Expectations of risk and return among household investors: Are their Sharpe ratios countercyclical?

Abstract

Data obtained from special questions on the Michigan Survey of Consumer Attitudes over several years are used to analyze stock market beliefs and portfolio choices of household investors. Consistent with other survey results, expected future returns appear to be extrapolated from past realized returns. The data also indicate that expected risk and return are strongly influenced by economic prospects. When investors believe macroeconomic conditions are more expansionary, they tend to expect both higher returns and lower volatility, which implies that household Sharpe ratios are procyclical. Separately, perceived risk in equity returns is found to be strongly influenced by household investor characteristics, consistent with documented behavioral biases. These expectations reported by respondents are given credence by the finding that the proportion of equity holdings in respondent portfolios tends to be higher for those who report higher expected returns and lower uncertainty. Finally, the finding of procyclical expected returns holds up when we instead condition on conventional business cycle proxies such as the dividend yield and CAY, which yields a stark contrast with the inferences from studies based on actual returns.

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Expectations of risk and return among household investors:
Are their Sharpe ratios countercyclical?

Gene Amromin and Steven A. Sharpe*


Federal Reserve Bank of Chicago and Federal Reserve Board


This draft**: February 2009


Abstract

Data obtained from special questions on a series of Michigan Surveys of Consumer
Attitudes are used to analyze stock market beliefs and portfolio choices of household investors.
We find that expected risk and returns are strongly influenced by expected economic conditions.
When investors believe macroeconomic conditions are more expansionary, they tend to expect
both higher returns and lower volatility. This finding is sharply at odds with the canonical view
that stock market returns should compensate investors for exposure to macroeconomic risks. We
further find that perceived risk in equity returns (though not the expected returns) is strongly
influenced by a number of well-documented behavioral biases. The relevance of investors’
reported expectations is supported by the finding that portfolio equity positions tend to be higher
for those respondents that anticipate higher expected returns and lower uncertainty.



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*The authors thank Joshua Schwartzstein and Daniel Rawner for outstanding research assistance. We also thank,
without implicating, Tobias Adrian, Sean Campbell, Long Chen, Joshua Coval, Dan Covitz, Eric Engstrom, David
Laibson, David Marshall, Matt Pritsker, Paul Seguin, Tyler Shumway, Justin Wolfers, Ning Zhu and seminar
participants at the Federal Reserve Board, the Chicago Fed, the University of Minnesota, 2005 EFA, the 2005
Wharton Conference on Household Portfolio Choice and Decision-Making, and the 2006 WFA meetings for their
comments. All remaining errors are our own. The views expressed in this paper are solely the responsibility of the
authors and should not be seen as reflecting the views of the Board of Governors of the Federal Reserve System or
of any other employee of the Federal Reserve System. Email addresses for the authors are gamromin@frbchi.org
and steve.a.sharpe@frb.gov.
** The previous incarnation of this paper was titled “From the Horse’s Mouth: Gauging Conditional Stock Returns
from Investor Surveys”

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1. Introduction
Rising stock market participation rates and the ongoing shift to defined contribution
pension plans have made millions of American households their own de facto investment
managers. Even with delegation of most day-to-day investment tasks to mutual funds,
households retain the ultimate responsibility of choosing magnitudes and timing of flows
between various asset classes. These decisions derive from expectations of future asset
performance and are presumably also made with an eye towards broad macroeconomic and
sectoral trends, household’s own employment prospects, etc. Yet, surprisingly little is known
about the way in which household expectations of equity market performance and, ultimately,
their investment decisions are related to their views of future economic conditions.
The paucity of knowledge about household beliefs stands in stark contrast with the large
body of research on the equilibrium relationship between systematic variation in stock returns
and the business cycle. That research, motivated by the apparent predictability of stock market
returns at business cycle frequencies, has advanced the view that expectations of future equity
returns tend to be high when the economy is expected to perform poorly. This interpretation, in
turn, has required a more nuanced asset-pricing theory. As summarized by Cochrane (2001, pg.
466), “most solutions introduce something like a ‘recession’ state variable [that] makes stocks
more feared than pure wealth bets” because stocks do poorly at particularly inopportune times.
In particular, it is argued that, the equity risk premium is higher in the recession state because
effective risk aversion is unusually high – such as in models with a slow-moving habit stock
(Campbell and Cochrane, 1999) – or because individual household income risk is unusually high
(Constantinides and Duffie, 1996).
The assumptions behind these theoretical models can be tested directly by focusing on
households’ measured expectations and actions instead of inferring them from observed
equilibrium outcomes. This research strategy is employed, for instance, by Brunnermeier and
Nagel (2008), who evaluate the plausibility of time-varying risk aversion by analyzing responses

