Can financial theory make sense of the factor zoo?

EDHEC PhD in Finance Newsletter - November 2019 

Editorial signed by Laurent Calvet, PhD, Chaired Professor of Finance, EDHEC Business School, and CEPR.

Can financial theory make sense of the factor zoo?

Over the past decades, researchers have uncovered hundreds of firm characteristics associated with persistent deviations from the Capital Asset Pricing Model, as well as linkages between these characteristics (Cochrane 2011, Harvey, Liu, and Zhu 2016). This vast body of empirical findings has prompted the rise of factor-based investing (Ang 2014) and a deep reassessment of asset -pricing theory. Omitted risk factors, such as time variation in investment opportunities, labour income, and liquidity, have been proposed as possible explanations for the properties of stock returns. Given the abundance of deviations from the Capital Asset Pricing Model (CAPM) and related explanations, the next step for financial economists is to develop integrated models that jointly generate a number of anomalies and their linkages to economic fundamentals (Cochrane 2008, 2017).

In a recent paper, Sebastien Betermier, Evan Jo, and I, propose that the cross-sectional properties of stock returns are natural consequences of the interaction of supply and demand forces in financial markets. The key ingredients of the model are (i) multiple firms operating production technologies with decreasing returns to scale and (ii) the exposure of firm cash flows to forms of “state risk” that are priced by investors. For instance, state risk represents macroeconomic risk to which firm cash flows and investor labor income are jointly exposed. Through the firms' cost of capital, general equilibrium creates linkages between production decisions and firm exposures to state risk.

The model immediately explains the positive intercept and flatness of the security market line documented in Asness, Moskowitz, and Pedersen (2013), Black, Jensen, and Scholes (1972), and Fama and MacBeth (1973). The relationship between risk and return is upward-sloping if firms are primarily heterogeneous in expected profitability, as is the case under the CAPM, and downward-sloping if heterogeneity in state risk exposure dominates.

The model generates the size, value, investment, and gross profitability anomalies. Consistent with Berk (1995), firms with highly exposed cash flows have high discount rates and therefore small market values. In general equilibrium, a reinforcing mechanism is that a high discount rate also implies a low market-to-book ratio and low capital expenditures, which further reduces firm size. Hence large firms with high investment and high market-to-book ratios have low alpha. Moreover, among firms with similar market-to-book ratios, profitable firms have high state risk exposure and therefore high alpha, as is evident in the data (Hou, Xue, and Zhang 2015, Novy-Marx 2013).

The paper has powerful implications for the allocation of capital and the cost of equity across firms. It predicts that a) growth stocks are generally larger than value stocks, b) the distribution of market values has a fatter upper tail than the distribution of book values, c) expected return and volatility decrease with firm size, and d) a stock's market correlation increases with firm size. All these implications, which hold both in partial and general equilibrium, are supported by the data.

We provide guidance for future research. Classic deviations from the CAPM arise naturally in general equilibrium, and they come as a pack. Since the security market line is flatter than the CAPM predicts, any variable driving a firm’s size also impacts the firm’s correlation to the market portfolio and therefore alpha, which explains the vast abundance of factors documented in the literature. In particular, a firm's alpha may not solely originate from exposure to state risk but may also be driven by average profitability and other firm characteristics. Thus, the factor zoo is a natural consequence of general equilibrium, which should be of help in structuring future empirical research.

References

Ang, Andrew, 2014, Asset Management: A Systematic Approach to Factor Investing, Oxford University Press.

Asness, Clifford S., Tobias J. Moskowitz, and Lasse H. Pedersen, 2013, Value and momentum everywhere, Journal of Finance 63, 929-985.

Berk, Jonathan, 1995, A critique of size-related anomalies, Review of Financial Studies 8, 275-286.

Black, Fischer, Michael Jensen, and Myron Scholes, 1972, The Capital Asset Pricing Model: Some empirical tests, in Michael Jensen ed., Studies in the Theory of Capital Markets, Prager (New York).

Cochrane, John, 2008, Financial Markets and the Real Economy, in R. Mehra, ed. Handbook the Equity Risk Premium, Elsevier Science, 237-325.

Cochrane, John, 2011, Presidential address: Discount rates, Journal of Finance 66, 1047-1108.

Cochrane, John, 2017, Macro-Finance, Review of Finance 21, 945-985.

Fama, Eugene F., and James MacBeth, 1973, Risk, return, and equilibrium: Empirical tests, Journal of Political Economy 81, 607-636.

Frazzini, Andrea, and Lasse Heje Pedersen, 2014, Betting against beta, Journal of Financial Economics 111, 1-25.

Harvey, Campbell, Yan Liu and Heqing Zhu, 2016, ... and the cross-section of expected returns, Review of Financial Studies 29, 5-68.

Hou, Kewei, Chen Xue, and Lu Zhang, 2015, Digesting anomalies: an investment approach, Review of Financial Studies 28, 650-705.

Liu, Ruomeng, 2018, Asset pricing anomalies and the low-risk puzzle, Working paper, Rice University.

Novy-Marx, Robert, 2013, The other side of value: The gross profitability premium, Journal of Financial Economics 108, 1-28.

About the author: Professor Laurent Calvet is Chaired Professor of Finance at EDHEC Business school and teaches Empirical Methods in Finance in the EDHEC PhD in Finance programme. He also serves as dissertation advisor for several PhD candidates. He is Research Fellow at the Center for Economic Policy Research and Founding Member of the Household Finance Network, and Fellow at the Center for Financial Studies at Goethe University.

Specialist in asset pricing, household finance, and volatility modelling, his research has appeared in leading economics and finance journals such as American Economic Review, Journal of the American Statistical Association, Journal of Finance, Journal of Financial Economics, Journal of Political Economy, and Quarterly Journal of Economics.

Laurent Calvet pioneered, with Adlai Fisher, the Markov-Switching Multifractal model of financial volatility, which is increasingly used by financial practitioners and central banks to forecast volatility, compute value-at-risk, and price derivatives. This approach is summarized in their book “Multifractal Volatility: Theory, Forecasting and Pricing”.

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