Borrowing Costs and the Demand for Equity over the Life Cycle

TLDR: The authors construct a life cycle model that delivers realistic behavior for both equity holdings and borrowing, where the key model ingredient is a wedge between the cost of borrowing and the risk-free investment return.

Abstract: We construct a life cycle model that delivers realistic behavior for both equity holdings and borrowing. The key model ingredient is a wedge between the cost of borrowing and the risk-free investment return. Borrowing can either raise or lower equity demand, depending on the cost of borrowing. A borrowing rate equal to the expected return on equity—which we show roughly matches the data—minimizes the demand for equity. Alternative models with no borrowing or limited borrowing at the risk-free rate cannot simultaneously fit empirical evidence on borrowing and equity holdings.

Figures

Figure 5: Average equity demand as a function of borrowing rate. Baseline parameter settings for a household from the pooled sample. [figb1]

Figure 6: Life-cycle equity holdings with and without labor income risks using pooled sample and baseline parameter settings.[figa6]

Table 5: Average Equity Demand and other Statistics, Alternative Specifications [tabx3]

Table 6: Equity Demand and other Statistics over the Life Cycle [tabx7]

Figure 4: Life-cycle liquid wealth at various borrowing rates. Baseline parameter settings for a household from the pooled sample and no labor income risk. [figa3]

Figure 3: Life-cycle borrowing at various borrowing rates. Baseline parameter settings for a household from the pooled sample and no labor income risk. [figa2]

Full text

NBER WORKING PAPER SERIES
BORROWING COSTS AND THE DEMAND FOR
EQUITY OVER THE LIFE CYCLE
Steven J. Davis
Felix Kubler
Paul Willen
Working Paper 9331
http://www.nber.org/papers/w9331
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
November 2002
We thank seminar participants at the 2002 Minnesota Macroeconomics Summer Institute, the 2002 NBER
Summer Institute, the 2002 NBER Economic Fluctuations Program Meeting in Chicago, Notre Dame
University and the University of Chicago for many helpful comments, Amir Yaron and Muhammet Guvenen
for thoughtful remarks, Jonathan Parker for providing parameters of the income processes in Gourinchas and
Parker (2002), Nick Souleles for directing us to data on charge-off rates for consumer loans and David
Arnold, Jeremy Nalewaik and Stephanie Curcuru for able research assistance. Davis and Willen gratefully
acknowledge research support from the Graduate School of Business at the University of Chicago. The views
expressed herein are those of the authors and not necessarily those of the National Bureau of Economic
Research.
© 2002 by Steven J. Davis, Felix Kubler, and Paul Willen. All rights reserved. Short sections of text, not
to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including ©
notice, is given to the source.

Borrowing Costs and the Demand for Equity Over the Life Cycle
Steven J. Davis, Felix Kubler, and Paul Willen
NBER Working Paper No. 9331
November 2002
JEL No. D91, G11, G12
ABSTRACT
We analyze consumption and portfolio behavior in a life-cycle model with realistic
borrowing costs and income processes. We show that even a small wedge between borrowing costs and
the risk-free return dramatically shrinks the demand for equity. When the cost of borrowing equals or
exceeds the expected return on equity – the relevant case according to the data – households hold little
or no equity during much of the life cycle. The model also implies that the correlation between
consumption growth and equity returns is low at all ages, and that risk aversion estimates based on the
standard excess return formulation of the consumption Euler Equation are greatly upward biased. The
demand for equity in the model is non-monotonic in borrowing costs and risk aversion, and the standard
deviation of marginal utility growth is an order of magnitude smaller than the Sharpe ratio.
Steven J. Davis Felix Kubler Paul Willen
Graduate School of Business Department of Economics Graduate School of Business
University of Chicago Stanford University University of Chicago
1101 East 58th Street Stanford, CA 94305-6010 1101 East 58th Street
Chicago, IL 60637 fkubler@stanford.edu Chicago, IL 60637
and NBER paul.willen@gsb.uchicago.edu
steve.davis@gsb.uchicago.edu

