Time Flies and Statistics Lag: Thoughts on Factors

Behavioral finance 14 Aug 2012

Clifford Asness and Andrea Frazzini, in a working paper prepared last year, have illustrated how tricky it can be to address issues of factor pricing and behavioral finance in a rigorous way.

Specifically, they show that an important detail in the way scholars go about studying these questions, the use of book-to-price data using both book and price data with the same lag, is seriously flawed.

The question of when and how often an analyst should update price in calculation of B/P sounds “innocuous and un-exciting,” the authors concede, but it is worth “305 basis points annually in the US since 1950.”

The construction method they target was pioneered by Eugene  Fama and Kenneth French in an influential 1992 paper, “The Cross-Section of Expected Stock Returns,” in which Fama and French contended that firm size and B/P between them do a lot to capture the cross-sectional variation in average returns, especially those of the period 1963 to 1990. Those two factors, added to the market risk factor adopted from the capital asset pricing model, leave Fama and French with what is accordingly known as the “three factor model” of market returns.

Another term for the book-to-price factor is High Minus Low (HML), a phrase that captures the Fama-French contention that value stocks (those with high B/Ps) routinely outperform growth stocks. Thus the name of the Asness-Frazzini paper is “The Devil in HML’s Details.”

Three Factors or Five

Asness and Frazzini prefer a five-factor model. In essence, market return can be modeled more effectively by adding to the three Fama-French models a consideration of momentum on the one hand and a short term reversal factor on the other.

The simple seeming method of B/P computation used by Fama and French involves updating value once a year on June 30, using the book value and price as of the preceding December 31, and then holding those values constant until the next June 30.  In short: once-a-year updates and a six month lag.

There has to be a lag in terms of the calculation of book value simply because we do not know on June 30 of any year what the book value of XYZ Inc. as of June 30 is. But (here the tricky bit arises) we don’t absolutely need a lag in market price at all. When XYZ is a public listed company, we know perfectly well what its June 30 value is on June 30.

Still: since we must employ a lag for B, common sense suggests a lag for P too. If you are going to create a ratio between the two, why wouldn’t you want them for the same date?

Asness and Frazzini contend that you don’t want them for the same date. They ask you to consider a stock whose value has fallen 75 percent during the last six months as of the June 30 rebalance. Their findings indicate that this fall makes it likely the stock is at present a “true value stock” so a measure that takes this fall into account is superior to one that ignores it. Thus: keep price current, and measure B/P despite the apparent timing mismatch that results.

The Take-Away

They also found, as you can see from Panel B of their Table II above, that international results are consistent with US results “and highly supportive of our proposed method of computing B/Ps over the standard specification (although based on a shorter sample),” as their text puts it.

In writing on this subject Asness, one of the cofounders in 1998 of AQR Capital Management, is returning to the subject of his Ph.D. dissertation from 1994, “Variables that Explain Stock Returns.” This paper cites that dissertation as authority for the proposition that momentum strategies have “long been shown to be efficacious.”  So has value investing, though the two strategies are negatively correlated. Thus, there should be an extra benefit in “doing them together.”

Still, for non-quants the take-away from this paper will be that small differences in method can make big differences in results, that there is a sort of chaos-theoretic butterfly effect in factor pricing scholarship.

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