Valuation Risk and Asset Pricing

• Published date: 01 December 2016
• Author: VICTOR XI LUO,SERGIO REBELO,RUI ALBUQUERQUE,MARTIN EICHENBAUM
• DOI: http://doi.org/10.1111/jofi.12437
• Date: 01 December 2016

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 6 •DECEMBER 2016

Valuation Risk and Asset Pricing

RUI ALBUQUERQUE, MARTIN EICHENBAUM, VICTOR XI LUO,

and SERGIO REBELO∗

ABSTRACT

Standard representative-agent models fail to account for the weak correlation be-

tween stock returns and measurable fundamentals, such as consumption and output

growth. This failing, which underlies virtually all modern asset pricing puzzles, arises

because these models load all uncertainty onto the supply side of the economy. We

propose a simple theory of asset pricing in which demand shocks play a central role.

These shocks give rise to valuation risk that allows the model to account for key asset

pricing moments, such as the equity premium, the bond term premium, and the weak

correlation between stock returns and fundamentals.

IN STANDARD REPRESENTATIVE-AGENT ASSET pricing models, the expected return

to an asset reflects the covariance between the asset’s payoff and the agent’s

stochastic discount factor (SDF). An important challenge to these models is

that the correlation and covariance between stock returns and measurable

fundamentals, especially consumption growth, is weak at both short and long

horizons. Cochrane and Hansen (1992), Campbell and Cochrane (1999), and

Cochrane (2001) call this phenomenon the correlation puzzle. More recently,

Lettau and Ludvigson (2011) document this puzzle using different methods.

According to their estimates, the shock that accounts for the vast majority

of asset price fluctuations is uncorrelated with consumption at virtually all

horizons.

The basic disconnect between measurable macroeconomic fundamentals and

stock returns underlies virtually all modern asset pricing puzzles, including

∗Albuquerque is with Boston College, CEPR, and ECGI; Eichenbaum is with Northwestern Uni-

versity, NBER, and the Federal Reserve Bank of Chicago; Luo is with Northwestern University;

and Rebelo is with Northwestern University, NBER, and CEPR. We benefited from the comments

and suggestions of Fernando Alvarez, Ravi Bansal, Frederico Belo, Jaroslav Borovicka, John Camp-

bell, John Cochrane, Lars Hansen, Anisha Ghosh, Ravi Jaganathan, Tasos Karantounias, Howard

Kung, Junghoon Lee, Dmitry Livdan, Jonathan Parker, Alberto Rossi, Costis Skiadas, Ivan Wern-

ing, and Amir Yaron. We thank Robert Barro, Emi Nakamura, Jun Steinsson, and Jose Ursua

for sharing their data with us and Benjamin Johannsen for superb research assistance. Albu-

querque gratefully acknowledges financial support from the European Union Seventh Framework

Programme (FP7/2007-2013) under grant agreement PCOFUND-GA-2009-246542 and from the

Foundation for Science and Technology-FCT under grant PTDC/IIM-FIN/2977/2014. A previous

version of this paper was presented under the title “Understanding the Equity Premium Puzzle

and the Correlation Puzzle,” http://tinyurl.com/akfmvxb. The authors have read the Journal of

Finance’s disclosure policy and have no conflicts of interest to disclose.

DOI: 10.1111/jofi.12437

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2862 The Journal of Finance R

the equity premium puzzle, Hansen and Singleton (1982)-style rejection of

asset pricing models, violation of Hansen and Jagannathan (1991) bounds, and

Shiller (1981)-style observations about excess stock price volatility.

A central finding of modern empirical finance is that variation in asset re-

turns is overwhelmingly due to variation in discount factors (see Campbell and

Ammer (1993) and Cochrane (2011)). A key question is: how should we model

this variation? In classic asset pricing models, all uncertainty is loaded onto

the supply side of the economy.In Lucas (1978) tree models, agents are exposed

to random endowment shocks, while in production economies they are exposed

to random productivity shocks. Both classes of models abstract from shocks to

the demand for assets. Not surprisingly, it is very difficult for these models to

simultaneously resolve the equity premium puzzle and the correlation puzzle.

We propose a simple theory of asset pricing in which demand shocks, arising

from stochastic changes in agents’ rate of time preference, play a central role in

the determination of asset prices. These shocks amount to a parsimonious way

of modeling the variation in discount rates stressed by Campbell and Ammer

(1993) and Cochrane (2011). Our model implies that the law of motion for

these shocks plays a first-order role in determining the equilibrium behavior

of variables like the price-dividend ratio, equity returns, and bond yields. Our

analysis is disciplined by the fact that the law of motion for time preference

shocks must be consistent with the time-series properties of these variables.

