Dividend Dynamics, Learning, and Expected Stock Index Returns

• Author: BINYING LIU,RAVI JAGANNATHAN
• Date: 01 February 2019
• Published date: 01 February 2019
• DOI: http://doi.org/10.1111/jofi.12731

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 1 •FEBRUARY 2019

Dividend Dynamics, Learning, and Expected

Stock Index Returns

RAVI JAGANNATHAN and BINYING LIU∗

ABSTRACT

We present a latent variable model of dividends that predicts, out-of-sample, 39.5%

to 41.3% of the variation in annual dividend growth rates between 1975 and 2016.

Further, when learning about dividend dynamics is incorporated into a long-run

risks model, the model predicts, out-of-sample, 25.3% to 27.1% of the variation in

annual stock index returns over the same time horizon, with learning contributing

approximately half of the predictability in returns. These findings support the view

that investors’ aversion to long-run risks and their learning about these risks are

important in determining stock index prices and expected returns.

THE AVERAGE RETURN ON EQUITIES has been substantially higher than the aver-

age return on risk-free bonds over long periods of time. For instance, between

1946 and 2016, the S&P500 earned 66 basis points more per month than 30-day

T-bills (i.e., over 7% annualized). Over the years, many dynamic equilibrium

asset pricing models have been proposed in an attempt to understand why risks

in equities require such a large premium and why risk-free rates are so low.

A common feature in most of these models is that the risk premium on equi-

ties does not remain constant over time, but rather varies in a systematic and

stochastic manner. Given a large number of studies find evidence of such pre-

dictable variation in the equity premium, Lettau and Ludvigson (2001, p. 842)

conclude that “it is now widely accepted that excess returns are predictable by

variables such as price-to-dividend ratios.”1

∗Ravi Jagannathan is with Kellogg School of Management, Northwestern University, and

NBER, ISB, and SAIF. Binying Liu is with the Hong Kong University of Science and Technology.

Neither of the authors have any relevant or material financial interests that relate to the research

described in this paper. We are grateful to Kenneth Singleton, an anonymous Associate Editor,

and two anonymous referees at the Journal of Finance for critical advice. We thank Jonathan

Berk, Jules van Binsbergen, Ian Dew-Becker, Wayne Ferson, Lawrence Harris, Gerard Hoberg,

Kai Li, Lars Lochstoer,Narayan Naik, and seminar participants at the 2017 AFA Meeting, HKUST,

London Business School, Purdue University,Norges Bank Wealth Management, Norwegian School

of Economics, Texas A&M University, and University of Southern California for helpful comments

and suggestions. Jiaqi Zhang provided valuable research assistance.

1See, among others, Campbell and Shiller (1988b), Breen, Glosten, and Jagannathan (1989),

Fama and French (1993), Glosten, Jagannathan, and Runkle (1993), Lamont (1998), Baker and

Wurg ler (2000), Lettau and Ludvigson (2001), Campbell and Vuolteenaho (2004), Lettau and Lud-

vigson (2005), Polk, Thompson, and Vuolteenaho (2006), Ang and Bekaert (2007), van Binsbergen

DOI: 10.1111/jofi.12731

401

402 The Journal of Finance R

Goyal and Welch (2008) argue, however,that while variables such as price-to-

dividend ratios are successful in predicting stock index returns in-sample, they

fail to predict returns out-of-sample. The difference between in-sample and

out-of-sample prediction comes down to the assumption made on investors’ in-

formation set. Traditional dynamic equilibrium asset pricing models assume

that, although investors’ beliefs about investment opportunities and economic

conditions change over time and drive the variation in stock index prices and

expected returns, these investors nevertheless have complete knowledge of the

parameters describing the economy. For example, these models assume that

investors know the true model and model parameters governing consumption

and dividend dynamics. This assumption has been only a matter of analyt-

ical convenience, and as Hansen (2007, p. 2) asks, “how can we burden the

investors with some of the specification problems that challenge the econome-

trician.” Motivated by this insight, a recent but growing literature focuses on

the role of learning in asset pricing models. Timmermann (1993) and Lewellen

and Shanken (2002) demonstrate via simulations that parameter uncertainty

can lead to excess predictability and volatility in stock returns. Johannes,

Lochstoer, and Mou (2016) propose a Markov-switching model for consumption

dynamics and show that learning about the consumption process is reflected in

asset prices. Croce, Lettau, and Ludvigson (2014) further show that a long-run

risks model that features bounded rationality and limited information can gen-

erate a downward-sloping equity term structure. Collin-Dufresne, Johannes,

and Lochstoer (2016) provide a theoretical model in which parameter learning

can be a source of long-run risks under Bayesian learning.2We add to this

literature.

