Question

A bond has a yield to maturity of 4.5%, a duration of 14 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 -6.70 percent 7.66 percent -7.66 percent

Answer 1

The correct answer would be option 2 or -6.70 percent

Let us now understand the calculation

Step 1 : Calculation of Price Volatility or Modified Duration

= D / (1+r)

where D = Duration i.e. 14 years

r = YTM i.e. 4.5%

Therefore Price Volatility or Modified Duration

= 14 / (1 + 0.045)

= 14/1.045

= 13.40 %

Now as stated Interest rate increases by 0.50%

When interest rate increases bond price is expected fall

Therefore Percentage fall in bonds price

= (13.40 * 0.50)

= -6.70%

The change in bond price as it falls is shown by Negetive Sign and for that reason it is -6.70 percent.