Large number of exposure units

Insurance is not magic. It is arithmetic that only works at scale.

The workbook's first requirement of an insurable risk is a large number of exposure units. Large groups of similar, though not necessarily identical, units must be subject to the same peril or group of perils.

Here is why that matters. An insurer runs a common pool. Everybody in the pool pays a premium. Only a few are expected to suffer a loss in any one year. So the insurer's liability falls on a handful while the contributions come from everybody.

Shrink the pool and the arithmetic breaks. The same total loss now has to be met by fewer premium payers, so each premium has to rise.

Push that far enough and the cover becomes unviable for both sides. The insured cannot afford it, and the insurer cannot price it.

The workbook makes this point with numbers, using its merchant ships example.

The merchant ships example, which the whole chapter is built on. In the 19th century, London merchants sent ships to India each month; a round trip took about 30 days, and some ships were lost at sea.

The fund exactly meets the two claims. Each merchant has secured a Rs 10,00,000 sum assured for Rs 20,000 — a ratio of 50 to 1.

Now shrink the pool, which is the workbook's own stress test. Suppose only 40 merchants agree to pay. The expected loss has not changed: two ships, Rs 20,00,000.

Rs 20,00,000 divided by 40 merchants = Rs 50,000 each

The premium rises from Rs 20,000 to Rs 50,000, two and a half times, for exactly the same cover. And the workbook adds the sting that makes it worse: it is not certain that the two lost ships will belong to the 40 who paid rather than to the 60 who did not. The premium has gone up and the fund may still face claims it cannot fund from its own subscribers.

Where this sits among the requirements. Section 1.2.1 lists seven requirements of an insurable risk, and this is (a). The others are insurable interest; the loss being accidental and unintentional; the loss being determinable and measurable; no prospect of gain or profit, which carries the principle of indemnity; the chance of loss being calculable; and the premium being economically feasible.

Two of those connect directly to this one. Chance of loss must be calculable requires the insurer to compute average frequency and average severity of future losses with some accuracy — which a large pool makes possible and a small one does not. And premium must be economically feasible says premiums must be not only affordable but far less than the value of the risk covered, or the insured will simply retain the risk instead of transferring it. At Rs 50,000 against a Rs 10,00,000 exposure the ratio is still 20 to 1; keep shrinking the pool and it stops being worth buying.

Note the exact wording. Similar, though not necessarily identical. The units need not be the same ship, the same house or the same age of person. They need to face the same peril.

Work the workbook's own figures in an Indian setting. A trade body in Kochi proposes a marine cover pool for 100 members, each with a consignment worth Rs 10,00,000, with 2 total losses expected in a year.

The expected loss is constant at Rs 20,00,000. Only the number of people sharing it changes, and the premium moves inversely with that number.

Where it stops being insurance. At 10 members the premium is 20% of the sum assured every year. A member paying Rs 2,00,000 a year for five years has paid Rs 10,00,000 — the whole value of the consignment. At that point the workbook's seventh requirement fails: the premium is no longer far less than the value of the risk covered, so retaining the risk becomes the more feasible option.

And the uncertainty the small pool adds. With 100 members, two losses among a hundred is a stable expectation. With 10 members, either nil or two losses in a year is perfectly possible. The insurer can no longer calculate average frequency and severity with any accuracy, so the sixth requirement fails too.

The counterpart on the life side. The workbook's King's employees example runs the same arithmetic for people: 500 employees, each earning Rs 2,00,000 a year for 10 years, so gross earnings of Rs 20,00,000 each; 2 deaths expected in the year, a total income loss of Rs 40,00,000; the king contributes Rs 8,000 per employee, which is 4% of the annual salary, and 500 x Rs 8,000 = Rs 40,00,000. Same structure, different peril — and it only works because there are 500 of them.

Chapter 1 (Basics of Insurance), section 1.2.1(a), is the first of seven requirements of an insurable risk, and it is taught through the merchant ships example set up in section 1.1. Section 1.2.1(f) and (g) — chance of loss must be calculable, and premium must be economically feasible — depend on it.

Expect a list question on the requirements of an insurable risk, and the arithmetic itself: if only 40 of the 100 merchants participate, the premium rises to Rs 50,000. The exact wording similar, though not necessarily identical is also tested, because candidates assume the units must be identical.

• Similar, not identical. The units must face the same peril; they need not be the same kind of object or the same age of person.
• The premium moves inversely with the pool size, not with the loss. In the workbook's stress test the expected loss stays at Rs 20,00,000 and only the number of payers changes, taking the premium from Rs 20,000 to Rs 50,000.
• A small pool is doubly bad. The premium rises and it is still uncertain whether the losses will fall among those who paid.
• This is a requirement of insurability, not a pricing technique. Without a large pool the risk is not insurable at all, however the premium is calculated.
• Do not confuse it with risk transfer or risk retention. Those are the two ways of dealing with a risk. This is a condition the risk must satisfy before transfer is even possible.
• Nor with reinsurance. Reinsurance spreads an insurer's own exposure across other insurers; this requirement is about the number of insureds in the original pool.
• The King's employees figures are a different example. 500 employees, Rs 8,000 premium each, Rs 40,00,000 fund. Mixing them with the merchant ship figures is an easy slip in a recall question.