Is it better to play it safe or to place bets that risk bankruptcy?

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Financial options are difficult to value. It isn’t really the maths that is the problem. The Black-Scholes formula, which can be used to help value some of them, may look arcane to people who struggled with school algebra but is not – as they say – rocket science. (Rocket science is not very close to the frontier of mathematical knowledge either. Nor does Black-Scholes really solve the valuation question, though it is worth knowing that many people think it does). The problem is that the valuation of options exposes difficulties humans encounter in assessing risks and uncertainties.

While options were invented recently, their pricing and evaluation is a question as old as time When hunter-gatherers went out in search of prey, they were often in danger of becoming prey themselves. No doubt some prudent hunters took weapons to fend off predators, scoured the ground carefully for hostile animals or tribes and stayed at home when it was too dangerous. Others, less prudent, chose not to buy or exercise these options. They took more risks and caught more prey.

Back around the campfire, was it the meagre haul of the prudent, or the full bags of those of the imprudent who returned, that won the admiration of the tribe? Were the young women of the tribe more impressed when the cautious described their uneventful days, or when the bold recalled their heroic escape from danger? And did mothers warn their daughters that marriage to brave hunters might end in widowhood, or urge them to seek husbands who would enable them to breed well-fed grandchildren?

Like all attempts to account for our behaviour by delving into our evolutionary past, this story should be taken with a large pinch of salt. But there does not have to be any historic truth in my narrative for its fundamental premise to be true. People who take foolish risks which mostly come off are likely to appear attractive mates and leaders. Our heroes are often drawn from precisely that population.

Our villains also. Some of the most spectacular recent business failures have been companies which braved the tigers, and were eaten alive. AIG feasted on the profits from credit default swaps, assuring analysts that the jungle was tiger-free. Equitable Life wrote guaranteed annuities for its prospective pensioners, confident that the tigers in the far distance were only shadows.

Accountants have always struggled with the problem of how to record transactions which carry a small risk of large loss. The perennial problem of how to make appropriate loss provisions in the banking sector is the best known illustration.

Such events can sensibly be assessed at their expected value if you have a large portfolio whose losses are uncorrelated – as with motor insurance. But this lack of correlation among risks is the exception, not the rule. It is not true of bank lending or credit default swaps on asset-backed securities or Equitable Life’s guaranteed annuities. And it was not true for the mortgages issued by Fannie Mae and Freddie Mac, or of the US government’s implicit guarantee of its liabilities.

Although transactions with low probability of large loss and high probability of small gain carry the potential for disaster, they can appear attractive for a very long time – perhaps for ever. They appeal to anyone in business or politics with a short time horizon: which is today most people in business or politics. The benefits can be brought into account now. The costs – if there are any – will probably fall to be met by someone else.

The UK government’s Help to Buy scheme admirably meets these criteria – it creates a class of happy borrowers at no apparent, and certainly no immediate, cost to government. It is not surprising that special advisers are in love with the policy.

Or there is the pledge from Mario Draghi, president of the European Central Bank, to do “whatever it takes” to save the euro – an assurance that costs nothing to give, spreads immediate balm on the markets and may never require any action. But if “whatever it takes” did not have the potential to be costly, the pledge would be redundant; we can already expect that the ECB will do what is cheap and easy.

Financial regulators warn that dealing in options is for sophisticated players only and carries a risk of total loss. It is a lesson everyone should take to heart.

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