For about three decades, the working asset pricing model was the capital asset pricing model (CAPM), with beta—specifically market beta—being its sole factor. Then, in 1993, the Fama-French three-factor model—which added size and value—replaced the CAPM as the workhorse model.
By eliminating two major anomalies (the outperformance of small stocks and of value stocks), it improved the model’s explanatory power from about two-thirds of the differences in returns of diversified portfolios to more than 90%. Thus, it was a major advance.
In 1997, momentum was added as a fourth factor. It too improved the explanatory power of the asset pricing model by eliminating another large anomaly. The next major advance came from Robert Novy-Marx in 2012.
In his paper, “The Other Side of Value: The Gross Profitability Premium,” he proposed a fifth factor, which also improved the model’s explanatory power while eliminating another important anomaly—the outperformance of stocks with higher profitability.
Since then, what might be called the “battle of the factor models” has occurred, with parsimony considered a major virtue—the fewer factors needed, the better. Kewei Hou, Chen Xue and Lu Zhang—authors of the October 2012 study, “Digesting Anomalies: An Investment Approach”—proposed a new four-factor model, the q-factor model. It included market beta, size, investment and profitability, and went a long way to explaining many anomalies.
In 2015, Eugene Fama and Kenneth French proposed a new five-factor model, using their original three factors and adding somewhat different definitions of investment and profitability.
Robert Stambaugh and Yu Yuan, authors of the January 2016 paper “Mispricing Factors,” add to the literature by proposing another four-factor model that includes two “mispricing” factors in addition to the factors of market beta and size. The authors note: “Factor models can be useful whether expected returns reflect risk or mispricing.”
By incorporating these mispricing factors, they are better able to accommodate 11 well-known anomalies. These anomalies, which represent violations of the Fama-French three-factor model, are:
Stambaugh and Yuan construct their two mispricing factors by average rankings within two clusters of anomalies whose long/short return spreads exhibit the greatest co-movement. Anomalies one through seven are in the first cluster of factors, and anomalies eight through 11 are in the second.
They then average a stock’s rankings with respect to the available anomaly measures within each of the two clusters. Thus, each month, a stock has two composite mispricing measures.
The authors constructed their mispricing factors by applying a 2×3 sorting procedure—sorting all stocks by P1 (and then P2) and assigning them to three groups, using as breakpoints the 20th and 80thpercentiles of the combined NYSE, AMEX and Nasdaq universe.
They chose 20th and 80th percentile breakpoints rather than at the 30th and 70th percentiles because mispricings tend to occur more in the extremes of the deciles. They then created value-weighted portfolios. Combining these two factors (P1 and P2) with the market and size factors creates a four-factor model.
Stambaugh and Yuan’s approach was motivated by the fact that “anomalies in part reflect mispricing and that mispricing has common components across stocks, often characterized as sentiment. A mispricing interpretation is consistent with evidence that anomalies are stronger among stocks for which price-correcting arbitrage is deterred by greater risks and impediments.” This is often referred to as limits to arbitrage.
Their study covers the period 1967 through 2013. Following is a summary of their findings:
Stambaugh and Yuan note that because higher idiosyncratic volatility (IVOL) implies greater arbitrage risk, mispricings should get corrected less among stocks with high IVOL. That’s exactly what they found, providing further support for their results.
For investors, it’s important to note that the authors’ finding that there is more uncorrected overpricing than uncorrected underpricing doesn’t mean a mutual fund would have to short a stock that’s overpriced to benefit. It can benefit by avoiding purchasing the overpriced stocks, creating a filter to screen out stocks with the characteristic that creates the mispricing.
Thus, passively managed long-only mutual funds can put this knowledge to work. Dimensional Fund Advisors (DFA) is likely the most well-known firm that has long used screens to eliminate certain stocks from its eligible buy list. (Full disclosure: My firm, Buckingham, recommends DFA funds in constructing client portfolios.)
Through their research, financial economists continue to advance our understanding of how financial markets work and how prices are set. The Fama-French three-factor model was a significant improvement on the CAPM. Mark Carhart moved the needle further by adding momentum as a fourth factor. And the creators of the q-factor model made further significant advancements, which in turn motivated the development of the competing Fama-French five-factor model.
Now we have a new four-factor model that incorporates anomalies and appears to have greater ability to explain the differences in returns of diversified portfolios than some prominent alternatives.
The competition to find superior models is what helps advance our understanding not only of the markets, but of our understanding about which factors to focus on when selecting the most appropriate investment vehicles and developing portfolios.
This commentary originally appeared May 11 on ETF.com
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