Uncorrelate to accumulate

Consider two assets, A and B, with different payoffs in three equally likely states of the world. In state 1, A pays out 30, in state 2 20 and in state 3 12. Asset B pays 10 in state 1, 12 in 2 and 30 in 3; my table summarises these payoffs.

You now have to chose how to invest £60. But you have only two options. You could split the money 52-8 in favour of asset A. Or you could split it 26-34 in favour of B. What do you do?

Now, let's consider a second choice. There are two assets, C and D, with payoffs to the same equally probable states shown in my second table. You can only choose one asset. Which is it - C or D?

If you chose the 52-8 split in my first choice, you're in the majority; 97 per cent of people, when offered this choice by messrs Weizsacker and Eyster, chose A.

If you did this, though, then you must also choose asset C in our second choice. This is simply because asset C has the same payoff as the 52-8 split between assets A and B, while asset D has the same pay-off as the 2634 split. The choice between D and C is the same as that between the 52-8 and 26-34 splits.

So, did you choose 52-8 and C? If not, you're in a large minority. Messrs Weizsacker and Eyster found that, in a choice between C and D, half of subjects chose C and half D.

This is irrational. Yes, it's entirely reasonable to choose the 52-8 split over the 26-34 one, as it has the higher expected return. And it's also reasonable to choose D over C, as it gives the best worst-case payoff and so appeals to the risk-averse chooser. What's not rational, though, is that, having preferred 52-8 to 26-34, we then prefer D to C. But lots of people do just this.

This is where correlations come in. People fail to see that assets A and B are negatively correlated and so a combination of the two creates the low-risk asset D. "People tend to ignore correlation," says Dr Eyster.

This leads to two errors, he says. When correlations are negative people under-diversify because they fail to see that negative correlations offer good ways to spread risk. And when correlations are positive, they over-diversify and think they have spread risk when in fact they haven't.

This mistake could be expensive. If you hold 30 assets each with a standard deviation of 30 percentage points - equivalent to a relatively safe equity or some specialist funds - the risk of a 10 per cent loss is almost 10 times greater if correlations between them are 0.5 than it is if they are zero. If you ignore correlations, then, you might be taking a lot more risk than you think.

One particular group of investors, I fear, might be especially prone to this correlation neglect - those of you who invest in lots of funds. Take two of the most popular investment trusts: Alliance Trust and Foreign & Colonial. Over the last 10 years, the correlation between monthly price changes in these two has been 0.89. They move almost in lockstep, which means they offer almost no diversification at all. This is simply because diversified portfolios of equities are correlated with the stock market and therefore with each other. This fact overwhelms the chance that fund managers will have varying degrees of luck or skill.

Herein, though, lies a clue as to how we can look out for correlations. The answer lies in the notion of implied covariance.

The idea here is that shares move together because both are sensitive to a common factor - moves in the global stock market in the case of Alliance and F&C. The correlation between two assets depends upon their sensitivities to various common factors.

But what are these factors? If we lived in the simple world of the capital asset pricing model, where the risk of the stock market falling was the only systematic risk, there'd be just that one.

Important as this is, though, it's not the only one. Some others are:

■ Interest rate risk. Highly-geared companies, or companies serving highly-geared customers, might all suffer together if borrowing costs rise.

■ Liquidity risk. An ending of central banks' easy money policy might hurt lots of assets: I suspect there's a common risk to gold, emerging market equities and commodity stocks here.

■ 'Cyclical' risk. A downturn in the economy hits 'cyclical' stocks together. This introduces a correlation between some smaller stocks and high-yielding stocks.

Which brings us back to where we started. The key to thinking about correlations is to consider their likely payoffs in different possible states of the world; a market crash state, a tight money policy state, and so on. If you hold a bunch of assets whose payoffs might be similar in these different states, then you might well be underestimating correlations and so overestimating the safety of your portfolio.