Shiller's CAPE: Market Efficiency and Risk

DOIhttp://doi.org/10.1111/fire.12167
Date01 November 2018
Published date01 November 2018
The Financial Review 53 (2018) 741–771
Shiller’s CAPE: Market Efficiency and Risk
Valentin Dimitrov
Rutgers University
Prem C. Jain
Georgetown University
Abstract
Robert Shiller shows that Cyclically Adjusted Price to Earnings Ratio (CAPE) is strongly
associated with future long-term stock returns. This is often interpreted as evidence of market
inefficiency. We present two findings contrary to such an interpretation. First, if markets are
efficient, stock returns should be higher than the risk-free rate. Wefind that even when CAPE
is in its ninth decile, future 10-year stock returns, on average, are higher than future returns on
10-year U.S. Treasurys. Thus, the results are largely consistent with market efficiency. Second,
consistent with a risk–return tradeoff, we find that CAPE is negatively associated with future
stock market volatility.
Keywords: C APE,market efficiency, stock returns, risk, market timing, market volatility
JEL Classifications: G11, G12, G14, G40
Corresponding author: Rutgers Business School, Rutgers University, Newark, NJ 07102;
Phone: (973) 353-1131; E-mail: vdimitr@business.rutgers.edu.
We thank Reena Aggarwal, Michael Alles, John Campbell, Sandeep Dahiya, Vladimir Gatchev, Aloke
Ghosh, Suresh Govindaraj, Zhaoyang Gu, Gilles Hilary,Srinivasan Krishnamurthy (the Editor), Subir Lall,
Jim Marrocco, Darius Palia, Deepannshu Pandita, Stephen Perrenod, Reining Petacchi, Srini Sankaragu-
ruswamy, Sheri Tice, Lawrence Weiss, Joanna Wu, an anonymous referee, and workshop participants
at Georgetown University, Rutgers University, and Indian School of Business, Hyderabad, for helpful
comments and discussions. Prem C. Jain acknowledges financial support from the McDonough Chair of
Accounting and Finance.
C2018 The Eastern Finance Association 741
742 V.Dimitrov and P. C. Jain/The Financial Review53 (2018) 741–771
1. Introduction
Among various marketvaluation indicators proposed over the history of the stock
market, one of the most popular ones is Robert Shiller’s Cyclically Adjusted Price to
Earnings Ratio (CAPE). CAPE is defined as the current price of the Standard & Poor’s
(S&P) 500 index divided by the S&P 500 index’s 10-year average inflation-adjusted
earnings. John Campbell and Robert Shiller analyze the relation between CAPE and
future stock returns in a series of papers.1They show that future 10-year stock re-
turns on the S&P 500 index are negatively associated with CAPE. Shiller (1996,
p. 2) concludes that “ . .. the association seems so strong as to suggest that this re-
lation is not consistent with the efficient markets or random walk model.” Shiller’s
interpretation is that fads, greed, and fear push stock prices away from fundamen-
tals (i.e., earnings), resulting in predictable fluctuations in both CAPE and future
stock returns. In contrast, proponents of market efficiency argue that this evidence
is consistent with “rational swings in expected returns” (Fama, 1991, p. 1581). In
this paradigm, CAPE proxies for risk: when expected stock return volatility (variance
[VAR]) is low (high), risk-averse investors are willing to pay a higher (lower) pre-
mium relativeto earnings to invest in stocks, resulting in high (low) CAPE. The debate
continues unabated to this day and interest in understanding CAPE remains high.2
We present two sets of analyses to shed light on this ongoing debate on market
efficiency. First, if markets are efficient, knowing CAPE should not help investors
earn superior future returns by selling (buying) stocks and buying (selling) a risk-
free asset when CAPE is high (low).3In other words, market timing strategies using
CAPE should not be profitable. However, we are not aware of any formal tests of
such strategies. Wefind that with the exception of periods when CAPE is in the upper
half of its 10th decile (CAPE higher than 27.6), on average, it is not beneficial to time
the market. For the most part, investors cannot profit from the evidence that CAPE
is associated with future 10-year stock returns.4We conclude that CAPE levels do
1Campbell and Shiller (1988a,b, 1998, 2001); Shiller (1996, 2000). Many authors have modified Shiller’s
original method to compute CAPE. Two notable contributions in this area include Asness (2012) and
Siegel (2016).
2Eugene Fama and Robert Shiller discuss these opposing views in their 2013 Nobel Prize acceptance
speeches (http://www.nobelprize.org).For a recent discussion on CAPE, see “Heard on the Street: Shiller’s
Powerful Market Indicator is Sending a False Signal about Stocks this Time,”by Justin Lahart, Wall Street
Journal (10/5/2016).
3Fama (1970) argues that market efficiency is always tested with an explicit or an implicit returns
generating model. Tobe specific, our implicit model is that regardless of CAPE, 10-year stock returns, on
average, are higher than the corresponding returns on 10-year U.S. Treasurys. Webelieve that this simple
model captures how many investors think of market efficiency. In more sophisticated models, investors
might use CAPE to rebalance their portfolios between stocks and U.S. Treasurys even if stock returns
always exceed returns on U.S. Treasurys (e.g., see Campbell and Thompson, 2008).
4We select a 10-year horizon because shorter horizons are noisy as pointed out by Shiller (1996). In
particular, Shiller (1996, p. 4) states, “In looking at one-year returns, one sees a lot of noise but overlonger
time intervals, this noise effectively averagesout, and is less important.”

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