# Financial markets and the real economy

FINANCIAL MARKETS AND THE REAL ECONOMY

John H. Cochrane

Working Paper 11193

http://www.nber.org/papers/w11193

NATIONAL BUREAU OF ECONOMIC RESEARCH

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Cambridge, MA 02138

March 2005

This review will introduce a volume by the same title in the Edward Elgar series “The International Library of Critical Writings in Financial Economics” edited by Richard Roll. I encourage comments. Please write promptly so I can include your comments in the final version. I gratefully acknowledge research support from the NSF in a grant administered by the NBER and from the CRSP. I thank Monika Piazzesi and Motohiro Yogo for comments. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.

© 2005 by John H. Cochrane. 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.

Financial Markets and the Real Economy

John H. Cochrane

NBER Working Paper No. 11193

March 2005, Revised September 2006

JEL No. G1, E3

ABSTRACT

I survey work on the intersection between macroeconomics and finance. The challenge is to find the right measure of "bad times," rises in the marginal value of wealth, so that we can understand high average returns or low prices as compensation for assets' tendency to pay off poorly in "bad times." I survey the literature, covering the time-series and cross-sectional facts, the equity premium, consumption-based models, general equilibrium models, and labor income/idiosyncratic risk approaches.

John H. Cochrane

Graduate School of Business

University of Chicago

5807 S. Woodlawn

Chicago, IL 60637

and NBER

john.cochrane@gsb.uchicago.edu

1

Introduction

Risk premia

Some assets oﬀer higher average returns than other assets, or, equivalently, they attract lower prices. These “risk premiums” should reﬂect aggregate, macroeconomic risks; they should reﬂect the tendency of assets to do badly in bad economic times. I survey research on the central question: what is the nature of macroeconomic risk that drives risk premia in asset markets?

The central idea of modern ﬁnance is that prices are generated by expected discounted payoﬀs,

pi = Et (mt+1 xi )

(1)

t

t+1

where xi is a random payoﬀ of a speciﬁc asset i, and mt+1 is a stochastic discount factor. t+1

Using the deﬁnition of covariance and the real riskfree rate Rf = 1/E(m), we can write the price as

Et (xi )

t+1

i

pt =

+ covt (mt+1 , xi ).

(2)

t+1

f

Rt

The ﬁrst term is the risk-neutral present value. The second term is the crucial discount for risk — a large negative covariance generates a low or “discounted” price. Applied to excess returns Rei (short or borrow one asset, invest in another), this statement becomes1 ei

ei

Et (Rt+1 ) = −covt (Rt+1 , mt+1 ).

(3)

The expected excess return or “risk premium” is higher for assets that have a large negative covariance with the discount factor.

The discount factor mt+1 is equal to growth in the marginal value of wealth, mt+1 =

1

VW (t + 1)

.

VW (t)

From (1), we have for gross returns R,

1 = E(mR)

e

i

j

and for a zero-cost excess return R = R − R .

0 = E(mRe ).

Using the deﬁnition of covariance, and 1 = E(m)Rf for a real risk-free rate, 0 = E(m)E(Re ) + cov(m, Re )

E(Re ) = −Rf cov(m, Re )

For small time intervals Rf ≈ 1 so we have

E(Re ) = −cov(m, Re ).

This equation holds exactly in continuous time.

1

This is a simple statement of an investor’s ﬁrst order conditions. The marginal value of wealth VW answers the question “how much happier would you be if you found a dollar on the street?” It measures “hunger” — marginal utility, not total utility. The discount factor is high at t + 1 if you desperately want more wealth at t + 1 — and would be willing to give up a lot of wealth in other dates or...

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