(This blog post is the third of a 4-part sequence based on my working paper fresh from the oven: "q-factors and investment CAPM, which is a solicited, analytical essay on the big-picture of the investment CAPM. Due to its length, I am splitting it into 4 parts on my blog. The link above gives the complete pdf, which also provides detailed references.)
As a disruptive innovation, the investment CAPM thinks about asset pricing very differently from the consumption CAPM and behavioral finance, with broad-ranging implications for academic finance research and asset management practice.
Complementarity with the Consumption CAPM
In his magnum opus, Alfred Marshall (1890, Principles of Economics [1961, 9th edition, p. 348]) writes: “We might as reasonably dispute whether it is the upper or under blade of a pair of scissors that cuts a piece of paper, as whether value is governed by utility or costs of production. It is true that when one blade is held still, and the cutting is affected by moving the other, we may say with careless brevity that the cutting is done by the second; but the statement is not strictly accurate, and is to be excused only so long as it claims to be merely a popular and not a strictly scientific account of what happens.”
Asset pricing theory is just value theory in microeconomics extended to uncertainty and over time. From this perspective, clearly, the consumption CAPM is conceptually incomplete. The crux is that it exclusively focuses on the demand of risky assets, while abstracting from the supply altogether. Alas, anomalies are primarily empirical relations between firm characteristics and expected returns. Without modeling firm characteristics, it is impossible to fully explain anomalies within the consumption CAPM. Even if an SDF specification is discovered that fits the consumption CAPM with anomaly portfolios, one still has to explain why the consumption betas would be aligned with investment-to-assets, Roe, book-to-market, momentum, and other anomaly variables. By focusing on the supply of risky assets, while abstracting from the demand altogether, the investment CAPM is the missing “blade” of equilibrium asset pricing, symmetrically and neatly complementing to the consumption “blade.” The investment CAPM and the consumption CAPM combine to form the pair of “scissors” of equilibrium pricing.
The glorious achievements of the consumption CAPM are well known. I interpret its major contribution as time-varying expected returns, which largely resolve Shiller’s (1981) excess volatility puzzle in aggregate asset pricing. But why does the consumption CAPM fail so badly in explaining anomalies in the cross section? Zhang (2017) blames the intractable aggregation problem. Investors are heterogeneous in preferences, beliefs, and information sets, all of which make the demand-based pricing extremely difficult. The Sonnenschein-Mantel-Debrew theorem in equilibrium theory says that individual rationality imposes essentially no restrictions on aggregate demand, meaning that the aggregation problem over heterogeneous investors is largely intractable (Kirman, 1992). It is possible that for aggregate, macro-level asset pricing, a representative agent still suffices but fails for micro-level asset pricing in the cross section. Who’s the marginal investor for Apple Inc.? Anyone’s guess is as good as mine.
Derived from the first principle of individual firms, the investment CAPM is relatively immune to the aggregation problem. Who’s the marginal supplier for Apple Inc. shares? Well, easy, that’s Apple Inc.. Tim Cook most likely has more impact on Apple Inc.’s market value via his operating, investing, and financing decisions than many Apple Inc. shareholders like me via portfolio decisions in their retirement accounts. The investment CAPM formalizes the linkage between corporate decisions and asset prices. The major contribution of the investment CAPM is cross-sectionally varying expected returns, which largely resolve anomalies in the cross section. In particular, the consumption CAPM anomalies are the investment CAPM regularities.
Because of the inescapable aggregation difficulty facing the consumption CAPM and no such challenge facing the investment CAPM, EMH must be detached from the consumption CAPM and reattached to the investment CAPM. How many more decades of the consumption CAPM failures do we have to endure to let the lesson sink in that firm characteristics are not even modelled? The step going from an individual investor problem to a consumption-based SDF that prices all assets requires aggregation, which is all but automatic. Asset pricing is not all about SDF, which is only demand-based. The overreaching tendencies of the consumption CAPM, detrimental to our Science, must stop. You don’t see me pretending that the investment CAPM has anything to do with personal finance, household finance, or portfolio allocation.
An EMH Counterrevolution to Behavioral Finance
The anomalies literature is the empirical foundation of behavioral economics. The investment CAPM shows that the empirical foundation is all but an illusion. Start with: Realized returns = expected returns + abnormal returns. When an anomaly variable forecasts realized returns, there are tautologically two parallel interpretations. One, which is the behavioral view, says that the variable is forecasting abnormal returns. As such, pricing errors are predictable, violating EMH. The other, which is the EMH view, says that the anomaly variable is related to expected returns, but the pricing errors are unpredictable. The consumption CAPM and the investment CAPM are both expected-return models. Both are consistent with EMH.
