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Exam April 2005 Q7(iii)

F

f888bet

Member
I'm struggling to follow the solution to this question. I understand how you get to R = 0.02 * Theta, and I also understand how
Capital = 115.12 / Theta. However, I don't the next bit of the solution.

Where does the bit

Theta = 10% * Capital / 10m, and the following

Theta^2 = 115.13m / 100m term come from?

This makes absolutely no sense to me - Anyone understand this?
 
You're happy that Capital = 115.13m/theta.

If we now think about the Return on capital (or profit) for Company A, we notice that:

Return on capital * Capital = theta * Expected claims

since theta is the security loading i.e. the extra amount loaded onto the premiums to represent the profit.

We know that the Expected claims = 10m (the loss cost for A)
We also know that the required Return on capital = 10%
so:
10% * Capital = theta * 10m
and so
Capital = (10m * theta) / 10%

Equating this with the fact that Capital = 115.13m/theta from above gives the result that
theta^2 = 115.13/100m
 
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