# key rates

Discussion in 'P1.T3. Financial Markets & Products (30%)' started by narayananvenkat, Aug 25, 2009.

1. ### narayananvenkatcfo

David..

Your tutorials on key rates are a treat to watch.

your spreadsheet on key rates is explicit and very well undersatandable. I have the foll qn

In the cols wherein you detail how rates are shocked under various periods(after 2 year,5 year etc.,,
1.What is the rationale(logiic) behind magnitude of shocks say after 2 years, 5 years etc., do you shock up and down over remaining period,ie how have quantified the shock %
2. In one slide you say effective duration is same as modified duration and some other slide define the differently if Iam not mistaken.

You may jhave answered similar qns humpteen times in forums etc., but please explain
venkat

2. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Hi venkat,

(thank you for liking the video. sincerely, I feel that is the highest compliment I could want because I *realize* it can be boring to sit through so much talking)

1. In a sense, it is arbitrary, by choice/design. It is merely Tuckman's choice: to select which key rates are shocked by one basis point, and then the "rule" about how the neighboring rates will be influenced. From the chart:

Tuckman uses a rule of "linear interpolation" so that, for example, the 2 year rate is fully shocked: period 4 = +1 basis point...
and then it is linear interpolation between:

period 4 at 1 basis point
...and...
period 10 at 0 basis points (b/c period 10 = 5 years and that is another key rate, so we can "anchor" at period 10; it will get its own +1 bps shock)

so the interpolation gives:
4: 0.01000%
5: 0.00833%
6: 0.00667%
7: 0.00500%
8: 0.00333%
9: 0.00167%
10: 0.00000%

but Tuckman says, "The fact that the shifts are linear between key rates is not essential. Quite the contrary: The arbitrary shape of the shifts is a theoretical weakness of the key rate approach. One might easily argue, for example, that the shifts should at least be smooth curves rather than piecewise linear segments. However, in practice, the advantage of extra smoothness may not justify the increased complexity caused by abandoning the simplicity of straight lines."

2. I treated them equivalently where we are looking at bonds without embedded options. As Fabozzi says, "Modified duration is the approximate percentage change in a bond’s price for a 100 basis point change in yield assuming that the bond’s expected cash flows do not change when the yield changes" .... but effective duration (option adjusted duration) does "takes into account both the discounting at different interest rates and how the expected cash flows may change." In other words, consider a MBS (or callable bond): at low yields, the bond prepays (or may be called). Consequently, yields changes may change cash flow. Effective duration accounts for this interaction between yields and cash flows; modified does not. However, for a plain vanilla bond (e.g., 6% coupon), yields won't change the cash flows, so the difference doesn't matter for plain vanilla bonds.

Hope this helps, David

3. ### narayananvenkatcfo

David..

it was me venkat who posted the qn and not (sudeep) . No matter . Thanks for the nice explanation.

venkat