Premium rate changes

[Cheng]

Hi! Hope someone can shed some light on premium rate changes, as I don't work in with a general insurer, I'm having some difficulty imagining how it's done and hence understand the readings.

From what I gathered from the readings, it's generally done to compare the premium rates at t1 and t2. Method 1,2 and 4 makes sense but I don't really get method 3, i.e. measure rate changes on individual renewals.

a) at renewals, don't insurers need to determine the premium to charge policyholders and hence would have premium at t2?

b) is this method usually used for policies with premium adjustments and hence premium at t2 can't be determined accurately?

c) from the ratio of E(Loss at t2) over E(Loss at t1), we determine Prem at t2/ Prem at t1 = Prem at t2 / [ Prem at t1 * {E(Loss at t2)/ E(Loss at t1)}]. I don't really understand this formula. Wouldn't it make more sense if Prem at t2 = Prem at t1* {E(Loss at t2)/ E(Loss at t1)}

d) from the readings it says that rate change for a group of renewed policies can be expressed as [ sum of Prem at t2 / sum of as-if prem at t1 -1]. Why do we adjust premium at t1 since we would already have prem at t1?

Lastly, one disadvantage of method4, is that there may be confusion around pure rate change and mis-pricing. Can you give another example of how this may arise or further explanation on the example given in the readings?

Thanks in advance!

 

[td290]

Hi Cheng,

4 A.M.! What on Earth are you doing studying premium rate changes at that God-forsaken hour?! I’ll answer your questions as helpfully as I can although my initial impression is that you might be at crossed purposes with the Core Reading. We are not talking about methods of determining premium rates; we are talking about monitoring past rate changes. In other words, the premiums at t1 and t2 will already have been determined and we have to work out the implied rate change. We are normally doing this to construct a rating index, which will give us an overall picture of how rates for a particular line of business have moved over time. Furthermore, we will normally want to strip out the effects of changes in the structure of the risk (i.e. limits, deductibles, etc.) and changes in the level of exposure in order to leave us with a rating index that shows movements in premium rates due to external factors. (Inside an insurance company you hear the phrase “rating environment” used a lot.)

Now the Core Reading discusses at various points the reasons why actual rates charged may differ from technical rates. In a subscription market, such as Lloyds’, these reasons are particularly apparent. The rates will generally be set by the lead underwriter, who will be approached by a broker with a particular risk and asked for a quote. At this point, the lead underwriter has a difficult juggling act to perform. He may have some analysis from actuaries that indicates a suitable technical rate. However he has other points to consider as well. If he sets the premium too high, the broker, who is the agent of the insured and will be under pressure to get his client a good price, is likely to look elsewhere and may also feel that, when placing future risks, showing them to this particular lead underwriter is likely to be a waste of time. Conversely, if the lead underwriter sets the price too low, he is compromising the profitability of his own syndicate and may also find that few underwriters from other syndicates are willing to sign on as following underwriters at that rate. The lead underwriter will also have in mind that he has a business plan that gives him a target amount of premium to write. If he doesn’t meet this target, his department may not cover its fixed expenses. Also, if any non-proportional reinsurance has been purchased that is subject to minimum premiums, the minimum amounts may start to take effect.

(Sorry, this is taking rather longer than I planned!) So after that lengthy explanation of market influences on premiums, what the insurer is trying to do is to measure the effect of influences such as these on previous years’ premiums, hence the motivation for constructing the rating index. Hopefully this goes some way to answering your questions a) and b).

Wouldn't it make more sense if Prem at t2 = Prem at t1* {E(Loss at t2)/ E(Loss at t1)}

This would happen if the premium charged was always equal to the pure risk premium. In this case there would be no rate changes. The whole point of the exercise though is to determine the element of the premium rate change that is not attributable to the change in limits, attachments, line size and exposure, i.e. not attributable to the change in the pure risk premium. In other words, we want to know the element of the rate change attributable to external factors such as those discussed above. So we calculate an “as-if” premium at t1, i.e. the original premium at t1 adjusted for all the effects we want to strip out. We then compare the actual premium at t2 with the “as-if” premium at t1.

from the readings it says that rate change for a group of renewed policies can be expressed as [ sum of Prem at t2 / sum of as-if prem at t1 -1].

The same idea is at work here. We take a group of policies on which we wish to measure the average rate change. We start from the premiums at t1 and adjust them for changes in the structure of the risks or anything that might influence the pure risk premium. We then compare the total premium at t2 with the adjusted premium at t1.

Finally, you asked about this:

There may also be confusion around pure rate change and mis-pricing.

I must admit I’m not particularly clear on the point being made here. I suspect what the notes are saying is that the underwriter may not be 100% clear on the question being asked and reliability of the results may be compromised by a straightforward miscommunication.

(Some of the above is loosely plagiarised from http://www.actuaries.org.uk/sites/all/files/documents/pdf/cynic-and-idealist.pdf)