Chapter 6 Chapter 6

43
[1% change in YMT causes 1.81% change in bond price in opposite direction]
Q. No. 55 5 : Madhav buys a bond with 4 years maturity. Face value Rs100. Coupon
rate 9%. YTM 9%. What is the duration of the bond What will be the price of the
bond if YTM rises to 10%.
Answer
Period (X) PV of cash-in-flows (W) XW
1 9 x 0.917 8.253
2 9 x 0.842 15.156
3 9 x 0.772 20.844
4 109 x 0.708 308.688
∑W = 99.95 ∑XW = 352.941
Duration = ∑XW /∑W = 352.941/99.95 = 3.53
% change in bond price = - [Duration/(1+YTM/n)] x (Δ BP/100)
= - [3.53/(1.09)] x (100/100)] = -3.24
When YTM rises to 10%, the price of the bond decreases by 3.24%. Hence new price
= 99.95 – 99.95(0.0324) = Rs.96.71
Q. No. 56 5 : The following data are available for a bond:
Face value
Rs.1,000
Coupon bonds 16%
Years to maturity 6
Redemption value
Rs.1,000
YTM 17%
What is the current market price, duration and volatility of this bond Calculate the
expected market price, if increase in required yield by 75 basis points. (Nov. 2005)
Answer
X W XW
1 160 x 0.855 = 136.80 136.80
2 160 x 0.731 = 116.96 233.92
3 160 x 0.624 = 99.84 299.52
4 160 x 0.534 = 85.44 341.76
5 160 x 0.456 = 72.96 364.80
6 1,160x0.390 = 452.40 2714.4
Total 964.40 4091.20
Current market price = Rs.964.40
Duration = 4091.20/964.40 = 4.24
Volatility = % change in bond price = - [Duration/(1+YTM/n)]
= -[4.24/(1.17)] = - 3.62 %
% change in bond price = - [Duration/(1+YTM/n)] x (Δ BP/100)
= - [4.24/(1.17)] x (75/100)] = - 2,72%