Question about duration and convexity

[korchamp]

Dear David,


Hello. I have watched your video in youtube on how to find YTM and find it very useful. However I am working on question to find the duration and convexity of bonds. :



Calculate the duration and convexity of a portfolio comprised of the following bonds
Years remaining to maturity Coupon Principal
10 8 150
8 3 100
5 10 50
7 0 120

The question does not provide the price and also i don't know if it is annual or semi annual period.
Any suggestion on what should I do to solve this question? (I need to solve them using excel_

Cheers,
Champ

 

[David Harper CFA FRM]

Hi Champ,

I agree you aren't given compound assumption (and principal amounts at 120 and 50 are odd), but even if you assume annual coupons, I do not see how there is a solution: you need yields, or prices to infer the yields. For example, the last zero-coupon bond has a Mac duration of 7.0 years but a mod duration (assume annual so k = 1) of: duration = 7.0/(1+y/1) = ?
i.e., duration is variant to yield (is lower as yield increases).

vanilla bonds have 5 variables (see the 5 TVM keystrokes on the TI/HP calculator). With respect to a bond, in general, you need four to solve for the fifth. You have 3 inputs, so unless yield is elsewhere stated (?), each of those bonds has technically several possible durations.

I hope that helps, thanks, David

 

[korchamp]

Thank you very much. Your advice really helps me.
I have 1 more question. There are couple of advantages for duration like 'speculating the interest rates' or 'matching risk to investors' taste'. But are there any disadvantages for duration? Thanks

 

[David Harper CFA FRM]

korchamp, great. Yes, two salient disadvantages are (i) it's a linear approximation with guaranteed error as it neglects the convexity (curvature) and (ii) even with convexity, it's a single-factor model treating the entire yield curve simultaneously (assumes a parallel shift in the yield-curve). So, analytical convenience at the cost of approximation (i) and not realistic w.r.t. term structure (ii).

Thanks, David