Question

The following information is for zero-coupon bonds with $1,000 maturity value. Maturity (years) Bond Price ($) 970 940 910 a) Derive the yield curve that is consistent with the above data. b) Assume the liquidity preference hypothesis holds and the liquidity premium for each period is constant at 1%. What is the “true” three-year spot rate?

Answer 1

Solution:

The face value of the zero-coupon bond = 1000

1-Year bond price = 970

1-year spot rate = Face value / 1-year price -1 = 1000/970 -1 = 3.09%

2-Year bond price = 940

2-year spot rate = (Face value / 1-year price)^(1/2) -1 = (1000/940)^(1/2) -1 = 3.14%

3-Year bond price = 910

3-year spot rate = (Face value / 1-year price)^(1/3) -1 = (1000/910)^(1/3) -1 = 3.19%

Part A )

Yield curve

A B C D E к Spot Rate 3.20% 4 Year 3.18% Spot Rate 1 3.09% 2 3.14% 3 3.19% 3.16% 3.14% 3.12% 3.10% 3.08% 3.06% 3.049 Spot Rate

Part B )

It is given that the liquidity premium is 1% for all the periods hence real 3-year spot rate = 3.19% - 1% = 2.19%