1 Introduction
This paper analyzes consumption and portfolio behavior in a life-cycle model with
borrowing costs that exceed the risk-free investment return. The agents have stan-
dard time-separable preferences with modest risk aversion and mild impatience, face
realistic income processes, and can invest in risky and risk-free assets.
We show that a wedge between borrowing costs and the risk-free return has several
important effects on consumption and portfolio behavior. First, even a modest wedge
dramatically shrinks the demand for equity throughout the life cycle. Second, when
the borrowing rate equals or exceeds the expected return on equity – the relevant
case according to the data – households hold little or no equity until middle age.
Third, the correlation between consumption growth and equity returns rises with
age, but it is low at all ages for reasonable parameter choices. Fourth, risk aversion
estimates based on the standard excess return formulation of the consumption Euler
Equation are greatly upward biased. The bias diminishes, but remains large, for
“samples” of households with positive equity holdings. Fifth, households borrow to
finance consumption but not to finance large equity positions. In each respect, the
introduction of a realistic wedge between borrowing costs and the risk-free return
greatly improves the fit between theory and empirical evidence.
Table 1 reports data on the size of the wedge. The bottom two rows show that
household borrowing costs on unsecured loans exceed the risk-free return by about six
to nine percentage points on an annual basis, after adjusting for tax considerations
and charge-offs for uncollected loan obligations. Since 1987, roughly two percentage
points arise from the asymmetric income tax treatment of household interest receipts
and payments. However, the bulk of the wedge arises from transactions costs in the
loan market. Despite the evident size of these transaction costs, they have been largely
ignored in theoretical analyses of life-cycle consumption and portfolio behavior. They
have also been ignored in most empirical studies of asset-pricing behavior.
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Aside from the wedge between borrowing costs and the risk-free return, our life-
cycle model is entirely standard. None of our results rely on strong risk aversion, a
high degree of impatience, habit formation, other types of nonseparability, self-control
problems or myopia. Nor do they rely on equity market participation costs, informa-
tional barriers, time-varying asset returns, enforcement problems in loan markets, or
hard borrowing limits (other than the lifetime budget constraint).
According to our analysis, the cost of borrowing and the shape of the expected
life-cycle income profile are key determinants of equity accumulation. The variance of
undiversifiable labor income shocks also has important effects on equity holdings, and
the risky nature of labor income is an important source of cross-sectional heterogeneity
in consumption and asset holdings conditional on age.
Our analysis also highlights several other results. First, equity holdings and mar-
ket participation rates are non-monotonic in the cost of borrowing, both reaching a
minimum where the borrowing cost equals the expected return on equity. As this
result suggests, the properties of our model are not “in between” those of the canon-
ical model with equal borrowing and lending rates and alternative models with hard
borrowing limits. Second, relative to a model with a no-borrowing constraint, house-
holds defer equity market participation when faced with realistic borrowing costs.
As a consequence, households accumulate less equity over the life cycle when faced
with realistic borrowing costs as compared to a no-borrowing constraint. Third, eq-
uity holdings and participation rates are non-monotonic in the degree of risk aversion
when borrowing costs exceed the risk-free return. Fourth, once we consider realistic
borrowing costs, neither sizable deviations from optimal portfolio shares nor delayed
participation in equity markets until, say, age 50 involves large welfare costs.
On the asset-pricing front, our analysis helps resolve two closely related aspects
of the equity premium puzzle: Why do people hold so little equity when faced with
a substantial equity premium? And, why is the covariance between consumption
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growth and asset returns so low? Answers to both question follow from the high
borrowing costs reported in Table 1. These data imply a small or negative “leverage”
premium on borrowed funds that are invested in the stock market. This fact, when
combined with upward sloping income profiles or mildly impatient consumers, means
that households accumulate little or no equity until middle age, and they can have
modest equity holdings even on the verge of retirement.
The paper proceeds as follows. The balance of the introduction discusses related
research and reviews some well-established facts about life-cycle consumption and
portfolio behavior. Sections 2 and 3 describe the model and the choice of parameters.
Section 4 discusses life-cycle portfolio choice and consumption in our model, and
section 5 compares model implications with empirical evidence. Section 6 offers some
concluding remarks, and an appendix describes our numerical solution method.
1.1 Relationship to the Literature
Our model departs modestly from the seminal work on life-cycle portfolio behavior by
Merton (1969) and Samuelson (1969). Indeed, our model is identical to Samuelson’s
discrete-time setup except for three elements: the wedge between borrowing costs and
risk-free returns, the presence of undiversifiable income shocks, and the use of realistic
income profiles. The wedge and the undiversifiable labor income shocks necessitate
a computational approach to the analysis, which we pursue using the same methods
as in Judd, Kubler and Schmedders (2002).
We also build on other research in finance and macroeconomics. Brennan (1971)
shows that a wedge between borrowing costs and risk-free returns is easily handled in
the standard one-period model of mean-variance portfolio choice. The wedge implies
that households cannot attain points above and to the right of the tangency portfolio
along the standard capital market line. Higher borrowing costs reduce the demand for
equity in the one-period setting, given standard mean-variance preferences. Heaton
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Frequently asked questions

Q1. What are the contributions in "Nber working paper series borrowing costs and the demand for equity over the life cycle" ?

The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. 

Q2. What have the authors stated for future works in "Nber working paper series borrowing costs and the demand for equity over the life cycle" ?

Their analysis points to several directions for future research. The authors plan to evaluate this richer version of the model against a number of facts about consumption, home ownership, wealth accumulation and portfolio choice over the life cycle. These implications can be tested using now-standard econometric methods applied to ( synthetic ) panel data on consumption and portfolio holdings.