Question

A bond with a 8-year duration is worth $1071, and its yield to maturity is 7.1%. If the yield to maturity falls to 7.03%, you would predict that the new value of the bond will be approximately

Answer 1

Solution :

Inference for Duration or Volatility: For every one percentage increase in the yield or interest rate, price of the bond will decrease by the ( percentage of increase * duration ).

For every one percentage decrease in the yield or interest rate, price of the bond will increase by the ( percentage of decrease * duration. )

In the given case the bond yield is decreasing by ( 7.1 % - 7.03 % ) = 0.07 %

If the bond's yield decreases by 0.07 % then the market price will increase by = Duration * Percentage of decrease

= 8 * 0.07 % = 0.56 %

= 0.56 % ( when rounded off to two decimal places )

Thus the new bond price = $ 1071 + 0.56 % = ( 1071 * 1.0056 )

= $ 1076. 9976 ( when rounded off to four decimal places )

= $ 1077 ( when rounded off to the nearest whole number )

Thus the new value of the bond is approximately $ 1077, if the YTM fall from 7.1 % to 7.03 % .