US Stock Market Correlations: What the data tell us about Portfolio Risk

Correlations Matter

Managing correlation risk is an important part of portfolio management. Diversification allows a more stable trajectory by buffering volatility of individual investment. Whether it’s Markowitz’ model or a Sharpe Ratio calculation, risk reduction through offsetting price movements is a key feature of good portfolio design.

How stable are Correlations, and what drives their change?

How stable and reliable are correlations? Can we make better decisions in the original choice and do such correlations change over time?

In this note we use machine learning tools to understand how correlations in the US stock market evolved and how we can use this information to our advantage.

We can divide the universe of US stocks into 5 distinct ‘Clusters’ of correlated stocks. The clusters are result of KMeans clustering (an unsupervised machine learning technique), which groups stock of similar behaviour. In this note, Cluster # 5 has the highest (positive) correlation, and Cluster #1 will have the lowest (potential negative) correlation.

Whilst correlations are not fully stable, each cluster does somewhat remain in a range, which indicates that we can make decisions on our stock selection on the correlation risk profile we want to chose.

By setting correlation changes against market volatility (proxied by S&P 500 Standard Deviation), a pattern emerges in that volatility is a driver for correlation

There is a clear relationship and the higher volatility, the higher correlations in the market. However, we can still see that in the lowest correlation cluster, the correlations turn from negative to around zero — zero correlation is still beneficial from a diversification effect.

The models clearly show however, that to stress-test our portfolios, we not only need to stress test price changes, but we need to assume a significant jump in correlations at times of stress. In other words, our portfolio will become significantly less diversified in times of stress.

We can take another perspective on the behaviour of the market, by looking at the size of each correlation cluster (measures as % of pairwise correlation as percent of the total)

This chart shows that particularly in times of stress, both the level of correlation and the number of shares in the top correlation cluster increases.

Whilst it does increase, it also seems to return to lower levels, which means that irrespective of the price movement, correlation behaviour seems to return to a previous path.

Conclusions

When we assess the diversification of our portfolio, we must stress test our assumptions against situations where both the size of volatility and the correlations of assets are stressed. US Stocks are significantly more correlated in times of stress than otherwise.

However, it is also clear that low or negative correlations provide a useful framework for portfolio construction, that remain of benefit in a wider diversified portfolio even if the market is under duress.

In our next notes, we will look at longer time history, investigate if up or down volatility behaves differently, and if either the market cap or industry have an impact on portfolio behaviour.