Question

Consider a 3-year bond with 14 percent semi-annual coupon payments and currently priced to yield 12 per cent per annum.

1. Calculate duration of the bond.
2. What is the percentage of price change if interest rate increases to 12.15% per annum?

Answer 1

Assuming the Face value of the Bond $1000

A	Semi annual Period (w)	Cash Flows (x)	Discounting fator @ YTM 6%	PV of cash flows (x)	w*x
	1	70	0.9434	66.04	66.04
	2	70	0.8900	62.30	124.60
	3	70	0.8396	58.77	176.32
	4	70	0.7921	55.45	221.79
	5	70	0.7473	52.31	261.54
	6	1070	0.7050	754.31	4,525.85
			Price of Bond	1,049.17	5,376.13
			Duration = Sum(w*x)/Sum(x)
			=(5376.13/1049.17)/2	2.56	Years
			Volatility of Bond=( Duration/ YTM)
			=(2.56/1.12)	2.285714286
			If Yeild changes by 1% the Bond price will change by 2.285%
B			If Yeild is increased by .15% then price of bond
			=1049.17*(.15/100)*(2.2857)	3.60
			Price of the bond(1049.17-3.60)	1045.57
			Percentage decreae in price(1045.57/1049.17)-1	-0.343%