2016.Fall Q15 Redone

This calculation is the same as explained on PrLiabs but with numbers from E (2016.Fall #15)

APD	CumPd	IncrPd	setup for PVfctr	setup for PVfctr w/ MfAD
(2)	(3)	(4)	(6) = (4) / 1.02^(2)	(9) = (4) / 1.015^(2)
0.5	10%	10%	9.90%	9.93%
1.5	60%	50%	48.54%	48.90%
2.5	100%	40%	38.07%	38.54%
			(10) Total = 0.9651	(10) Total = 0.9737

PV factors:

PVfctr @ 2.0% = 0.9651 x (1.02)^{(0.5 - 1/3)} = 0.9683

PVfctr @ 1.5% = 0.9737 x (1.015)^{(0.5 - 1/3)} = 0.9760

Macaulay duration:

Step 1: Take the SUMPRODUCT of columns (2) and (6) DIVIDED by the SUM of column (6) to get 1.7919 (This is the same method as for claim liabilities.)

(It's the weighted average of the time from column (2) where the weights are the PV factors from column (6))

Step 2: This is an extra step in the duration calculation for the premium liabilities to adjust for the FAD (Future Accident Date). It's easy, just subtract (0.5 - 0.3333):

The final Macaulay duration is:

1.7919 - (0.5 - .3333) = 1.6252

And the modified duration is:

1.6252 / (1.02) = 1.5933

To finish solving the problem as in the examiner's report but with this new duration, you have to recalc the duration of the total liabilities (claims + premium):

duration of liability = ( 24,350 x 0.8565 + 10,752 x 1.5933 ) / ( 24,350 + 10,752 ) = 1.0822

Then the final value for the capital required for interest rate risk is:

[ 49,000 x 2.367 x 1.25% ] - [ 35,102 x 1.0822 x 1.25% ] = 975

Something that makes my brain itchy:

Why do they keep using the term (0.5 - 1/3)? Isn't this just 1/6? I suppose I do see why they do it – it makes the reasoning behind the adjustment for future accident date clearer (kind of). Anyway, it's a small point. Ok, I feel better now that I've scratched my brain.

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