Trying to make sense of a correlation matrix for a wide range of asset classes (see below) is a complicated task – too many numbers and too much detail can hide the bigger picture. Looking at individual correlations – between Japanese equities and emerging market debt (EMD), for instance – isn’t particularly important for a multi-asset investor; we need to see how an asset class behaves relative to all the other asset classes we hold (we therefore look at a full column of the matrix) and relative to a total portfolio.
There are newer quantitative methods however that promise more intuitive, graphical access to the data. We call them our correlation galaxies given that asset classes (the dots or 'stars') are clustered and arranged in a way to visually reflect the complex correlation matrix. If we just consider one asset class – we try to place it close to all asset classes that it has a high and positive correlation with, and far away from those assets where it has a low or even negative correlation.
The axes themselves have no particular meaning; we only need to worry about the distance between the stars. The methodology places all stars simultaneously to achieve a close fit in the distances between the dots and the correlations between each combination. In addition, the strongest positive links between assets are shown as dotted, dashed and solid lines.
The above chart has pretty much the same information as the large correlation matrix above but is so much clearer. We see various clusters (galaxies) of assets that are closely linked, as well as asset classes (intergalactic stars) that seem to have no strong links to the rest of the asset universe. There are many interesting conclusions we can draw from this chart, but I’ll just highlight a few points:
- Regional equities are highly correlated and thus sit closely together, although the gaps between markets suggest some differentiation exists. Japanese and frontier market equities are the most diversifying equity markets
- The same applies to nominal bonds (and to a lesser degree to inflation-linked bonds)
- Bonds and equities are at the polar opposite sides, which implies on average a very low or negative correlation
- The interesting asset classes, from a multi-asset perspective, are the intergalactic stars: high yield, EMD hard currency debt, EMD local currency debt, infrastructure, UK direct property, and commodities provide the most tangible diversification enhancements. In our minds, this group also includes global REITs whose performance is linked to equities in the short term but more in line with the underlying property assets over the long term.
- Currencies (and gold) are in a separate corner. I’ll look at them separately in a future post.
While all of the above is very intuitive, there are two main 'issues' here. First, there is a statistical one as the standard correlation assumes that returns are well behaved (follow a normal distribution) which we know isn't true. A possible solution for this problem is to use 'rank correlation measures' such as Kendall’s tau or Spearman’s rho.
Second, the idea that we can simply rely on some historic relationship to predict the future isn’t holding up well in the data. Rolling five-year numbers (below and covered by Daria) show that the correlation within the main asset class 'blocks' is consistently high and relatively stable. But there is huge variation between the main galaxies (between equities, bonds, etc) and some correlations swing from positive to negative and vice versa. So what reduces risk over some periods is adding to risk over another.
A time-lapse video of our analysis shows how the main galaxies (regional equities, bond markets, etc.) stay together, while their relative location and links between the blocks move around a lot. Worryingly, the relatively stable structure clearly breaks during the global financial crisis in 2008/2009 when diversification benefits that investors may have banked on previously didn't materialise. This should be a concern for anyone relying purely on correlations to make investment decisions.
What are the implications of this research? Some may argue that we can continue to use correlations as we are unlikely to see a sharp break in asset relationships over the short term, but that misses the point as it is exactly in these unexpected events (such as the 2008 financial crisis) when we need the benefits of diversification the most.
Our own approach is to combine those asset classes with stable correlations – as this helps to reduce the complexity. But we want to take into account that there may be no stable link between these clusters (which means that we do not rely on the correlations between the clusters, and this is where we deviate strongly from risk parity approaches). Instead, we spend much of our time and effort to understand the changing pattern of behaviours and look for robust solutions. For risk management purposes, we use scenarios and tail risk analysis to test portfolio outcomes when markets go rogue.