Limited Risk Sharing and International Equity Returns

• Date: 01 April 2021
• DOI: http://doi.org/10.1111/jofi.12994
• Published date: 01 April 2021
• Author: SHAOJUN ZHANG

THE JOURNAL OF FINANCE •VOL. LXXVI, NO. 2 •APRIL 2021

Limited Risk Sharing and International Equity

Returns

SHAOJUN ZHANG*

ABSTRACT

Limited stock market participation can potentially explain the disconnect between in-

ternational asset prices and macro quantities. An incomplete markets model in which

risk sharing for stockholders is high generates highly correlated equity returns and

relatively smooth exchange rates. Risk sharing for nonstockholders is limited because

of their nonparticipation in stock markets and borrowing constraints, reducing the

aggregate consumption correlation and the correlation between aggregate consump-

tion differentials and exchange rates. Financial integration widens the disconnect

by benef‌iting stockholders but hurting nonstockholders. Survey data indicate that

international risk sharing for stockholders is better than that for nonstockholders,

consistent with the predictions.

INTERNATIONAL ASSET PRICES AND QUANTITIES are disconnected. In the

post–Bretton Woods period, quarterly equity returns of the United States have

a correlation of 0.7 with those of the United Kingdom, whereas the corre-

lation between the f‌inancial income of the two countries is 0.14 and that of

nondurable consumption growth is 0.18. This large spread between the cross-

country equity correlation and consumption correlation is known as the inter-

national equity premium puzzle. Similarly, the correlation between the differ-

ences in home and foreign aggregate consumption growth rates (or consump-

tion differentials) and real exchange rate changes is −0.06 between the United

States and United Kingdom, whereas the correlation predicted by theoretical

models is often close to one. This discrepancy is known as the Backus and

*Shaojun Zhang is with The Ohio State University. This paper is based on Chapter 1 of my

doctoral dissertation at NYU Stern School of Business. I thank my advisors Matteo Maggiori,

Thomas Mertens, Stijn van Nieuwerburgh, and Robert Whitelaw for their training and guid-

ance. I acknowledge helpful comments from Rui Alburquerque (discussant); Redouane Elkamhi

(discussant); Aurel Hizmo; Kewei Hou; Christopher Telmer (discussant); Alexi Savov; Lu Zhang;

and seminar participants at CKGSB, Georgetown McDonough, HKU, Hofstra, Minnesota Carl-

son, NYU Stern, OSU Fisher,PSU Smeal, Purdue Krannert, SMU Lee K ongChian, and Tsinghua

PBC seminars, European Financial Association Annual Meeting 2015, American Financial Associ-

ation Annual Meeting 2016, and China International Conference in Finance 2016. I am especially

indebted to the editor Wei Xiong and two anonymous referees for many constructive criticisms

that substantially improved the paper. The author does not have potential conf‌licts of interest to

disclose as def‌ined in The Journal of Finance’s disclosure policy. All remaining errors are my own.

Correspondence: Shaojun Zhang, The Ohio State University.e-mail: zhang.7805@osu.edu.

DOI: 10.1111/jof‌i.12994

© 2020 the American Finance Association

893

894 The Journal of Finance®

Smith (1993) puzzle. Finally, under complete markets and power utility, a high

equity premium and relatively smooth exchange rates imply high international

risk sharing and highly correlated pricing kernels, but the consumption data

indicate otherwise (Brandt, Cochrane, and Santa-Clara (2006)).

A large literature attempts to reconcile international asset prices and quan-

tities under the assumption of complete markets.1Because of modeling con-

venience and data restrictions, the heterogeneity within a country is largely

abstracted away. As a fundamental departure from the literature, I study the

heterogeneity in asset market participation in this paper.

Empirically, using household-level consumption survey data for the United

States and United Kingdom from January 1988 to March 2017, I show that

stockholders achieve better international risk sharing than nonstockholders.

First, stockholders’ cross-country fourth-quarter (Q4-Q4) consumption growth

correlation is as high as 0.56, whereas the aggregate consumption correlation

is only 0.32 and nonstockholders’ consumption correlation is 0.15. Second, the

Backus-Smith correlation, which is the correlation between real exchange rate

changes and consumption differentials, is −0.11 for the aggregate population,

0.15 for stockholders, and as low as −0.22 for nonstockholders. The appar-

ent lack of risk sharing at the aggregate level can therefore be potentially at-

tributed to nonstockholders.

