Measures of Price Sensitivity Based on Parallel Yield Shifts

[Imad]

Hi David,

Hope you are well.
I have a question related to exemple on page 19 of your market risk study notes. In the exemple about the calculation of Macaulay duration, you got "k*price" as $1,702.
I did not understand how you calculated this. I assume that K = 7.
Please advise.

Thanks
Imad

 

[David Harper CFA FRM]

Hi Imad,

Thanks I hope you are well, too!

That should be more clear. k = 2. It is the same (k) as found in: Modified duration = Mac duration / (1 + yield/k), where typically our (k) is 2. It is the number or coupon periods per year; 2, in the case of semi-annual. If the coupons paid monthly, k = 12

Macaulay duration is the weighted average maturity of the bond, where the weights are the PV of the cash flows. As the example is a 10-year bond with semi-annual (k = 2) coupons, there are 20 cash flows. The Mac duration is weighting these periods (1, 2, ... 20) by the associated PV of cash flows (not easy to follow, but once you see it, Mac duration isn't too terrible!). In order to weight the periods, since the weights should sum to 1.0, we need to divide by 2*price (there are 2* too many cash flows, in a sense).

It's probably easier to see this weighting in http://www.bionicturtle.com/how-to/spreadsheet/3.b.3-hulls-duration
(note the next-to-last column H has the pure weights). Same formula but more direct.

I hope that explains, thanks! David