Factor Models

Structural Estimation

Factor models only explore directional predictions of the investment CAPM. In structural estimation, one takes the model’s key equation directly to the data for econometric estimation and evaluation. Hansen and Singleton (1982) conduct the first such test for the consumption CAPM. Liu, Whited, and Zhang (2009) perform the first structural estimation for the investment CAPM. Although by no means perfect, their first stab yields much more encouraging results than Hansen and Singleton’s at the consumption CAPM. The baseline investment CAPM with only physical capital manages to explain value and post-earnings-announcement drift separately, albeit not jointly. Liu and Zhang (2014) show that the baseline model can explain Jegadeesh and Titman’s (1993) momentum separately, but not simultaneously with value.

The joint estimation difficulty has been largely resolved by Goncalves, Xue, and Zhang (2020), who introduce working capital into the investment CAPM. With plausible parameter estimates, the two-capital investment CAPM manages to explain the value, momentum, investment, and Roe premiums simultaneously. Aggregation also plays an important role. Liu et al. (2009) and Liu and Zhang (2014) construct portfolio-level predicted returns from portfolio-level accounting variables to match with portfolio-level stock returns. In contrast, Goncalves et al. (2020) use firm-level accounting variables to construct firm-level predicted returns, which are then aggregated to the portfolio level to match with portfolio-level stock returns.

A surprising insight from Goncalves et al. (2020) is that value and momentum (as well as investment and ROE) are driven by closely related mechanisms. Intuitively, current investment and expected investment are locked in a “tug of war” in the investment CAPM. When current investment overpowers expected investment, the model predicts the value and investment premiums. When expected investment overpowers current investment, the model predicts the momentum and ROE premiums. The predicted value and investment premiums are long-lived, persisting over three to five years after portfolio formation. The predicted momentum and ROE premiums are short-lived, vanishing within a year after portfolio formation. The model dynamics are intriguingly consistent with the dynamics in the data.

Quantitative Theories

Zhang (2005) constructs the first neoclassical investment model for the cross-section of returns in the spirit of real business cycles (Kydland & Prescott, 1982; Long & Plosser, 1983). Instead of estimating the first-order conditions formally in structural estimation, quantitative theory studies fully specify a dynamic model, calibrate and simulate it, and compare its implied moments with observed moments in the data. Zhang (2005) highlights the role of costly reversibility in explaining the value premium. Intuitively, value firms are burdened with more unproductive capital in bad times, finding it more difficult to downsize so as to yield more cyclical and riskier cash flows and earn higher expected returns than growth firms. In contemporaneous and independent work, Cooper (2006) shows closely related mechanisms at work in a real options model. Also in a related real options model, Carlson, Fisher, and Giammarino (2004) emphasize the role of operating leverage in driving the value premium. The Zhang framework, recently characterized by Clementi and Palazzo (2019, p. 282) as “the dominant paradigm,” has served as a launching pad for a large subsequent, theoretical literature on the cross-section of returns. A full review of this literature is far beyond this short, analytical article.

A long-standing controversy in this theoretical literature is that the CAPM alpha of the value premium in Zhang’s (2005) model is economically small, although the average value premium itself matches that observed in the data. Subsequent studies have attempted to explain the failure of the CAPM in explaining the value premium in the post-Compustat sample, by breaking the tight link between the stochastic discount factor (SDF) and the market factor with multiple aggregate shocks. Prominent examples include short- and long-run shocks (Ai & Kiku, 2013), investment-specific technological shocks (Kogan & Papanikolaou, 2013), and stochastic adjustment costs (Belo, Lin, & Bazdresch, 2014). However, these two-shock models all fail to explain the long sample evidence from 1926 onward that the CAPM alpha of the value premium is economically small and statistically insignificant.

