Joint dynamics of stock returns and cash flows: A time‐varying present‐value framework

• Published date: 01 September 2023
• Author: Deshui Yu,Yayi Yan
• Date: 01 September 2023
• DOI: http://doi.org/10.1111/fima.12433

DOI: 10.1111/fima.12433

ORIGINAL ARTICLE

Joint dynamics of stock returns and cash flows: A

time-varying present-value framework

Deshui Yu1Yayi Yan2

1College of Finance and Statistics, Hunan

University, Hunan, China

2School of Statistics and Management,

Shanghai Universityof Finance and Economics,

Shanghai, China

Correspondence

YayiYan, School of Statistics and Management,

Shanghai Universityof Finance and Economics,

Shanghai, China.

Email: yanyayi0812@gmail.com

Fundinginformation

National NaturalScience Foundation of China,

Grant/AwardNumbers: 72303060,

72303142; The Ministry of Education of the

People’sRepublic ofChina, the Humanities

and Social Sciences YouthFoundation,

Grant/AwardNumber: 22YJC790156;

FundamentalResearch Funds for the Central

Universities, Grant/AwardNumbers:

2022110877, 2023110099

Abstract

This paper proposes a novel time-varying present-value

model to analyze the joint dynamics of stock returns and

cash flows periodically. We use a nonparametric time-

varying vector autoregressive model to examine the eco-

nomic implications of the time-varying present-value model.

By conducting several nonparametric tests, we reject the

stability of multivariate forecasting models and the null

that stock returns and cash flows are simultaneously unpre-

dictable in any given period. Additional bootstrap analyses

show that under the null of unpredictable returns, dividend

growth is highly predictable. Finally, the proposed time-

varying present-value frameworkholds robustly for both the

dividend–price ratio and the earnings–price ratio.

KEYWORDS

bootstrap analysis, localized and global joint nonparametric tests,

locally stationary process, time-varying present-value model, time-

varying vector autoregression

1INTRODUCTION

A fundamental question in asset pricing is whether stock prices change in response to news about discount rates

or to news about expected cash flows. In a seminal work, Campbell and Shiller (1988a) show that the log dividend–

price ratio can be approximated as the present value of future stock returns (discount rates) and future dividend

growth (cash flows). This identity implies that changes in the dividend–price ratio should arise from changes in dis-

count rates, changes in cash flows, or both. Although the present-value model has motivated a vast literature that

studies predictability features based on predictive regressions of stock returns and cash flow growth on the lagged

© 2023 Financial Management Association International.

Financial Management. 2023;52:513–541. wileyonlinelibrary.com/journal/fima 513

514 YU ANDYAN

dividend–price ratio, the extant results present many discrepancies (see, e.g., Ang & Bekaert, 2007; Cochrane,2008;

Lettau & Nieuwerburgh, 2008; Liu et al., 2021; Ma et al., 2022; and Welch & Goyal, 2008).

The time-series properties of the dividend–price ratio play a significant role in determining the present-value

relation. A keyassumption in the present-value model of Campbell and Shiller ( 1988a)i s that the dividend–price ratio

(or other price-scaled ratios) is covariance stationary, and the accounting identity is derived by expanding around

the long-run mean of the ratio. However, empirical evidence suggests that the dividend–price ratio is extremely

persistent.1In particular, Lettau and Nieuwerburgh (2008), Favero et al. (2011), and Yu et al. (2023) attribute the

highly persistent movements in the dividend–price ratio to its time-varying levels. Along this line, Campbell (2008)

and Dybvig and Zhang (2018) point out that the extremely high persistence of the dividend–price ratio can lead to

severe convergence issues with the Taylor series expansion of period returns, making the traditional present-value

identity of Campbell and Shiller (1988a) less reliable.

In this paper, we propose a noveltime-varying present-value framework to reanalyze the joint dynamics of stock

returns and cash flows, which forms the main contribution of our paper. First, we adopt a flexible, locally stationary

framework to relax the assumption of stationarity imposed on the dividend–price ratio, which allows for statistical

properties of a time series, such as the mean and persistence, to vary smoothly overtime.2Based on the locally station-

ary assumption, we then perform the Taylorexpansion of the dividend–price ratio at a local level for each time point

rather than at the long-run sample average as done in Campbell and Shiller (1988a), which ought to reduce approx-

imation errors of the Taylor expansion according to Dybvig and Zhang (2018). Finally, the proposed time-varying

present-value model is formulated as follows:

dpt≃−

∞



j=0

𝜌j

tkt+j+

∞



j=0

𝜌j

tEtrt+1+j−

∞



j=0

𝜌j

tEtΔdt+1+j,

where dptis the log dividend–price ratio, rt+1is the log stock return, Δdt+1is the log dividend growth, and ktand 𝜌tare

functions of time-varying (local) mean of the dividend–price ratio. An important feature of the time-varying present-

value model is that the time-varying characteristicsof the dividend–price ratio, including its mean and persistence, are

intimately linked to time variations in expectedfuture stock returns and expected future cash flows.

The time-varying present-value framework provides important economic implications for stock return and cash

flow predictability.First, the dividend–price ratio is approximated as the discounted value of future expected discount

rates and cash flows but with time-dependent “discount factors,” 𝜌j

t. Hence, the forecasting relationship should be

time-dependent, consistent with ample empirical evidencethat attempts to predict stock market returns or cash flows

areplagued by instability in the underlying predictive regression models (Chen et al., 2012; Paye & Timmermann, 2006;

Smith&Timmermann, 2020; Yan & Cheng, 2022). Therefore, the time-varying present-value model suggests detecting

patterns in return or cash flow predictability at any local time, consistent with Chen et al. (2012) and Farmer et al.

(2023).3

Second, the time-varying stock return predictability driven by the dividend–price ratio should not be tested in

isolation; instead, it should be studied jointly with the time-varying cash flow predictability and time-varying depen-

dence properties of the dividend–price ratio. In specific, at any local time, the variation of the dividend–price ratio

should come from the variation in expected future discount rates and/or cash flows. As a result, the dividend–price

1See,for example, Campbell and Yogo (2006), Chen and Hong (2012), Cai and Wang (2014),andYuandHuang(2023).In addition, the dividend–price ratio is

overalldeclining on average since the 1970s, consistent with the phenomenon of so-called “disappearing dividends” (Fama & French, 2001).

2The locally stationary assumption carries robustness with respect to the changing time-series properties of the predictors (see Chen & Hong, 2012;Chen

etal., 2018; Dahlhaus, 1996,1997; Vogtet al., 2012; Yousuf & Ng, 2021;Yu&Huang,2021,e.g.). That is, it does not contain a unit root across time, ruling out

thebubbles in asset prices, and it captures time variation in the mean and persistence of predictors. By performing the statistical tests proposed by Ya n et al.

(2021) and Zhang and Wu (2011), we show that the hypothesisof smooth changes in the mean and persistence of the dividend–price ratio is well supported

bythe real data over the sample from 1927 to 2019.

3Traditional predictability tests commonly use linear predictive models. However,as pointed out by Farmer et al. (2023), “inference on the resulting

coefficientsmay yield misleading and unstable results, since return predictability shifts over time.”