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 further look at correlation, this time through the prism of 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.
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 intrument. 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:
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.