Why premium size matters (more than you think)

Most people involved with insurance recognise that more premium is better (ceteris paribus of course). This is usually true (and occasionally not) but while some of the reasons are obvious, there are a variety of more subtle factors to take into account. This post will cover many of these factors, and point out a few cautionary tales around seeking large average premium size above all else.

When is value created?

For a particular product-type, it is usual for larger premiums to be more profitable than smaller premiums. By profitability here I mean the increase in shareholder wealth resulting from having sold that additional policy. The value creation at time of sale arises from:

  1. A customer relationship has been confirmed and cemented through an agreement to do business for a few months or many years. The customer relationship was already in the process of being developed in the period up to the sale (from broad advertising campaigns, brand-development, specific distribution channel contact and the quotation process). However, this is also true for any other industry, so we will restrict the analysis in this post to the “point of sale”.
  2. This customer relationship means that for short-term or annually renewable business, there is a non-zero probability of renewal, and this probability is likely to be higher than the probability of a random individual with no previous contact with the insurance company buying a new product under the same conditions.
  3. The costs of renewing an existing policy are usually lower than those of creating a new policy. (Policyholder and risk details are already captured on the system, the sales process is quicker, legal and regulatory compliance (for example, around identifying customers) is already complete and payment details / credit checks have been performed.
  4. For life insurance business, a long-term, legal contract has been entered into. Traditionally, these contracts can be cancelled at the option of the policyholder (usually with a fair and sometimes controversially unfair penalty). In spite of the cancellation option, signing a long-term contract provides some evidence that the policyholder has an intention to enter into a long-term agreement with the insurance company.

This list isn’t exhaustive, but it covers some important bases.

So why are larger premiums better?

Larger premiums are more profitable because:

  • Some marginal costs are fixed per policy
  • Larger policies are usually more persistent
  • Larger policies usually imply greater wealth, which usually means lower morality (check below for caveats!)
Some marginal costs are fixed per policy

Many actual marginal costs really are fixed per policy:

  • Policy form, posting, printing, filing etc.
  • Ongoing reporting and communication with the policyholder
  • Bank charges related to processing premium receipts and claim payments
  • Calls to the call centre
  • Valuation modelling costs (PC / Mainframe running time, purchase costs, electricity, coding, debugging)

Since the costs are fixed per policy, the greater absolute charges are matched against lower costs yielding a higher margin.

Larger policies are usually more persistent

No question this is subjective, but one only needs to consider the 25% – 50% first year lapse rates on low-income products with small sums assured and small premiums. Large policies are likely to be sold to educated consumers who are less likely to be hoodwinked by smooth-talking commission-driven salespersons.

One can understand logically how this could be true, and the data supports these conclusions as well.

Larger policies usually imply greater wealth, which usually means lower mortality

Fairly standard actuarial knowledge this. Higher income means better access to healthcare for current ailments. More importantly, high income now is strongly correlated with high income in the previous years, which implies consistently better access to good healthcare and thus better overall life expectancy. Moreover, higher income is correlated with higher education. Education is correlated with family having money, which is correlated with good healthcare since birth, which is positive for life expectancy. Certain diseases (particularly heart disease) are related to stress and high cholesterol, which are positively correlated with wealth and income and act in the opposite direction.

Lower mortality both means lower claims experience (for non-annuity risk products) but also means, very marginally, that persistency will be higher since dead policyholders don’t pay premiums. Since a portion of all premiums is earmarked for the repayment of initial expenses, the more premiums paid the higher the overall margin will be.

And what about the impact of discounted rates?

Absolutely right. Higher premiums often attract discount rates, including lower asset management fees, higher allocation rates and lower mortality charges. These cost elements shouldn’t be ignored in the analysis, but experience usually shows that the benefits outweigh these costs. Results may vary!

An element that is often forgotten is medical underwriting. Most underwriting manuals have limits below which certain components of the comprehensive underwriting process are omitted because they aren’t cost effective. Thus, for the largest policies, the underwriting cost are often the highest. Analysis of actual experience and the costs involved for this should provide reasonable estimates of this cost.

One final, even more subtle impact is that of statistical variation. Individual policyholders will die (and we are continuing with the focus on non-annuity risk products here) with a certain probability at each age. Thus, the overall distribution of the number of deaths in a year should follow a binomial distribution, ignoring catastrophes and the slight theoretical correlation between deaths of spouses. Since the number of deaths follows a binomial distribution, we can determine likely variation from the expected number of deaths using basic statistical methods. What this also shows us is that as the number of policyholders increases, so the percentage variation from the mean decreases due to the diversification benefit. I’m not going to go into the detail of this for now – those familiar with insurance should be comfortable so far.

So, ideally we want lots of policies. If we also want to hold the premium constant between two comparable companies (S and B) but where S has small premiums per policy and B has big premiums per policy, then S will have a greater number of policyholders than B and will experience less volatility in financial results through better diversification of risks. You can also think of this like every Rand (or Pound or Dollar or Euro) of benefit for a particular policyholder is perfectly correlated with every other unit of currency for that same policyholder. Either the policyholder lives and all units of currency don’t get paid, or the policyholder dies and every single unit of currency is paid out as the total Sum Assured. Thus, larger premiums make larger benefits make more correlation and less diversification. This slightly unusual way of looking at the problem is what most people are familiar with as concentration risk, except here we are considering concentration within individual policyholders. This increase in risk increases the economic capital required (and often the regulatory capital too) which will likely have a cost to be considered.

So large premiums matter

Most people involved in life insurance will intuitively feel that larger premiums are “better” or more profitable – here are some of the reasons why. Most of these reasons are familiar to actuaries, and if you give an actuary a little bit of time he or she will likely come up with these and some others as well. However, this article has focussed on premium size in the absence of other factors and incentives. I’ll post soon on an example of how the external environment can distort this natural operational conclusions.

2 Replies to “Why premium size matters (more than you think)”

  1. Nice blog! And a good analysis of the larger policies question – one point on your lack of diversification point – at least with large policies you can go for reinsurance – get all the other benefits, without increasing your variability of profits to a point you are uncomfortable with.

    (came from David Maister’s site)

  2. Great point, Jennifer. Giving up a little profit by using some surplus-style proportional reinsurance will give you most of the benefits of larger policy sizes, without the added concentration risk and greater profit than an otherwise similar small policy. Thus, the risk and economic capital hit from larger policies can be managed through reinsurance.

    You do add in the credit risk of the reinsurer to your total enterprise risk, but given the relative credit rating of direct insurers and reinsurers, this is pretty marginal for almost all insurers. Depending on your financial reporting basis, there is likely to be some more work there in valuing liabilities and a reinsurance asset and the related disclosures. The regulator may also require approval of the reinsurer or the reinsurance programme, and there will always be some administrative overhead in setting up the treaties or negotiating facultative terms on a case-by-case basis.

    Reinsurers can also provide some valuable services through underwriting manuals and pricing, but this can’t be considered as a separate benefit because it is ultimately priced into the reinsurance rates either implicitly or explicitly.

    Reinsurance is a great area for discussion – I’ll be sure to blog about it in the near future.

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