Many investors diversify too much – for perhaps surprising reasons. To see why, think about what happens when you add assets to your portfolio. As you do so, you reduce the contribution any single asset makes to your total returns. But you increase the importance of correlations between assets. If you had an infinite number of assets each would make an infinitesimally small contribution and your returns would depend only upon the covariances between them.
We can quantify this with the help of the concept of the tracking error, which measures the variation in relative returns. For a typical larger mid-cap stock, this tracking might be around 30 percentage points, meaning that there’s a two-thirds chance of its annual return being within 30 percentage points of the market’s return. If you hold 30 of these stocks, and the average correlation of their relative returns is zero (so if one beats the market there’s only a 50:50 chance of another doing so), then the tracking error of your portfolio is5.5 percentage points. Which means there’s a two-thirds chance of annual returns being within 5.5 percentage points of the market’s – and only a one-in-six chance of you beating the market by more than this.
If you hold safer stocks or more of them your tracking error will be lower than this. And if you hold funds (which tend to have low tracking errors because of the above logic) it could be very low indeed. In such cases your best hope of significant outperformance is that your holdings will do well at the same time. But this usually entails taking on some extra risk. The risk might be greater exposure to recession risk. Or it might be the risk that previously profitable strategies (such as backing monopoly-type stocks) will turn bad.
Many of you, then, have unwieldy equivalents of tracker funds. And these are expensive. You’re paying fund management changes that compound horribly over time. You’re incurring dealing charges. And then there’s the cost of time and effort in monitoring your portfolio.
Such calculations, however, miss an important point. Risk isn’t only a matter of numbers. It’s also about feelings. If you hold only a single global tracker fund your equity investments will be well diversified (although of course you need non-equity assets to protect you from market risk). But it will feel riskier than a portfolio of many stocks and funds.
Some experiments by Ola Mahmoud at the University of St Gallen in Switzerland have shown what’s going on here. She finds that people are willing to pay to diversify even if doing so does not reduce mathematical risk.
This corroborates another fact. To see it, imagine I were to ask you to bet on whether I would draw a red or white ball out of a bag containing 60 red balls and 40 white. What would you do? The best strategy is to put five bets on red. Many people, though, don’t do this. Instead as Ariel Rubinstein showed in a series of experiments at Tel Aviv University, they spread their bets even when it is wrong to do so.
We see in the laboratory, therefore, the same thing we see in our portfolios. People diversify even when it costs them money,
Why? My cat, Lucius, provides one possible answer. Like most cats, he sleeps in different places in a typical day. Cats have evolved to do this as a way of avoiding predators and reducing viral load if they sleep in an infected place.
A similar thing might be true of humans, says Dr Mahmoud. Mixed strategies – varying what we eat or where we hunt – are what kept the human species alive. Diversification is what got us here. So why shouldn’t we continue with it? Like cats, we have evolved an instinct to diversify, even if this costs us money in modern environments.
You might object that if you avoid fund managers’ changes and hold only stocks the cost of over-diversification is small.
If this were all, over-diversification would be low on the list of mistakes we make. But it might not be. I fear that, in some cases, it arises from more expensive errors.
One problem is that if you keep buying stocks while being reluctant to sell, you’ll end up over-diversified without intending to. And if it is losing stocks you hold onto in the hope that they’ll come good you are exposing yourself to negative momentum effects – to the tendency for past losers to continue falling.
Also, stock-pickers don’t have many good ideas. The LSE’s Christopher Polk and colleagues show that the typical fund manager has only a handful of decent buying ideas at any one time. Stock markets might be inefficient – but they are not ‘that’ inefficient. If you buy lots of stocks, then, you are probably overestimating your ability to pick good ones. You are overconfident. And we know that overconfidence is an expensive mistake as it can cause us to take on too much risk, incur excessive charges as we trade to much, and buy expensive funds as we overestimate our ability to spot good fund managers. Even if over-diversification is a cheap mistake, therefore, the things that lead us to be over-diversified might be more expensive ones.
Our portfolios, then, are like our garages. They need a regular clear-out.
