Our article "The Economics of Security Analysis" (Hou, Mo, Xue, and Zhang 2022) has been accepted at Management Science.
An intriguing finding is that top-20 (about 1%) active, equity funds outperform by holding high expected growth, low investment stocks at the expense of other funds who hold the opposite sides of the trades in equilibrium. In particular, top-20 active fund portfolios have significantly positive expected growth and positive (albeit insignificant) investment factor loadings, whereas aggregate active fund portfolios have significantly negative loadings on both factors.
Please see the latest draft, the internet appendix, slides, as well as video presentation below:
I am honored and pleased to deliver my 2022 FMCG keynote on "Asymmetric Investment Rates." A big thank-you to Prof. Philip Gharghori at Monash Business School for the kind invitation.
Please see below for the article, slides, and video presentation:
We have just completed a massive empirical paper "Asymmetric investment rates" (Bai, Li, Xue, and Zhang 2022), with 128 pages short. The main data work is to construct firm-specific current-cost capital stocks (the replacement costs) for the entire Compustat sample.
The headline result is that the firm-level current-cost investment rate distribution is heavily right-skewed, with a small fraction of negative investment rates, 5.51%, but a huge fraction of positive investment rates, 91.64%.
The histogram below (Figure 4 in our paper) shows that the firm-level asymmetry is comparable with, if not more impressive than, the Cooper-Haltiwanger (2006) plant-level evidence (their Figure 1).
I've also put some slides together for my upcoming keynote at the 2022 Financial Markets and Corporate Governance Conference (FMCG) organized by Monash Business School.
We have just updated our q-factors and expected growth factor through December 2021. The data are available at the Factors page of global-q.org. We expect to get our testing portfolios updated within four weeks.
The article on "Searching for the Equity Premium" (Bai and Zhang 2022) has just been published in the February 2022 issue of Journal of Financial Economics. Our key insight is that a DSGE model with recursive utility, search frictions, and capital accumulation is a good start to forming a unified theory of asset prices and business cycles.
Please see the article, slides, and presentation:
This work is the latest development in our research program that aims to integrate macro labor with asset pricing in order to explain the equity premium puzzle in general equilibrium production economies.
Prior contributions in this research program include "Endogenous Disasters" (Petrosky-Nadeau, Zhang, and Kuehn 2018) at American Economic Review. Please see the article, slides, codes, and presentation:
Another contribution in this research program is "Solving the Diamond-Mortensen-Pissarides Model Accurately" (Petrosky-Nadeau and Zhang 2017) at Quantitative Economics. Please see the article, slides, codes, and presentation:
Asset pricing is in a Kuhnian crisis. And it has been since 1992.
The asset pricing theory that one would read in doctoral textbooks is the consumption CAPM, and the theory in MBA textbooks is the class CAPM. Alas, we know the CAPM fails in the data, and the consumption CAPM performs often worse than the CAPM.
Where do we go from here?
A prominent answer in the prior literature is the joint-hypothesis problem. There could be nonmarket risk factors absent in the CAPM. However, what counts as a risk factor is controversial.
The joint-hypothesis problem is a specific example of the Duhem-Quine thesis in philosophy of science. The thesis says that when we test a specific hypothesis, we are in effect testing a whole web of beliefs underlying its development.
In the context of the CAPM, a long list of assumptions, including metaphysical presuppositions, has been made in its derivation. Where exactly do we pin the blame for the model’s failure?
I blame the metaphysical presupposition of the consumption CAPM that the marginal investor is the marginal agent who determines asset prices. More specifically, I blame the assumption of homogeneous expectations (beliefs) for investors in the CAPM and the existence of a representative investor in the consumption CAPM.
Ontology is a branch of philosophy that studies the fundamental structure of reality.
Consider the following two possible worlds. Which world do you think is closer to the mind-independent reality we are living in?
Possible World 1:
At the end of each September (fiscal yearend) of calendar year t, all shareholders of Apple Inc. elect a marginal investor, who represents the best interests of all shareholders. The marginal investor then marches into Tim Cook’s office in Cupertino and dictates to Tim the cost of equity for Apple Inc. in the next fiscal year. After receiving the cost of equity, Tim and his management team then work out Apple’s operating, investing, and financing decisions for the next fiscal year.
Possible World 2:
Tim Cook and his management team do whatever they want to maximize the shareholder value to the best of their abilities. While paying attention to external capital markets, they already have a sense of what their cost of equity is likely to be. Some shareholders will approve what the management is doing and buy and hold Apple shares. Others who disagree can feel free to leave by selling their shares. Unless facing a major decline of Apple’s share price, Cook and his team continue to do whatever they feel is the right thing to do.
If you find Possible World 1 absurd, keep in mind that is exactly the ontology presupposed in the academic finance literature, often without us consciously aware that we are doing so.
Thus when teaching capital budgeting in corporate finance and equity valuation in accounting, we take the cost of equity as a free parameter. We then tell students to take a course on investments to pin down the parameter with a factor model. (Though curiously, most empirically efficacious factor models are built on firm characteristics, not investor preferences. Although the 3-factor model is dead, the CAPM is deader.)
Thus in the theoretical asset pricing literature, we have the metaphysical presupposition “Asset pricing is all about the pricing kernel” declared as incontrovertible truth. This decree ensures an ill-founded hegemony of the consumption CAPM over the investment CAPM.
