Asset pricing puzzles in an OLG economy with generalized preference

• Author: Mira Farka,Amadeu DaSilva
• Date: 01 June 2018
• DOI: http://doi.org/10.1111/eufm.12133
• Published date: 01 June 2018

DOI: 10.1111/eufm.12133

ORIGINAL ARTICLE

Asset pricing puzzles in an OLG economy with

generalized preference

Amadeu DaSilva

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Mira Farka

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1

Department of Finance, California State

University, Fullerton. 800 N. State

College Blvd., Fullerton, CA 92834, USA

Email: adasila@fullerton.edu

2

Department of Economics, California

State University, Fullerton. 800 N. State

College Blvd., Fullerton, CA 92834, USA

Email: efarka@fullerton.edu

Funding information

This research was sponsored by the Faculty

Research Grant of California State

University, Fullerton.

Abstract

We seek to explain a number of asset pricing anomalies –the

equity premium puzzle, the risk-free rate puzzle, and portfolio

allocation puzzle –in a parsimonious overlapping generations

(OLG) model with two key features: borrowing constraint and

Epstein–Zin–Weil (1989) preference. The model goes a long

way towards the resolution of these puzzles, and is able to

simultaneously match asset pricing moments and individual

portfolio decisions using reasonable values of parameters

governing behavior. We find that the main driver of savings

behavior, equity returns, and asset allocation is the relative

difference between the two parameters: the level of relative

risk aversion and the inverse of the elasticity of substitution.

KEYWORDS

equity premium puzzle, generalized preferences, overlapping

generations model, portfolio allocation

JEL CLASSIFICATION

G0, G12, D10, E21

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INTRODUCTION

Over the past threedecades a vast body of work has consistently documenteda number of puzzles related

to asset prices and portfolioallocation. Broadly speaking, empirical regularitiesobserved in asset price

data appear to be at odds with the predictionsof standard, reasonably parametrized general equilibrium

We are grateful to two anonymous referees and the editor, John Doukas, for insightful comments and suggestions, which greatly

improved the manuscript. We also thank John Donaldson, Valerio Poti, Arthur Petit-Romex, conference participants of the 2015

European Financial Management Association, and conference participants of the 2016 World Finance Conference for helpful

comments and suggestions. This research was sponsored by the Faculty Research Grant of California State University, Fullerton.

Eur Financ Manag. 2018;24:331–361. wileyonlinelibrary.com/journal/eufm © 2017 John Wiley & Sons, Ltd.

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models. In their seminal work, Mehra and Prescott (1985) identify the now well-understood equity

premium puzzle,showing that the equity premium observed in U.S. data was difficultto reconcile with a

standard consumption-based asset pricing model. Weil (1989) documents a second related puzzle, the

risk-free rate puzzle:per capita consumption growth is too high to reconcile with the observedlow risk-

free rate if agents are averse to intertemporal substitution in consumption to the extent observed. Not

surprisingly,standard models also fail to match other key empiricalstatistics, such as the Sharpe ratio or

the price–dividendratio, historically observed in the UnitedStates. In addition, LeRoy and Porter (1981)

and Shiller (1981) argue that the observed volatility in stock prices is too high to be matched by the

smoothed dividend process observed in the data.

A parallel literature in asset pricing has documented another related puzzle: the portfolio allocation

puzzle. Standard models, calibrated at moderate levels of risk aversion and historical (high) levels of

risk premium deliver optimal portfolios that are significantly more heavily skewed towards risky assets

than what is observed in the data. In most cases, the models predict that households invest almost their

entire wealth in equities over the life cycle, which contradicts casual and formal empirical evidence. In

fact, recent empirical work has shown that the average share of stocks in financial portfolios is slightly

above 50% (Bertaut & Starr-McCluer, 2002; Gomes & Michaelides, 2005). Other studies document a

clear life-cycle pattern of the risky asset share in the optimal portfolio, with the largest share reaching

45–55% by middle age (Fagereng, Gottlieb, & Guiso, 2013; Guiso, Haliassos, & Japelli, 2002).

A large body of literature has focused on different aspects of the puzzles. On reconciling the

predicted equity premium with empirical data, several generalizations of the standard neoclassical

model have been employed, with various degrees of success, including preference modifications,

1

disaster events and survivorship bias,

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behavioral models,

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incomplete markets,

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market

imperfections,

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and tax distortions.

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On the portfolio allocation front, promising avenues involve

simultaneous extensions of several key aspects of the standard model, such as preference

heterogeneity, incomplete markets, borrowing constraints, uninsurable labor income risk, stock

market participation costs, and housing investment.

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Though enormous progress towards the

resolution of the puzzles has been made, strikingly, most works either tend to match one statistic at a

time (equity premium, portfolio allocation, or participation) or, when simultaneously matching more

than one dimension of the puzzle, tend to assume unrealistic parameter values (high risk aversion, high

elasticity of intertemporal substitution, or unrealistic patterns for wealth accumulation).

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This paper contributes to the literature by seeking to explain the observed equity premium, asset

allocation, and other key asset price statistics in a parsimonious overlapping generations (OLG) model

with two key features: borrowing constraints and Epstein–Zin–Weil preferences (Epstein & Zin [EZ],

......................................................................................................................................................................................................................................

1

See, for example, Abel (1990), Constantinides (1990), Benartzi and Thaler (1995), Lauterbach and Reisman (2004), and

DaSilva, Farka, and Giannikos (2011).

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See, for example, Rietz (1988) and Julliard and Ghosh (2012).

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See, for example, Barberis, Huang, and Santos (2001).

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See, for example, Constantinides and Duffie (1996) and Heaton and Lucas (1996).

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See, for example, He and Modest (1995) and Constantinides et al. (CDM, 2002).

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See, for example, McGrattan and Prescott (2005).

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See, for example, Heaton and Lucas (1996), Cocco (2005), Cocco, Gomes, and Maenhout (2005), Gomes and Michaelides

(2005, 2008), and Storesletten, Telmer, and Yaron (2007).

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Generally speaking, financial market frictions (e.g., borrowing constraints, market segmentation, participation costs) have

proven largely successful in mitigating asset price puzzles because, through these frictions, the marginal investor model

differs from the representative agent model where the stochastic discount factor depends on the aggregate consumption

process.

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