Age‐Dependent Increasing Risk Aversion and the Equity Premium Puzzle

• Date: 01 May 2019
• Author: Christos Giannikos,Mira Farka,Amadeu DaSilva
• Published date: 01 May 2019
• DOI: http://doi.org/10.1111/fire.12191

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

Abstract

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: efarka@fullerton.edu.

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.

C2019 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

(2017).

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).