Thus in the empirical asset pricing literature, the joint-hypothesis problem only covers missing risk factors, while leaving the question why we should waste more time on the pricing kernel (risk factors) to begin with unanswered.
Possible World 2 is the ontological foundation of the investment CAPM, which it shares with corporate finance and accounting. Alas, for the most part, the latter two fields have largely ignored their own impact on cross-sectionally varying expected returns (asset prices).
Possible World 2 is much closer to our reality. While still germinating in my brain, I am gradually arriving at the philosophical position that the corporate manager, not the marginal investor, is the marginal agent (causal power) that determines the asset price of the manager’s own equity.
It is conceivable that a venture capitalist can bully his way with the manager of a private equity or a microcap public equity. (I say “his” because most bullies I have encountered in life are male.) But I doubt Tim Cook can be bullied by anyone.
All in all, the fundamental structure I have in mind is a powerful manager on one side and a diffuse assemblage of shareholders, who are best at bickering among themselves, on the other. Which side do you think is more causally powerful for the asset price of the manager’s own stock?
If my carving of the fundamental structure of finance is more accurate than that of our forefathers, then we should clear the rubbish (at least substantially revise) what we call equilibrium asset pricing theory (i.e., the consumption CAPM) from our textbooks.
Partial equilibrium theories remain valid from the demand side, but general equilibrium theories fail. There is just no such entity called the marginal investor.
I accept the importance of behavioral biases in partial equilibrium theories of investors, both retail and institutional. But I remain dubious about their impact on equilibrium asset prices. Imposing behavioral biases on the marginal investor to do equilibrium asset pricing commits the same aggregation fallacy as the consumption CAPM.
All in all, our current edifice of equilibrium asset pricing theory is built on sand, shifting sand. The causal power called the marginal investor simply doesn’t exist in reality. Time to rebuild our edifice on the causal power that does exist, i.e, the corporate manager, via the investment CAPM.
Corporate finance and accounting colleagues of the world, unite! You have nothing to lose but your chains forced upon you by fallacious asset pricers.
In my recent interview with Jack Forehand and Justin Carbonneau, I discuss the related scientific debate within asset pricing.
The demise of empiricism.
The clash between the 3-factor model and the q-factor model is a clash between two philosophies of science and two visions for the future of asset pricing. And an epic struggle for its soul.
The 3-factor model is a product of empiricism. This philosophy of science dates back to David Hume in the 18th century, arises as logical positivism of the Vienna Circle in the 1930s, and modifies as logical empiricism in the 1950s and 1960s.
Empiricism is built on the verification principle, which insists that all scientifically meaningful statements must be verifiable (testable) with our senses, facts, and data. The verification principle emphatically rejects metaphysics, including theories of causation beyond Hume’s constant conjunctions (correlations).
After reaching its heyday in the 1960s, philosophers today generally regard empiricism as defunct. Most tellingly, the verification principle itself is not verifiable, meaning that it is itself an unfalsifiable metaphysical presupposition. Oops. As far as philosophy goes, this defect is insurmountable... All in all, theory is indispensable.
In asset pricing, empiricism has also crashed to the ground, albeit only recently.
The 6-factor paper states (2018, p. 237): “We include momentum factors (somewhat reluctantly) now to satisfy insistent popular demand. We worry, however, that opening the game to factors that seem empirically robust but lack theoretical motivation has a destructive downside: the end of discipline that produces parsimonious models and the beginning of a dark age of data dredging that produces a long list of factors with little hope of sifting through them in a statistically reliable way (my emphasis).”
Seriously? The beginning of a dark age? Isn’t it really the end of the dark age ushered in by the 3-factor paper in 1993? The q-factor model published in 2015 has ended the dark age. And the 6-factor paper merely confirms the end of the dark age via a form of doublespeak.
The creation of the q-factor model is an imaginative, retroductive, and iterative fusion between asset pricing theory and asset pricing empirics. The q-factor model asks: What the fundamental structure of capital markets must be like for us to observe asset pricing anomalies? The starting point is theoretical (transcendental). After I identify the causal powers of investment and profitability in 2005, it then takes another 10 years to put the empirics together. Contrary to Hume’s induction, the scientific inference is retroduction (closely related to abduction, i.e., inference to the best explanation).
Far from Hume’s empiricism, the philosophy of science embodied in the q-factor model is Roy Bhaskar’s critical realism. In addition to the domain of the empirical (observed events, the only reality accepted in empiricism), critical realism also allows the domain of the real (causal powers, causal structures, and causal mechanisms).
All in all, theory plays an important, if not major, role in science. About time to take causation seriously in asset pricing.
If the 3-factor model is like the alpha variant of Covid-19, the 5-factor model would be the delta variant, and the 6-factor model the wimpy delta+. While Covid-19 infects our lungs, the 3-factor virus eats our brains and turns us into zombies, who refuse to dig any deeper than observed events and even actively deny the need of doing so. As evidenced by the quote above from the 6-factor paper about "popular demand," the 3-factor virus has turned our beloved science into a dystopian Oceania.
The q-factor model is like the Pfizer vaccine. It borrows the factor form from the 3-factor virus but neutralizes its rotten, poisonous core of defunct empiricism. And the expected growth factor is our booster.
I have no conflicts of interest to declare. My only objective in life is the pursuit of scientific knowledge. The state of Ohio couldn’t care less about whether my results come out one way or another. And I couldn’t care less about any investment company’s assets under management.
Truth is fragile. Freedom is not free.
To protect ourselves from the delta surge, please consider taking the vaccine to ensure a brighter future.
