Dividend Dynamics and the Term Structure of Dividend Strips

• Author: FREDERICO BELO,ROBERT S. GOLDSTEIN,PIERRE COLLIN‐DUFRESNE
• DOI: http://doi.org/10.1111/jofi.12242
• Date: 01 June 2015
• Published date: 01 June 2015

THE JOURNAL OF FINANCE •VOL. LXX, NO. 3 •JUNE 2015

Dividend Dynamics and the Term Structure of

Dividend Strips

FREDERICO BELO, PIERRE COLLIN-DUFRESNE, and ROBERT S. GOLDSTEIN∗

ABSTRACT

Many leading asset pricing models are specified so that the term structure of dividend

volatility is either flat or upward sloping. These models predict that the term struc-

tures of expected returns and volatilities on dividend strips (i.e., claims to dividends

paid over a prespecified interval) are also upward sloping. However, the empirical ev-

idence suggests otherwise. This discrepancy can be reconciled if these models replace

their proposed dividend dynamics with processes that generate stationary leverage

ratios. Under such policies, shareholders are forced to divest (invest) when leverage

is low (high), which shifts risk from long- to short-horizon dividend strips.

RECENT ADVANCES IN CONSUMPTION-based asset pricing models have created an

embarrassment of riches in that several competing frameworks are now able

to capture many salient features of security prices that were once considered

puzzling (e.g., high excess returns and volatilities for stocks, low levels and

volatilities for interest rates). Due to these successes, there has been a push to

identify additional empirical moments in the hope of distinguishing between

the different frameworks. For example, recently there has been considerable

interest in the pricing and return properties of so-called dividend strips, which

are claims to dividends paid over a prespecified time interval in the future.

These assets provide information regarding the term structures of both the

∗Belo is with the University of Minnesota and the NBER. Collin-Dufresne is with the Swiss

Finance Institute at EPFL and the NBER. Goldstein is with the University of Minnesota and

the NBER. This paper was previously entitled “Endogenous Dividend Dynamics and the Term

Structure of Dividend Strips.” We thank the Editor, Cam Harvey, as well as the Associate Editor

and an anonymous referee for excellent suggestions. We also thank our discussants Lukas Schmid

(AFA discussant), Jakub Jurek (WFA Discussant), Ivan Shaliastovich (CAPR and NFI workshop

discussant), and Francisco Palomino (Minnesota Macro-Asset Pricing conference discussant) for

detailed comments, as well as Ravi Bansal, Jules van Binsbergen, Murray Carlson, Long Chen,

John Cochrane, Darrell Duffie, Adlai Fisher, Murray Frank, Dana Kiku, Ralph Koijen, Dimitris

Papanikolaou, Ivan Shaliastovich, Jessica Wachter,Jianfeng Yu, and seminar participants at Aalto

University/Hanken School of Economics, BI Norwegian Business School, Central Bank of Portu-

gal, Cheung Kong Graduate School of Business, Dartmouth College (Tuck), Hong Kong University,

University State Arizona (W.P. Carey), University of Pennsylvania (Wharton), University of Min-

nesota (Carlson), University of British Columbia (Sauder), University of North Carolina at Chapel

Hill (Kenan-Flagler), University of Southern California (Marshall), Vanderbilt University (Owen),

American Finance Association 2013, Western Finance Association 2012, Minnesota Macro-Asset

Pricing 2012 conference, and the 2012 CAPR/NFI workshop on Time-Varying Expected Returns

for many helpful comments. All remaining errors are our own.

DOI: 10.1111/jofi.12242

1115

1116 The Journal of Finance R

price and quantity of risk in the economy, and thus may be useful for help-

ing us understand how asset prices are determined in equilibrium. While the

return on a portfolio of all dividend strips replicates stock returns, return

characteristics of the individual strips provide an out-of-sample test for these

competing frameworks.

Indeed, while successful in capturing the asset pricing properties mentioned

above, many leading asset pricing models, such as Campbell and Cochrane

(CC, 1999), and Bansal and Yaron (BY, 2004), predict that the term structure

of expected returns and volatilities on dividend strips are strongly upward

sloping. Yet the empirical evidence reported in van Binsbergen, Brandt, and

Koijen (BBK, 2012) and van Binsbergen et al. (BHKV,2013) suggests otherwise.

Adding to the puzzle, they also report that short-horizon dividend strips possess

low CAPM market betas, high CAPM alphas, and high Sharpe ratios. While

Boguth et al. (2011)1question some of the findings in these papers, all seem to

agree that the strongly upward-sloping term structures predicted by BY and

CC are inconsistent with the historical evidence on returns of dividend strips.