In the anomalies literature (and in asset management industry), the behavioral view is extremely popular. Behavioral finance has gained its prominence by documenting the CAPM alphas and sticking labels such as under- and over-reaction to them. While rejecting the CAPM is the more accurate interpretation of the evidence, the interpretation of rejecting EMH altogether certainly appears to be more impactful. More important, for a long time, the consumption CAPM is the only asset pricing theory in the land. Given the exclusive focus on investors, it’s not unreasonable to interpret the failure of the consumption CAPM as investor irrationality.
The investment CAPM has changed the big picture in its entirety. I deal with Fama’s (1991) joint-hypothesis problem by replacing the consumption CAPM with the investment CAPM. With the suppliers of risky assets at the center of analysis, the anomalous evidence is largely consistent with the NPV rule in Corporate Finance. Remember EMH only says that pricing errors are not predictable. The investment CAPM alphas are mostly small and unpredictable. And the expectations of the investment CAPM are entirely rational.
I separate EMH from investor rationality. Again, EMH only says that pricing errors are not predictable. It doesn’t say all investors are rational. A common counterargument against my EMH defense is that if investors set a firm’s equity price too high, its manager will just blindly adjust her investment decisions per her first-order condition. As a result, both the equity price and investment are wrong. This argument is specious at best. It ignores the powerful equilibrating role of the supply side. Some investors might be optimistic and attempt to bid up the equity price too high. But with a manager’s cool head, the supply of risky shares goes up, flooding cold water over the fire of irrational exuberance. The wrong price will drop toward the equilibrium price. In the special case of no adjustment costs, in particular, Tobin’s q will forever be one, regardless of how irrational investors are. This equilibrating role of the supply side seems to have been greatly underappreciated by academics and practitioners alike.
I should concede that the complex equilibrating process between demand and supply is largely unknown. I have seen models of heterogeneous investors, and separately, models of heterogeneous firms. But I have yet to see a model with both heterogeneous investors and heterogeneous firms, likely because of its computational intractability. As such, all we can do is to use simpler models to gain insights. Behavioral finance relies on dysfunctional, inefficient markets for its mechanisms to work. With the investment CAPM, I view anomalies as regularities from the NPV rule in well functioning, efficient markets. As such, the argument that anomalies must necessarily imply investor irrationality is wrong. Anomalies most likely have less to do with investors and more to do with managers. The NPV rule is as fundamental an economic principle as diversification. Capital markets obey standard economic principles!
However, because the complex equilibrating process between demand and supply is unknown, and perhaps even unknowable, I cannot say that the observed prices are completely deprived of wrong decisions from investors. However, remember the Sonnenschein-Mantel-Debrew theorem says that investor rationality and aggregate rationality are completely detached. Investors can be irrational, but the marginal (aggregate) investor might not, and vice versa. As such, the failures of the consumption CAPM might have nothing to say about EMH. Behavioral economists can hide behind this aggregation problem all they want and claim relevance. But it’s no coincidence that a coherent behavioral theory has yet to appear after 35 years since De Bondt and Thaler (1985). Given the time test, I feel that such a theory likely doesn’t even exist.
While I contend that behavioral finance has almost nothing to say about equilibrium asset prices, I do think that it has a major role to play in areas like personal finance and household finance. Identifying and rectifying investor mistakes in these areas are enormously important for human welfare. However, these areas are partial equilibrium in nature. Without dealing with aggregation, these fields have limited implications for equilibrium asset prices.
How I Defend Fama
A watershed article is Fama and French (1992). It is this paper from the EMH inventor that abandons the CAPM, which is largely the only asset pricing theory at the time, thereby stimulating the development of behavioral finance. Although Fama and French (1993) quickly attempt to patch up the hole with their 3-factor model by adding SMB and HML into the CAPM, the floodgate has been opened. Fama (1998) tries to contain the resulting tsunami but to little avail. With a wrong hammer in their hands (as firm characteristics are all condensed into a Lucas tree), theorists have largely stood on the sidelines looking on, with precious little to say about the EMH versus behavioral finance debate.
It is informative to compare Fama’s (1998) EMH defense 20 years ago with my current defense based on the investment CAPM. Fama makes 2 points. First, apparent overreaction is about as common as underreaction. As anomalies seem to split randomly between underreaction and overreaction, Fama claims that EMH wins. Second, anomalies are sensitive to changes in measurement. Anomalies with value-weighted returns are smaller than with equal-weighted returns. Also, calendar-time 3-factor regressions are more reliable than long-horizon event studies. Kothari (2001) echoes Fama in emphasizing the sensitivity of measurement and the need of coming up with a theory of inefficient markets as null hypotheses.