Please see my latest interview below with Jack Forehand and Justin Carbonneau on my recent adventure into philosophy of science in the context of scientific debates within asset pricing.
I had much fun today discussing "Dissecting Green Returns" (Pastor, Stambaugh, and Taylor 2021) at the webinar hosted by the Jacobs Levy Equity Management Center for Quantitative Financial Research at the Wharton School. The webinar is available at this Wharton link, which contains Rob's presentation and my discussion.
Because the webinar is available only through 12/2/2021, I have posted a remake of my discussion on YouTube (slides):
I've just come across a new textbook written by Umberto Sagliaschi and Roberto Savona titled "Dynamic Corporate Finance: An Equilibrium Approach." Despite corporate finance in the book title, the authors provide a cool introduction to investment-based asset pricing.
The textbook seems to be freely downloadable from SpringerLink.
I highly recommend this book. The crux is that I sense many research opportunities from integrating investment-based asset pricing with dynamic corporate finance. So far in the former literature only the asset side of the balance sheet has been studied. And the liability side is wide open. On the other hand, corporate finance has traditionally worked with risk neutrality, with little contact with asset pricing. How time-varying and cross-sectionally varying expected returns are jointly determined with corporate decisions (beyond just investment) emerges as a potentially fecund research direction.
Please also check out my prior vlog on "Two Highly Cited Articles."
I am happy to report that two of our recent publications have just made the highly cited lists in their respective journals: "Which Factors?" (Hou, Mo, Xue, and Zhang 2019) at the Review of Finance list and "Replicating Anomalies" (Hou, Xue, and Zhang 2020) at the Review of Financial Studies list.
"Which Factors?": Article; Slides; and Presentation:
"Replicating Anomalies": Article; Slides; and Presentation (repost from Vlog: Replicating Anomalies):
Take a look at the picture below. What animal do you see?
Source: Rabbit–duck illusion Wikipedia
Philosophers of science such as Kuhn (1962) and Feyerabend (1975) call the shift from duck to rabbit (and vice versa) as "gestalt switch." The drastic change of perspectives spells trouble for scientific progress. The crux is that competing research programs interpret the available facts in entirely different, incompatible ways based on their different yardsticks of scientific success (the incommensurability problem).
The prior literature in asset pricing has largely perceived anomalies as indicating dysfunctional capital markets as a result of systematic investor mistakes and trading frictions (that prevent these mistakes from being eliminated). In contrast, my body of work has viewed anomalies as indicating well-functioning capital markets as a result of the net present value rule in capital budgeting on the part of managers. The change in perspective seems like a "gestalt switch."
Back in the picture above, the animal cannot be a duck and a rabbit simultaneously. "Dubbit" doesn't exist. The real world is more ambiguous, though one can still ask the question which one of the two perspectives outlined above offers a more accurate description of capital markets in reality. Time will tell.
The presentation below delves into the "gestalt switch" based on Liu, Whited, and Zhang (2009, Journal of Political Economy, "Investment-based Expected Stock Returns," see also article and slides):
The latest word on GMMing investment returns is in Goncalves, Xue, and Zhang (2020, Review of Financial Studies, "Aggregation, Capital Heterogeneity, and the Investment CAPM," see article, slides, and the presentation below):
Zhang (2005), titled "The Value Premium," is back in the news in academic circles. As flattered as I am with the latest attention, most of which I didn't exactly ask for, it occurs to me that I should check the Web of Science cites. While I do follow Google Scholar, which is only one click away, the last time I checked Web of Science was in December 2009, when I was putting a dossier together to come to Ohio State.
Back in the late 1990s and early 2000s, after the publication of Fama and French (1993, 1996), one of the more pressing tasks facing asset pricing theorists is to explain the value premium. Many of their works in this wave of theorizing were published around 2005. With 15+ years of time test, the table below shows the scorecard based on citations (that are at least objective):
I have put a recording together for "The Value Premium," in which I reflect on the methodological choices (largely implicit in this article) as well as open challenges in this theoretical literature. See below please as well as slides:
In the next-to-last section of the presentation above, I share my take on the recent disappointing performance of the value premium in the data:
First, the high-minus-low decile on book-to-market earns on average only 0.3% per month (t = 1.58) from January 1967 to December 2020. However, the high-minus-low decile on operating cash flow-to-market earns 0.8% (t = 4.18) in the same sample period. I view the evidence as saying that (i) book equity fails to capture intangibles per Lev's influential body of work. And (ii) the value of intangibles can still be ascertained, effectively, from cash flows (Penman 2009).
Second, as in book-to-market, operating cash flow-to-market has also suffered from poor recent performance (though to a lesser degree). Barring from the Covid shock, the past decade has been the longest boom in history. The causal mechanism based on costly reversibility and countercyclical price of risk in Zhang (2005) would predict that the value premium should come back going forward. (The expected value premium is countercyclical.) To invoke Karl Popper, this prediction is highly falsifiable. Time will tell.
Finally, please see below for a video presentation on "The CAPM Strikes Back? An Equilibrium Model with Disasters" (Bai, Hou, Kung, Li, and Zhang 2019) as well as slides. Among other things, this article extends Zhang's (2005) industry equilibrium to general equilibrium with heterogeneous firms.