Bai, Hou, Kung, Li, and Zhang (2019) embed disasters into a general equilibrium model with heterogeneous firms to induce strong nonlinearity in the SDF to explain the CAPM failure. Intuitively, when a disaster hits, value firms are burdened with more unproductive capital, finding it more difficult with costly reversibility to reduce capital than growth firms. As such, value firms are more exposed to the disaster risk than growth firms, giving rise to a high average value premium. However, in a finite sample, in which disasters are not realized, the estimated market beta fails to fully capture the disaster risk embedded in the value premium. Consequently, the CAPM fails to explain the value premium in a finite sample without disasters.

In their general equilibrium model, a nonlinear consumption CAPM holds by construction, yet the standard consumption CAPM fails badly in simulated data from the model. Intuitively, the aggregate consumption growth is a poor proxy for the SDF based on recursive utility. Their correlation in simulated data is close to zero. Surprisingly, the onset of disasters is not associated with particularly low contemporaneous consumption growth, and the onset of recoveries is not associated with particularly high consumption growth.

The crux is consumption smoothing. Intuitively, when a disaster hits, the SDF spikes up immediately because investors anticipate multiple years of high marginal utility (bad times). However, consumption smoothing immediately kicks in, with forward-looking real investment falling drastically to prevent consumption from falling too fast. Consequently, consumption only falls cumulatively over multiple years, making the contemporaneous consumption growth a bad proxy for the SDF. Relatedly, consumption smoothing also explains why the CAPM performs better than the consumption CAPM. Because stock prices are forward-looking, the market factor is much more correlated with the SDF than the contemporaneous consumption growth.

A more recent controversy concerns the quantitative performance of the Zhang model. Clementi and Palazzo (2019) argue that upon hit by adverse shocks, U.S. public firms have “ample latitude” to divest their unproductive assets. Specifically, “each quarter on average 18.2% of firms record negative gross investment” (p. 282), suggesting that “plenty of firms downsize, at all times” (p. 287), and there exists “no sign of irreversibility” (p. 289). Clementi and Palazzo (2019) argue that for the standard investment model to explain the average value premium, its implied investment rates must be counterfactual, with a tiny fraction of negative rates and a cross-sectional volatility that is an order of magnitude smaller than that in the data.

Bai, Li, Xue, and Zhang (2019) reexamine the evidence of costly reversibility in U.S. public firms. The firm-level investment rate distribution is highly skewed to the right, with a small fraction of negative investments, 5.79%, a tiny fraction of inactive investments, 1.46%, and a large fraction of positive investments, 92.75%. This firm-level evidence is even stronger than the prior plant-level evidence in Cooper and Haltiwanger (2006). Sample criteria likely play an important role. Cooper and Haltiwanger include only relatively large manufacturing plants in continuous operations throughout their 1972–1988 sample. For comparison, Bai, Li, et al. (2019) follow the standard sample criteria in empirical asset pricing and include virtually all Compustat firms in different industries (not just manufacturing), with no restrictions on size or age.

With a careful replication effort, Bai, et al. (2019) trace the differences between their evidence and Clementi and Palazzo’s (2019) to three sources. First, both studies measure gross investment rates as net investment rates plus depreciation rates. Both measure net investment rates as the net growth rates of net PPE in Compustat. However, Bai, Li, et al. (2019) measure depreciation rates as Compustat’s depreciation over net PPE, depreciation rates that are embedded in net PPE. In contrast, Clementi and Palazzo (2019) use industry-level geometric depreciation rates estimated by Bureau of Economic Analysis, depreciation rates that are internally incompatible with net PPE in Compustat.

Second, Clementi and Palazzo (2019) impose sample criteria that are nonstandard in empirical asset pricing, such as removing firm-years with mergers and acquisitions, in which the target’s assets are more than 5% (a low cutoff) of the acquirer’s. The nonstandard sample criteria curb the right tail of the asymmetric firm-level investment rate distribution. Finally, Clementi and Palazzo (2019) also cut off the right tail of the quarterly investment rate distribution at 0.2. This research practice is highly questionable because the right tail is the “smoking gun” evidence in support of costly reversibility (Cooper & Haltiwanger, 2006).

