Age‐Dependent Increasing Risk Aversion and the Equity Premium Puzzle

Date01 May 2019
AuthorChristos Giannikos,Mira Farka,Amadeu DaSilva
Published date01 May 2019
The Financial Review 54 (2019) 377–412
Age-Dependent Increasing Risk Aversion
and the Equity Premium Puzzle
Amadeu DaSilva
California State University, Fullerton
Mira Farka
California State University, Fullerton
Christos Giannikos
Baruch College, City University of New York
We introduce a new preference structure—age-dependent increasing risk aversion
(IRA)—in a three-period overlapping generations model with borrowing constraints, and
examine the behavior of equity premium in this framework. We find that IRA preferences gen-
erate results that are more consistent with U.S. data for the equity premium, level of savings
and portfolio shares, without assuming unreasonable levels of risk aversion. We find that the
relative difference between the two risk aversions (howmuch more risk-averse old agents are
relative to the middle-aged) matters more than the average risk aversionin the economy (how
much more risk-averse both cohorts are). Our findings are robust with respect to a number of
model generalizations.
Corresponding author: Department of Economics, Mihaylo College of Business and Economics,
California State University, Fullerton, 800 N. State College Blvd., Fullerton, CA 92834; Phone: (657)
278-7281; Fax: (657) 278-3097; E-mail:
We thank John Donaldson, Stijn Van Nieuwerburgh, John Geanakoplos, Rajnish Mehra, John Doukas,
and conference participants of the Financial Management Association, Annual Meeting 2005, Conference
on Research on Economic Theory and Econometrics 2006, European Financial Management Association
2015, the WorldFinance Conference 2017, and International Finance and Banking Society 2018. We also
thank Richard Warr (editor), and an anonymous reviewerfor their constructive suggestions on the paper.
This research was sponsored by the Faculty Research Grant of the Mihaylo College of Business and
Economics, CSUF, and the Graduate Research Program, Department of Economics, Columbia University.
All remaining errors are our own.
C2019 The Eastern Finance Association 377
378 A. DaSilva et al./The Financial Review 54 (2019) 377–412
Keywords: equity premium puzzle, overlapping generations model, increasing risk aversion,
portfolio allocation
JEL Classifications: D10, E21, G0, G12
1. Introduction
The equity premium puzzle, first presented in the seminal work of Mehra and
Prescott (1985), underscores the inability of standard, reasonably parameterized
representative-consumer exchange models to match the historical equity premium
observed both in the United States and in international markets. The essence of the
puzzle is driven by the definition of risk: the model parsimoniously links the risk
premia of financial assets with per capita consumption growth. As it is now well
understood, this covariance is typically one order of magnitude lower than what is
needed to generate the observed equity premium, implying that the price of risk must
be implausibly high to reconcile model predictions with its historical counterpart.
Subsequent studies have shown that the puzzle is robust (Campbell, 1996; Kocher-
lakota, 1996), and it is neither a country-specific phenomenon (Campbell, 2003;
Mehra and Prescott, 2003) nor a period-specific one (Siegel, 1992).
Aspects of the equity premium puzzle are manifested in the failure of standard
models to replicate other key empirical regularities. For example, the observed stock
price volatility is too high to be matched by the smoothed dividend process observed
in the data (Shiller, 1981). Moreover, standard models, calibrated at historical (high)
levels of equity premium and moderate (known) levels of risk aversion, produce a
counterfactually high demand for equity forcing theoretically optimal portfolios to
be much more heavily invested in stocks than what the data suggest. In most cases,
these models predict that the appropriate proportion of wealth invested in the risky
asset is close to 100% (Benzoni, Collin-Dufrense and Goldstein, 2007), while the
average share of stocks in financial portfolios in the data is only slightly above 50%
(Bertaut and Starr-McCluer, 2002).
Not surprisingly, the equity premium puzzle has spawned a voluminousbody of
research aimed at reconciling the high equity premium observed in the data with the
theoretical findings of plausibly specified asset pricing models. Several generaliza-
tions of the key features of the Mehra and Prescott (1985) model have been proposed,
ranging from preference modifications, lower tail risks, survival bias, incomplete
markets, market imperfections, limited participation, macroeconomic shocks, long-
run growth prospects, and behavioral explanations.1Many of these generalizations
have contributed importantly to our understanding of the puzzle and the dynamics
1See, for example, Rietz (1988), Weil (1989), Constantinides (1990), Epstein and Zin (1990), Telmer
(1993), Heaton and Lucas (1997), Basak and Cuoco (1998), Campbell and Cochrane (1999), Constan-
tinides, Donaldson and Mehra (2002), McGrattan and Prescott (2003), Bansal and Yaron (2004), Barro
A. DaSilva et al./The Financial Review 54 (2019) 377–412 379
driving asset pricing. However, even though enormous progress has been made in
reconciling facts with theory, no single unified theory appears to have solved all
aspects of the puzzle.
This paper explores whether the equity premium puzzle can be explained in
a parsimonious asset pricing model with preference heterogeneity over the life cy-
cle and borrowing constraints. Our basic framework is the overlapping generations
(OLG) model of Constantinides, Donaldson and Mehra (CDM) (2002) with bor-
rowing constraints. The novelty of this study lies in introducing a new preference
structure—age-dependent increasing risk aversion (IRA)—in this setting: agents be-
come more risk-averse as they age. This type of preference heterogeneity is motivated
by a large number of empirical and survey-based studies that have routinely docu-
mented a strong positive relation between age and risk aversion.2
Following CDM (2002), we assume that there are three age cohorts (young,
middle-aged, and old), each facing different sources of uncertainty on wage and
equity income. The attractiveness of equity depends on the stage of the life cycle.
The young, for whom equity is attractive as a hedge against future consumption
fluctuations, would like to borrow to invest in equity but are unable to do so due to
the borrowing constraint. Equity does not have the same appeal for the middle-aged
given that consumption fluctuations are driven entirely from fluctuations in equity
income. Therefore, the constraint reduces the risk-free rate (because the young are
unable to borrow) and increases equity returns (because the middle-aged require a
higher premium) resulting in a higher premium. However,even though it goes a long
way, the borrowing constraint fails to fully account for key aspects of the data: the
predicted equity risk premium falls short of the historical average, the levelof savings
is higher than observed, and portfolio shares tend to be more heavily skewed toward
the risky asset than they are in practice.
These shortcomings are largely resolved once we introduce age-dependent IRA
into the standard CDM framework with borrowing constraints. We find that the
introduction of IRA preferences in a life cycle model plays a key role in determining
the price of risk in the economy, matching the equity premium while simultaneously
delivering portfolio allocations that are more closely aligned with the data: the equity
premium is in line with the historical average (6–7%), and the portfolio share of
the risky asset is in the 40–50% range. Importantly, these results are obtained for
fairly moderate levels of risk aversion.These results are generally robust with respect
to a number of model extensions (correlation structure, scale changes, growth, and
pension schemes) and the main message from this work—that an OLG model with
(2006), Guvenen (2009), DaSilva, Farka and Giannikos(2011), G ˆ
arleanu and Panageas (2015), and Abbot
2See, for example, Morin and Suarez (1983), Riley and Chow (1992), Bakshi and Chen (1994), Lee and
Hanna (1995), Palsson (1996), and Sung and Hanna (1996).

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