I have just put a recording together for the published version of "Replicating Anomalies" (Hou, Xue, and Zhang 2020, Review of Financial Studies). See below please as well as slides:
Please also see below Jack Forehand and Justin Carbonneau's "Excess Returns" Podcast Episode 73 on our article:
Nir Kaissar at Bloomberg wrote a cool article on "Amazon and Other Tech Giants Buck the Empire Trap." Nir's article draws the difference between our investment factor and our expected growth factor. Our factor series are available at our global-q data library.
Because our expected growth factor is relatively new, I thought I could elaborate its intuition against the background of our investment factor. The investment CAPM (a reformulation of the Net Present Value rule in corporate finance) says that the discount rate equals the marginal benefit of investment divided by the marginal cost of investment. And the marginal benefit includes expected profitability and expected growth.
The investment factor is built on tangible investment, which is measured as the growth rates of book assets on the balance sheet. Tangible investment has little impact on expected growth. And the investment CAPM implies a negative relation between tangible investment and the cost of capital (captured by our investment factor).
However, the expected growth factor is (mostly) built on operating cash flow, which accounts for some of the most reliably measured intangible investment at the firm level, such as R&D. Intangible investment raises expected growth. And the investment CAPM implies a positive relation between intangible investment and the cost of capital (captured by our expected growth factor).
These economic insights are explained in depth in the latest draft of our security analysis paper.
The expected growth factor is from our 2021 RoF article. Please see Slides and the video presentation:
We have just released the codes for the globally nonlinear projection algorithm developed in Petrosky-Nadeau and Zhang (2017) titled "Solving the Diamond-Mortensen-Pissarides Model Accurately" published at Quantitative Economics.
Please see Codes as well as Article, Slides, and the video presentation:
The codes for our 2018 article "Endogenous Disasters" at American Economic Review have already been released. Please see Codes as well as Article, Slides, and the video presentation:
I am honored to deliver my keynote on "Toward A Theory of Everything?" at the 6th Annual University of Connecticut Finance Conference this morning. The talk summarizes my scientific research program that aims to explain the equity premium puzzle in general equilibrium production economies, by integrating macro labor with asset pricing.
Please see below for the video presentation, which might help with insomnia.
While on the subject of vlog, I repost below my keynote on ”The Investment CAPM: Latest Developments” delivered at Swedish House of Finance Annual Conference on August 19, 2019.
A wise man advises me that I should elaborate on the epistemological issues raised toward the end of my last post “Is Asset Pricing Scientific?” (April 3, 2021). This post is my response.
The Fama-French 3-factor model is arguably the most important work in asset pricing in the past 25 years. It is thus not surprising that the new way of thinking epitomized in the q-factor model has been met with high hurdles, one after another. To make sense of my professional predicament in the past decade, I have recently started to explore philosophy of science. Kuhn (1977, p. 357) describes five virtues that scientists must consider when deciding between an established theory and an upstart competitor. In particular, how should one choose between the Fama-French 3-, 4-, 5-, and 6-factor models on one side and the q-factor model and its extension, the q5 model, on the other?
First, Kuhn says that a theory should be accurate: “within its domain, that is, consequences deducible from a theory should be in demonstrated agreement with the results of existing experiments and observations.”
The head-to-head factor spanning tests reported in my last post clearly show that the q-factor model is more accurate than the 6-factor model. In fact, we have been reporting such evidence since 2014 (first with the 5- then with the 6-factor model).
Second, Kuhn says that a theory should be consistent, “not only internally or with itself, but also with other currently accepted theories applicable to related aspects of nature.”
The q-factor model is internally consistent. It is built from, and consistent with, the net present value rule in corporate finance. The rule says that, uncontroversially, investment policy is the first-order determinant of firm value.
Riding on the first principle of firms, the q-factor model is also consistent with, and complementary to, the consumption CAPM. The investment versus consumption CAPM debate is only about the scope of applications, not a matter of theory replacement (like the q- versus 6-factor model).
In my view, the 6-factor model falls short of the consistency criterion, both internal and external. Internally, it is not clear how UMD arises from valuation model. In addition, expected investment and expected return correlate positively in the model, not negatively (Hou, Mo, Xue, and Zhang 2019). Externally, the theoretical linkage between common factors and ICAPM-APT state variables is tenuous (Zhang 2017).
Third, a theory should have broad scope in that “a theory’s consequences should extend far beyond the particular observations, laws, or subtheories it was initially designed to explain.”
The q-factor model is broad. In particular, Hou, Xue, and Zhang (2015) write “the consumption model and the investment model of asset pricing are equivalent in general equilibrium, delivering identical expected returns. While the consumption model says that consumption risks are sufficient for accounting for expected returns, the investment model says that characteristics are sufficient. We take the latter prediction seriously and confront the q-factor model with a wide array of anomaly variables that are not directly related to investment and profitability (p. 658, footnote 8).”
In other words, just like only beta matters in the CAPM, only investment and profitability matter for the cross-sectional expected-return dispersion in the q-factor model. In Popperian (1962) terms, this conjecture is very bold and highly refutable. Yet, the evidence largely confirms our conjecture. Popper would have liked the q-factor model.
Fourth, a theory should be simple, “bring order to phenomena that in its absence would be individually isolated and, as a set, confused.”
I started out with complicated modeling in Zhang (2005), simplified substantially to Euler equation tests in Liu, Whited, and Zhang (2009), and finally arrived at the investment and profitability factors in Hou, Xue, and Zhang (2015). It is simple to be complicated and complicated to be simple. Each layer of simplification comes with, I think, a deeper layer of understanding of the inner workings of capital markets. In the end, only the net present value rule is left standing.
