View Full Version : WM 14 Ken's New Problem 5

04-09-2011, 09:20 PM
I'm pretty lost on this problem from how the current premium is being calculated to how the Current Variable premium is calculated.

It seems to relate to the "Calculating new rates for an existing product" section, but I'm even more lost when I look at that section especially when it introduces the discounts in addition to the R1 R2.

Any help for how its calculated?

Even the R1 and R2 being 1 and A, with 6000 exposures, I can't figure out how its 3M, while the R1 and R2 being 2 and A is 5.5M

Vorian Atreides
04-09-2011, 10:22 PM
Without seeing the whole problem, I'll offer a few bits that may (or may not) help.

Note that "variable premium" is usually made in the context where an expense fee is charged (that is, Fixed Expenses are a separate charge and not built into the rates). So the "current variable" premium will be total premium less the charged expense fee.

For example, if total premium = $6,000,000 and the expense fee = $50 per exposure, with 6,000 exposures; then the variable premium = 6M - 50*6k = 5.7M.

If you're looking at effecting a rate change in this scenario, what is needed is the approximate affect of making the various changes to each rating variable (the material of Ch 11) and then estimate the total rate effect these changes have already made. Let's say that the average effect of changes made to R1 is +3.2% and the average changes made to R2 is -1.1%; with no changes made to any discounts. The net effect of these changes is approximately (1+0.032)*(1-0.011)-1 = 2.1% to the variable premium.

Suppose, using the info provided above, that the indicated change is +5% overall. This means that you need to increase rates so that an additional 6M*5% = 300k is produced. But this would then necessitate that variable premiums increase by 300k/5.7M = 5.3% since we're assuming that the expense fee is adequate and not excessive.

Since the changes in the rating plan has already resulted in a 2.1% increase, we only need to increase the (variable) base rate by (1+0.053)/(1+0.021)-1 = 3.1%.

So, if the current (variable) base rate is $110.50, then the proposed base rate should be $113.93.

As for the discounts, deal with them as if they were another rating factor (with one more level than discounts provided; that extra level is simply those who don't qualify for any level of the given discount) and convert the discount to a decimal form. For example, a 15% discount == 0.85 factor. So if the plan for a rate change was to increase this discount to a 20% discount, this would effectively be saying that those have the discount would be seeing a -5.9% change (= 0.80/0.85 - 1.0). If 2,300 of the 6,000 exposures have this discount, the net impact of this rate change would be -2.3% change (= -5.9%*2.3/6.0 + 0.0*3.7/6.0) to the total variable premium.