Question

A $1,000 par value, 10% annual coupon bond matures in 3 years. The bond is currently priced at $1,106.92 and has a YTM of 6.0%.

a. What is the Macaulay duration?

b. What percentage will the bond's price change if market interest rates decrease by 1%?

Answer 1

Duration will be calculated using following formula:

Duration = [(1+Y) / Y] - [{(1+Y) + T(C-Y)} / C{(1+Y)^T - 1} + Y]

where Y = YTM

C = coupon rate

n = years to maturity

Duration = [(1+6%) / 6%] - [{(1+6%) + 3(10% - 6%)} / 10%{(1+6%)^3 - 1} + 6% ]

= 17.6667 - 14.9175

= 2.75years

b)

change is measured by volatality = Duration / (1+Y)

= 2.75 / (1+6%)

= 2.59%

if interest rate decrease by 1% bond price will increase by 2.59%

percentage change = 2.59%

(answers are rounded to two decimals)