On the trail of a good bet

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We evaluate risks poorly – whether it comes to insurance, speculation or beef scares. These mistakes cost us all money in the long run.

As we all contemplate the remote prospect that the bowl of chilli con carne we ate in 1987 might give us Creutzfeldt Jacob disease, it is a timely moment to focus on our attitudes to risk.

Do you think that if mad cow disease could be completely eradicated at modest cost – say £1m – the government should do it, however low the probability is that it will do humans any harm? Would you consider taking out extra insurance before engaging in a high risk activity, like scuba diving or hang gliding? Do you think that companies that engage in speculative ventures, like oil exploration or new drug development need to earn a higher rate of return than firms which are in safer businesses, like electricity generation or retailing?

Do you regard it as important that your personal possessions, like your bicycle and your holiday bags, are properly insured? Do you believe that people who want to keep risk to a minimum should always avoid speculative securities like futures, options and other derivatives? Do you take a flutter on the national lottery?

Most people will have answered yes to all these questions. But if you have been trained in financial economics, and are familiar with the concept of expected utility maximisation and the structure of modern portfolio theory, you will think that the correct answer to all of them is no. Most people will probably conclude that this only shows how little economics and economists relate to the real world. They may be right. But let me put the economist’s case.

The financial economist contends that few of us really understand the concept of probability which underpins any systematic analysis of risk. Begin with the easiest mistake – taking out special insurance when you go hang gliding. If your family will suffer from your premature demise, they will suffer just as much if you die from something that is unlikely to happen – you are struck by a meteorite while walking in the street – as if you die from something which is much more probable, like falling out of the sky while hang gliding. That means that if you insure your life at all, you should insure it cheaply against low probability risks and not just insure it expensively against high probability risks.

Another possibility, of course, is that you, recognise the dangers of hang gliding, and think the policy looks cheap. You look at the odds the insurance company offers and fancy a bet. A bet that you will be killed. If this is what you believe, a wiser course would be not go hang gliding at all. If the insurance company knows its business, you will lose. And if it doesn’t know its business you will lose even more.

Since insurance companies and betting shops are profitable, and those who run them study risks all the time, it is a sound starting point to assume that the odds you are being offered are ones at which the other side expects to make money. So why then insure at all? The financial economist’s answer is that some bets may have a positive value to you even if they have on average, a negative expected cash return. You may find the prospect of a £100 premium distressing, but a £1000 loss may be more than ten times as distressing.

But – the financial economist goes on to say – that is only likely to be true if the £1000 is a large part of your personal wealth. And that is why you are wise to insure against your house burning down, but foolish to insure your bags or your bicycle. You would do better to put a little money into the building society every year to buy a new bicycle when your current one is stolen, and escape any need to find the insurance company’s profits and administrative costs. Only insure things you really cannot afford to lose.

So in thinking about risk you ought to look at the whole portfolio of risks you face, not at each risk in isolation. That is why adding a single speculative item – like a bet on the movement of the FT all-share index – might actually reduce, not increase, the risk of your overall portfolio. The guaranteed bonds issued by insurers and building societies are often based on derivatives, and so are fixed rate mortgages.

And that is also why the risk of an oil company’s dry hole, or a drug company’s failed development, is really nothing like as costly as it seems. That risk is spread over a very large number of people, none of whom should, if they are behaving sensibly, have a large part of their wealth in any particular activity of this kind. And when risks are distributed and diversified in this way their costs fall substantially. BP’s dry well is a penny less on all our pensions. The uncertainties associated with electricity generation – which cannot be diversified because they reflect general movements in the economy – is actually more costly.

But there is another, yet nearly universal, confusion in our attitude to risk. Our minds tend to dwell on unlikely outcomes, attaching an importance to them which may be far out of line with the probability that they will actually occur. That is how we feel about winning the national lottery, or about contracting BSE. The financial economist cannot prove that you are irrational to think in this way. All that he can say is that if you do think in this way, it will prove very expensive. That is why the national lottery is able to raise so much money for the government and good causes. And it is why eliminating mad cow disease is going to cost us all a fortune.

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