First, though, let's see why over-diversification matters. Let's begin with the simple maths of portfolio variance. This tells us that the volatility of our portfolio is a weighted average of two things: the volatility of our individual holdings; and the covariances between them. The more shares you add to your portfolio, the more its volatility depends upon the covariances and the less it depends upon the volatility of the individual assets. But if we're thinking about performance relative to the market, these covariances are very low; if the chances of one stock beating the market are independent of the chances of another doing so, the covariance is zero.
This implies that adding shares to your portfolio can quickly lead you to something like a tracker fund. Take, for example, a bundle of stocks with an annualised standard deviation of returns relative to the market of 30 percentage points, implying that they have a one-in-six chance of beating the market by 30 percentage points, which is roughly the case for many well-established stocks. If you have 30 such stocks and the correlation of their relative performance is zero, then your portfolio has a standard deviation of relative returns of 5.5 percentage points. That is, there's a two-thirds chance its returns will be within 5.5 percentage points of the market.
You might wonder what's wrong with this. Aren't I a big advocate of trackers? I am. But a portfolio like this incurs dealing costs - and the costs of researching stocks - which a tracker doesn't.
And if you're investing in funds, things are much worse. For one thing, these are less likely to deviate from the market by much because of the maths I've just described. This means only a few of them will give you tracker-like performance. But you'll incur big costs for doing so. An extra percentage point of charges - roughly the difference between active and passive fees - compounds to huge money over time. The power of compounding returns is a great friend to investors - but the power of compounding fees is a great enemy.
Why, then, do so many investors incur the costs of over-diversification? I suspect there are several cognitive biases at work.
One is something you might have seen during the World Cup. In penalty shoot-outs, you'll have noticed that, quite often, goalkeepers dive only to see a penalty go down the centre of the goal which they would have saved had they stood still. This corroborates what Israeli researchers have found - that keepers dive too much. This is an example of the action bias - the urge to do something even when standing still would be a good idea. Investors are prone to the same bias, a belief that being useful requires them to do something.
Unfortunately, though, there's an asymmetry in this bias. On the one hand, we like buying. In doing so we can convince ourselves that we're onto the next big thing; the combination of overconfidence and wishful thinking is a powerful one. But on the other hand, we hate to sell losing stocks. This could be because doing so means acknowledging our failure. Or it could be because we hope it will return to the price we bought it at - as if shares remember the price you bought them at. Or it might be because of regret aversion; we'd kick ourselves if we sold and the stock then rose.
This tendency to want to buy but not sell means that the number of stocks in our portfolio will rise over time. For this reason, it seems to be the most experienced investors who tend to over-diversify. There are some mistakes you can only make with experience.
A further bias is the framing effect. This was pointed out back in 1995 by Richard Thaler and Shlomo Benartzi. They showed that when pension fund investors were offered plenty of equity funds but few bond funds they tended to hold lots of equities, whereas if they were offered many bond funds and a few equities they held lots of bonds. This shows that our investment choices are shaped by the framework of those choices. And because we are faced with a choice of thousands of stocks and funds, we are tempted to buy a lot of them.
The answer to this is to change your frame. Economic theory tells us that, under some reasonable conditions, an efficient portfolio comprises just two assets: a tracker fund plus a safe asset such as cash. If we begin from this frame, the question is: why hold anything else? There are good answers to this question - but not such good ones as to require one to buy dozens of shares, and still less funds.
Granted, over-diversification isn't the worst mistake investors can make - it might not even be as bad as under-diversification. But it is a costly one, and it can be avoided.
