(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.)ChallengesWhile 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 ClassesAn 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. ConclusionI 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.
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## Lu Zhang
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June 2021
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