While Clementi and Palazzo’s (2019) evidence is flawed, their point of matching investment and returns moments jointly in quantitative studies is well taken. Using simulated method of moments (SMM), Bai, et al. (2019) estimate four parameters (the upward and downward adjustment cost parameters, the fixed cost of production, and the conditional volatility of firm-specific productivity) to target seven data moments (the average value premium, the cross-sectional volatility and skewness of individual stock excess returns, the cross-sectional volatility, skewness, and persistence of investment rates, as well as the fraction of negative investment rates). The SMM estimation strongly indicates costly reversibility and operating leverage in U.S. public firms. The downward adjustment cost parameter is estimated to be 508.2 (t-value = 13.39), which is substantially higher than the upward parameter, 0.63 (t-value = 4.6). The fixed cost of production is estimated to be 0.0637 (t-value = 4.24). The model matches the average value premium of 0.43% per month (t-value = 1.97) in the 1962–2018 sample. For investment rates, the cross-sectional volatility is 62% per annum (58.5% in the data) and the fraction of negative investments 5.78% in the model (5.79% in the data). The overidentification test fails to reject the model with the seven moments (p-value = 0.59).

The Consumption CAPM is Incomplete

In his 1890 magnum opus, Alfred Marshall (1890, 1961) reconciles the costs of production theory of value with the marginal utility theory of value, using a famous “scissors” simile. Marshall 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” (p. 348).

Asset pricing theory is just value theory in microeconomics extended to uncertainty and multiple periods. From this perspective, clearly, the consumption CAPM is conceptually incomplete. The crux is that it blindly focuses on the demand of risky assets, while abstracting from the supply. Alas, anomalies are primarily empirical relations between firm characteristics and expected returns. Without modeling characteristics, it is impossible to fully explain anomalies.

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. Modeling these characteristics takes one right back to the investment CAPM. 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. The investment “blade” is exactly symmetrical and neatly complementary to the consumption “blade.” The investment CAPM and the consumption CAPM combine to form the pair of “scissors” of equilibrium asset 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. Alas, 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 demand-based pricing exceedingly difficult. The Sonnenschein–Mantel–Debreu theorem in equilibrium theory says that individual rationality imposes no restrictions on aggregate demand, meaning that the aggregation problem over heterogeneous investors is essentially 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. Above all, the consumption CAPM anomalies are the investment CAPM regularities.

Because of SDF’s far-reaching influence in asset pricing (Cochrane, 2005), my intellectual abandonment of SDF in the investment CAPM warrants further clarification. The first ever general equilibrium model in Fisher (1930) provides a symmetric treatment of the impatience and investment opportunity theories of equilibrium interest rates. Fast forward to 2020, both consumption and investment Euler equations are in every modern DSGE model and are well understood to be equally important in equilibrium theory.

Yet in asset pricing, classic theorists such as Markowitz, Sharpe, and Lintner put investors at the center of inquiry and never look back. In the late 1970s, Rubinstein, Lucas, and Breeden derive the consumption CAPM from the consumption Euler equation, while continue ignoring firms. Their key argument is that as long as consumption is consistent with the optimality conditions of firms left outside the model, consumption betas should be sufficient in pricing assets. This argument is theoretically correct. Alas, empirically, again fast forward to 2020, other than a few diehards with seemingly no listening skills, most people would consider the consumption CAPM as a colossal failure. Otherwise, the anomalies literature would not be called the “anomalies” literature to begin with.

