Monday, October 28, 2013

Eugene Fama explained. Kind of. Part 3: Performance measurement

If we don’t think too much about EMH, but instead view the CAPM and the Fama–French models as models of expected returns, it’s clear that we can use alphas (linear regression intercepts) from these models as a way of managing the performance of investment managers. The return on an investment fund or strategy is just another return and we should be able to use the same models of expected returns to analyze them, so if a mutual fund has positive alpha, we can say that the manager is good and we should invest in him or her, especially if returns are measured after deducting expenses. If alpha is negative, we are dealing with a bad manager and should move funds away. If alpha is zero and/or negative, we might as well invest with a passively managed index fund.

It’s not quite that simple: model alphas are theoretical entities based on population regressions, but in the real world we have to estimate alpha from messy real world data. A common way to estimate alpha is to regress a year of daily excess returns on daily observations of the factors (daily market returns and daily high-minus-low and small-minus-big returns).

Suppose we find a mutual fund that has statistically significant positive alpha based on that year of returns, or even based on the past 10 years of data. What’s to say that the same mutual fund will continue to have positive alpha next year, or the next 10 years? That would only be true if mutual fund alphas are persistent. If they are not persistent, or not persistent enough, it’s all well and good that the fund had positive alpha over the past year, but we can’t use that for anything when deciding when to invest in now.

Hendricks, Patel and Zeckhauser (1993) found some evidence that mutual fund performance is persistent over a one-year time horizon. I’ve mentioned the Carhart momentum factor before; the actual paper where Carhart introduces this result is about the persistence of mutual fund returns. He find that the persistence can be explained by a momentum factor, inspired by previous research on momentum in stock returns.

What exactly do we mean by “can be explained by”? Without the momentum factor, alphas were significant and positive. Adding a momentum factor, that’s no longer true. If we adopt Mark Carhart’s model for evaluating performance managers, we are adopting the value judgment that they should not be rewarded for taking advantage of the known cross sectional factor of momentum.

In the same way, if we dump CAPM and use the Fama–French 3-factor model, we are saying that managers should not be rewarded simply for investing in value stocks or small stocks. Why? The literature offers several different rationales, the simplest being that these are well known risk premia that any idiot could obtain, so we shouldn’t pay investment managers any extra for them. You don’t necessarily have to agree on a reason for value and size premia to share this view.

If we decided to add more factors to the benchmark models, we would be further raising the bar for our investment managers and excluding yet more things that they shouldn’t be rewarded for. Do non-US stocks have a higher expected returns than US stocks? Add an international stock index. Do bonds? Add a bond index. Does real estate have higher returns? Add a real estate index. It becomes more and more difficult to show positive and persistent alpha as we keep on adding more factors; we could add in all the significant principal components of returns for good measure.

Where does Fama himself come down on all this? In a 2010 Journal of Finance paper, a lot of which is about the statistical difficulties of answering the question, Fama and French conclude that very few actively managed funds have abnormal returns that are high enough to outweigh their high fees.

Robert Shiller had an op-ed in the New York Times with this interesting observation:
It’s interesting that Professor Fama is also the intellectual father and major adviser of an investment company that has, by many accounts, been beating the market. The company, Dimensional Fund Advisors, has impressed investors with its performance so much that its assets under management have grown to $296 billion, as of Aug. 31. 
So, how does D.F.A. reconcile the successes with Professor Fama’s efficient-markets theory? 
The D.F.A. Web site refers to the “dimensions” of investing, reflecting the name of the company. First on the list of dimensions are “size” (the stock returns of small companies tend to do better) and “value” (low-priced companies tend to have better returns as well). Indeed, Professor Fama’s work with Kenneth French of the Tuck School of Business at Dartmouth has shown that historically, these dimensions could be used to deliver higher return for investors.
I haven’t actually calculated the alpha of DFA fund returns against the 3-factor and 4-factor models because I am lazy. However, if we take them at their word—that they are simply mimicking the factors rather tha trying to deliver alpha—then by Fama and French’s own standards, we should not expect them to outperform other mutual funds.

(It’s worth looking more closely at that first link. The returns of various DFA funds are compared to benchmarks that capture their investment strategy. For example, DFA US Micro Cap Portfolio (DFSCX), is compared to the 9th and 10th deciles of the CRSP cap-based portfolio indexes, a well constructed family of indexes that is often used by academics.)

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