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Please could someone explain why the amount is 1.08xRP and not 0.08RP?

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asked Oct 29, 2016 in BUS 1003H - Introduction to Financial Risk by anonymous
edited Oct 29, 2016 by simon_rigby

The question deals with pricing and the risk margin is 8% of the risk premium and instead of 0.08 they use 1.08 and I don't understand why.

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Solution:

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1 Answer

+1 vote
answered Oct 30, 2016 by Rowan (3,200 points)
selected Nov 12 by Richard van Gysen
 
Best answer

For this question, the definition of the Risk Premium (RP) is what is important. The RP is the portion of the premium which covers the expected cash outflow due to claims. Therefore, if we find the present value of the RP it is equivalent to the expected present value of claims.

Now consider the following equation:

\(EPV(OP) = EPV(Claims) + EPV(Expenses) + EPV(Profit) + EPV(Risk)\)

For this question, these values are as follows: (where i is the effective monthly rate)

\(EPV(OP) = 275 \ddot{a}_{\bar{12|}i}\)

\(EPV(Claims) = PV(RP) = RP\ddot{a}_{\bar{12|}i}\)

\(EPV(Expenses) = 150 + 0.05EPV(OP) = 150 + 0.05 \times 275 \ddot{a}_{\bar{12|}i}\)

\(EPV(Profit) = 0.1EPV(OP) = 0.1 \times 275 \ddot{a}_{\bar{12|}i}\)

\(EPV(Risk) = 0.08PV(RP) = 0.08 \times RP\ddot{a}_{\bar{12|}i}\)

Thus, when you combine the \(EPV(Claims)\) and the \(EPV(Risk)\) you end up with the 1.8 times the present value of the RP.

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