Eugene Fama and Kenneth French deserve enormous respect for the work they did in legitimizing an equity investors’ consideration of risk factors beyond the stock market itself and in identifying those factors. But to use factors as effectively as we can, we’ll have to use a framework that meets our client-centered concerns, which are not necessarily the same as those of academicians.
From CAPM to Fama-French
Factor analysis starts with the capital asset pricing model (CAPM), which describes return in terms of (i) the component associated with a risk-free investment and (ii) the component associated with the equity market. The initial three-factor model presented by Fama-French retained the market factor and added two more: size and valuation. Eventually, they brought the number of factors to five by adding profitability and conservatism (or investment); momentum was later recognized as an additional factor.
All variations conform to the following framework:
R = a + (b1*F1) + (b2*F2) +. . . + (bN * FN)+ e
R = return
a = constant (a risk-free factor)
F = factor (a risky factor)
B = a loading associated with each factor F
e = the residual error – that which the model missed
But however many factors we use, and however simply or elaborately each factor is defined, we’re ultimately seeking to describe the overall market. We want changes in the right side of the equation to describe changes on the left and achieve a correlation as close as possible to 1.00, and we want the error term to be as close to zero as possible.
An explosive – but obsolete – controversy
For practitioners, as opposed to academicians, if liquidity is a concern (as would be the case if one were managing many billions of dollars), it would be unrealistic to deviate much if at all from the market. You buy everything in proportion because you pretty much have to. But a client, or even the sum total of all clients in most practices, is not so big as to force the manager’s hand in this regard. Hence, advisors have the ability to build portfolios that reflect goals other than tracking the market.
I know, I know, I know… active investing is crazy. Countless trees have given their lives to publication and dissemination of study after study showing such endeavors to be pointless (with surviving tress grateful for digitization).
Get ready for a bombshell: I don’t care.
We’re in a different world. We no longer sit in brokerage offices and watch ticker tapes. We no longer wait patiently for the monthly S&P guide to arrive in the mail so we can look up basic information on companies. We no longer get inky fingers and tired eyes thumbing through the Wall Street Journal looking up stock prices. We no longer sit on hold waiting for brokers to get back on the phone to confirm that our trades are “done.” And we no longer trudge our way to the SEC or a library lugging suitcases full of coins to copy 10-Ks and 10-Qs, nor do we beg companies to send them faster than by third-class mail.
We know things now – quickly and cheaply. For the even moderately computer literate, we know them easily.
That has opened up a new way of doing things. Any one of us can quickly and easily complete studies that once took academicians many months and countless graduate-student person-hours to accomplish. We can use fresher data in our studies (Did you really believe once-per year is the ideal rebalancing period, or might it be that annual data was all the non-paying professors could squeeze from the data vendors?) Screening and ranking are available to anybody with a will to work this way.
The old binary world that pitted passive buy-the-market investors against active-inspired-by-my-personal-genius investors is dead. The research that shows passive investing being better than active has lost its usefulness. The question is top-down index investing versus bottom-up-rules-based strategies. Eventually, researchers will study and come up with insight into this new topic.
Factors and Moneyball
The one thing I really hate about the way I work (using objective rules-based data-driven methods) is that I don’t have a catchy label for it. So I’ll borrow from Billy Beane and Michael Lewis and call it Moneyball. Beane used data-driven algorithms to supplant seat-of-the-pants and eyeball-based judgment to build baseball-team rosters and succeeded to turn the Oakland Athletics into a championship-caliber team. Data-driven algorithms supplant the special genius, unique inspiration and seat of the pants hunches to create stock portfolios that beat the market.
Data is the raw material. Factors are the value-added materials built from individual data points.
Freedom from Fama-French – A case study using value
Because I build portfolios for investors who are not required (e.g., by liquidity considerations) to track the market, I don’t care about my residual error or need a high correlation. In fact, the lower the correlation and the higher the residual error, the better the portfolio if its risk-adjusted returns are better than those of the market.
Here’s what this means in a practical sense.
Fama-French concluded that value is a relevant factor. They defined value in terms of book-to-market, but other metrics work too. I’ll use the P/E ratio.
Following Fama-French, you would assume that you’re better off owning lower P/E stocks, but -- in practice -- that there are times that the markets does not perform this way. It’s tempting and easy to explain those deviations by saying how styles go in and out of favor, or that value is out or “cold” right now, but that over the long term it has been shown to be effective.
But a more precise understanding of the operation of the value factor starts with the dividend-discount model (DDM):
P = D / (R – G)
P = price
D = dividend
R = required rate of return
G = expected dividend growth rate
While we all recognize the unimpeachable logic of a stock being worth the present value of its future dividends and the mathematical expression that presumes an infinite holding period, this formula cannot be used in stock section. But we can and do work with approximations that make it more likely than not that a stock is reasonably valued relative to the DDM ideal.
One generally accepted approximation is to substitute E (earnings per share) for D. We pretend that all earnings accrue directly to shareholders and that the stock can be valued without reference to a voluntary decision they collectively make to reinvest all or some of that back into the business. This allows us to recast the DDM as follows:
P = E / (R – G)
Now, we can compute a fair P/E ratio by dividing each side of the equation by E.
P / E = 1 / (R – G)
Since G is a negative term in the denominator, we know as G rises, so does PE. That is the inspiration for the well-known PEG (P/E-to-Growth) ratio. This alone destroys any notion that low P/E makes for better value. A P/E of 35 for shares of a company that is growing briskly may be “cheaper” than a P/E of 12 for shares of a company whose earnings are declining.
