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

• Author: Amadeu DaSilva,Mira Farka
• DOI: http://doi.org/10.1111/eufm.12063
• Date: 01 September 2017
• Published date: 01 September 2017

Retracted

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

E-mail: adasilva@fullerton.edu

Mira Farka

California State University, Fullerton, Department of Economics, 800 N. State College Blvd., Fullerton,

CA 92834

E-mail: efarka@fullerton.edu

Abstract

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 find 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 findings

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’,first 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, 1–29

doi: 10.1111/eufm.12063

© 2015 John Wiley & Sons Ltd

Retracted

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 findings of

reasonably specified asset pricing models. Several generalisations of the key features of

the Mehra-Prescott (1985) model have been proposed, ranging from preference

modifications, lower tail risks, survival bias, incomplete markets, market imperfections,

limited participation, macroeconomic shocks, and behavioural explanations.

1

Though

enormous progress has been made in reconciling facts with theory, no single unified

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) find that the

average share of stocks in financial 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) find 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 profile, 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 infinite

and finite 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

investment.

2

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

1

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.

(2011).

2

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