On equity correlations

My table gives an idea of what I mean. It shows correlations between annual changes in a few equity assets (in sterling terms) since 1999. I say 'idea' because these are of course only a handful of the thousands of correlations between all equities.

The first thing to note here is that all these correlations are positive, implying that if one falls there is a higher than 50:50 chance that the other will too. This warns us that we cannot spread risk very much by diversifying across equities alone.

What's more, many of the correlations are very high. That between the All-Share index and MSCI's Europe ex UK index is 0.93, implying that the two move almost in lockstep. For practical purposes, UK and European assets are much the same.

Correlations between some UK sectors and emerging markets are also high. For miners, it is 0.81 and for Aim stocks it is 0.73, implying that it is overwhelmingly likely that losses on emerging markets will be accompanied by losses on these. In fact, miners and Aim stocks have a beta with respect to emerging markets of 1.1, implying that on average they will fall slightly more than emerging markets in bad times*. In this sense, you have exposure to emerging markets even if you are not investing in them directly.

There's a caveat here. Correlations aren't everything. If one asset rises 20 per cent when another rises 10 per cent but falls 10 per cent when the other falls 20 per cent, it is obviously the better investment even though the two have a correlation of one.

This tendency can be measured by the asset's alpha - that portion of its returns that can't be explained by its co-movement with other assets. Unless you know those co-movements, though, you cannot know what alpha is.

My table shows the simplest measure of alpha - the annual returns that cannot be explained by the asset's co-movement with the MSCI world index. Take, for example, miners. Despite their recent slump, these have had an alpha since 1999 of 7.2 percentage points, implying that if the MSCI world index were flat they would have risen 7.2 per cent per year on average.

Interpreting this, though, is tricky. Does it mean miners were a genuine bargain? Or does it mean they were especially risky, and so gave extra returns to compensate for this risk?

My table can shed light on this. To see how, recall the basic capital asset pricing model (CAPM). It predicts that the only systematic risk affecting share prices is market risk - a share's co-movement with the general market. We can test this prediction by comparing our actual correlations with the correlations that would exist if assets co-moved only because of their correlation with MSCI's world index**. If the correlations are higher, it is a sign that two sectors are both vulnerable to a risk other than market risk. If the correlations are lower than the CAPM predicts, it's a sign that the two sectors react in opposite directions to a particular risk.

Sure enough, some correlations are higher than the CAPM implies. This is true for emerging markets' correlations with miners, oil producers and the FTSE 250. This suggests that the global economic cycle is a risk. In good times, these assets all rise together, and in bad times they fall together.

Also, Aim stocks are more highly correlated with emerging markets and tech stocks than the CAPM predicts. For me, this implies that sentiment risk matters: positive investor sentiment raises all three assets, and negative sentiment depresses them by more than ordinary market moves imply.

What's more, the All-Share index, Aim and FTSE 250 are all more highly correlated than we'd expect from their co-movements with the MSCI world index. This suggests there is UK-specific risk: UK-based assets move together by more than they should.

However, some correlations are lower than the CAPM predicts. This is the case for pharmaceuticals' correlations with emerging markets or the FTSE 250. This could be because they are to some degree counter-cyclical; they do relatively well in recessions, when emerging markets fall a lot. Also, utilities are less well correlated with Aim or tech stocks than the CAPM implies. This could be because their relatively defensive nature means they hold up relatively well when investors' sentiment worsens, and relatively badly when it improves.

Now, all this is rather simple. I'm considering only a few of the countless possible co-movements between equity assets. And I'm overlooking the fact that these co-movements themselves can vary over time. What I'm hoping to do, though, is give you an idea about managing risk when buying equities, so that you avoid buying similar assets by mistake, thus ending up with a more volatile portfolio than you intended.

In doing this, I'm actually making a deeper point. It's easy to get the impression from the media that financial economics is simply pompous middle-aged men pontificating about the future. It's not. It's about understanding risks better, and so being able to better manage them.

*You can calculate betas from my table. Multiply the correlation between two assets by their standard deviations. Then divide this by the square of the standard deviation of the asset you want as the basis of your beta.

**The CAPM-implied covariance between two assets is simply the product of their two betas, multiplied by the variance of the MSCI world index (the square of the standard deviation). To get the implied correlation, you then divide this by the product of the two assets' standard deviations.