They studied the UK market between 1975 and 2011 and found that, on average in this period, you could have removed 90 per cent of stock-specific equity risk by holding 21 shares. (This doesn't, of course, mean you eliminate all risk by doing so, because a portfolio of 21 stocks would rise and fall as the general market rises and falls.)
If you had wanted to reduce tail risk - that is, cutting losses in the worst 1 per cent of days - you could have done so on average with just 16 stocks.
However, the investor concerned to reduce the variance of his long-term wealth needed many more shares to do so - more than 60 on average.
There's a reason for these differences. Short-run tail risk is largely idiosyncratic; if a share falls sharply, for example because of a profit warning, it's unlikely that others will fall a lot at the same time. Such risk can be diversified easily. (The big exception to this came in the crash of 1987, when shares not only fell but all fell at the same time, which meant that even dozens of shares didn't protect us.)
By contrast, in the long run shares face a common risk - that market forces or technical change will destroy the advantage that incumbent companies have; the long-term death rate for companies is high. This creative destruction risk means shares face a common danger. And common dangers can't be diversified away so easily. This implies that a long-term investor - a young person building a pension pot, for example - would be better off with a tracker fund than with a portfolio of individual shares, because the latter will be badly diversified against long-term risk.
However, it could be that even these numbers overstate the number of individual stocks the retail investor really needs, for three reasons.
First, the calculations are based upon taking shares at random. But we can improve our chances of diversifying well by overweighting defensives stocks which have lower than average volatility - although even defensives might not protect so well from long-run risk.
Second, you don't need to add individual stocks to diversify idiosyncratic risk. You can do so quickly and easily by using a tracker fund.
Third, you might not want to reduce as much as 90 per cent of diversifiable risk. Spreading risk reduces the chance of good returns as well as bad. If you really fancy your chances of beating the market, you'll want to take on diversifiable risk - which would mean holding fewer stocks.
Retail investors, then, should probably hold less than 20 stocks - especially if individual shareholdings are accompanied by fund holdings that diversify idiosyncratic equity risk anyway.
This poses the question: why do most unit trusts hold many more than 20 stocks? One big reason is liquidity risk. If a decent-sized fund tried to concentrate its holdings it would have large stakes in a few companies which would be difficult to sell without moving prices against itself. Retail investors, however, don't have this excuse.
