Question

Given the following information:Bond Par valueTime to maturityAnnual Coupon Bond price(Semi-annual PMT)$100.000.50$0.00$95.00$100.001.00$0.00$92.00$100.001.50$6.20$99.00$100.002.00$8.00$98.00a) Calculate the 2-year zero rate.b) Calculate the 2-year forward rate.

Answer 1

Bond par value	Time to maturity	Annual coupon	Bond price
100.00	0.50	0.00	95.00
100.00	1.00	0.00	92.00
100.00	1.50	6.20	99.00
100.00	2.00	8.00	98.00

First, we calculate the YTM of the bonds

Using excel function rate

YTM = 2* Rate(2*Time to maturity,Annual coupon/2,-Bond price,Par value)

Here we multiply by 2 as the bond is a semi-annual coupon

nper = 2*Time to maturity

PMT= Annual coupon/2

PV = -Bond price

FV = Par value

Bond par value	Time to maturity	Annual coupon	Bond price	Yield to maturity
100.00	0.50	0.00	95.00	10.526%
100.00	1.00	0.00	92.00	8.514%
100.00	1.50	6.20	99.00	6.913%
100.00	2.00	8.00	98.00	9.116%

a) Two years zero rate is the Yield to maturity on a bond with a maturity of 2 years

Hence, Two years zero rate = 9.112%

b) 2- year forward rate (1.5 years from now)

The 2-year forward rate in this case f(1.5,2)

(1+f(0,2)/2)^4 = [(1+f(0,1.5)/2)^3 ] * [(1+f(1.5,2)/2)]

(1+0.09112/2)^4 = [(1+0.06913/2)^3 ] * [(1+f(1.5,2)/2)]

We get, f(1.5,2) = 15.78%