to maturity on 1-year zero coupon bond) [we will have to use the exact intermediate values to arrive at this answer]

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Part d)

If there is a liquidity premium, the expected holding period return will be higher, that is, it will be greater than 5.14%.

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