Anticipating correlations

Anyone who either tries to construct a portfolio with determinable risk parameters or tries to trade by taking cues from other markets faces a seemingly insurmountable problem: correlations vary over time. For instance, sometimes the bond and stock markets are negatively correlated, but there are times that they move in lockstep. Sometimes U.S. equities move up when the dollar is weak, other times when it is strong. What’s a person to do?

Robert F. Engle gave a three-day lecture series at the Econometric Institute of the Erasmus School of Economics in Rotterdam, subsequently published as Anticipating Correlations: A New Paradigm for Risk Management by Princeton University Press (2009). The Dutch are known for their command of the English language, but they probably didn’t have to work too hard here since the English text serves largely to connect statistical formulas. Since I am not comfortable in the world of econometrics, I’ll stitch together a little post from the linking text and some general observations.

The risk of a portfolio as well as its optimal hedge depends in large part on the future correlations and volatilities of its constituents. For example, in the case of the notorious CDOs correlations between defaults were the key determinants of valuation, yet virtually nobody who bought CDOs or tranches of CDOs had a reliable method for figuring out just how correlated these defaults were.

Engle hypothesizes that shifting correlations are responses to fundamental news. Even when it would seem that trading rather than news moves correlations—for instance, when hedge funds unwind similar positions or deleverage their holdings, Engle claims that this distinction is semantic rather than real.

Engle explores and evaluates a range of models for predicting correlations and comes down on the side of the FACTOR DCC model, analysis for quants only. I’ll skip to the end where the author concludes: “The models developed in this book have the potential to adapt to unforeseen changes in the financial environment and hence give a dynamic picture of correlations and volatilities. These methods are naturally short-run methods focusing on what can happen in the near future. Risk management must necessarily also be concerned with the longer run. Conveniently, the factor versions of these models allow us to model the determinants of factor volatilities, which are the primary determinants of longer-term volatilities and correlations.” (p. 140)

For those who don’t aspire to be risk managers at an investment bank but who want to manage risk in their portfolio, it is important to monitor both volatility and correlation on an ongoing basis. We may not have fancy models, we may not be able to predict with any measurable probability where volatility and correlation will be in the future, but we can devise matrixes to know where we are. Are we in a high volatility or a low volatility environment? Are traditional correlations shifting? What are the fundamental reasons for these shifts? Once we know the answers to these questions, we can start to position size and hedge accordingly.