Theoretically, I begin by deriving analytically closed-form results in an in-

complete markets model that features limited risk sharing analytically. I then

turn to a richer quantitative model. Specif‌ically, I f‌irst study a simple analyti-

cal framework with two goods, two countries, and stochastic labor and f‌inancial

income in each country. Agents have power utility that exhibits home bias in

goods and receive a constant fraction of domestic labor income. Stockholders

further receive f‌inancial income. Markets are complete for stockholders, and

nonstockholders live in f‌inancial autarky.

Because of the home bias in goods, following positive home income shocks,

home stockholders’ consumption increases more than foreign stockholders’

consumption to achieve a Pareto optimal allocation. As the demand for foreign

goods increases, foreign goods become more expensive to clear the goods mar-

kets. As such, stockholders’ consumption differentials are perfectly positively

correlated with real exchange rate changes. This is the complete markets role

of real exchange rates.

Second, I analytically study nonstockholders. Following positive home la-

bor income shocks, the income effect leads home nonstockholders’ consump-

tion to increase one-for-one. However, the appreciation of the real exchange

rate makes home nonstockholders’ consumption basket more expensive, damp-

ens the magnitude of their consumption increase, and increases nonstockhold-

ers’ risk sharing. This is the so-called relative price effect (Cole and Obst-

feld (1991)). In contrast, following positive home f‌inancial income shocks, non-

stockholders receive no direct endowment shocks, but the real exchange rate

1Prominent examples include Dumas (1992), Farhi and Gabaix (2008), Verdelhan (2010), and

Pavlova and Rigobon (2007,2012).

Limited Risk Sharing and International Equity Returns 895

appreciation dampens home nonstockholders’ consumption. This adjustment

moves in the opposite direction of the Pareto optimal allocation. In other words,

the relative price effect now reduces risk sharing for nonstockholders and

can lead to a negative cross-country consumption correlation and a negative

Backus-Smith correlation for nonstockholders. In sum, under limited partici-

pation, the tension between complete markets for stockholders and the relative

price effect in incomplete markets for nonstockholders can help reconcile inter-

national asset pricing puzzles.

I next study whether limited participation can lower the aggregate risk shar-

ing enough to resolve the international asset pricing puzzles quantitatively.

The model features an inf‌inite-horizon two-country, two-good economy similar

to the analytical model, but with more realistic asset markets. The economy

has three assets, namely, a home stock, a foreign stock, and a zero net supply

real global bond. The f‌inancial income is the dividend stream of stocks. In this

case, nonstockholders can trade only in the bond market subject to borrow-

ing constraints, whereas stockholders can trade in all asset markets. Markets

are incomplete because of limited stock market participation, borrowing con-

straints, and incomplete spanning of asset markets.

The model generates rich risk-sharing patterns that are consistent with

the data. Risk sharing is high for stockholders but low for nonstockholders

and for the aggregate population. In the aggregate, the model simultane-

ously solves the international equity premium, Backus-Smith, and Brandt-

Cochrane-Santa-Clara puzzles. Stockholders are marginal investors and the

key to generating both high stock return correlations and low exchange rate

volatility. Quantitatively, markets are almost complete for stockholders, as

their Backus-Smith correlation is close to one. Stockholders’ consumption

growth rates are almost perfectly correlated across countries. Equity returns

are also almost perfectly correlated across countries. Because the f‌inancial in-

come is volatile, stockholders’ consumption is also highly volatile. Jointly, the

volatile but highly correlated stochastic discount factors (SDFs) for stockhold-

ers generate high and volatile equity premia and low exchange rate volatility,

thereby solving the Brandt-Cochrane-Santa-Clara puzzle.

Nonstockholders are the source of the apparent lack of aggregate risk shar-

ing. Because of limited participation, real exchange rate variations can provide

only limited risk sharing for nonstockholders through the relative price ef-

fect as in the analytical model. Furthermore, because of their nonparticipation

in equity markets and borrowing constraints, nonstockholders receive limited

risk sharing from asset markets. As a result, nonstockholders’ consumption

growth rates are poorly correlated across countries and their Backus-Smith

correlation is negative.

Comparative statics show that the quantitative success of the model comes

from the tension between complete markets for stockholders and incomplete

markets for nonstockholders. In particular, the income heterogeneity in the

form of f‌inancial income shocks sharpens the tension. First, the access to

international stock markets increases market completeness for stockholders.

Quantitatively, when stock markets are closed, markets are incomplete for all