Prompted by some thoughts from Nassim Taleb, David Einhorn (who compared VaR to “an airbag that works all the time, except when you have a car accident.”) and Ralph Vince (“The Leverage Space Trading Model”, pp 61-65), I decided to take a look at asset correlation during high volatility.

The motivation is, as before, to explore ways to limit variability in returns to provide more breathing room for leverage: raise returns by limiting volatility of returns.

# Base Case

For this exploration I used a 38 instrument portfolio with a variety of currencies, softs, energies, metals, interest rates and stock indices. First I calculate the overall correlation matrix for the entire history (1995 – present):

I take each instrument and filter it for the days when its daily percent change in closing price is in the 5th percentile or lower (i.e. volatile downwards), the 95th percentile or higher (i.e. volatile upwards) or the absolute value of the change is in the 95th percentile. Then I build a correlation matrix for those days and plot the results on a heat map.

Here’s what we get – the prefix “V-” implies that the filtering was done based on the volatility of this instrument. For example, the row labelled “V-S&P …” tells us what the correlation is between S&P and other instruments when the S&P met the volatility requirements:

# High Up and Down Volatility

The two charts below show higher magnitudes in the correlation coefficients (the histograms are more spread out). But, I have to say, not as much as I expected.

# Very High Absolute Volatility

This final chart shows a clear increase in the magnitude of the correlation coefficients when the volatility of one of the components is high. The histogram in the color key is wide. The chart as a whole suggests “risk assets” on the one hand and “safe assets” – US Dollar, treasuries and short term rates, on the other.

If anyone has any thoughts on why the distinction is not so clear in the charts separated by upward and downward volatility I would love to hear them. My only thought is that the absolute volatility chart is looking at even more extreme regions (2.5% / 97.5%) than the upward / downward charts (5% / 95%).

Using the absolute chart of correlation coefficients to limit total correlated positions, appeals to both simplicity (I don’t have to worry about whether to use the upward or downward chart) and conservatism (the values are larger anyway).

In the future I plan on running Monte Carlo simulations of the proposed portfolio when contemplating a trade. Then I can establish the empirical distribution of portfolio variability and use that to limit positions. Right now, I don’t have the computing power to back-test that way.

I disagree with pumpernickel.

You only need to test liquid stuff. At the local microbrewery I go to, there's a bunch of different bags of hops stacked up. Is that gonna change the fact that everyone sitting in the bar got paid on the last friday of the month?

Pumpernickel,

I agree 100%, and I would like to get me some! I am learning to walk right now, running comes later – and I am going to need a bigger budget to acquire a lot more data.

It would be interesting to examine the markets by region and as a whole to see if the relationship between volatility and correlation functions on a regional basis (containment) or a world-wide basis (contagion). It might be interesting (but not actionable) to see how these relationships have evolved through time: has the world got smaller / more inter-connected?

The markets you studied are all traded at US exchanges — geographically nondiverse. I bet you could seriously increase diversification / lower correlation if you mixed in a bunch of non-US-exchange-traded markets such as Paris Milling Wheat, Swiss Govt Bonds, Tokyo Rubber, Malaysian Crude Palm Oil, and some of the less well known national stock index futures such as the Amsterdam EOE, the Milan MIB, the Johannesburg ASI, the Paris CAC40, the MSCI Taiwan @SGX, etc. Diversification is the only free lunch on Wall Street, get you some.