Question on Duration

[srinu2singaraju]

Hi David,

Please help me in solving this question.

Q: The information in the table below is for a callable corporate bond traded in the secondary market. What will be the bond’s percentage price change if its yield declines by 0.50%?


Bond A

Coupon rate 8.30%
Price 101.56
Effective Duration 4.23
Yield Based DV 01 0.0445
Modified Duration 4.39
Macaulay Duration 4.56


The Answer is: 2.12% (how?)

(What is effective duration and when should we use this?)

Thanks in advance !!

Srinivas

 

[liordp]

Hi Srinivas

In my opinion the Calculation is = 0.5%*4.23=2.115% ~2.12%

The Explanation is Related to fact that Effective Duration recognize that cash flow may change because of embeeded option

Callable corporate bond is like plain vanila bond with option so we need to use it in order to calculate the change

Hope it's help

 

[David Harper CFA FRM]

H Convexity,

I agree with Srinivas. (Can i ask the source of the question, as this would be an usual question?)
The embedded call changes the cash flows because, for example, at a low yield the bond will be called and this alters and complicates the cash flows compared to a simple re-pricing for a plain vanilla bond that assumes the same coupons until the final principal at maturity. "Effective duration" utilizes more advanced re-pricing (e.g., binomial tree) to handle the embedded call, but then it has the same general form and meaning as "modified duration" (not Macaulay duration; it is generalized modified duration). At low yields, the callable bond will exhibit both negative duration and (related) an effective duration that is lower than the modified duration (i.e., so the 4.23 less than 4.39 is credible). The determination of effective duration is beyond the FRM scope (not really covered by Tuckman) and so this question would be a tad bit unusual but still good to know. Is covered by Fabozzi - David

 

[srinu2singaraju]

Thanks david.

Thanks convexity.

I found the above question from the FRM practice exams

regards
srinivas