In philosophy of science, the no miracles argument for scientific realism says that the predictive success of science would be a miracle if predictively successful scientific theories were not at least approximately true (Putnam 1975). In asset pricing, this argument implies that the strong explanatory power of the simple q-factor model would be a miracle if its underlying theory (the investment CAPM) was not at least approximately true in capital markets.
Fifth, a theory should be fruitful of new research findings: “it should, that is, disclose new phenomena or previously unnoted relationships among those already known.”
Lakatos (1970) defines a scientific research program as “progressive” as long as its theoretical growth keeps predicting novel facts with some success. A program is “degenerate” if its theoretical growth lags behind its empirical growth, that is, it gives only ex post, ad hoc explanations of facts anticipated by, and discovered in another program. If a research program progressively explains more than a rival, then it supersedes the rival. And the rival program can be eliminated.
In Lakatosian terms, the q-factor model is one exemplar from a scientific research program that I call the supply theory of value. The “hard core” of this program is to price assets based on the first principles of their suppliers. To make contact with data in the real world, this hard core is supplemented with a variety of “protective belt.” The belt includes the measurement of investment, profitability, and expected growth as well as factor construction; specifications of marginal product of capital and adjustment costs as well as structural estimation via GMM; and specifications of the pricing kernel and productivity as well as quantitative investigation. I feel that this research program is “progressive” in that it has successfully addressed a wide range of important issues, including factor models, scientific explanations of asset pricing anomalies, linking factor premiums to fundamentals via structural estimation, and the equity premium puzzle, etc.
[I know, I know, my academic colleagues and I disagree on what accounts as an explanation. I will get to this important issue in due time. But for now, briefly, I am using the unification definition of explanation (Kitcher 1989).]
I will leave it to the reader to decide where the Fama-French program of the 3-, 4-, 5-, and 6-factor models resides in the Lakatosian degenerate-progressive spectrum. Where I stand is an open secret.
In short, evaluated with Kuhn’s five virtues (accuracy, consistency, scope, simplicity, and fruitfulness), I feel that the q-factor model is the rightful heir of the Fama-French 3-factor model. The q-factor model inherits everything cool about the 3-factor model, especially its empirical methods, but fills its glaring lack of theoretical foundation.
American Finance Association Code of Professional Conduct and Ethics (2016, 3 (a)) says: “Financial economists should work to provide an environment that encourages the free expression and exchange of scientific ideas. They should promote equal opportunity and treatment for all their colleagues, regardless of age, gender, race, ethnicity, national origin, religion, sexual orientation, disability, health condition, marital status, parental status, genetic information, or any other reason not related to scientific merit. More senior members of the profession have a special responsibility to facilitate the research, educational, and professional development of students and subordinates. This includes providing safe, supportive work environments, fair compensation and appropriate acknowledgement of their contribution to any research results (p. 1-2, my emphasis).”
Alas, I view the Code as normative only. “Ought” doesn’t mean “is.” If “is” is already achieved, there is no need to set up “ought” to begin with.
Whether a theory change from the 3-factor model to the q-factor model occurs, and if yes, how long it will take, are left for future historians, who, presumably, will try to reconstruct how scientific academic finance really is. I no longer worry about such things. I enjoy my work. And that’s all that matters to me.
Hou, Kewei, Chen Xue, and Lu Zhang, 2015, Digesting anomalies: An investment approach, Review of Financial Studies 28 (3), 650-705.
Hou, Kewei, Haitao Mo, Chen Xue, and Lu Zhang, 2019, Which factors? Review of Finance 23 (1), 1-35.
Kitcher, Philip, 1989, Explanatory unification and the causal structure of the world, in P. Kitcher and W. C. Salmon: Scientific Explanation, University of Minnesota Press.
Kuhn, Thomas S., 1977, Objectivity, value judgment, and theory choice, in T. S. Kuhn: The Essential Tension, University of Chicago Press.
Lakatos, Imre, 1970, Falsification and the methodology of scientific research programmes, in I. Lakatos and A. Musgrave: Criticism and the Growth of Knowledge, Cambridge University Press.
Liu, Laura Xiaolei, Toni M. Whited, and Lu Zhang, 2009, Investment-based expected stock returns, Journal of Political Economy 117 (6), 1105-1139.
Popper, Karl R., 1962, Conjectures and Refutations: The Growth of Scientific Knowledge, Basic Books.
Putnam, Hilary, 1975, What is mathematical truth? In H. Putnam: Mathematics, Matter and Method, Collected Papers Vol. 2. Cambridge University Press.
Zhang, Lu, 2005, The value premium, Journal of Finance 60 (1), 67-103.
Zhang, Lu, 2017, The investment CAPM, European Financial Management, 23 (4), 545-603.
We have just released the latest q-factors data library that has been updated through December 2020. The table below shows that the Hou-Xue-Zhang (2015) q-factor model continues to fully subsume the Fama-French (2018) 6-factor model in the extended sample from January 1967 to December 2020.
The Fama-French 6-factor model cannot explain the q-factors. The investment premium is 0.33% per month (t = 4.1), with a 6-factor alpha of 0.09% (t = 2.55). The return on equity (Roe) premium is 0.51% (t = 4.96), with a 6-factor alpha of 0.25% (t = 4.09). The Gibbons-Ross-Shanken (1989, GRS) test strongly rejects the 6-factor model with the null hypothesis that the 6-factor alphas of the investment and Roe premiums are jointly zero (p = 0.00).
