Question

What is the duration of a 2 year bond that pays a 5% annual coupon with a 9% YTM? Use $1000 as the face value of the bond. Using the duration, what is the expected change in the bond if rates are expected to drop by 25 basis points?

Answer 1

Solution:

The duration of the bond is = 1.9507 years

Please find the attached screenshot of the excel sheet containing the detailed calculation for the solution.

As per the information given in the question

The Duration of the bond = 1.9507 years

Yield to maturity = 9 %

The YTM and price of a bond are inversely related. This relationship is explained by calculating the volatility of the bond.

Thus the volatility = Duration / ( 1 + Interest rate )

= 1.9507 / ( 1 + 0.09 ) = 1.9507 / 1.09 = % = 1.7896 % ( when rounded off to two decimal places )

Inference for volatility : For every one percentage change in the YTM the bond price will change by 1.7896 % .

Thus,

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

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

As per the information given in the question the interest rates or YTM are expected to decrease by 25 basis points

Thus since the interest rate is decreasing by 0.25 % , the price of the bond will increase by

= 0.25 * 1.7896 %

= 0.4474

= 0.45 %

Thus the price of the bond will increase by 0.45 %

Thus the predicted price change in the bond =   0.45 %