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Hire a wealth manager, and one of their first tasks will be to work out your attitude to risk. If you are not sure exactly what this means, the questions are unlikely to help. They range from the inane (“How do you think a friend who knows you well would describe your attitude to taking financial risks?”) to the baffling (“Many television programmes now have a welter of fast whizzing images. Do you find these a) interesting; b) irritating; or c) amusing but they distract from the message of the programme?”). This is not necessarily a sign that your new adviser is destined to annoy you. Instead, it hints at something fundamental. Risk sits at the heart of financial markets. But trying to pin down precisely what it is, let alone how much of it you want and which investment choices should follow, can be maddening.

To get around this, most investors instead think about volatility, which has the advantage of being much easier to define and measure. Volatility describes the spread of outcomes in a bell-curve-like probability distribution. Outcomes close to the centre are always the most likely; volatility determines how wide a range counts as “close”. High volatility also raises the chances of getting an extreme result: in investment terms, an enormous gain or a crushing loss. You can gauge a stock’s volatility by looking at how wildly it has moved in the past or, alternatively, how expensive it is to insure it against big jumps in the future.

All this feels pretty risk-like, even if a nagging doubt remains that real-life worries lack the symmetry of a bell curve: cross the road carelessly and you risk getting run over; there is no equally probable and correspondingly wonderful upside. But set such qualms aside, pretend volatility is risk and you can construct an entire theory of investment allowing everyone to build portfolios that maximise their returns according to their neuroticism. In 1952 Harry Markowitz did just this, and later won a Nobel prize for it. His Modern Portfolio Theory (MPT) is almost certainly the framework your new wealth manager is using to translate your attitude to risk into a set of investments. The trouble is that it is broken. For it turns out that a crucial tenet of MPT—that taking more risk rewards you with a higher expected return—is not true at all.

Elroy Dimson, Paul Marsh and Mike Staunton, a trio of academics, demonstrate this in UBS’s Global Investment Returns Yearbook, an update to which has just been released. They examine the prices of American shares since 1963 and British ones since 1984, ordering them by volatility and then calculating how those in each part of the distribution actually performed. For medium and low volatilities, the results are disappointing for adherents of MPT: returns are clustered, with volatility having barely any discernible effect. Among the riskiest stocks, things are even worse. Far from offering outsized returns, they dramatically underperformed the rest.

The Yearbook’s authors are too thorough to present such results without caveats. For both countries, the riskiest stocks tended to also be those of corporate minnows, accounting for just 7% of total market value on average. Conversely, the least risky companies were disproportionately likely to be giants, accounting for 41% and 58% of market value in America and Britain respectively. This scuppers the chances of pairing a big long position in low-volatility stocks with a matching short position in high-volatility ones, which would be the obvious trading strategy for profiting from the anomaly and arbitraging it away. In any case, short positions are inherently riskier than long ones, so shorting the market’s jumpiest stocks would be a tough sell to clients.

Yet it is now clear that no rational investor ought to be buying such stocks, given they can expect to be punished, not rewarded, for taking more risk. Nor is the fact that they were risky only obvious in hindsight: it is unlikely that the illiquid shares of small firms vulnerable to competition and economic headwinds ever looked a great deal safer. Meanwhile, lower down the risk spectrum, the surprise is that more people do not realise that the least volatile stocks yield similar returns for less risk, and seek them out.

Readers may not be flabbergasted by the conclusion—that investors are not entirely rational after all. They might still wish to take another look at the racier bits of their portfolios. Perhaps those are the positions that will lead to a gilded retirement. History, though, suggests that they might be speculation for speculation’s sake. Call it return-free risk.■

Read more from Buttonwood, our columnist on financial markets:
Uranium prices are soaring. Investors should be careful (Feb 28th)
Should you put all your savings into stocks? (Feb 19th)
Investing in commodities has become nightmarishly difficult (Feb 16th)

Also: How the Buttonwood column got its name