Correlation in the tails - You will be surprised at the limited convexity

For some, the devil is in the details - for investors, the devil is in the tails!

The only free lunch is diversification except if you are in the distribution tails.

An investor will look at buying assets that have lower correlation with their main equity holdings; however, it is critical to look the conditional correlations in the tails. Investors need diversification the most in the left-hand tail of equity market extremes. We try to visualize the problem through looking at the left and right tail correlation for a wide set of assets, hedge fund styles, and factor. As a first pass, we use the data appendix from the Financial Analyst Journal article "When Diversification Fails" from December 2018. 

We look at a map of right and left tail correlations divided into a 2x2 grid. In a perfect world, investors would like an asset that has positive correlation in up markets and a negative correlation in down markets. This is represented by quadrant III. If correlations are the same in both up and down markets, the values will be on the 45-degree straight line. 

Most assets fall above the 45 degree line and in quadrant I and II. These tells us the correlation in the left-tail (5th percentile) is higher than the right-tail (95th percentile) of the equity return distribution. The only notable exception is with Treasuries in quadrant I where the right-tail correlation is positive and the left-tail is negative. This suggests that investors should always hold Treasuries as their diversifier; however, the relationship has not held during periods of higher inflation and has not always been stable.

Looking at this differently, we created a simple measure of correlation convexity by taking the difference between the right-tail and left-tail correlations, (correlations in the 95th minus 5th percentiles of the equity return distribution). If correlations are the same, the value will be zero. If an investor receives more downside diversification, the value of the index will be positive. Most assets have negative values or worsening diversification in market downturns.

Investor should look at correlation risks; the fact that the unconditional correlation is not the same as the conditional correlations in the extremes. If you have to hold this correlation risk, you should be compensated with higher returns. More time should be focused on these correlation risks and their impact on portfolio hedging and diversification.