More important, the Hou-Xue-Zhang q-factor model fully subsumes the Fama-French factors. The HML, CMA, and RMW premiums are on average 0.24%, 0.27%, and 0.27% per month (t = 1.76, 3.05, and 2.77), but their q-factor alphas are virtually zero, -0.01%, 0.01%, and 0.02% (t = -0.09, 0.39, and 0.3), respectively. UMD is on average 0.62% (t = 3.63), but its q-factor alpha is only 0.18% (t = 0.86). The GRS test fails to reject the q-factor model with the null that the q-factor alphas of HML, CMA, RMW, and UMD are jointly zero (p = 0.7).
So, is asset pricing scientific? Popper's (1959) demarcation between science and non-science hinges on falsifiability. Lakatos (1970) says that a scientific research program should be "progressive" in that it needs to explain empirical puzzles with few ad hoc fixes. Despite his early "mob psychology" regarding theory choice in Structure (1962), Kuhn (1977) later characterizes a good theory in terms of its accuracy, consistency, scope, simplicity, and fruitfulness. Finally, Feyerabend (1975) argues that science is an anarchic enterprise with no particular epistemic order.
While conscientious about external forces at work, we are determined to show Feyerabend is wrong about asset pricing.
Feyerabend, Paul, 1975, Against Method, New Left Books.
Kuhn, Thomas S., 1962, The Structure of Scientific Revolutions, University of Chicago Press.
Kuhn, Thomas S., 1977, Objectivity, value judgment, and theory choice, in T. S. Kuhn, The Essential Tension, University of Chicago Press.
Lakatos, Imre, 1970, Falsification and the methodology of scientific research programmes, in Criticism and the Growth of Knowledge, I. Lakatos and A. Musgrave (eds.), Cambridge University Press.
Popper, Karl, 1959, The Logic of Scientific Discovery, Hutchinson & Co.
The article “Searching for the equity premium” (with Hang Bai) is now forthcoming at Journal of Financial Economics (paper, slides).
For its motivation and overview of key results, please see my last blog posted on 10/18/2020.
A surprising insight from our revision is the properties of investment and hiring returns. Despite a high average labor share in output calibrated to 74.6% (Gollin 2002), the capital share in the market equity is on average 92.6%! As such, even though labor market frictions play a central role in our search economy, the stock market is mostly for shareholders.
Panel A below shows the scatter-plot of the capital share in value against aggregate productivity in our economy. As in a Covid map, dark red means high density, and light green low density. The value-weight of capital exhibits countercyclical dynamics, approaching 100% in very bad times, meaning that the shadow value of labor goes to zero.
(In Panel B, the labor share in output is countercyclical, not surprisingly. Panel C shows an alternative labor share, in which wage equals the marginal product of labor, is weakly countercyclical, due to the CES production function.)
The 92.6% estimate of the value-weight of capital has broad implications beyond this paper. In the cross section, the prior literature has mostly examined investment returns due to severe limitations of firm-level labor data. If we are right in that stock returns primarily consist of investment returns, prior cross-sectional results based on investment returns are likely to survive extensions to labor.
Finally, I wish to acknowledge a weakness of the model (see Section 4.5). It turns out the postwar US sample is not representative at all from the model's perspective. In 10,000+ simulations, we could not find a single path with the equity premium no lower than, but the consumption volatility no higher than that in the postwar US sample. I suspect that a similar problem might also be present in the Rietz-Barro exogenous disaster literature, although I have not seen an explicit discussion yet. So the search continues...
Hang Bai (UConn) and I have just circulated our new working paper titled “Searching for the equity premium” (paper, slides).
We view this work as a solid progress report toward the holy grail of macro-finance, which (in our view) is a unified theory of asset prices and business cycles.
The persistence of the Mehra-Prescott (1985) equity premium puzzle in general equilibrium production economies has given rise to a long-standing dichotomy in macro-finance. Finance specifies “exotic” preferences and exogenous cash flow dynamics to match asset prices but ignore firms (Campbell and Cochrane 1999; Bansal and Yaron 2004; Barro 2006). Macroeconomics analyzes full-fledged dynamic stochastic general equilibrium (DSGE) models but ignore asset prices with primitive preferences (Christiano, Eichenbaum, and Evans 2005; Smets and Wouters 2007).
This macro-finance dichotomy has left many important questions unanswered. What are the microfoundations underlying the exogenously specified, often complicated cash flow dynamics in finance models (Bansal, Kiku, and Yaron 2012; Nakamura, Steinsson, Barro, and Ursua 2013)? What are the essential ingredients in the production side that can endogenize the key elements of cash flow dynamics necessary to explain the equity premium? To what extent do time-varying risk premiums matter quantitatively for macroeconomic dynamics? How large is the welfare cost of business cycles in a general equilibrium production economy that replicates the equity premium?
We embed the standard Diamond-Mortensen-Pissarides search model of equilibrium unemployment into a DSGE framework with recursive utility and capital accumulation.
Highlights of our quantitative results include:
In all, the DSGE model with recursive utility, search frictions, and capital accumulation is a good start to forming a unified theory of asset prices and business cycles.
Our article titled “Aggregation, capital heterogeneity, and the investment CAPM” (Goncalves, Xue, and Zhang 2020) has just appeared in the June 2020 issue of Review of Financial Studies. A free copy is here as well as the internet appendix.
