Causal Modeling and Quantitative Investing

May 21, 2007 7:40 AM

When I was a professor at Columbia University, I taught quantitative analysis (basically experimental design, statistics and econometrics) to masters’ level students in the program in Environmental Science, Policy, and Management. What made this course interesting is that environmental science is one of the most multi-disciplinary fields imaginable. With my background in the social sciences, teaching a course in statistics to students with backgrounds ranging from electrical engineering to art history became an exercise in understanding how different fields approach quantification. A physics undergraduate myself, I knew that under certain circumstances, mathematical modeling offered enormous predictive power, but as a professor in politics, I could also tell that there were times when quantification severely tested one’s suspension of disbelief.

In the social sciences (sociology, political science, and some psychology), statistical methods are most often used to test causal hypotheses. Without highly controlled experiments - some of which would be unethical to perform even if feasible - one can never truly escape from the challenge that correlation is a necessary but not sufficient condition to establish causality, and the result is that statistical analysis in the social fields is only a supplementary analysis to other qualitative forms of argument: it is never definitive. The essence of statistical analysis was to search for evidence of “what causes what” in the presence of extraneous noise from other sources, and a major part of the analysis was making sure the quantitative model was specified in a way that genuinely reflected the researcher’s understanding of what was actually going on.

As I moved to financial analysis, however, it was striking how little causal analysis appears in quantitative finance. The essence of finance can be boiled down to the fact that no sustainable return on investment can exceed the so-called risk free rate without taking on some level of risk, risk being defined, at minimum, as the possibility of earning less than this rate. Intelligent investing thus boils down to the efficient use of risk exposure: given that one must take risk to gain excess returns, is one getting as much return as possible for the amount of risk that is taken. In other words: given that there is risk, is the investor profiting from intelligent educated guesses, or is he or she just taking big chances and hoping to get lucky (what most people refer to as speculating).

As a result, much statistical analysis in finance focuses more on how much noise remains in the system, rather than on how much return can be predicted using specific causal models. Variables are used to predict returns, to be sure, but the analysis of how and why they should affect returns often seems amazingly thin. This initially came as a surprise, since good investors presumably make good predictions of future events. And predictability and residual noise are obviously related, insofar as having more of one leads to less of the other. However, a key insight of portfolio theory points out that better causal understanding of return drivers is not the only way to remove risk from the system.

Since the key issue is how efficiently an investor can convert his or her exposure to risk into some kind of expected return, minimizing residual noise can be almost more important than predicting expected returns, and whether one has a causally accurate model may actually seem less critical than whether one’s prediction equation is simply stable over time and reasonably accurate. But quantitative finance has also found that the correlation between asset returns is a key to reducing overall risk, and it is the use of these correlations to reduce an investment portfolio’s risk that has probably been modern portfolio theory’s most significant insight over the last 50 years. The use of correlation, diversification, and hedging has made it possible to reduce risk exposures dramatically without substantially reducing available returns.

For example, if one has two assets that are perfectly negatively correlated, one can potentially lock in a return with zero risk. That’s right, zero. It is not necessary to understand the causal structure guiding these assets’ valuations - it is sufficient to establish that they are negatively correlated. If one can establish that there is indeed a perfect negative correlation, it is possible to argue that they should return no more than the value of the risk free rate, or else one would have a perpetual money-making machine, which is logically inconsistent. In effect, the rate of riskless moneymaking would become the new risk-free rate, and other asset values would readjust accordingly. If this weren’t the case, and such a correlation existed, it would lead to return at zero risk (arbitrage), and since it should be possible to leverage an investment to increase returns, one could, theoretically, generate any payoff imaginable.

The key issue here is that none of this profit depends on a causal model that drives asset returns, other than the observation that two assets are negatively correlated, and possibly a causal understanding of why one price would be inversely related to another. The fact that one can improve the efficiency of risk exposure by exploiting these correlations has meant that the causal perspective has tended to be neglected in quantitative finance, because it has been possible - and profitable - to improve risk efficiency without requiring an understanding of causal effects.

Does this mean that a causal modeling perspective is useless for quantitative financial professionals? I don’t think so, especially in a changing global economy. In the past few decades, economists have focused on equilibrium models over causal models because of the problems in concluding causality from correlations, a logical step which equilibrium models do not require. Finance professionals may have simply followed suit and found that the equilibrium approach generates sufficiently handsome profits. However, the exclusion of potentially causal ideas from standard modeling practice simply because they are “mutable“ or soft comes back to haunt ”hard quants“ in the form of “regime shifts,” where the key parameters relevant to investing (e.g. correlations) can change suddenly. It is true that causal models may or may not be able to predict these regime shifts, but the causal perspective does include a greater self-awareness of what external conditions or events might make a model applicable or not, because a large part of the causal perspective is asking whether a particular model’s specification maps correctly to the modeler’s understanding of the way the world works.

Behavioral finance, a relatively new branch of finance and economics, has started to bring causality back into the equation. I will talk more about behavioral finance and other causal approaches in a future blog.