Fall 2009 #7

[bosactuary]

Nov '09 #7 is an asset share question. I'm confused why Y3 the Premium is lapsed differently than the Y3 # of policies.


Given:
Market premium is $3000, discount is 15%
Y1 Lapse 0.4
Y2 Lapse 0.3
Y3 Lapse 0.3

In solutions, it shows:
Premium by Year
1=3000
2=3000*(1.0-0.4)x(1.15)=2070
3=2070*(1.0-0.6)x(1.15)=1666

# of Policies by Year
1=1
2=1*(1.0-0.4)x=0.6
3=(0.6)*(1.0-0.3)=0.42


Why isn't Y3 premium=Y2premium*(1-Y2lapse), which would be 2070*(1.0-0.3)x1.15. They seem lapsing logically for # of policies but not premium. What's the deal?!

[MATE Seminars]

That is just a typo. It should be 0.3, and they actually used 0.3 to get their answer:
2070 * (1.0 - 0.3) * 1.15 = 1,666.

[Actuarialness]

I just noticed another error in this solution. The last step calculates ROE as the PV of after-tax profit over the required capital, except that equation doesn't produce the answer they give. The answer of 3.18% is just the PV of after-tax profit over PV of premium. The answer to their equation is 15.9%.

I'm confused as to why the Cost of Capital percentages given in the model are never used in the solution. Do we just ignore that since they gave us the total required capital of 20%?

[MATE Seminars]

The cost of capital percentages are not used because capital is reflected instead as the equity in the ROE calculation. So adding in that cost of capital would be double counting in a way.

If on the other hand we were calculating present value of profits as a percent of premium, then those cost of capital assumptions could be used (although many past exam problems have done this calculation without any cost of capital assumption provided in the problem).

For the syllabus source on this topic, see the last paragraph of chapter 5 of the Individual Health Insurance book. It isn't perfectly clear there, but it is the best there is on the syllabus to guide us on this question.

[Actuarialness]

That makes sense. Thanks for the help!