Capital Share Risk in U.S. Asset Pricing

• Date: 01 August 2019
• DOI: http://doi.org/10.1111/jofi.12772
• Published date: 01 August 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 4 •AUGUST 2019

Capital Share Risk in U.S. Asset Pricing

MARTIN LETTAU, SYDNEY C. LUDVIGSON, and SAI MA∗

ABSTRACT

A single macroeconomic factor based on growth in the capital share of aggregate

income exhibits significant explanatory power for expected returns across a range of

equity characteristic portfolios and nonequity asset classes, with risk price estimates

that are of the same sign and similar in magnitude. Positive exposure to capital

share risk earns a positive risk premium, commensurate with recent asset pricing

models in which redistributive shocks shift the share of income between the wealthy,

who finance consumption primarily out of asset ownership, and workers, who finance

consumption primarily out of wages and salaries.

CONTEMPORARY ASSET PRICING THEORY REMAINS in search of an empirically rele-

vant stochastic discount factor (SDF) linked to the marginal utility of investors.

This study presents evidence that a single macroeconomic factor based on

growth in the capital share of aggregate income exhibits significant explana-

tory power for expected returns across a wide range of equity characteristic

portfolio styles and nonequity asset classes, with positive risk price estimates

of similar magnitude. These assets include equity portfolios formed from sorts

on size/book-to-market, size/investment, size/operating profitability, long-run

reversal, and nonequity asset classes such as corporate bonds, sovereign bonds,

credit default swaps, and options.

Why should growth in the share of national income accruing to capital (here-

after the “capital share”) be a source of systematic risk? After all, a main-

stay of contemporary asset pricing theory is that assets are priced as if there

were a representative agent, leading to an SDF based on the marginal rate of

∗Martin Lettau is with Haas School of Business, University of California at Berkeley. Sydney

Ludvigson is with the Department of Economics, New York University. Sai Ma is with the Board

of Governors of the Federal Reserve System. Ludvigson received financial support from the C.V.

Starr Center for Applied Economics at NYU, a member of the Economic Advisory Panel of the

Federal Reserve Bank of New York, which meets twice per year to discuss policy areas of interest

to the president of the bank; this position is unpaid. We are grateful to Federico Belo; John Y.

Campbell; Kent Daniel; Lars Lochstoer; Hanno Lustig; Stefan Nagel; Dimitris Papanikolaou; and

to seminar participants at Duke, USC, the Berkeley-Stanford joint seminar, the Berkeley Center

for Risk Management, Minnesota Macro-Asset Pricing Conference 2015, the NBER Asset Pricing

meeting on April 10, 2015, the Minnesota Asset Pricing Conference May 7–8, 2015, and the 2016

Finance Down Under Conference for helpful comments. The views expressed are those of the

authors and do not necessarily reflect those of the Federal Reserve Board or the Federal Reserve

System. The authors have read the Journal of Finance disclosure policy and have no conflicts of

interest to disclose.

DOI: 10.1111/jofi.12772

1753

1754 The Journal of Finance R

substitution over aggregate household consumption. Under this paradigm, the

division of aggregate income between labor and capital is irrelevant for the pric-

ing of risky securities once aggregate consumption risk is accounted for. The

representative agent model is especially convenient from an empirical perspec-

tive, since aggregate household consumption is readily observed in national

income data.

But there are reasons to question whether average household consump-

tion is the appropriate source of systematic risk for the pricing of risky

financial securities. Wealth is highly concentrated at the top, and limited

securities market participation remains pervasive. The majority of house-

holds own no equity but even among those who do, most own very lit-

tle. In particular, while just under half of households report owning stocks

either directly or indirectly in 2013, the top 5% of the stock wealth

distribution owns 75% of the stock market value.1It follows that any rea-

sonably defined wealth-weighted stock market participation rate should be

much lower than 50%, as we illustrate below. Moreover, unlike the av-

erage household, the wealthiest U.S. households earn a relatively small

fraction of income as labor compensation, implying that income from the

ownership of firms and financial investments, that is, capital income, fi-

nances much more of their consumption.2Consistent with this point, we

find that the capital share is strongly positively related to the income

shares of those in the top 5% to 10% of the stock market wealth distribu-

tion, but negatively related to the income shares of those in the bottom

90%.

These observations suggest a different approach to explaining return premia

on risky assets. Recent inequality-based asset pricing models imply that the

capital share should be a priced risk factor when risk-sharing is imperfect

and wealth is concentrated in the hands of a few investors or “shareholders,”

while most households are “workers” who finance consumption primarily out

of wages and salaries (e.g., Greenwald, Lettau, and Ludvigson (2014, GLL)).

In these models, redistributive shocks that shift the share of income between

labor and capital are a source of systematic risk for asset owners. In the extreme

case in which workers own no risky asset shares and there is no risk-sharing

between workers and shareholders, a representative shareholder who owns the

entire corporate sector will have consumption in equilibrium equal to Ct·KS

t,

where Ctis aggregate (shareholder plus worker) consumption and KS

tis the

capital share of aggregate income.3The capital share is then a source of priced

risk.