A recurring critique of my structural estimation line of work started in Liu, Whited, and Zhang (2009) is that the parameter estimates appear unstable across different testing portfolios. This fair and important critique has guided our effort in the past five years. Thank you for arguing with me.
Figure 2 from our latest publication replicates this difficulty. The parameter instability manifests itself as the failure of the baseline investment model in explaining value and momentum simultaneously (Panel A). The baseline model fits momentum but gets value upside down. Not surprisingly, the joint estimation failure persists once we add asset growth and return on equity deciles (Panel B).
Figure 3 shows that the joint estimation difficulty has largely been resolved within an extended two-capital model with working capital and fixed, physical capital. Our article also offers a range of improvements in terms of measurement and econometric specifications. Perhaps the most important improvement is to calculate the "fundamental" (model implied) stock return at the firm level before aggregating it to the portfolio level to match with the portfolio-level stock return.
Many important questions remain open. The measurement is all based on historical-cost accounting. Curious to see what happens with current-cost economic measurement. What about employment data? International data? Is it possible to develop ex-ante expected return measures out of this economic model that can compete with the prestigious and immensely important literature on implied costs of capital in accounting? Not sure, but I am eager to find out...
The q-factors library at global-q.org has just been updated through December 2019. The table below reports the latest head-to-head factor spanning tests: The Hou-Xue-Zhang (2015) q-factor model continues to dominate the Fama-French (2018) 6-factor model in the January 1967--December 2019 sample.
On the one hand, the 6-factor model cannot subsume the q-factors. The investment premium is 0.36% per month (t = 4.45), with a 6-factor alpha of 0.09% (t = 2.65). The return on equity (Roe) premium is 0.54% (t = 5.46), with a 6-factor alpha of 0.26% (t = 4.25). The Gibbons-Ross-Shanken (1989, GRS) test strongly rejects the 6-factor model based on the null hypothesis that the 6-factor alphas of the investment and Roe premiums are jointly zero (p = 0.00).
On the other hand, the q-factor model fully subsumes the Fama-French factors. The HML, CMA, and RMW premiums are on average 0.3%, 0.29%, and 0.28% per month (t = 2.29, 3.24, and 2.82), but their q-factor alphas are tiny, 0.04%, 0.01%, and 0.03% (t = 0.35, 0.23, and 0.35), respectively. The momentum factor, UMD, is on average 0.63% (t = 3.66), but its q-factor alpha is small, only 0.15% (t = 0.66). The GRS test fails to reject the q-factor model based on the null that the q-factor alphas of HML, CMA, RMW, and UMD are jointly zero (p = 0.79).
Don't take my word for it. Go ahead and replicate the numbers. If your replication fails, I am the jerk. Otherwise, how about using the better factor model from now on?
That's right. Ten years on, it seems that the q-factor model is indeed "A Better Factor Model That Explains More Anomalies." My apologies for taking so long, but please know that we're doing the best we can.
Our working paper titled "An augmented q-factor model with expected growth" (with Kewei, Haitao, and Chen) is now forthcoming at Review of Finance. The paper is formerly titled "q5." Alas, who knew that the compiled output of the LaTeX source code "$q^5$" would be invisible to Google Scholar? Oh well, live and learn.
The expected growth factor, its 2 by 3 benchmark portfolios on size and expected growth, the expected growth deciles, and the 3 by 5 testing portfolios on size and expected growth are all available to download at global-q.org. We're waiting for Compustat to update its data in early February. Once the data become available, we will update and circulate the testing portfolios on all 150 anomalies examined in our q5 paper.
Conceptually, in the investment CAPM, firms with high expected investment growth should earn higher expected returns than firms with low expected investment growth, holding current investment and profitability constant. Intuitively, if expected investment is high next period, the present value of cash flows from next period onward must be high. Consisting mainly of this present value, the benefit of current investment must also be high. As such, if expected investment is high next period relative to current investment, the current discount rate must be high to offset the high benefit of current investment to keep current investment low.
Empirically, we estimate expected growth via cross-sectional forecasting regressions of investment-to-assets changes on current Tobin’s q, operating cash flows, and changes in return on equity. Independent 2 by 3 sorts on size and expected growth yield the expected growth factor, with an average premium of 0.84% per month (t = 10.27) and a q-factor alpha of 0.67% (t = 9.75). The t-values far exceed any multiple-testing adjustment that we are aware of.
We augment the q-factor model (“q”) with the expected growth factor to form the model (“q5”). We then perform a large-scale horse race with other recently proposed factor models, including the Fama-French (2018) 6-factor model (“FF6”) and their alternative 6-factor model (“FF6c”), in which the operating profitability factor is replaced by a cash-based profitability factor, as well as several other factor models.
As testing portfolios, we use the 150 anomalies that are significant (|t| ≥ 1.96) with NYSE breakpoints and value-weighted returns from January 1967 to December 2018 (Hou, Xue, and Zhang 2019). The large set includes 39, 15, 26, 40, and 27 across the momentum, value-versus-growth, investment, profitability, and intangibles categories.
The q5 model is the best performing model. The figure below shows the fractions of significant alphas across all and different categories of anomalies. Across all 150, the q5 model leaves 15.3% significant, a fraction that is lower than 34.7%, 49.3%, and 39.3% across the q, FF6, and FF6c model, respectively. In terms of economic magnitude, across the 150 anomalies, the mean absolute high-minus-low alpha in the q5 model is 0.19% per month, which is lower than 0.28%, 0.3%, and 0.27% across the q, FF6, and FF6c model, respectively.
