Is insurance worth paying for? Probably

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Think probabilities and be detached. It’s hard advice to follow. That is why the financial services industry is better off than its customers.

Scott Fitzgerald claimed that the mark of first-rate intelligence was the ability to hold two contradictory ideas in mind at the same time, and still function. Thinking in terms of probabilities is a technique for managing Fitzgerald’s problem.

Probabilistic thinking is particularly relevant to insurance and investment. While it is vexing to have your television stolen, or to lose your bag on holiday, insurance will not bring back either. The financial loss from a stolen television or lost bag is probably smaller than you will incur on a bad day on the stock market.

So you should think probabilities when you take out insurance. But so does the insurance company, which knows the probabilities well. It has estimated the expected value of claims and, if the expected value was not less than the premiums, it would not stay in business. Worse still, much of the premium on policies that insure against these minor contingencies goes not to pay policyholders but to the administrative costs of small claims.

So insure only those things you cannot afford to lose. You need insurance against your house burning down, but not for replacing the bedroom carpet. You need insurance against being hospitalised in the US, but not for an extra night’s accommodation because your plane is delayed.

Many people struggle with this advice. Insurers find their customers have little appetite for policies that rarely pay out, even though low probability risks are those most appropriate for insurance. Policyholders like the reassurance of occasional small cheques even if

such cheques add up to much less than their premiums.

You will be financially better off if you can be detached and learn to control these emotions. But even people educated in intelligent investment find it hard to exercise such control. If you can’t refrain from kicking yourself, or your spouse can’t refrain from kicking you, when an uninsured television set is stolen, then you should take out the policy.

This strategy is, however, likely to cost you considerably more in premiums than you received in claims.

The stock market throws up similar probabilities. Last week, I wrote about Robb Caledon, a bankrupt shipyard in the 1970s. Its shareholders would receive £1 per share if the company was nationalised, but otherwise would lose their money. Its shares were standing in the market at 40p. These shares were a good buy if you thought the nationalisation bill would succeed. But they were also a good buy if you thought the nationalisation bill might not succeed.

The expected value of a gamble such as an investment in Robb Caledon is measured by multiplying the possible outcomes by their probabilities. If you thought the probability that the bill would pass was 0.5, then the expected value of a share was 50p – 10p more than the market price.

In spite of the name, the expected value is not what you should expect, and the expected profit is not the profit you should expect, either. A year after a purchase, you would either have lost your whole investment or made 60p of profit. Still, if you use expected values, you will sometimes win, sometimes lose. But over time, the overall outcome will approach the expected value. In the long run, using probabilities and calculating expected values is likely to leave you better off.

Thinking probabilities does not come naturally to humans, though. Although the ancient Greeks developed mathematics and gambled incessantly, they never discovered probability, which appeared only in the 18th century.

Probabilistic thinking requires emotional detachment. We worry more about risks we cannot control than those we can. Many people are nervous about flying, but fewer are nervous about driving, even though driving is more dangerous. We feel comfort that we hold the steering wheel, even though the airline pilot is better trained than we are.

Sometimes involvement gives pleasure – a rush of excitement from the horse race or the roulette wheel.

Sometimes involvement causes pain – as for those who spent sleepless nights worrying about the shipbuilding nationalisation bill.

Whether pleasurable or painful, the experience of engagement is costly. The thrill of the race and the glamour of the casino are paid for by the majority of punters who lose. Sleepless nights worrying about risks we do not control cause distress, to no purpose.

These failures of detachment lead us away from expected values, and enable others to make money at our expense. That is why a diversified portfolio of individually risky investments can yield higher returns with less risk.

So think probabilities and be detached. It’s hard advice to follow. That is why the financial services industry is better off than its customers.

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