Question

Bond Principal ($)	Time to Maturity (years)	Annual Coupon ($)	Bond Price ($)	Coupon Payment Frequency
100	1.00	0	97
100	2.00	4	100.0	(A)
100	3.00	5	99.0	(A)
100	4.00	6	100.0	(A)
100	5.00	6	98.0	(A)

A = Annual

1. Compute the continuously compounded yields of these five bonds.
2. Compute the continuously compounded zero rates for maturities of 1,2,3,4, and 5 years.

Answer 1

The calculation of zero rates is based on the formula:

for 2 year maturity:

c1*e^(-z1*1)+(c2+b2)*e^(-z2*2) = p2

where;

c1 = cash flow/coupon at the end of year 1

c2 = coupon at the end of year 2

b2 = bond principal with maturity if 2 years

z2 = zero rate for maturity of 2 years

z1 = zero rate for maturity of 1 year

p2 = price of bond with maturity 2 years