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of household portfolio allocations to fluctuations in wealth.1 This paper pursues a similarly
disaggregated approach to assess whether individual investors behave in accordance with the
central tenet of theoretical models. Namely, do investors expect (demand) higher returns for
holding equities when macroeconomic conditions are expected to be poor?
To that end, we employ time-series and cross-sectional data from surveys of household
investors to examine how these investors’ expectations of risks and returns on stocks relate to
perceived and actual macroeconomic conditions. The data is drawn from two sources: (i) the
Gallup/UBS poll of mutual fund investors that provides a monthly snapshot of household stock
market expectations from 1998-2007, and (ii) a special supplement to the Michigan Survey of
Consumer Attitudes, included in 22 monthly surveys from 2000-2005. To our knowledge, the
latter is the first survey to provide information on household-level portfolio allocations together
with investors’ expectations of both risk and returns on stocks. Also unique and critical to this
analysis is the accompanying regular Michigan Survey data that measures perceptions about
current and future economic conditions. These facilitate an analysis of how business-cycle
factors influence expected returns and risk and, by extension, the demand for equities.
Our analysis begins by examining the time series characteristics of household investors’
expected returns on stocks from the Gallup UBS survey. We document that the survey-based
measures of expected returns are correlated with the most popular proxies for the “recession
state” – the aggregate dividend yield and the consumption-wealth ratio (CAY). Indeed, these
two conditioning variables are found to explain over 50 percent of the variation in our 10-year
time series of average expected year-ahead returns. However, both of these variables are
negatively correlated with investors’ expected returns – the opposite of both the theoretical
predictions and the empirical literature that uses realized returns as proxy for ex ante
expectations. This result begs the question: how do household investors’ expectations evolve
with the business cycle? In particular, does the existing consensus have it backwards?

1 Other papers that study whether consumption or investment choices over time are consistent with habit-formation
include Dynan (2000), Lupton (2003), and Ravina (2005).

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To tackle this question, we employ the household-level Michigan survey data. Although
the data spans a period of only five years, it encompasses several significant events – the
bursting of the Internet stock bubble, the terrorist attacks of September 2001, the spate of
corporate scandals in 2002, the start of the Iraq war, and hurricane Katrina – each of which
caused substantial swings in respondents’ economic outlook. The fluctuations in average
reported expectations and the uncertainty surrounding those expectations are complemented by
substantial cross-sectional heterogeneity in views, which together provide ample sources of
variation for identification.
Like the time-series results from the Gallup-UBS data, the findings from the Michigan
data provide a stark contrast with the extant literature on return predictability. In particular, we
find that when investors have a more favorable assessment of short- or medium-term
macroeconomic conditions, they tend to expect higher returns. This does not appear to reflect an
anticipated-news effect that could arise from cross-sectional disagreement among respondents.
On the contrary, the consensus (monthly average) assessment of economic conditions has an
even stronger positive effect on an investor's forecast of stock market returns.
Furthermore, the perception of more favorable economic conditions is found to have a
strong negative effect on expected stock market risk. Together with the expected-return results,
this suggests that for most household investors forward-looking Sharpe ratios are higher when
the economy is expected to be strong – a finding that appears to fly in the face of the
conventional view that stock market returns should compensate investors for exposure to
macroeconomic risks. Finally, we find that the households’ portfolio equity allocation is indeed
systematically related to their reported expectations. Specifically, portfolio equity positions are
significantly higher for those respondents who anticipate higher returns and lower uncertainty.
Taken together, these findings lend support to a behavioral explanation for time-varying
expected returns. In particular, while not necessarily ruling out time-varying risk aversion as a
contributing factor, the results suggest that equity valuations are low during recessions – and the

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subsequent returns are high – because at such times household investors become unduly
pessimistic about future stock returns. The converse occurs during an economic boom.
The rest of the paper is structured as follows. Section 2 summarizes some of the related
research. Section 3 documents the relationship between the time series data on expectations
from the UBS/Gallup survey and the key conditioning variables from the literature on stock
return predictability. Section 4 describes the Michigan survey instrument and data construction.
Sections 5 and 6 focus on time-series and cross-sectional determinants of investors’ expectations
of risk and returns in the equity market, while section 7 analyzes the relationship between
investors’ reported beliefs and their portfolios. Section 8 concludes.

2. Previous Research
Our findings add to a growing body of research on the determinants of investor
expectations of prospective stock market returns and their asset-pricing implications. Fisher and
Statman (2002) and Vissing-Jorgensen (2003) both analyze the first few years of data from the
UBS/Gallup survey of mutual fund investors. These studies find that respondents tend to
forecast continuation of recent performance. Vissing-Jorgensen also documents that expected
returns reported by wealthier respondents follow the same time-pattern as the expectations of
less wealthy respondents, even though the former group's average expectations were consistently
somewhat lower during the period under study (1998-2003). In a recent paper, Malmendier and
Nagel (2009) find that investor memories of past performance can be very long-lived.
Specifically, they show that experiencing periods of low (high) equity returns early in one’s life
has lasting negative (positive) effects on stock market participation and equity share decisions.
Dominitz and Manski (2004, 2005) use data from the Michigan Survey of Consumer
Attitudes to examine determinants of expected stock market performance, measured as the
“probability that a typical diversified stock mutual fund will increase in value over the coming
year” – a metric that conflates risk and expected return. With this measure, they document a
positive correlation between expected market returns and expected business conditions over the