Allowing for risk using the risk discount rate

[MLC]

In the second reserving chapter the notes say that in some countries premiums are set using realistic assumptions with risks to the company being allowed for in the risk discount rate. The notes also mention that for riskier projects a higher discount rate should be used.

However for life insurance products (other than annuities) premiums are received first and benefits paid out at a later date. So by using a higher risk discount rate it would reduce the present value of the benefit payments by a greater extent than the premiums and so make such products look more profitable.

For example suppose we have a without-profits 15 year endowment for a policy holder aged 50 with SA of 2000 and we want a NPV of 100 (ignoring expenses).

If we thought the product was higher risk and so decided to use a risk discount rate of 6%, then this would mean a premium of 95.88 would be required to satisfy to above conditions.

But if we thought the product was less risky and so used a risk discount rate of 4% then this would require a premium of 109.59.

So in this case the more risky product gives a lower required premium.

Please could someone point out what I'm missing here.

Thanks,

Max

 

[Lindsay Smitherman]

Hi Max

Risk discount rates are used when pricing is being done via the cashflow projection approach. That is, when we are discounting future profits. (Broadly, profit = premiums + investment earnings - claims - expenses - increase in reserves.) Higher discount rate -> lower present value of profits -> higher premium rate.

As explained in Section 1.7 of Chapter 17, allowing for risk using a risk discount rate is not an available technique if the formula approach is used, which is basically what you are doing here (ie PV premiums = PV benefits + PV expenses). For the formula approach, we would have to deduct a margin from the investment return used. The course notes consider such an example, so probably worth having another read through that section.