Question

ECON 354 Problem Set 3 1. (Total 4 points, 2017 Final) The current yield curve for default-free zero-coupon bond is as follows: Maturity (years) Yield-to-maturity (%) 1% 2% 3% (a) What is the price of three-year zero coupon bond with the par value being $1,000 and the coupon rate being 2%? Assume that this coupon bond has no default risk and that one coupon payment is made every year (b) What are the implied one-year forward rates? (c) What is the expected yield-to-maturity of one-year zero coupon bond next year under the expectation hypothesis? (d) Suppose that investors prefer short-term investment and that the current liquidity premium for the next year is known to be 1%. Then, what is the expected yield- to-maturity of one-year zero coupon bond next year under the liquidity preference hypothesis?

Answer 1

Part a:

We will determine the cash flow for each of the three years and then discount them at the corresponding spot rate.

Coupon payment is assumed to be made at the end of the year = 2% * 1000 = 20

The calculation is given in the table below:

Maturity (yrs)	YTM (%)	Cash Flow	PV of Cash Flow
1	1%	20	20/(1+1%) = 19.80
2	2%	20	20/(1+2%)2 = 19.22
3	3%	1020	1020/(1+3%)3 =933.44
		Total	972.47

Price of the bond = $972.47

Part b:

To calculate the forward rates we will use the formula

F_T1,T2 = (R2*T2 -R1*T1) /( T2-T1)

Calculation is given in the table below:

Maturity (yrs)	YTM (%)	Implied forward rate (R2T2-R1T1) / (T2-T1)
1	1%
2	2%	3.00%
3	3%	5.00%

Part c:

The implied zero coupon rate of one year zero coupon bond next year is the implied forward rate.

Hence the answer is 3.00%

Part d:

Liquidity preference theory states that investors must be paid a “liquidity premium” to hold less liquid, long-term debt

The formula to calculate expected ytm is given below:

ytm = liquidity premium + ytm1 = 1% + 1% = 2%