The separation from SDF in the investment CAPM is exactly symmetrical to the separation from firms in the consumption CAPM. As long as the SDF is consistent with the optimality conditions of the marginal investor left outside the model, a few firm characteristics should be sufficient in pricing assets. If the marginal investor is risk neutral, the discount rate backed out from the NPV rule would just be the risk-free rate. And in an economy with only idiosyncratic shocks, there would still be factors that capture comovements in stock returns, but the long-short factor premiums would just be zero. The beauty is that in general equilibrium theory, the consumption CAPM and the investment CAPM deliver identical expected returns (Zhang, 2017). In this sense, the investment CAPM is an asset pricing paradigm, which is separate from, but complementary to, the consumption CAPM. Most important, the investment CAPM works.

Because of the intractable 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 does one have to suffer to let the lesson sink in that firm characteristics are not even modeled? 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, which are detrimental to our science, must stop. No one has ever pretended 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 has served as 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 overreaction to them. While rejecting the CAPM is the more scientificially accurate interpretation of the evidence, rejecting EMH altogether certainly appears more impactful. More important, for a long time, the consumption CAPM was the only asset pricing theory in the land. Given the exclusive focus on investors, it’s not entirely unreasonable to interpret the failure of the consumption CAPM as investor irrationality.

The investment CAPM has changed the big picture. 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 inquiry, the anomalous evidence is largely consistent with the NPV rule in corporate finance. Remember EMH only says that pricing errors are unpredictable. The investment CAPM errors are mostly small and unpredictable. And the expectations in the investment CAPM are entirely rational.

I separate EMH from investor rationality. Again, EMH only says that pricing errors are unpredictable. 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, the manager will just blindly adjust investment decisions per the 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. The investment CAPM says that anomalies are in fact 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 little to do with investors and everything to do with managers. The NPV rule is as fundamental an economic principle as diversification. Capital markets obey standard economic principles!

Alas, 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. With this caveat in mind, I emphasize that individual rationality and aggregate rationality are completely detached per the Sonnenschein–Mantel–Debreu theorem. Individuals can be irrational, but the marginal (aggregate) investor might not, and vice versa. Thus, the failures of the consumption CAPM might have nothing to say about EMH. Behavioral economists can hide behind aggregation 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 sense 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 believe 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 originator that abandons the CAPM, which is largely the only asset pricing theory at the time, thereby opening the floodgate of behavioral finance. Although Fama and French (1993) quickly attempt to patch up the hole with their three-factor model by adding SMB and HML into the CAPM, the floodgate has forever been breached. Fama (1998) tries to contain the resulting tsunami but to no 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 over 20 years ago with my current defense based on the investment CAPM. Fama makes two 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 three-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 in empirical work.

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 questions, 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 et al. (2020).

Alas, I do not find Fama’s (1998) chance argument persuasive. Anomalies do not just randomly split between under- and overreaction 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 et al. (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 stopped them from adding it into their factor model until 2018 (Fama & French, 2018). It is statistically correct to view SMB, HML, and perhaps even UMD as risk factors from the intertemporal CAPM 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 whole concept of covariance superfluous. Yes, the consumption CAPM is all about covariances, 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 premium. If a long-short factor earns a significant premium in the time series, its underlying characteristic is likely significant in cross-sectional regressions. 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. Stock returns of firms with similar investment-to-assets comove together because their investment returns are similar as a result of similar investment-to-assets. Stock returns of firms with similar ROE comove together because their investment returns are similar due to their similar ROE. And stock returns of firms with expected investment growth comove together because their investment returns are similar due to their similar expected investment growth. In all, 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, and 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 comovement. To the extent that size, book-to-market, and momentum are not modeled within the consumption CAPM, these factors have been (wrongfully, in my view) perceived as ad hoc, arising from “fishing” expeditions.

The investment CAPM instead offers a new, microeconomic perspective of “factors.” Again, the comovement of stock returns among stocks with similar investment, profitability, and expected growth arises from the comovement of their similar investment returns. Characteristic-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, consumption 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,” meaning that 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 (2014) maintain: “[T]he efficient market hypothesis predicts that most fundamental analysis is doomed to failure” (p. 356, original emphasis). In a recent interview with Bloomberg on November 5, 2019, Fama even calls equity research on Wall Street “business-related pornography.”

