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.

Taxes – more than just a cost

Apparently, it was Benjamin Franklin who said “In this world, nothing can be said to be certain, except death and taxes.” Without going into a detailed analysis of whether death is certain, and whether there are tax-haven countries with sufficiently low taxes to stretch the point a little, I have some comments to make on the throw-away use of the word “certain”.

Taxes are not certain. Even if some amount of tax is unavoidable, the actual tax payable is not certain. This is not a massively complex idea, but does require a shift in mindset to consider taxes as something other than merely a cost that must be paid, something that reduces profits and returns to the owners of a business. I’m not even talking about optimising the amount of tax paid through careful tax structuring (which can be a good idea, if it is legal, and if the loophole stays open long enough to be beneficial, and if the extent of structuring makes business and moral sense).

I’m talking about considering the impact that tax has on business strategy, target market selection, business mix choices and competitive advantage.

A current example for me is the taxation of life insurance companies in Lebanon. Corporate tax on profits is 15% in Lebanon. However, for life insurers, the tax authorities have deemed it too difficult to nail down a clear measure of insurer profitability (another point for another blog, but in fairness to the tax authorities, insurers are rather notorious for adjusting actuarial reserves to arrive at the desired financial result …). Thus, insurers are taxed on “assumed profit” which is set to be 5% of revenue (mostly premiums written, which are considered as revenue, and investment income).

Some things to note:

  • The tax calculation is thus simple, which for most business is a good thing.
  • The effective rate of tax is then 15% x 5% x revenue = 0.75% x revenue.
  • If a company can make a higher margin than 5% of revenue, then they will benefit from the simplified tax system. If a company’s margins are thin and their net profit is less than 5% of premiums, they will pay a disproportionately large amount of tax.

The last point is where tax becomes interesting, and this is particularly ironic because in this case tax is more certain than usual (given it depends only on a single factor, revenue, rather than revenue and expenses). I’ll expand in my next posts on two important impacts this has for insurers and the economy as a whole.

The place of analysis for entrepreneurs

Entrepreneurs are hailed as saviours of modern society. The current international paradigm (and one which is growing ever stronger in South Africa) is biased towards the idea that career success requires one to create something new and build up something from scratch – head out on one’s own and conquer the earth.

OK, this doesn’t apply to everyone, but the start work at a large company, rise within the ranks to senior management then retire and die doesn’t have the same allure as it used to. I was discussing this with some very bright friends recently. We agreed (in our pop psychology way) that probably one of the causes of this change in attitude was the decrease in loyalty offered by large companies to its employees over the last 30 years. It might be simply a matter of survival that has created this idea that you’ve only made it once you’ve made it your own way.

So increasing numbers of engineers are heading out on their own to form small engineering consulting businesses. Even actuaries are departing the safe and comfortable world of life insurance or pensions for the wild wastelands of “entrepreneurial world-saving activities”. These are entrepreneurs with extensive theoretical training, rigourous mathematical and problem-solving abilities, and (particularly actuaries) a huge array of analysis tools and a deep-seated understanding of risk. Are these skills of benefit or hindrance to these professionals in their new-found living-on-the-edge lives?

Jawwad Farid (an actuary in Pakistan with extensive education in the States, including an MBA) takes a view on this in his blog on the new Image of the Actuary site. (The tagline for the Society of Actuaries is “Risk is Opportunity”, which I quite like as a slogan for actuaries, since we are used to using risk rather than just getting rid of it.) I get the impression that Mr Farid is not a typical actuary in his risk-taking exploits, but he does explain the twin concepts that reduce actuaries’ willingness to take risks:

  1. Possible higher risk aversity (the obvious, but not necessarily all-powerful factor)
  2. Higher opportunity cost of taking risk (more to leave behind in terms of virtually guaranteed good income)

Factor 1 comes from several possible areas. Maybe only risk averse people are attracted to studying actuarial science. Maybe only the risk averse ones make it. Maybe the very process of writing (and passing…) the exams kills off part of the soul of actuaries, leaving them nervous shells of their former beings in the process. While I’m sure these all make a contribution, there can be no question that virtually all actuaries start out as risk averse. In their career choice (at school-leaving age now, mostly) they choose to study a course that is difficult (has a high cost) but reasonably certain rewards (provided they make it). Thus, they are paying a high price to reduce risk. This is a classic definition of risk aversity. As it turns out, many probably underestimate the amount of risk involved in actually getting through the exams. Let it not be said that actuarial students don’t back themselves to meet challenges! Overestimation of one’s abilities is one of the important components of Behavioural Finance and related behavioural studies. (Interestingly, many of these studies show that the extent of overestimation of one’s abilities increases as one’s abilities increase. The frightening fact may be that as actuaries and other “experts” become more qualified, they are more susceptible to overestimating their skills.)

But all those last few paragraphs are something of a digression. The point of this blog is to pose the question: “Does analysis have a place for entrepreneurs?” If it does, then actuaries (and similarly other analytical professionals) should have an advantage, even if it is muted by the dangersr of analysis paralysis. If, on the other hand, the advantage of analysis is so slight in the face of huge uncertainty and the need for brace, gut-based decisions, then actuaries should do well to stay clear.

There is no doubt in my mind that analysis is key to success in business, but I’m an actuary after all.

Almost Famous

Not quite rockstar material yet, but my fame is spreading, at least in The Actuary, the magazine of the UK’s actuarial profession.

Check out the mention of my involvemet in the launch of the South African version of the Actuarial Modelling course (CA2) in Pretoria during July. Overall, it went pretty smoothly – results are expected shortly. I’ll post a link when they come out if one is available.

exam results now available