SA3 April 2021 Q2

[Kieran Rowles]

Hi all,

I’ve been getting confused by the concept of rate change again and was hoping someone could help me with the following questions about SA3 April 2021 Q2:


1) For Q2 iii) the ASET solution say that anything that could potentially distort premium rate changes could be considered (as a factor that would reduce the credibility of premium rate changes in a reserving exercise). By distort, does this just mean any factor that could lead to a change in how the premium rates were calculated between times t1 and t2. For example, if the rating basis changed between times t1 and t2 it would make a comparison of the premiums between those times less relevant?


2) From the SP8 course notes premium rates are a measure of how profitable a policy or segment is. So a measure of premium rate could be the premium as a percentage of claims whereas the premium itself is the absolute amount that the policyholder is being charged. Question iv) talks about factors that might affect premium rates, so any factor that would make the business more or less profitable.

THe solutions seem to largely refer to things that would cause the actual premiums to change e.g. a change in level of exposure or nature of the risk. However shouldn’t premium rate changes strip out the effects of changes in the nature of the risk and changes in the level of exposure, as the rate change should be comparing the premiums charged for like for like polices at different times?


3) Finally (and linked to point 2), in part iv) when the solutions talk about factors that will lead to rate change for business d) ‘Rolling monthly mobile phone insurance policies written through a binding authority’ it mentions that:

“Some policyholders will sell their phone during the month, but as cover is monthly, will still have paid the premium, thus increasing profits and potentially reducing rates”

If premium rate is a measure of the profitability of business then wouldn’t a policyholder selling their phone mid-way through a month increase profitability as expected claim costs will decrease whilst premiums won't (so premium rate will rise).


I don’t know if I should be interpreting premium rate as a measure of the profitability of a premium rate, or the actual premium charged and I think this might be why I’m getting into such a mess.


Apologies for the long questions and thanks!

 

[Busy_Bee4422]

Hi

Regarding your questions:

1. I generally take distortion to mean anything that causes a lack of correspondence between two numbers you want to compare to each other as a result of a change in the internal and/or external environment or policy coverage. This causes unadjusted comparisons to be misleading. It normally is a result of some change discussed in the chapter on risk and uncertainty in sp8/7. With SA3 the trick is to tailor your answers to the specific scenario in the question.
2. The solution is ok. Premium rates are the cost per unit of exposure that is multiplied by the exposure to get the premium. Bear in mind that the rating structure can be complicated with different rates for different factors that are then combined to produce the premium. Anything that causes a change in the premium will also cause a change in the rate so you can discuss anything that causes premium changes.
3. Pricing is the process of coming up with the premium rates. The underwriter, using the rates and the proposal form/submission determines the premium. The profit margin is the measure of profitability.

Have a look at a rating manual if you work for an insurer. It will help clarify a lot of issues.

 

[Busy_Bee4422]

Hi

Just a follow-up. I was doing some reviews at work and it got me thinking about the point in SP8 that premium rates are a measure of profitability. I agree with that point. Because the premium rate is the premium per unit of an appropriate measure, the level of the premium rate can tell you how profitable a contract/book of busiess is. For example, if we know that we need a rate of 100 to break even if our rate is 98 we know we are not selling profitable business and vice versa.

 

[Kieran Rowles]

Hi

Just a follow-up. I was doing some reviews at work and it got me thinking about the point in SP8 that premium rates are a measure of profitability. I agree with that point. Because the premium rate is the premium per unit of an appropriate measure, the level of the premium rate can tell you how profitable a contract/book of busiess is. For example, if we know that we need a rate of 100 to break even if our rate is 98 we know we are not selling profitable business and vice versa.

Thanks for the follow up.

Unfortunately I think I’m still struggling to get my head around things. I get that premium rates are premium per unit of exposure. I was thinking back to SA3 April 2021 Q2 iv). It list a load of things that impact rate change for example changes in the layer structure of a non-proportional property treaty or an increase in climate change. However:

• If the layer structure changed for the non-proportional property treaty the exposure would change (e.g. an increase in the attachment point would reduce exposure), but wouldn’t the premium also decrease to reflect the lower level of coverage.
  • So overall the exposure and premium have decrease so the premium rate (premium per unit of exposure) might be broadly neutral
• Similarly, if the climate risk rose the exposure for the policy will rise as the level of risk has risen, but then wouldn’t the premium increase to reflect the increased level of risk, so again the premium rate would be broadly neutral.

Or is the point that a lot of these changes will change the exposure but the premium won’t initially change, so there will lead to a sudden change in premium rate (i.e. the adequacy of premiums). However, as rate change is normally measured for example at renewal then changes in these factors over the year should be incorporated into the new premium set. Unfortuantely I wasn't able to find a rating manual to support my understanding.

Is the rate change based on actual exposure (meaning it can change after the premiums have been set) or expected exposure?

Thanks.

 

[Busy_Bee4422]

Hi
Normally the rate changes when some dimension of the risk changes meaning you now expect more or fewer claims per unit of exposure excluding changes driven by underwriting cycle effects. I am not sure I would use the term "neutral" because the generally used pricing formula is that expected income should equal expected outgo. This means that in general, your premium will go up or down if the expected outgo goes up or down respectively. All this question is really focussing on is what may lead to a change in that relationship. Changes can happen on either side of the equation.

The exam report is brief on the matter of the attachment point but I see it as more its a move to a different section of the loss distribution where your expected claims experience will be different. The shape of the loss distribution will determine the rate. If you are using a burning cost approach you will have to include or exclude claims in your pricing leading to a new rate.

Regarding the climate risk, your claims experience would be expected to change if you previously were not exposed to such a risk. In the event that a rate change occurs, it is likely that you will now have an adjustment to the rate upwards to now factor in these new claims experience from a new source eg if the rate was previously 100 it may have to move to 110 to include the new claims. Not adjusting your rate is effectively reducing your rate.