Question

In bond valuation, we learned that bond price volatility was a function of years to maturity and size of coupon – e.g., the longer the term to maturity (TTM) or the smaller the coupon, the greater the bond price volatility. “Duration” is a measure of “effective maturity,” accounting for both term-to-maturity and coupon size. Given: A $,1000 face-value, 20% coupon bond has 5 years remaining to maturity. Prevailing market rates (applicable yield to maturity) is 10%. Find the bond’s

1) Duration: _________________________.

2) % volatility/change in price for small changes in the rates): _________________________.

Answer 1

To calculate the duration first we shall calculate the market price of the bond as follows:

   = 200 (PVIFA10%, 5yrs) + 1000 (PVIFA10%, 5yrs)

   = 200 * 3.791 + 1000 * 0.621

= 758.16 + 620.92

= 1379.08

(1) Duration:

Years	Cash Flows	P.V. @ 10%	Proportion of Bond value	Proportion of Bond value * Time (Years)
1	200	0.909	181.80	0.24	0.24
2	200	0.826	165.20	0.22	0.44
3	200	0.751	150.20	0.20	0.60
4	200	0.683	136.60	0.18	0.72
5	1200	0.621	124.20	0.16	0.80
			758.00	1.00	2.80

Duration of the Bond = 2.80 years

(2) Volatility = Duration /(1+YTM)

=2.80/1.1

=2.55%