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OPINION

Luck or skill?

Luck or skill?
January 22, 2015
Luck or skill?

Economists at Ohio State University show that foreign exchange day-traders tend to increase their borrowing and activity after a week of modest profits - of the sort that could easily be due to random good luck - but don't react to modest losses. This suggests they are prone to a self-serving bias: they attribute profits to skill but losses to bad luck. This is dangerous because it can lead to overconfidence and excessive risk-taking. As that great economist Arsene Wenger once said: "When you give success to stupid people, it makes them more stupid sometimes."

This is not the only evidence that investors misinterpret past returns to see skill where none exists. Economists at the University of Mannheim have shown that investors see skill in fund managers' performance where there might only be luck, and so overinvest in expensive funds that subsequently do badly.

Bjorn-Christopher Witte at the University of Bamberg has shown that this can lead to systematic market failure. If investors favour big but lucky performers over smaller, stabler and more skilful ones then the market will select against skill. We'll see survival not of the fittest but of the stupidest. This might not be the case for unit trusts - where the problem is that many are closet trackers - but it might explain banks' excessively risky behaviour in the run-up to the 2008 crisis, and could be true for some hedge funds.

All this poses the question: how can we protect ourselves from these sorts of mistakes? We do so by asking of returns: are they due to noise or signal? A useful measure here is the tracking error, which measures the volatility of returns relative to the benchmark.

The idea here is simple. We'd expect returns on any fund or portfolio to deviate from the market's return to some extent simply by chance. Tracking error helps us quantify this.

For a reasonably active UK all companies unit trust, tracking error is around 6 per cent. One reasonable interpretation of this is that it implies that a fund has a one-in-six chance of beating the market by six percentage points or more over a 12-month period simply by chance. Because one-in-six chances come up quite often, we shouldn't interpret such modest outperformance as proof of skill; it might be evidence of it, but not proof. What's more, even if no fund had any skill, we'd expect one-sixth of them to beat the market by six percentage points or more simply by luck. (In fact, fewer all companies unit trusts have done so, because many have a smaller tracking error.)

For retail investors, most of whom hold more concentrated portfolios, tracking errors are bigger - which means that there's a bigger chance of beating the market by a long way simply by chance.

Another handy measure in this context is the information ratio, which is relative returns divided by the tracking error. The higher this ratio is, the more likely it is that a fund's returns are due to skill.

However, even very respectable information ratios fall short of proof of skill. For example, in the last three years the best-performing fund in Trustnet's database of all companies' funds (in terms of raw performance) has been Standard Life's unconstrained fund. It has an information ratio of 1.3. One reasonable interpretation of this is that there's a 10 per cent chance that such returns could be due to luck. That's higher than the cut-off point for what social scientists conventionally consider to be statistical significance.

Of course, it's not just the size of performance that matters, but consistency. We would usually consider consistent performance to be a mark of competence.

If returns were random and there were no skill, it would be easy to measure this. Ex ante, the chance of beating the market would be 50 per cent in one year, 25 per cent in each of two years, 12.5 per cent in each of three years and so on. (I say 'ex ante' because if small caps outperform mega caps then most stocks will beat the market which means that a monkey picking stocks at random has a better than 50:50 chance of beating the market. Let's ignore this wrinkle.)

However, things aren't so simple. There's momentum in share prices. This means that a fund manager who got lucky one year might do well the following year, simply because stocks that do well one year go on to outperform the next. Even consistent performance, then, isn't necessarily due to skill. Correcting for this momentum effect is tricky in theory, and harder in practice, given that the extent to which shares have momentum varies over time.

Such problems mean that, in practice and in most cases, it is almost impossible for retail investors to be confident that good performance is due to skill.

But do we really need to know? Take, for example, mid-cap funds. Many of these are at the top of the rankings for five-year performance. In considering whether to invest in them the question of whether their managers are skilful isn't the only issue. We should also ask whether mid-cap shares will continue to do well. If you think the sector will do badly, you might reasonably avoid such funds even if you believe the managers are genuinely good stock-pickers.

We should also ask: what is the cost of being wrong? In the absence of hard proof, efficient market fundamentalists can maintain that there's no skill - or at least none that can be identified in advance - while overconfident investors can believe that they have ability to pick genuinely good stocks or funds. Both views might be wrong. I suspect, however, that more money is lost through overconfidence than is lost through believing that markets are efficient.