AT THE end of 2011 small investors who had bought mutual funds that focused on index-linked gilts were feeling pretty smug. It was the best-performing British sector of that year. But woe betide them if they then hung on to the funds all the way through 2012. The sector was last year’s worst performer.

The difficulties facing investors when selecting individual mutual-fund managers are well known. Past returns may be a result of luck, not skill, and a smart manager may be hired away by a rival firm. But perhaps past data can still be of some use for asset-allocation purposes, if only as a contrarian indicator?

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To test the principle Ed Moisson of Lipper, an information provider, analysed the records of British mutual funds over the past 30 years. At The Economist ’s request, he compared the records of the best-performing, median and worst-performing British sectors over one-, three- and five-year periods (see chart).

The analysis shows two forces at work. The first is momentum, the tendency for shares that have performed well to continue to do so. Momentum is a long-established phenomenon at the level of individual stocks and is a puzzle for those who believe that markets are efficient. How can information that is widely available, like past price performance, be a useful guide to future price movements? Theory suggests that the momentum effect should be quickly arbitraged away.

The persistence of momentum has been explained by the relationship between investors and the fund managers who look after their money. Investors choose fund managers on the basis of past performance. When those fund managers get new money from clients, they invest in their favourite stocks. Because those managers have been successful, their favourite stocks are likely to be those that have already performed well.

The chart suggests momentum also exists at the sectoral level. Buying a fund in the best-performing sector of the previous year earns a higher average return over the next year than either the worst or the median performer. Extend that period forwards by another four years, and the best sector in the prior year outperforms the worst by close to 30 percentage points.

The second force is reversion to the mean. Assets can become overvalued: think of Japanese shares in the late 1980s or dotcom stocks in the late 1990s. As values return to normal, the assets underperform.

The reversion-to-the-mean effect shows up most over longer periods. Investors selecting a sector on the basis of its prior five-year performance would have earned much higher returns over the following five years by selecting the worst-performing sector than the best. The gap is more than 30 percentage points. In the long term it pays to be contrarian.

It may seem surprising that the reversion-to-the-mean effect is not stronger over shorter periods. But mutual-fund sectors are not equal: some asset classes are likely to have a higher average return than others. Equities are more volatile than bonds or cash and have accordingly paid a premium return to investors over time. In the tables showing the one-year past performance, there are more equity sectors (22) in the best category than in the worst (19); by contrast, there are more bond and cash sectors (9) in the worst list than in the best (6). That gives funds in the top sectors a natural upward bias.

Any momentum or contrarian strategy is likely to focus on equities, and in specialist sectors where the swings are wildest. Technology and telecoms funds were the best performers over five years on four occasions in the 1990s, and the worst performers four times in the first decade of the 21st century. Funds focusing on smaller firms have been the best annual performers on nine separate occasions and the worst on eight others.

So what are the momentum and contrarian bets for 2013? The best British sector last year was UK smaller companies. Investors betting that the trend will continue will need strong nerves: the FTSE SmallCap index trades on a price-earnings ratio of 37 and offers a dividend yield of just 2.7%, almost a point below the yield on blue chips in the FTSE 100. And the contrarian bet? The worst-performing sector over the past five years was property, a popular investment a decade ago. Perhaps the attractions of an asset that offers a decent income and a hedge against inflation will come back into fashion.