The main contributions of our paper are as follows. We present a model for

aggregate dividends of the stock index, based on simple economic intuition,

which explains large variation in annual dividend growth rates out-of-sample.

We show that, when learning about dividend dynamics is incorporated into a

long-run risks model, the model predicts large variation in annual stock index

returns out-of-sample. This not only addresses the Goyal and Welch (2008)

critique and significantly revises upward the degree of return predictability

relative to the existing literature, but also lends support to the view that both

investors’ aversion to long-run risks and their learning about these risks play

important roles in determining asset prices and expected returns.3,4

To study the effect of learning about dividend dynamics on stock index prices

and expected returns, we first need a dividend model that is able to realistically

and Koijen (2010), Chen, Da, and Zhao (2013), Kelly and Pruitt (2013), van Binsbergen et al.

(2013), Li, Ng, and Swaminathan (2013), Da, Jagannathan, and Shen (2014), and Martin (2017).

2Instead of learning, an alternative approach that researchers have used is to introduce pref-

erence shocks. See, for example, Albuquerque, Eichenbaum, and Rebelo (2015).

3Our paper is also consistent with the argument in Lettau and Van Nieuwerburgh (2008)

that steady-state economic fundamentals, or in our interpretation, investors beliefs about these

fundamentals, vary over time and that such variation is critical in determining asset prices and

expected returns.

4Following existing literature, we adopt the stock index as a proxy for the market portfolio.

Dividend Dynamics, Learning, and Expected Stock Index Returns 403

capture how investors form expectations about future dividends. Inspired by

Lintner (1956) and Campbell and Shiller (1988b), we develop a model of divi-

dend growth rates that adds information in corporate payout policy to the latent

variable model used in Cochrane (2008), van Binsbergen and Koijen (2010), and

others. Our model predicts 42.4% to 46.4% of the variation in annual dividend

growth rates between 1946 and 2016 in-sample and 39.5% to 41.3% of the vari-

ation in annual dividend growth rates between 1976 and 2016 out-of-sample.

Based on these results, we comfortably reject the null that expected dividend

growth rates are constant and show that the superior performance of our divi-

dend model over alternative models in predicting annual dividend growth rates

is statistically significant and economically meaningful.

We further document that uncertainty about parameters in our dividend

model, especially parameters surrounding the persistent latent variable, is

high and resolves slowly. In particular, such uncertainty remains substantial

even at the end of our 71-year sample, which suggests that learning about

dividend dynamics is a difficult and slow process. Moreover, when our dividend

model is estimated at each point in time based on data available at the time,

model parameter estimates fluctuate over time, some significantly, as more

data become available. In other words, if investors estimate dividend dynamics

using our model, we expect their beliefs about the parameters governing the

dividend process to vary significantly over time. We show that these changes

in investors’ beliefs can have large effects on their expectations of future div-

idends. Thus, through this channel, changes in investors’ beliefs about the

parameters governing the dividend process can contribute significantly to the

variation in stock prices and expected returns.

We next provide evidence that investors behave as if they learn about divi-

dend dynamics and price stocks using our model. First, we define stock yields

as discount rates that equate the present value of expected future dividends to

the current prices of the stock index. Based on the log-linearized present value

relationship of Campbell and Shiller (1988a), we specify stock yields as a func-

tion of price-to-dividend ratios and long-run dividend growth expectations.5

We show that, assuming investors learn about dividend dynamics, these stock

yields explain 18.7% of the variation in annual stock index returns between

1975 and 2016. In comparison, stock yields, assuming full information, predict

a statistically significantly lower 13.0% of the same variation over the same

horizon. Next, we embed our dividend model into a dynamic equilibrium asset

pricing model that features Epstein and Zin (1989) preferences, which capture

preferences for the early resolution of uncertainty, and consumption dynamics

similar to the long-run risks model of Bansal and Yaron (2004). We refer to this

model as our long-run risks model. We find that, assuming learning, our long-

run risks model predicts 25.3% to 27.1% of the variation in annual stock index

5See Jagannathan, McGrattan, and Scherbina (2001) for the dynamic version of the Gordon

(1959) growth model that gives an expression for stock yield in levels. When expected dividend

growth rates vary over time, according to the present value relationship, we show that stock yield,

that is, the long-run expected return on stocks, is the current dividend yield plus a weighted

average of expected future one-period dividend growth rates.