A bond currently sells for $1,250, which gives it a yield to maturity of 7%. Suppose that if the yield increases by 22 basis points, the price of the bond falls to $1,228.


Required:
What is the duration of this bond?

20

To calculate the duration of a bond, we need to use the concept of modified duration. Modified duration measures the percentage change in a bond's price in response to a change in its yield to maturity.

First, we need to calculate the dollar change in price corresponding to a 22 basis point increase in yield.

Step 1: Calculate the basis point value of the bond:
Yield change = 22 basis points
Basis point value = Yield change in decimal form * Bond price
= 0.22% * $1,250
= $2.75 (approx.)

Step 2: Calculate the new price of the bond after the yield change:
New price = Old price - Dollar change in price
= $1,250 - $2.75
= $1,247.25 (approx.)

Step 3: Calculate the percentage change in price:
Percentage change in price = (New price - Old price) / Old price
= ($1,247.25 - $1,250) / $1,250
≈ -0.0018 (approx.)

Step 4: Calculate the modified duration:
Modified duration = Percentage change in price / Yield change in decimal form
= -0.0018 / 0.0022
≈ -0.82 (approx.)

The duration of the bond is approximately -0.82.