Retracted: Portfolio Allocation and Asset Returns in an OLG Economy with Increasing Risk Aversion

AuthorAmadeu DaSilva,Mira Farka
Date01 September 2017
Published date01 September 2017
Portfolio Allocation and Asset Returns
in an OLG Economy with Increasing
Risk Aversion
Amadeu DaSilva
California State University, Fullerton, Department of Finance, 800 N. State College Blvd., Fullerton,
CA 92834
Mira Farka
California State University, Fullerton, Department of Economics, 800 N. State College Blvd., Fullerton,
CA 92834
We examine asset returns,equity premium and portfolio allocation in a three-period
OLG model with increasing risk aversion (IRA). IRA preferences generate results
that are more consistent with US data for the equity premium, level of savings and
portfolio shares,without assuming unreasonable levels of risk aversion.We nd that
the relative difference between the two risk aversions (how much more risk-averse
old agents are relative to the middle aged) matters more than the average risk
aversion in theeconomy (how much more risk averse both cohortsare). Our ndings
are robust with respect to a number of model generalisations.
Keywords: equity premium puzzle, overlapping generations model, increasing risk
aversion, portfolio allocation
JEL classification: G0, G12, D10, E21
1. Introduction
The equity premium puzzle,rst presented in the seminal work of Mehra and Prescott
(1985), underscores the inability of standard, reasonably parametrised representative-
consumer exchange models to match the historical equity premium observed both in the
We thank John Donaldson for numerous comments and suggestions. We also thank Stijn
Van Nieuwerburgh, Christos Giannikos, John Geanakoplos, Rajnish Mehra, and conference
participants of the 2014 European Financial Management Association. We are also grateful
to an anonymous referee for detailed comments and suggestions. This research was
sponsored by the Faculty Research Grant of California State University Fullerton and the
Graduate Research Program, Columbia University. Correspondence: Mira Farka.
European Financial Management, Vol. 9999, No. 9999, 2015, 129
doi: 10.1111/eufm.12063
© 2015 John Wiley & Sons Ltd
USA and in international markets. Since then, a large body of literature has focused on
reconciling the high equity premium observed in the data with the theoretical ndings of
reasonably specied asset pricing models. Several generalisations of the key features of
the Mehra-Prescott (1985) model have been proposed, ranging from preference
modications, lower tail risks, survival bias, incomplete markets, market imperfections,
limited participation, macroeconomic shocks, and behavioural explanations.
enormous progress has been made in reconciling facts with theory, no single unied
theory appears to have solved all aspects of the puzzle.
Unresolved (or partially resolved) questions in asset pricing theory are, in a sense,
manifestations of unresolved issues in portfolio choice theory, which have also been
documented extensivelyin the literature. Early models based on the dynamicframework of
Merton (1969), and Samuelson(1969) predict a constant optimal share of the risky asset in
the portfolio over the life-cycle, independent of age and wealthand dependent only on the
level of risk aversion and on the moments of asset returns. However, when calibrated
to historical values of asset returns, predicted optimal portfolio shares of equity holdings
derived from these models appear unreasonably high, ranging from 42% in Netherlands
to over 100% for Germany (73% forthe USA) (Jorion and Goetzmann, 2000). This is the
portfolio-allocation version of the equity premium puzzle: calibrated at historical (high)
levels of equity premium and moderate (known) levels of risk aversion, these models
produce counter-factually high demand forequities forcing theoretically optimalportfolios
to be much more heavily invested in stocks than what is observed in data.
These discrepancies are further highlighted by a large body of empirical work which
has consistently found that the share of the risky asset in household portfolios is
considerably below 100%. For example, Bertaut and Starr-McCluer (2002) nd that the
average share of stocks in nancial portfolios in the USA is around 54%. Similarly,
Gomes and Michaelides (2005) estimate the equity share at 54.8% based on the Survey of
Consumer Finances (SCF). Other studies document a pronounced life-cycle pattern of the
risky asset share in the portfolio: Fagereng et al. (2013) nd that households hold a
remarkably stable share of risky assets (around 39%) up until the age of 50, which is then
reduced to around 30% by the time of retirement. Andersson (2001) shows that the
fraction of risky asset follows a hump-shaped age prole, while the share of the safe asset
has a distinct U-shaped pattern.
Not surprisingly, a vast body of work has addressed the portfolio allocation puzzle.
Standard models have been extended to analyse asset allocation decisions in both innite
and nite horizon models and include a number of key features such as uninsurable labour
income risk, preference heterogeneity, market participation costs, precautionary and
retirement savings, bequest motives, small probability of disastrous events, and housing
While these works have vastly improved our understanding of the nature of
the puzzles, most studies tend to address one key statistic at a time: matching either shares
(or participation) or asset returns. In those cases when a number of key statistics are
See, for example, Weil (1989), Constantinides (1990), Epstein and Zin (1990), He and
Modest (1995), Heaton and Lucas (1997), Shrikhande (1997), Campbell and Cochrane
(1999), McGrattan and Prescott (2003), Lauterbach and Reisman (2004), and DaSilva et al.
See, for example, Heaton and Lucas (1997), Bertaut and Haliassos (1997), Cocco et al.
(2005), Gomes and Michaelides (2005), and Storesletten et al., Telmer and Yaron (2007).
© 2015 John Wiley & Sons Ltd
2A. DaSilva and M. Farka

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