Question

Regarding a 3-year bond with 14 percent semi-annual coupon payments and with a current price 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

i)

Let face value of bond be 100

Maturity of bond = 3 years

Annual Coupon Rate = 14%

Coupon frequency = semi-annual

Semi Annual Coupon = 14%*100/2 = 7

yield, r = 12%

Macaulay Duration is given by the formula

Where Ct is the cash flow for each period

r is the yield

t is the time period of the cash flow

Calculation for duration is shown below

Macaulay Duration = 2.5641

ii)

Modified Duration = Macaulay Duration /(1+yield/n)

Where n is the number of compounding per year

As coupon is paid semi-annually, n = 2

Modified Duration = 2.5641/(1+12%/2) = 2.5641/ 1.06 = 2.418961

New yield = 12%

Change in yield rate = 12.15% - 12% = 0.15%

% Change in bond price = - Modified Duration * Change in yield

= -2.418961*0.15% = -0.3628%

Hence the bond price will reduce by 0.3628%