The q5 model is also the best performer in each of the categories. In particular, in the momentum category, the fraction of significant alphas in the model is 10.3%, in contrast to 28.2%, 48.7%, and 35.9% across the q, FF6, and FF6c model, respectively. In the investment category, the fraction of significant alphas in the q5 model is 3.9%, in contrast to 34.6%, 38.5%, and 30.8% across the q, FF6, and FF6c model, respectively.
While bringing expected growth to the front and center of empirical asset pricing, we acknowledge that the (unobservable) expected growth factor depends on our specification, and in particular, on operating cash flows as a predictor of future growth. While it is intuitive why cash flows are linked to expected growth, we emphasize a minimalistic interpretation of the q5 model as an effective tool for dimension reduction.
The Fractions of Significant (|t| ≥ 1.96) Alphas Across Different Categories of Anomalies
The paper titled "Unemployment Crises" (with Nicolas Petrosky-Nadeau) is now forthcoming at Journal of Monetary Economics.
Our historical time series for U.S. unemployment rates and labor productivity (January 1890-December 2017) as well as vacancy rates (January 1919-December 2017) are available to download at this link. Nicolas and I have been as careful as we can when compiling the historical series, by building on the latest economic history literature.
The following picture is the U.S. historical Beveridge curve. The convexity clearly indicates the congestion externality arising from matching frictions in the labor market. More important, the prewar observations, especially those from the Great Depression, make the Beveridge curve substantially flatter than it otherwise would have been. The 2007-2009 Great Recession is well aligned with the overall curve even without the Great Depression.
Theoretically, we show that a search model of equilibrium unemployment, when calibrated to the mean and volatility of the postwar unemployment rates, implies empirically plausible persistence and unconditional probability of unemployment crises (states with the unemployment rates above 15%).
We also implement a Cole-Ohanion style accounting exercise for the Great Depression, but within the search framework. With a measured negative labor productivity shock that amounts to a magnitude of 3.4 unconditional standard deviations in the postwar sample, the model predicts a 35.8% drop in output from 1929 to 1933 and a high unemployment rate of 32.9% in June 1933. Both are empirically plausible. We also demonstrate the impact of detrending on the accounting exercise, a point that has not been emphasized in the prior literature.
All in all, we suggest that a unified search model with the same parameters is a good start to understanding labor market dynamics in both the pre- and post-war samples simultaneously.
(This blog post is the last 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.)
While many open questions remain in the investment CAPM literature, due to space limitations, I only discuss what I perceive as the two most important challenges in this essay.
A Risky Mechanism of Momentum
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). However, 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), while its loadings on the other 3 factors are insignificant. In the structural estimation of Goncalves, Xue, and Zhang (2019), the investment CAPM explains value and momentum simultaneously, and the “tug of war” between current investment and expected investment plays a key role in the model’s performance.
Nevertheless, a major gap in our knowledge exists. What exactly are the risks underlying momentum? 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) has tied the value premium to business cycle risks. Alas, I am aware that momentum, and equivalently, the Roe factor premium are both significantly negative in that model. Also in partial equilibrium, Johnson (2002) ties momentum to expected growth and argues that expected growth is risky. Sagi and Seasholes (2004) 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 framework. A unified model imposes internal consistency that is vital for theories. Li (2018) is the only exception 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, failures in explaining returns of different asset classes are definitely worse than failures in explaining just stock returns. Behavioral under- and overreaction apply to different asset classes (Asness, Moskowitz, and Pedersen, 2013). But sticking labels 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. Because of aggregation, to me, SDF is the source of all ills in asset pricing and should be avoided at all costs.
I am ready to answer the fundamental questions raised at the beginning of this essay. What explains all the consumption CAPM anomalies? Well, the consumption CAPM anomalies are the investment CAPM regularities, all of which conform to the NPV rule in Corporate Finance. Capital markets obey standard economic principles. Anomalies in fact indicate well functioning, efficient capital markets. The world makes sense! The consumption CAPM fails so badly because of the well known aggregation problem (Kirman, 1992). The pain of aggregation is likely manageable for aggregate asset pricing (and for DSGE models, unless you want to study wealth inequality). However, the pain is insurmountable for the cross section, which is in essence a microeconomic problem. And our ubiquitous representative investor is out of depth.
Despite its enormous, ever-lasting influence in practice, Graham and Dodd’s (1934) Security Analysis has yet to find its rightful home in finance theory. We’re blind to this parallel universe (otherwise known as practice) because of the consumption CAPM’s single-minded, dogmatic focus on demand. Graham and Dodd are squarely on supply. And the NPV rule is the first place one would go to put the 2 and 2 together. Characteristics-based factors are linear approximations to the nonlinear investment return equation in the investment CAPM. Characteristic factors are on as solid theoretical grounds in the investment CAPM as aggregate consumption growth in the consumption CAPM. Taking aggregation seriously, aggregate consumption growth is not even a factor. Neither are all other macroeconomic factors.
Post-earnings-announcement drift persists for 50 years since Ball and Brown (1968) because it is part of expected returns, as predicted by the investment CAPM (the Roe factor). Why has there not been a coherent behavioral theory for 35 years since De Bondt and Thaler (1985)? Because such a theory likely doesn’t exist. If a full menu of psychological biases gives rise to underreaction, and another full menu to overreaction, we have an embarrassment of riches. A “theory” that explains everything (with no discipline) explains nothing.