Question B6 Zero-rate curves for various dates are shown in the following table:
ID: 1172803 • Letter: Q
Question
Question B6 Zero-rate curves for various dates are shown in the following table: Term Year Year YearYear (years)o 2 3 4.1% 5.2% 5.8% | 7.2% | 8.2% | 8.8% | 9.9% | 10.4% | 10.1% |10.4% | 10.2% | 10.4% 2 3 Use this information to answer questions a)-b) below: a) An investor bought a 3-year zero-coupon bond in Year o, when the 1-year zero rate was 4.1% pa, the 2-year zero rate was 5.2% pa and the 3-year zero rate was 5.8% pa. The investor sold the bond two years later. What is the investor's holding period rate of return (pa)? b) Find the price (per $100 par value) of a default-free bond with annual coupon rate of 5% and exactly 3 years to maturity. Does the bond trade at par, at premium or discount? Would you expect the bond's yield to be equal to, greater or less than the coupon rate?Explanation / Answer
a) Assuming that the face value (FV) of the zero coupon bond is 100. In year 0 the price of the zero coupon bond can be written as:
PV=0/(1.0410)+0/(1.052)2+100/(1.058)3
= $ 84.43
After 2 years the bond will have one year left to maturity. Hence, the price of the bond:
PV=100/(1.099)
=$ 90.99
Therefore, holding period return:
((90.99-84.43)/84.43)*100
=7.77%
Annualized holding period return= (1+0.0777)1/2-1= 3.812%
b) Price of the bond :
5/(1.041)+5/(1.052)2+105/(1.058)3
=$ 97.98
Since the bond is trading at less than FV of 100 the bond is trading at a discount.
The bonds yield is greater than the coupon rate at 5.752%. Use the following inputs in your financial calculator to get I/Y
PV=-97.98
PMT=5
n=3
FV=100