Key Rate Shifts

[mathman]

Hi,

So I was looking at the example in Bruce Tuckman where he explains Key Rate Shifts and as per his example we have:

A semi annual payment mortgage to be retired in 30 years at a payment of 3250 per 6 months discounted at a 5% flat rate. This gives the PV to be 100,453.13

Now he says there is a key rate shift of an increase of 1 basis point in the 5 year rate. So I did that and linearly calculated the appropriate interest rates that should apply from the 2 year to 10 year period (that is going from 0 bp to 1bp from 2nd year to 5th year and then from 1bp down to 0bp from 5th year to 10th year). I adjusted them to the 5% rate and found that this value comes to 100, 442.487, which is not 100,449.36. I did this to test my understanding of the meaning of what is a key rate. Am I applying the formula correctly? You can see my working in the corresponding excel sheet I have attached. Please let me know what you think. Thanks.

 

[David Harper CFA FRM]

Hi Mathman,

Your method is correct and fine: you shock the 5-year spot with linear interpolation to each of the neighboring 2- and 10-year rates. Your 100,442.487 matches the value in our original XLS version. The difference is that Tuckman employs a shock to the par yield instead of the spot rate (because, according to him, par yields makes calculation of the hedging portfolio simpler), which produces a (slightly) diffferent PV. But the key rate is an "interest rate" that can validly be the spot, forward rate, or par yield. Here is our learning XLS with both versions, yours (shock spot) and reconciles with Tuckman (shock par yield): http://www.bionicturtle.com/how-to/spreadsheet/2012.5.b.3.-key-rate-shift/ Thanks,

 

[mathman]

Thanks David. It feels good to know I got it right.