Question

Sarah just used $98.71 purchased a Treasury bond. Assume that the yield rate for this bond is j₂ =4.43% p.a. and the duration of this bond is 3.17 years. Without actually calculating the new price for this bond, use the bond price and the duration value to estimate (use the price sensitivity formula) the change in price of this bond that would result from an increase in yield rate (j₂) of 15 basis points. Round your answer to four decimal places.

Answer 1

To find the answer we first need to find the Modified Duration of the Bond.

The formula for Modified Duration = Duration / (1 + YTM/2)

This value gives us the sensitivity of the price to the changes in yield.

From the given data, we can calculate that Modified Duration = 3.17 / (1+4.43%/2) = 3.1013

This value of 3.1013 means that for every 1% change in yield rates, the price of the bond changes by $3.1013.

Therefore we can find the change in on price when the yield changes by 0.15% (15 basis points) as below:

Modified Duration * Change in Yield Rate = 3.1013 * 0.15 = 0.4652.

Therefore, if the yield increases by 15 basis points, the bond price should fall by $0.4652