Like his EMH insight, Fama’s empirics has no peers. As acknowledged in Zhang (2017), the empirical design of the q-factor model, including its factor construction, formation of testing portfolios, econometric tests, and most important, the taste of the economic question, are all deeply influenced by Fama and French (1993, 1996). I also take the value- versus equal-weight lesson to heart and give it a demonstration on steroids in Hou, Xue, and Zhang (2019).
Alas, I do not find Fama’s (1998) chance argument persuasive. Anomalies do not just randomly split between under- and over-reaction camps. The two types of anomalies are systematically different. To a theorist, the systematic pattern is exciting, because it indicates hidden economic law(s) to be discovered. The hidden law turns out to be the investment CAPM (a restatement of the NPV rule in Corporate Finance), as demonstrated in Hou, Xue, and Zhang (2015). The “overreaction” anomalies are all just different manifestations of the investment factor, and the “underreaction” anomalies are all just different manifestations of the Roe factor.
I do not find Fama and French’s (1993, 1996) interpretation of risk factors for SMB and HML persuasive either. To their credit, the lack of a risk interpretation for momentum has stopped them from adding it into their factor model until 2018 (Fama and French, 2018). It is statistically correct to view SMB, HML, and perhaps even UMD as risk factors from the intertemporal CAPM and/or APT. However, the interpretation is on shaky economic grounds because size, book-to-market, and prior short-term returns are never modeled in the two theoretical frameworks. As such, the risk interpretation seems like a mere assertion.
This concern is why Hou, Xue, and Zhang (2015) interpret the q-factors only as common factors that summarize the cross-sectional variation of average stock returns. In particular, I find the concept of covariance superfluous. Yes, the consumption CAPM is all about covariance, but the investment CAPM is all about characteristics. If a characteristic is significant in cross-sectional regressions, its long-short factor is likely to earn a significant average return. And if a long-short factor earns a significant average return in the time series, its underlying characteristic is likely to be significant in cross-sectional regressions. As such, the q-factor model is simply a linear factor approximation to the nonlinear characteristics model of the investment CAPM.
Going from a characteristic to a factor is mostly mechanical, and vice versa. In particular, stock returns of firms with similar investment-to-assets tend to comove together because their investment returns are similar as a result of similar investment-to-assets. Stock returns of firms with similar Roe and expected growth tend to comove together because their investment returns are also similar for analogous reasons. Comovement is nothing mysterious.
More fundamentally, the investment CAPM advances a new perspective of “factors.” In the consumption CAPM, factor models are linear approximations of the intertemporal marginal rate of substitution for the representative investor. Aggregate variables such as the growth rate of industrial production, inflation rate, the default premium can be used to substitute out consumption, giving rise to the classic macroeconomic risk factor model of Chen, Roll, and Ross (1986). Because the consumption CAPM is in essence a macroeconomic model, factors are commonly perceived as aggregate, systematic sources of covariation. To the extent that size, book-to-market, and momentum are not modelled within the consumption CAPM, these factors have been (wrongfully, in my view) perceived as ad hoc, arising from “fishing” expeditions.
In contrast, the investment CAPM offers a new, microeconomic perspective of “factors.” The comovement of stock returns among stocks with similar investment, profitability, and expected growth arises from the comovement of their similar investment returns. Characteristics-based factors are on as solid economic grounds in the supply theory of asset pricing as aggregate consumption growth in the demand theory of asset pricing. If one takes aggregation seriously, aggregate consumption growth is not even a factor. Neither are most other aggregate variables.
Security Analysis within Efficient Markets
Graham and Dodd (1934) define Security Analysis as “concerned with the intrinsic value of the security and more particularly with the discovery of discrepancies between the intrinsic value and the market price (p. 17).” Their philosophy is to invest in undervalued securities that are selling below the intrinsic value “justified by the facts, e.g., the assets, earnings, dividends, and definite prospects (p. 17).” Alas, the intrinsic value is not exactly identified. To protect against its estimation errors, Graham (1949) advocates the “margin of safety,” i.e., investors only purchase a security when its market price is sufficiently below its intrinsic value.
EMH and Security Analysis have historically been viewed as diametrically opposite. On the one hand, the traditional view of academic finance, with the CAPM as its workhorse theory, dismisses security analysis as pure luck, likens security analysts to astrologers, and recommends investors to passively hold only the market portfolio. Bodie, Kane, and Marcus (2017) maintain: “[T]he efficient market hypothesis predicts that most fundamental analysis is doomed to failure (p. 356).” In a recent interview with Bloomberg on November 5, 2019, Fama even labels equity research on Wall Street as “business-related pornography.”