On the other hand, honoring the 50th anniversary of Graham and Dodd (1934), Warren Buffett (1984) showcases nine 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 behavioral finance, and view EMH as 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 one is allowed to talk about in academia (unless you’re a behavioral economist who is willing to say that the world is all crazy).

The investment CAPM once again changes the big picture. Recall the investment CAPM says: discount rates = (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 seem to mostly 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 four decades. Indeed, the random walk hypothesis (with a constant discount rate) is still the workhorse theory for EMH as late as the 1970s.

In the 1980s and 1990s, the consumption CAPM rises up to meet Shiller’s (1981) excess volatility challenge and move 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 (1981) 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 I attribute it to cross-sectionally varying expected returns, all within EMH.

Empirically, Hou, Mo, Xue, and Zhang (2019a) show that the $q^5$ 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, and Penman and Zhu’s (2014, 2018) expected return strategies. Also, the latest factor models cannot fully explain Buffett’s alpha, suggesting that discretionary, active management cannot be fully replaced by passive factor investing. Identifying sources of quality, quantifying their impact on expected returns, and evaluating to what extent a market price is a bargain price 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 trying to make a living 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 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 works 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 DSGE models in modern quantitative macroeconomics.

A Risky Mechanism of Momentum

Let me start by emphasizing that momentum is a success story for the investment CAPM. Recall from January 1968 to December 2018, UMD earns on average 0.64% per month (t-value = 3.73), but its q-factor alpha is only 0.14% (t-value = 0.61). The ROE factor does all the heavy lifting, as UMD has a large ROE-factor loading of 0.9 (t-value = 5.85). The loadings on the other three factors are insignificant. In the structural estimation of Goncalves et al. (2020), the investment CAPM explains value and momentum simultaneously. In the “tug of war,” expected investment dominates current investment and plays a key role in the model’s performance.

Nevertheless, a major gap in our knowledge exists. What exactly are the risks underlying momentum (and the ROE premium)? To answer this question, one needs more than factor regressions and Euler equation tests. Only fully specified quantitative theories are up to the task. Recall Zhang (2005) ties the value premium to business cycles. Alas, momentum, and, equivalently, the ROE premium are both significantly negative in his model. Also in partial equilibrium, Johnson (2002) ties momentum to expected growth and argues that expected growth is risky. Sagi and Seasholes (2007) argue that momentum winners have more growth options than momentum losers and that growth options are risky. An important, open question is how to combine Zhang’s value with Johnson’s and Sagi and Seasholes’ momentum mechanisms in a unified, general equilibrium framework. More generally, what sources of risks are behind the investment, Roe, and expected growth factors in the $q^5$ model in a unified, equilibrium setting? A unified model imposes internal consistency that is vital for theories. Li (2018) is the only exception (alas in partial equilibrium) that makes sense to me. More work is sorely needed.

Other Asset Classes

An advantage of the consumption CAPM, and more generally, the SDF framework, is that it can in principle be applied to different asset classes simultaneously. In contrast, the investment CAPM has so far been mostly applied to equity pricing. However, I caution that the consumption side’s advantage of applying to different asset classes should not be taken too literally. After all, failing to explain returns of different asset classes is definitely worse than failing to explain just equity returns. Behavioral under- and overreaction apply to different asset classes (Asness, Moskowitz, & Pedersen, 2013). But relabeling is no theory.

More important, any asset has suppliers, which must face certain tradeoffs in making optimal supply decisions. It seems straightforward to apply the investment CAPM to global stocks, country equity indices, corporate bonds, and real estates. Other asset classes such as currencies, government bonds, and commodities require additional, creative theorizing. The challenge is to cleanly separate the supply-side tradeoff from the SDF. To me, because of aggregation, SDF is the source of all ills in asset pricing and should be avoided at all costs.