In our model, the representative agent has recursive preferences of the type

considered by Kreps and Porteus (1978), Weil (1989), and Epstein and Zin

(1991). When the risk aversion coefficient is equal to the inverse of the elasticity

of intertemporal substitution, recursive preferences reduce to constant relative

risk aversion (CRRA) preferences. We show that, in this case, time preference

shocks have negligible effects on key asset pricing moments such as the equity

premium.

We consider two versions of our model. The benchmark model is designed to

highlight the role played by time preference shocks per se. Here consumption

and dividends are modeled as random walks with conditionally homoskedas-

tic shocks. However, while this model is useful for expositional purposes, it

suffers from clear empirical shortcomings, for example, the equity premium is

constant. We thus consider an extended version of the model in which shocks

to the consumption and dividend process are conditionally heteroskedastic. We

find that adding these features improves the performance of the model.1

We estimate our model using a Simulated Method of Moments (SMM) strat-

egy implemented with annual data for the period 1929 to 2011. We assume that

agents make decisions on a monthly basis. We then deduce the model’s implica-

tions for annual data, that is, we explicitly deal with the temporal aggregation

problem.2

1These results parallel the findings of Bansal and Yaron (2004), who show that allowing for

conditional heteroskedasticity improves the performance of long-run risk models.

2Bansal, Kiku, and Yaron(2013) pursue a similar strategy in estimating a long-run risk model.

They estimate the frequency with which agents make decisions and find that it is roughly equal to

one month.

Valuation Risk and Asset Pricing 2863

It turns out that, for a large set of parameter values, our model implies

that the SMM estimators suffer from substantial small-sample bias. This bias

is particularly large for moments characterizing the predictability of excess

returns and the decomposition of the variance of the price-dividend ratio pro-

posed by Cochrane (1992). In light of this fact, we modify the SMM procedure to

focus on the plim of the model-implied small-sample moments rather than the

plim of the moments themselves. This change makes an important difference

in assessing the model’s empirical performance.

We show that time preference shocks help explain the equity premium as long

as the risk aversion coefficient and the elasticity of intertemporal substitution

are both greater than one or both smaller than one. This condition is satisfied

in the estimated benchmark and extended models.

Allowing for sampling uncertainty, our model accounts for the equity pre-

mium and the volatility of stock and bond returns, even though the estimated

degree of agents’ risk aversion is moderate (roughly 1.5). Critically, the ex-

tended model also accounts for the mean, variance, and persistence of the

price-dividend ratio and the risk-free rate. In addition, it accounts for the cor-

relation between stock returns and fundamentals such as consumption, output,

and dividend growth at short, medium, and long horizons. The model also ac-

counts for the observed predictability of excess returns by lagged price-dividend

ratios.

We define valuation risk as the part of the excess return to an asset that is

due to the volatility of the time preference shock. According to our estimates,

valuation risk is a much more important determinant of asset returns than

conventional risk. Valuation risk is an increasing function of an asset’s matu-

rity, so a natural test of our model is whether it can account for the bond term

premia. We show that the model does a good job at accounting for the level and

slope of the nominal yield curve, as well as the standard deviation of nominal

yields. The upward-sloping nature of the nominal yield curve reflects the fact

that our model predicts an upward-sloping yield curve for ex ante real yields

on nominal bonds. In fact, in our model the slope of the yield curve is driven

entirely by valuation risk.

The last result contrasts sharply with leading alternatives such as the long-

run risk model, which generally predicts a downward-sloping real yield curve.

With this distinction in mind, we discuss evidence on the slope of the real yield

curve obtained using data for the United States and the United Kingdom. We

also show that the estimated nominal SDF for our model has the properties

that Backus and Zin (1994) argue are necessary to simultaneously account for

the slope of the yield curve and the persistence of bond yields.

An extant literature models shocks to the demand for assets as arising from

time preference or taste shocks. For example, Garber and King (1983)and

Campbell (1986) consider these types of shocks in early work on asset pric-

ing. Stockman and Tesar (1995), Pavlova and Rigobon (2007), and Gabaix and

Maggiori (2013) study the role of taste shocks in explaining asset prices in

open-economy models. In the macroeconomic literature, Eggertsson and Wood-

ford (2003) and Eggertsson (2004) model changes in savings behavior as arising