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20 May 2008

Matching Portfolios

Jointly with Dave Kane, an IQSS fellow and head of Kane Capital, I've been working on applying causal inference techniques to the financial problem of performance evaluation. We have a draft on SSRN up here.

The problem: how do you evaluate a stock portfolio's performance? This is usually done by comparing the returns on the manager's portfolio against those of a counterfactual portfolio of investments the manager could have chosen, but did not. A common choice is a passive portfolio like the S&P 500. If a manager can't perform at least as well as a passive benchmark like this, why not just invest in the S&P 500? But this may not be a fair comparison, since the S&P 500 contains only large-cap stocks, while the manager may actually have considered a wider universe of possibilities. Any difference in returns could be due to the portfolio's smaller capitalization rather than the manager's stock-picking ability.

Dave Kane and I view performance evaluation as a causal inference problem. We consider the treatment to be the manager's claimed advantage. Does he time the market? Does he pick hot sectors? Most commonly a manager claims an ability to pick stocks. Then the covariates are the set of confounding factors: observable characteristics of stocks, such as their capitalization, sector and country.

To get a better benchmark, we propose forming a matching portfolio of stocks with similar characteristics, but which are not held in the portfolio. In the leftmost figure above, the black dots represent the characteristics of holdings in a particular portfolio we considered (an equal-weighted portfolio based on the StarMine indicator). The gray dots represent non-holdings. We form the matching portfolio by matching each black dot to a nearby gray dot, using a propensity score method. When we're done, we end up with a well-matched portfolio -- the exposures are compared in the second figure, and they line up nicely. Notice from the figure that there are several possible matched portfolios -- we consider a random set of 100 of them, matching within a thin caliper, as part of our benchmark.

Finally, we compare the realized portfolio return against the returns of the matched portfolios. When we do that, we obtain the histogram below. The portfolio outperforms 75% of the matched portfolios, suggesting there's a moderate but not overwhelming amount of evidence for the stock-picking ability of the StarMine indicator.

In the paper we consider several extensions of this framework to situations with non-equal portfolio weights and to long-short portfolios. We employ the generalized propensity score of Imai and Imbens to form the matching portfolios in this case, treating the portfolio weights of the stocks as a continuous treatment.

We welcome any comments, thoughts or reactions to these ideas! The SSRN draft is linked above, and an accompanying R package is available here if you want to reproduce the computations.

Posted by Kevin Bartz at 11:10 PM