Modified Duration

[ExamTortoise]

The CAS model solution for Problem 31 of the 2005 exam calculates the modified duration as D/(1+ y/2), however, the CAS model solution for Problem 34 of the 2006 exam calculates the modified duration as D/(1 + y).

Does anyone know why? The problems look almost identical to me (i.e. both are semi-annual coupon bonds).

Thanks.

[Scooterpye]

Yeah, it looks like the model solution to 2006 #31 is incorrect. Modified duration should be Macaulay's divided by 1+y/2 for semi-annual bonds.

That question also has the extraneous information: "The current market interest rate is 5.0%."

The poor choice of words leaves the question open to legitimate confusion. Bonds are priced and duration is calculated based on market yields. If the "current" market yield is now 5%, then is the 5.5% yield-to-maturity quote out of date?

If they wanted to throw in extraneous information without creating confusion, they should've said something like, "The yield on three-year Treasury bonds was 5.0%," while making it clear that the bond you're pricing is not a Treasury bond.

[Becoming An Actuary]

Glad you guys posted. I was tripping out when I got this question wrong.

I think the D*=D/(1+y/2) is the way to go cause Goldfarb says so.

[Super Silver Haze]

The CAS model solution for Problem 34 of the 2005 exam calculates the modified duration as D/(1+ y/2), however, the CAS model solution for Problem 31 of the 2006 exam calculates the modified duration as D/(1 + y).

Does anyone know why? The problems look almost identical to me (i.e. both are semi-annual coupon bonds).

Thanks.
fixed
The poor choice of words leaves the question open to legitimate confusion. Bonds are priced and duration is calculated based on market yields. If the "current" market yield is now 5%, then is the 5.5% yield-to-maturity quote out of date?
To further confuse the issue, CSM does the 2006 question using the 5% market yield as the discount rate (i.e. 1.05^0.5, 1.05^1, 1.05^1.5, etc.) and then divides the duration by 1.055 to get the modified duration. I guess, like you said, the word "current" is the reason they used the market yield for discounting.

But yeah, I agree that if you're going to discount with 1+ y/2 to get the duration, you should be dividing by 1 + y/2 to get the modified duration.