R is a positive number in the denominator, so when it rises, P/E falls. Assuming, as I’m sure we can all agree to do, that R varies directly with interest rates, we notice the familiar-from-real-life phenomenon that P/E varies across-the-board inversely with rates. R also varies directly with risk, (as we would in a CAPM formulation, where higher beta makes for higher returns all else being equal), so increases here push P/E downward. Conversely, one has to pay up for risk protection in the stock market, just as one does in health care and auto liability.
We see what the Fama-French framework misses. Our DDM-based analysis shows that lower P/E is not inherently better. None of this has anything to do with fleeting changes in market sentiment. It does, on the other hand, have everything to do with why so many naïve investors get caught in value traps and why the performance of plain-vanilla value ETFs, such as value subsets of the S&P 500, the Russell 2000, etc., often fail to outperform a capitalization-weighted index. One who ignores G and R cannot assume lower valuation metrics are preferable. We should not be surprised to see value strategies falter when they become to heavily exposed to companies with too much risk and/or poor growth prospects.
Hence I never rely solely on low P/E to select stocks. Every model I create combines P/E, G and R. If there are times when value doesn’t “work,” I know I can’t brush that off to passing market fads. One possibility I must always consider is that I haven’t done a good enough job “specifying” the relevant factors (an often-challenging endeavor – see below). Or we may be experiencing a market-wide diminution in expectations for G and/or increases in expectations regarding R (based on risk and/or interest rates).
Therefore, I have no use for a Fama-French value factor. A value factor only has meaning if applied to a sub-universe that eliminates situations where poor growth and/or high risk are likely to prove troublesome.
How not to identify factors
Factor specification is a dangerous proposition if done empirically. Objective evidence of a factor’s relevance cannot be used to define the existence of a factor lest the exercise slide into dangerous data-mining quagmire discussed in this article by Michael Edesess and Kwok l. Tsui. Empirical study and testing is appropriate only as feedback on the efficacy of one’s attempt to specify a factor in an algorithmic manner.
How, for example, might we build a value model that limits consideration to companies whose risk and growth prospects do not sabotage the ideal impact of low P/E? This is no small matter. Our concern is with future risk and growth, but all the data we have relates to the past. Rather than being statistical analysts, play the role of a data detective or artist to come up with creative ways to find clues.
For example, rather than naively plugging in historical growth rates, consider a variety of measures such as trends in return on equity (a more persistent ratio that tells us something about a business’ capacity to grow) and analyst projections and revisions thereto, not so much for the number per se but as sentiment indicators that can stand in for qualitative growth assessments. We can’t even be sure P/E is the best price ratio to use. Graham and Dodd taught us to consider a company’s underlying earning power, which may vary, sometimes considerably, for any particular E figure.
There are countless ways to articulate the efficacy of a particular factor and testing provides valuable feedback in this area. But one should never test an item unless and until it is known, with complete certainty, to be a relevant factor. I have no idea if Fama and French knew ahead of time that size and value would be relevant. Kudos if they did. But if their research led them to discover it, then they got lucky.
Moreover, Fama-French style analysis falters even if one does stumble on something that should work. That sort of scientific control-for-everything methodology is the exact opposite of what real-world investors need. We have no interest in whether or how value per se is associated with future equity returns. We concern ourselves with how valuation ratios whose potential impact is not unraveled by other relevant factors (such as growth and risk) relate to future equity returns.
How factors should be identified
Every now and then, it can pay for even the most experienced among us to refresh ourselves on that which we have long since internalized.
Everything starts with the notion that a stock is worth the present value of its expected cash flows. There are many ways to formularize this idea, but the cleanest approach is the DDM.
This foundational but wildly impractical model is where the science of investment strategy stops and gives way to the art. Everything else we consider must be justifiable as something that makes it more probable than not that we’re looking at a stock whose market price is or is not reasonably in line with the unknowable ideal.
Hence we know value must be relevant because, well, that should be obvious in the way DDM can be adapted to use in defining an ideal P/E, and that can easily be expanded to address other valuation metrics. Most of the other Buffett- or guru-type fundamentals help us address growth and risk.
Even analyst data and technical analysis can help. Since we’re looking into the future, we should be open to qualitative assessments that cannot be captured by historical data. This doesn’t give us license to use anything and everything. But we can use information that meets the test of “That wouldn’t have happened unless they believe or expect...”
Whetting the appetite – I hope
Fama-Franch factor analysis (Moneyball Investing) is a vast field. I only scratched the surface.
I assumed that price should equal value (P = V). Actually, though, that’s oversimplified. Inspired by an intriguing 1984 Robert Shiller paper, Stanford’s Dr. Charles M.C. Lee explains that in equilibrium price equals value plus noise (P = V + N). The word “noise” here is not meant to refer to irritating rhetorical nonsense we assume can be conquered by better investor education but something which Fischer Black acknowledged is necessary and inventible to allow trading to take place. We can, should and do build models that help us understand the impact of N (which, believe it or not, can be quantified).
The nightmare scenario for Moneyball investing is that everybody discovers and uses all factors and profit opportunities are arbitraged out of existence. We are years, perhaps decades or even centuries, away from that, however. Moneyball is a very new phenomenon that came into existence with the proliferation of affordable access to data and the tools to quickly analyze it. Consider that, together with the scope of the field (Fama French studies would need to give way to countless other analyses of factors against who-knows-how-many-potential pre-qualified sub-universes against which they would have to be studied), and the fact that so many researchers remain unaware of the need to even study this sort thing (preferring, instead, to stay locked into the traditional but no longer helpful passive-versus-active controversy) suggest there will likely be more than enough ideas available to fill the expected lifespan of every reader of this site and then some.
Marc H. Gerstein is director of research at Portfolio123 and a specialist in rules/factor-based equity modeling and an attorney. Before joining Portfolio123, he served as an associate research director at Value Line and as director of investment research at Reuters.
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