Question

1. A bond has a yield to maturity of 4.5%, a duration of 16 years, and a 20-year maturity. By what percentage will the bond's price change if market interest rates increase by 0.5%?

   		6.70 percent
   		7.66 percent
   		-6.70 percent
   		-7.66 percent

Answer 1

Duration = Macaulay duration of bond = 16 years

Yield to maturity of bond = YTM = 4.5%

Modified duration of bond = Macaulay duration / ( 1 + YTM) = 16 / (1 + 4.5%) = 16 / 1.045 = 15.3110

As market rate increase by +0.5% , therefore Percentage change in market interest rate or YTM of bond = +0.5%

Modified duration gives the percentage change in price of bond for 1% percent change in YTM or market interest rate of bond

Therefore we can calculate the percentage change in price of bond by using modified duration

Percentage change in price of bond = - Modified duration x Percent change in market interest rate = -15.3110 x 0.5% = -7.6555% = -7.66%

Answer: - 7.66%