On the other hand, honoring the 50th anniversary of Graham and Dodd (1934), Warren Buffett (1984) showcases 9 famous investors and argues that their successful performance is beyond chance. Buffett goes on to say: “Our Graham & Dodd investors, needless to say, do not discuss beta, the capital asset pricing model or covariance in returns among securities. These are not subjects of any interest to them. In fact, most of them would have difficulty defining those terms (p. 7).” Buffett then mocks finance academics as out of touch with the real world: “Ships will sail around the world but the Flat Earth Society will flourish (p. 15).” Wall Street practitioners, not surprisingly, are overwhelmingly sympathetic to the behavioral view, and believe EMH to be a relic of the past. An old joke helps illustrate the schism between academics and practitioners. An asset manager asks an academic: “If you are so smart, why aren’t you rich?” to which the academic replies: “If you are so rich, why aren’t you smart?”
EMH is down in the dumps only because the consumption CAPM is a rundown dumpster truck. I have yet to meet an asset manager who even mentions the consumption CAPM, not even once, yet the consumption CAPM is virtually all we are allowed to talk about in academia (unless you’re a behavioral economist). The investment CAPM once again changes the big picture. Recall the investment CAPM says: Discount rate = (profitability + expected investment costs) / investment costs. In the denominator, investment costs equal Tobin’s q (marginal costs of investment equal marginal q). As such, the investment CAPM prescribes that to earn higher expected returns, investors should buy stocks with high quality (measured as high profitability and high expected growth) at bargain prices. This prescription is exactly what Graham and Dodd (1934) have been saying and what Wall Street asset managers have been practicing for 85 years. Finally, after such a long exile, Security Analysis has found its rightful home in finance theory.
However, my treatment of Security Analysis differs from Graham and Dodd’s (1934) in a fundamental way. Writing way, way before the arrival of equilibrium theory, Graham and Dodd largely have a constant discount rate in mind as the expected-return model. Their remarkable business acumen enables them to intuit their way to the ever-lasting investment truth of buying high quality stocks at bargain prices. Their monumental work predates academic finance by at least 4 decades. Indeed, in at late as the 1970s, the random walk hypothesis (with a constant discount rate) is still the workhorse theory for EMH.
In the 1980s and 1990s, the consumption CAPM rises up to meet Shiller’s (1981) excess volatility challenge and moves the needle from a constant discount rate to time-varying expected returns as the workhorse theory in EMH. With the investment CAPM, I am trying to move the needle once again to cross-sectionally varying expected returns. Shiller attributes all excess volatility to predictable pricing errors against EMH, but the consumption CAPM attributes it to time-varying expected returns within EMH. Analogously, Graham and Dodd (1934) attribute the performance of security analysis to predictable pricing errors against EMH, but the investment CAPM attributes it to cross-sectionally varying expected returns, all within EMH.
Empirically, Hou, Mo, Xue, and Zhang (2019c) show that their model goes a long way toward explaining prominent security analysis strategies, including Frankel and Lee’s (1998) intrinsic-to-market value, Piotroski’s (2000) fundamental score, Greenblatt’s (2005) “magic formula,” Asness, Frazzini, and Pedersen’s (2019) quality-minus-junk, Buffett’s Berkshire, Bartram and Grinblatt’s (2018) agnostic analysis, as well as Penman and Zhu’s (2014, 2018) expected-return strategies. Also, Hou et al. show that the latest factor models cannot fully explain Buffett’s alpha and interpret the evidence as saying that discretionary, active management cannot be fully replaced by passive factor investing. Identifying sources of quality and quantifying their impact on expected returns leave plenty of room for active management.
Rational Expectations Economics
Make no mistake. The investment CAPM is the latest product from the Lucas-Sargent rational expectations economics. While I no longer believe that the end stage of economics is a Fortran program, the Lucas-Sargent teaching of microfoundation is deeply embodied in the investment CAPM. My Wharton theoretical training has given me a strong immune system against behavioral finance, despite being embedded in the hostile territory of the anomalies literature for 20 years. If I cannot write down an optimization-based model to explain a stylized fact, I don’t understand the fact. A “model” with no optimization is just sticking labels to the fact to be explained. True to the nature of the anomalies literature, with my Rochester empirical training, I have also given life to the investment CAPM with the careful, empirical measurement in the Fama-French tradition. While there are still a few mopping-up operations left to do, the anomalies literature, which used to be a major embarrassment for rational expectations economics, is no more. On the contrary, I have turned it into a triumph of rational expectations. My macroeconomist compatriots can go on refining the all-important DSGE models, without worrying about all the fires of capital markets, as the investment CAPM has put them out, mostly.
I should clarify that my aggregation critique against the consumption CAPM applies to the specific context of anomalies in the cross section. For aggregate asset pricing, the consumption CAPM does well, although it remains to be seen to what extent aggregation would bite once the consumption CAPM is embedded into a full-fledged equilibrium model with production. Analogously, my aggregation critique does not apply, at least not directly, to the mainstream DSGE models in modern quantitative macroeconomics.
An aspiring economic philosopher