1Source: 2013 Survey of Consumer Finances.

2In the 2013 SCF,the top 5% of the net worth distribution had a median wage-to-capital-income

ratio of 18%, where capital income is defined as the sum of income from dividends, capital gains,

pensions, net rents, trusts, royalties, and/or sole proprietorships or farms.

3This reasoning goes through as an approximation even if workers own a small fraction of

the corporate sector and even if there is some risk-sharing in the form of risk-free borrowing

and lending between workers and shareholders, as long as any risk-sharing across these groups

is imperfect.

Capital Share Risk in U.S. Asset Pricing 1755

0123

Capital Share Beta

1

1.5

2

2.5

3

3.5

4

Average Quarterly Return in %

Panel A. Size/BM, H = 8

S1B1

S1B2S1B3

S1B4

S1B5

S2B1

S2B2

S2B3

S2B4

S2B5

S3B1

S3B2S3B3

S3B4

S3B5

S4B1

S4B2

S4B3

S4B4

S4B5

S5B1

S5B2

S5B3

S5B4

S5B5

R2 = 0.80

0123

Capital Share Beta

1

1.5

2

2.5

3

Average Quarterly Return in %

Panel B. REV, H = 8

REV1

REV2

REV3

REV4

REV5

REV6

REV7

REV8

REV9

REV10

R2 = 0.86

–1 0123

Capital Share Beta

1

1.5

2

2.5

3

3.5

Average Quarterly Return in %

Panel C. Size/INV, H = 8

S1I1

S1I2S1I3

S1I4

S1I5

S2I1

S2I2

S2I3

S2I4

S2I5

S3I1

S3I2

S3I3

S3I4

S3I5

S4I1

S4I2

S4I3

S4I4

S4I5

S5I1

S5I2

S5I3

S5I4

S5I5

R2 = 0.62

012

Capital Share Beta

1

1.5

2

2.5

3

3.5

Average Quarterly Return in %

Panel D. Size/OP, H = 8

S1O1

S1O2

S1O3

S1O4

S1O5

S2O1

S2O2

S2O3

S2O4

S2O5

S3O1

S3O2

S3O3

S3O4

S3O5

S4O1

S4O2

S4O3

S4O4

S4O5

S5O1

S5O2

S5O3

S5O4

S5O5

R2 = 0.76

–10123

Capital Share Beta

1

1.5

2

2.5

3

3.5

4

Average Quarterly Return in %

Panel E. All Equities, H = 8

S1B1

S1B2S1B3

S1B4

S1B5

S2B1

S2B2

S2B3

S2B4

S2B5

S3B1

S3B2S3B3

S3B4

S3B5

S4B1

S4B2

S4B3

S4B4

S4B5

S5B1

S5B2

S5B3

S5B4

S5B5

REV1

REV2

REV3

REV4

REV5

REV6

REV7

REV8

REV9

REV10

S1I1

S1I2

S1I3

S1I4

S1I5

S2I1

S2I2

S2I3 S2I4

S2I5

S3I1

S3I2

S3I3

S3I4

S3I5

S4I1

S4I2

S4I3

S4I4

S4I5

S5I1

S5I2

S5I3

S5I4

S5I5

S1O1

S1O2

S1O3

S1O4

S1O5

S2O1

S2O2

S2O3

S2O4

S2O5

S3O1

S3O2

S3O3

S3O4

S3O5

S4O1

S4O2

S4O3

S4O4

S4O5

S5O1

S5O2

S5O3

S5O4

S5O5

R2 = 0.74

Figure 1. Capital share betas. This plot depicts betas constructed from Fama-MacBeth (1973)

regressions of average returns on capital share beta for different equity characteristic portfolios or

using all equity portfolios together (size/BM, REV,size/INV, and size/OP). Hindicates the horizon

in quarters over which capital share exposure is measured. The sample spans the period 1963Q3

to 2013Q4. (Color figure can be viewed at wileyonlinelibrary.com)

With this theoretical motivation as backdrop, in this paper we explore

whether growth in the capital share is a priced risk factor for explaining cross-

sections of expected asset returns. We find that an asset’s exposure to short-

to medium-frequency (i.e., four-to-eight quarter) fluctuations in capital share

growth has strong explanatory power for the cross-section of expected returns

on a range of equity characteristic portfolios as well as other asset classes.

For the equity portfolios and asset classes mentioned above, we find that pos-

itive exposure to capital share risk earns a positive risk premium, with risk

prices of similar magnitude across portfolio groups. A preview of the results

for equity characteristic portfolios is given in Figure 1, which plots observed

quarterly return premia (average excess returns) on each portfolio on the y-

axis against the portfolio capital share beta for exposures of H=8 quarters on

the x-axis. The estimates show that the model fit is high across a variety of eq-

uity portfolio styles. (We discuss this figure further below.) Pooled estimations

of the different stock portfolios considered jointly and of the stock portfolios

combined with the portfolios of other asset classes also indicate that capital

share risk has substantial explanatory power for expected returns. In princi-

ple, these findings could be consistent with the canonical representative agent

model if aggregate consumption growth were perfectly positively correlated