Below,however, we demonstrate that the counterfactual implications of these

leading asset pricing models can be eliminated without altering their funda-

mental economic mechanisms. In particular,neither their proposed preferences

nor their consumption processes need be changed—hence, their pricing kernels

need not be altered. Instead, all that is necessary to make these models con-

sistent with many of the empirical findings of BBK is to replace their proposed

dividend dynamics with processes that are both more economically justifiable

and more consistent with the empirical properties of dividends that we identify

below. In particular, we show that the term structure of dividend volatility (i.e.,

the quantity of risk) is decreasing with horizon.2This evidence is important be-

cause, in contrast to the empirical evidence on dividend strips (for which data

are available for only a relatively short sample period), the empirical properties

of the term structure of dividend volatility can be estimated from more than a

century of data. Importantly, we show that our proposed changes to dividend

dynamics do not impact the ability of these frameworks to capture the salient

properties of stock returns mentioned previously. Intuitively, this property is

due to the dividend irrelevance argument of Modigliani and Miller (1961).

In this paper we consider dividend processes that are internally consistent

with capital structure policies that generate stationary leverage ratios. In do-

ing so, our model is able to capture two important properties that, at first blush,

seem contradictory. First, compared to unleveraged cash flows of a firm (which

we refer to as EBIT), dividends are a leveraged cash flow. It is thus not sur-

prising that claims to dividends (i.e., equity) are more volatile and have higher

average historical returns than claims to EBIT (i.e., debt plus equity). Second,

over long horizons, the dividend-EBIT ratio should be stationary,implying that

long-horizon dividends are no more volatile than long-horizon EBIT.

1See also Schulz (2013).

2Here, we are defining quantity of risk as total volatility, and not necessarily as risk that is

priced.

Dividend Dynamics and the Term Structure of Dividend Strips 1117

This apparent contradiction can be explained by noting that, when a firm

rebalances its debt levels over time to maintain a stationary leverage process,

shareholders are being forced to divest (invest) when leverage is low (high).

Thus, even if investors follow a static strategy of holding a fixed supply of stock,

their position is effectively being managed by the capital structure decisions

of the firm. Below, we show that these imposed investments/divestments con-

ceal the leveraged nature of dividends in that, even though dividends are cor-

rectly interpreted as leveraged cash flows, over the long run EBIT and divi-

dends are equally risky.

Interestingly, most leading asset pricing models ignore either the leveraged

nature of dividends or its cointegration with unleveraged cash flows (or both).

Moreover, even if they do account for leverage, they do so in a reduced-form

way by introducing free parameters that are not directly tied down to ob-

served leverage ratios. For example, for parsimony, CC specify consumption

and dividends as i.i.d. with the same drift, and therefore disregard leverage.

BY capture leverage by assuming that dividends have greater exposure to

shocks to expected growth rates than does consumption. However, their model

does not capture stationarity in the dividend-consumption ratio. Abel (1999,

2005) models cash flows to be of the form yλ, where λ=0 for fixed income se-

curities, λ=1 for EBIT, and λ>1 for dividends. Hence, this framework does

not capture stationarity in the dividend-EBIT ratio.

To demonstrate the impact of capital structure policies on the properties of

dividends in leading asset pricing models, we investigate modified versions of

the BY and CC economies. In particular, we replace their proposed dividend

processes by first specifying an unleveraged cash flow (i.e., EBIT) process (with

the same functional forms as the dividend processes in BY and CC), and then

combine it with a dynamic capital structure strategy that produces stationary

leverage ratios. These two ingredients generate an endogenously determined

dividend process that is internally consistent with the EBIT process. Claims

to this dividend process (i.e., equity) have higher expected returns and higher

volatilities than claims to EBIT (i.e., equity plus debt), yet this framework

generates a stationary dividend-EBIT ratio.

We investigate two different approaches to modeling joint dividend/leverage

dynamics. The first approach directly specifies leverage dynamics and then

identifies dividend dynamics from an accounting identity that equates the

firm’s cash inflows and outflows. Advantages of this framework are its intu-

itive nature and its tractability, as it provides analytic solutions for dividend

strip prices. Unfortunately, it generates counterfactually large correlations be-

tween short-horizon dividends and stock returns. As such, we also investigate

a second approach where dividend dynamics are directly specified and leverage

dynamics are determined from the accounting identity.In addition to matching

leverage dynamics and the term structures of dividend strips, this more flexible

framework can be calibrated to generate low CAPM betas, high CAPM alphas,

and high Sharpe ratios for the short-horizon strips, consistent with BBK and

BHKV.