Explicit Quantification Mfad(inv)
In the Dec 2009 CIA Mfad paper, the timing risk calculation example provided seems different from the examples provided in the Explicit_Quantification.pdf file from the guide, though they both yield similar results. The guide has change in duration % * discount factor (d) whereas the paper tries to solve d* (discount adjusted for timing risk) then the mfad = d - d*. Are both methods valid?
Comments
Yes, both methods should be valid based on the solution provided in the examiner's report. Below is the timing risk calculation using the method from the paper. You don't get exactly the same answer, but it's very close. (My simpler solution, based on the examiner's report, gives 91bps, and the method below gives 93bps.)
alternate approach to calc'ing timing risk margin:
where
d* = new discount rate (unknown)
D = original duration of liabilities
d = original discount rate
D* = shortened duration of liabs
Since:
d = 6.5%
D* = 0.86 x D or (1-shortening) x D
Because "D" cancels out, we can solve the equation from above and obtain:
d* = 5.57%
then the timing risk margin
= 6.50% - 5.57%
= 0.93%
= 93 bps
This answer is very close to the original approximation of 91bps using the much simpler method from the examiner's report.