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The Actuary The magazine of the Institute & Faculty of Actuaries

Life at the margins

At the margin is where it all happens’. This seven-year-old wisdom came from my honourable university economics lecturer, talking about supply and demand curves in a perfect market.
The margin is the promised land, where ‘it’ all happens. This is the crucial point where the economic world is in balance: where the borders blur, and bid and offer prices become equal; where the price is set for all, where demand equals supply, and from whence peace reigns in the land.
Taking artistic licence with the theory and omitting several important points, the people at the margin are the designated drivers to the economics party (they set the price and ‘break even’). Everybody else is having a wild time, celebrating because they have paid less or received more than they were expecting.

With the margin is where it all happens’
This piece of wisdom is distilled from various hallowed actuarial sources, and is at least 150 years old.
The pricing (and valuation) margins of an insurance company determine its profits, losses, and even its survival. Picture an idyllic market for insurance. In this market, our realistic expectations will be borne out in practice. In addition, let there always be customers for every company, and let no policy lapse. Further, let there be three insurers.

A tale of three citations
ZERO is a life company that prices its products using a realistic set of experience assumptions. Its name relates to the profits it expects to make. ZERO is the designated driver of the industry. No bonuses for its staff, no profits for its shareholders (and no parties for anyone). This is assuming that ZERO is allowed to operate at all under today’s regulations. For now, we will assume the regulators permit all companies to operate.
Looza is a life company that prices its products using optimistic assumptions. As its name implies, Looza is widely expected to make losses. No jobs for staff, negative returns for shareholders (and the only parties are those where people drown their sorrows).
RBA (RunByActuaries) is the third of the life companies in our life insurance market. RBA prices its products using conservative or prudent assumptions. As its name implies, it expects to make profits that emerge smoothly over time despite the constraints of fair value accounting and other legislation, which we will ‘assume away’. RBA is the party animal of all insurers its staff get bonuses and the shareholders get profits.

Basically, here’s what it’s all about
Table 1 illustrates the three bases used by our life companies. In our market, we need only three assumptions to have a full basis. Bear in mind that ZERO uses realistic assumptions.
Let’s ‘rephrase’ this table. Table 2 shows the implicit pricing margins each company is using:
In practice, no life company will be a Looza, ZERO, or an RBA. Every product of each life company will have optimistic, realistic, and prudent assumptions in its pricing basis.

Let’s take a different view
What is 9? 9 is an integer. It is also 10 plus a margin of 1. Rather than speaking of an assumption being optimistic, we can equally clearly speak of a realistic assumption with an optimistic margin. And vice versa for prudent assumptions um, prudent margins, that is.

Why bother?
When you price a policy, it is useful to know where you expect your profits to come from.
Once your pricing basis is set in terms that describe it relative to your realistic basis, it becomes clearer where your profits and losses are expected arise. On its own, that is pretty useful as it can take your analysis of surplus to a higher level. There is another benefit too this is a valuable tool that enables companies to manage their risk better.

An appetite for risk
Given a realistic basis, we can assign optimistic margins to some assumptions and prudent margins to others in order to a specific expected profit. In fact, we can vary our margins in this initial set quite widely and still obtain the same expected profit.
After all, each set of margins represents a different pricing basis, and each is expected to give the same profits. However, some assumptions are riskier than others. Coupling this with your company’s risk preferences allows you to choose where you want to take more risk.

Real fresh, live examples
Many companies that sell investment products do price their products using some form of this approach. For example, there are companies that are aware that they are undercharging for policy expenses and mortality risks. They hope to make up the losses from margins on their asset charges. In effect, they are choosing to take more risk on their expense and mortality experience than on their asset charge.
Here is another example. Most big companies are likely, at some point in time, to have lost money from mispricing. Sometimes this happens because their expectations are simply wrong. Other times, this occurs because pricing assumptions are not in line with with current realistic assumptions. Using this approach will bring the risk of the latter occurring to almost zero.

How would I use this?
In practice, I use optimistic margins in those areas where I want to take a greater risk of experience being worse than I expect. I recommend that you apply prudent margins on the assumptions likely to have the greatest impact on your profits. Even though my examples relate to life companies, this is just as applicable to other companies that pool risk, like general insurers and healthcare providers. o

Table 1 Our life insurers’ pricing bases

Table 2 Our life insurers’ pricing margins