Specification Error, Estimation Risk, and Conditional Portfolio Rules

• Author: Murray Carlson,David A. Chapman,Hong Yan,Ron Kaniel
• DOI: http://doi.org/10.1111/irfi.12110
• Published date: 01 June 2017
• Date: 01 June 2017

Specification Error, Estimation Risk,

and Conditional Portfolio Rules*

MURRAY CARLSON

†

,DAVID A. CHAPMAN

‡

,RON KANIEL

§

AND

HONG YAN

¶

†

Finance Division, Sauder School, University of British Columbia, Vancouver, British

Columbia, Canada,

‡

McIntire School, University of Virginia, Charlottesville, VA, USA,

§

Simon School of Business, University of Rochester and IDC Herzliya, and CEPR,

Rochester, NY, USA and

¶

Shanghai Advanced Institute of Finance, Shanghai Jiao Tong University, Shanghai,

China

ABSTRACT

In characterizing the data-generating process for excess returns, an investor

faces both parameter uncertainty (or “estimation risk”) and specification error.

We examine the trade-off between these two effects, in the context of an

optimal consumption/portfolio decision problem, by considering a minimal

extension of the standard assumption of a linear vector autoregression for

excess returns. The key additional assumption in our data-generating process

is a positive linear relationship between market volatility and lagged market

dividend yields. This simple specification is consistent with a long sample of

U.S. data. We show that volatility adjusted rules are substantially less sensitive

to variation in dividend yields, and volatility-related specification error is

economically significant –even when the decisions are based on sample

estimates from data sets of a realistic size.

I. INTRODUCTION

The impact of excess return predictability on optimal consumption and portfolio

choice has received a substantial amount of attention in the recent academic

literature. The emphasis has been on measuring the quantitative significance of

return predictability for specific utility functions that are common in the

* We would like to thank Brian Balyeat, Ravi Bansal, Alexandre Baptista, Michael Brennan, Yeung

Lewis Chan, John Cochrane, Ron Gallant, Lorenzo Garlappi, Rick Green, John Heaton, Eric Hughson,

Chris Jones, Chris Lamoureux, Jun Liu, Nathalie Moyen, Sheridan Titman, Stathis Tompaidis, Ross

Valkanov, two anonymous referees, and seminar participants at Cornell, HKUST, Arizona, UCLA,

Colorado, Indiana, North Carolina, Penn State, Texas, Texas A&M, Wisconsin, and the 2002 AFA

meetings for helpful comments on various stages of this research. We would also like to thank Sergey

Kolos for research assistance.

© 2016 International Review of Finance Ltd. 2016

International Review of Finance, 17:2, 2017: pp. 263–288

DOI: 10.1111/irfi.12110

theoretical asset pricing literature. One finding of the early papers in this area is

that optimal investment policies seem to be very responsive to the level of the

dividend yield (the predictor variable used in these analyses). For example,

Campbell and Viceira (1999, 2000) find that a constant relative risk aversion in-

vestor with a risk aversion coefficient of four allocates (roughly) 20% of her

wealth to the risky asset when the excess return is zero and 130% of her wealth

to the risky asset when it is 6%. Balduzzi and Lynch (1999) reach similar

conclusions.

1

The studies cited above estimate a particular data-generating process (DGP)

for market excess returns and the market dividend yield, and then they compute

the optimal policy at the point estimates of the parameters of the exogenous

DGP. Kandel and Stambaugh (1996) and Barberis (2000) point out that param-

eter uncertainty, alternatively called “estimation risk,”can have an important

impact on both the measurement of the economic significance of return pre-

dictability and on how aggressively an investor will trade on the apparent pre-

dictability found in a given sample of stock returns. In all of the studies

mentioned so far, excess returns evolve as a restricted version of a first-order vec-

tor autoregression (VAR) of market excess return and dividend yield, driven by

independent normally distributed shocks with constant variance. While this

choice has the virtue of simplicity, the specification of a constant excess return

variance is clearly inconsistent with the large empirical literature that docu-

ments time-varying volatility in stock returns. In addition, the effect of parame-

ter uncertainty on the economic significance of specification error is an

important open issue.

In this paper, we address two questions: (i) how big is the economic signifi-

cance, as measured by utility cost, of ignoring the volatility dynamics in the

DGP when investors make their portfolio allocations based on a mis-specified

model? and (ii) does the estimation risk of parameters mitigate the economic

significance of specification error? We examine these issues from the perspective

of a correctly specified DGP and assess the utility cost of a CRRA investor who

estimates a mis-specified model based on the data that are generated from the

true model. While our approach is decidedly non-Bayesian, it provides a reason-

able way to assess the economic consequence of a common practice of calibrat-

ing a pre-specified DGP for portfolio choice problems based on return

predictability.

The DGP that we use allows both excess return and dividend yield volatilities

to be linear functions of the lagged market dividend yield. This specification is a

small departure from the standard assumptions, and it has the considerable

advantage of simplicity, because mean and volatility dynamics are driven by a

single (observable) state variable. Furthermore, we demonstrate that these

volatility dynamics are qualitatively consistent with the properties of conditional

1 See Lynch (2001) and Campbell, Chan, and Viceira (2003) for multivariate extensions of these

studies.

International Review of Finance

© 2016 International Review of Finance Ltd. 2016264