Journal of Banking and Finance 93 (2018) 183–197 Contents lists available at ScienceDirect Journal of Banking and Finance journal homepage: www.elsevier.com/locate/jbf Estimating risk-return relations with analysts price targets  Liuren Wu Baruch College, Zicklin School of Business, One Bernard Baruch Way, New York, NY 10010, USA a r t i c l e i n f o Article history: Received 8 February 2018 Accepted 17 June 2018 Available online 22 June 2018 JEL classification: C13 C51 G12 Keywords: Risk-return relation Equity risk premium Analysts price targets a b s t r a c t Asset pricing tests often replace ex ante return expectation with ex post realization. The large deviation between the two drastically weakens the power of these tests. This paper proposes to use analysts con- sensus price target for a stock as the market expectation of the stock’s future price to directly construct the stock’s expected excess return. Analyzing the expected excess return behavior both over time and across different stocks shows that classic asset pricing theory works much better on ex ante return ex- pectations than on ex post realizations. The analysis also provides new insights on the pricing of common equity risk factors. © 2018 Elsevier B.V. All rights reserved. 1. Introduction Asset pricing theories generate implications on the relation be- tween the expected excess return of a financial security and its risk. Empirical asset pricing tests often replace the ex ante return expectation with ex post return realization. Realizations, however, can differ greatly and persistently from the expectation. The devi- ations can come from large surprises, expectation biases, or expec- tations of certain large, rare events that have not materialized yet in the test sample period (i.e., the peso problem). Regardless of the particular source, the large deviations can drastically weaken the power of the empirical tests (Lundblad, 2007). This lack of testing power contributes to the lack of empirical support for classic asset pricing theories. This paper proposes to test asset pricing implications using di- rect constructions of ex ante market expectation instead of using ex post return realization, thus mitigating the impact of ex post surprise on the estimated risk-return relation. Focusing on the U.S. equity market, the paper uses analysts consensus price target for a stock as the market expectation of the stock’s future price and constructs the stock’s ex ante expected excess return, or equity risk premium, as the log deviation between the price target and the stock price minus the one-year financing cost. Analyzing the equity risk premium behavior both over time and across different  The author thanks Carol Alexander (the editor), two anonymous referees, Peter Carr, Lin Peng, Jonathan Wang, and seminar participants at Baruch College for their comments and suggestions. E-mail address: liuren.wu@baruch.cuny.edu stocks shows that classic asset pricing theories work much better on ex ante return expectations than on ex post return realizations. Ex ante risk premium expectation can be constructed from sev- eral different channels, all of which can, in principle, be applied to replace ex post return realizations in asset pricing tests. For example, a large accounting literature derives the implied cost of capital (ICC) from current stock prices, various valuation model assumptions, and cash flow forecasts. 1 Pastor et al. (2008) and Lee et al. (2009) take the ICC approach to examine the in- tertemporal and international risk-return relations, respectively. Campello et al. (2008) construct expected equity returns using cor- porate bond yields by recognizing that bonds and stocks are con- tingent claims written on the same asset. More recently, several studies explore the idea of extracting risk premiums from option prices. 2 The main issue that prevents these implied approaches from broader adoption in testing asset pricing models is that they often involve many assumptions that can significantly alter the re- sults. For example, different combinations of valuation approaches and cashflow assumptions can generate many different sets of ICC estimates. 3 Extracting risk premium from options or other contin- gent claims such as bonds also necessitates strong assumptions on 1 See, for example, Claus and Thomas (2001), William et al. (2001), Easton (2007), Hou et al. (2012), Fama and French (2002), and Duarte and Rosa (2015). 2 Prominent examples include, among others, Bakshi et al. (2008), Bakshi and Wu (2010), Santa-Clara and Yan (2010), Backus et al. (2011), Duan and Zhang (2014), Ross (2015), and Carr and Wu (2016). 3 Several studies strive to evaluate the performances of alternative estimates, e.g., Botosan and Plumlee (2005), Easton and Monahan (2005), Guay et al. (2011), and Lee et al. (2015). https://doi.org/10.1016/j.jbankfin.2018.06.010 0378-4266/© 2018 Elsevier B.V. All rights reserved.