To see this, let's take three popular investment trusts: Foreign & Colonial, Templeton Emerging Markets and Standard Life UK Smaller Companies. Looking at monthly returns since January 2000, correlations between these three are all over 0.6, implying that a bad month for one is highly likely to be a bad month for the others. What's more, all three are also highly correlated with the FTSE All-Share index, with correlations of over 0.6.
Now, I haven't chosen these three because they are closet trackers. They are not; I could easily have found higher correlations. Instead, I've picked on them to show a general point - that even good funds which invest in different areas spread risk less well than you might think. This is because of the very fact of diversification.
Think about what happens when you add one stock to another. Naturally, the importance of the idiosyncratic merits or demerits of a particular stock becomes less important. This tends to reduce the volatility of your portfolio. But there's a limit to how far volatility can fall. This is set by the covariance between shares, the extent to which they move together. The more stocks you have, the more your portfolio will resemble the average covariance between the stocks.
But why do stocks move together? One massive reason is that they carry market risk - they rise and fall as the global stock market rises and falls. This means that funds - big bundles of stocks - will rise and fall with the general market and so with each other. Even the best funds can't avoid this problem. It's the mathematical effect of holding lots of stocks. And even funds in different sectors will move together because most shares covary with the global market.
This in turn means you can't spread risk much by diversifying across funds. Let's take a concrete example, which illustrates the general problem. Since 2000, the annualised volatility of F&C has been 19.8 percentage points; this means there's a roughly one-in-six chance of it falling 19.8 percentage points short of an average return over a 12-month period. Imagine - reasonably, I think - that there are lots of funds with this volatility, with correlations between them of 0.7. Then the maths of diversification means that if we hold 10 such funds annualised volatility falls only to 16.9 percentage points, and 30 funds takes us only to 16.6 percentage points.
You can't reduce risk much. This is simply because of the high covariances between funds. Worse still, if you're buying actively managed unit trusts, you're adding fees without much cutting risk.
You might reply here that risk isn't everything. Performance also matters. Of course it does. But this doesn't justify holding many funds.
By definition, there are only two ways a fund might do well: either because it takes some systematic risk; or because of the idiosyncratic fact that the fund picks good stocks.
The latter, though, obviously doesn't justify holding many funds. The more funds you hold, the more you dilute the contribution a good stock-picking fund manager can make to your wealth. Not all managers can beat the market, and the more of them you back, the more likely it is that your portfolio will have an average return.
There might be a case for holding several funds if you want exposure to systematic risk simply because this comes in many flavours. If you want cyclical risk, you can buy a small-cap or value fund; if you want illiquidity risk, you can try a private equity fund; if you want tail risk (among other things), you can buy an emerging markets fund. However, such funds will tend to have high correlations with each other, simply because they are also - unavoidably - exposed to market risk.
Now, I'm not saying that there's no place for funds. There's certainly a role for low-cost trackers as an easy way of getting exposure to the market. And some funds give you exposure to things you can't otherwise get easily - such as emerging markets and private equity funds.
You should, though, think of funds as a cook uses spices. They're great if used sparingly, but unpleasant if thrown everywhere.
