The Investment CAPM

• DOI: http://doi.org/10.1111/eufm.12129
• Published date: 01 September 2017
• Date: 01 September 2017

The Investment CAPM

Lu Zhang

Fisher College of Business, The Ohio State University, 760A Fisher Hall, 2100 Neil Avenue, Columbus

OH 43210; and NBER

E-mail: zhanglu@fisher.osu.edu

Abstract

A new class of Capital Asset Pricing Models (CAPM) arises from the first principle

of real investment for individual firms. Conceptually as ‘causal’as the

consumption CAPM, yet empirically more tractable, the investment CAPM

emerges as a leading asset pricing paradigm. Firms do a good job in aligning

investment policies with costs of capital, and this alignment drives many empirical

patterns that are anomalous in the consumption CAPM. Most important,

integrating the anomalies literature in finance and accounting with neoclassical

economics, the investment CAPM has succeeded in mounting an efficient markets

counterrevolution to behavioural finance over the past 15 years.

Keywords: investment CAPM, consumption CAPM, CAPM, asset pricing anoma-

lies, efficient markets, behavioural finance, aggregation, general equilibrium, joint-

hypothesis problem

JEL classification: D53,E22,G12,G14,G31

1. Introduction

Consider a two-period stochastic general equilibrium model. The economy has three

defining features of neoclassical economics: (i) agents have rational expectations; (ii)

consumers maximise utility, and firms maximise their market value of equity; and (iii)

markets clear.

There are two dates, tand tþ1. The economy is populated by a representative

household and heterogeneous firms, indexed by i¼1, 2,...,N. The representative

household maximises its expected utility, UC

t

ðÞþrEtUC

tþ1

ðÞ½, in which ris the time

preference coefficient, and Ctand Ctþ1are consumption expenditures in tand tþ1,

respectively. Let Pit be the ex-dividend equity, and Dit the dividend of firm iat period t.

This article was prepared for my keynote speech at the European Financial Management

Symposium on ‘Finance and Real Economy’at Xiamen University, China, in April 2017. I

thank seminar participants at the symposium, Shanghai University of Finance and

Economics, as well as Hang Bai, Zhengyu Cao, John Doukas (Editor), Alex Edmans,

Andrei Goncalves, Kewei Hou, Stephen Penman, Andreas Stathopoulos and especially

Chen Xue for helpful comments.

European Financial Management, Vol. 23, No. 4, 2017, 545–603

doi: 10.1111/eufm.12129

© 2017 John Wiley & Sons, Ltd.

The first principle of consumption says that:

Pit ¼EtMtþ1Pitþ1þDitþ1

ðÞ½)EtMtþ1rS

itþ1



¼1;ð1Þ

in which rS

itþ1Pitþ1þDitþ1

ðÞ/Pit is firm i’s stock return, and Mtþ1

rU0Ctþ1

ðÞ/U0Ct

ðÞis the stochastic discount factor. Equation (1) can be rewritten

as:

EtrS

itþ1



rft ¼bM

it lMt;ð2Þ

in which rft 1/EtMtþ1

½is the real interest rate, bM

it Cov rS

itþ1;Mtþ1



/Var Mtþ1

ðÞ

is the consumption beta, and lMt Var Mtþ1

ðÞ/EtMtþ1

½is the price of the consumption

risk. Equation (2) is the consumption CAPM, first derived by Rubinstein (1976), Lucas

(1978) and Breeden (1979). The classic CAPM, due to Treynor (1962), Sharpe (1964),

Lintner (1965) and Mossin (1966), is a special case of the consumption CAPM

under quadratic utility or exponential utility with normally distributed returns

(Cochrane, 2005).

On the production side, firms produce a single commodity to be consumed or invested.

Firm istarts with the productive capital, Kit, operates in both dates, and exits at the end of

date tþ1 with a liquidation value of zero. The rate of capital depreciation is set to be

100%. Firms differ in capital, Kit, and profitability, Xit , both of which are known at the

beginning of date t. The operating profits are given by Pit XitKit . Firm i’s profitability

at date tþ1, Xitþ1, is stochastic, and is subject to aggregate shocks affecting all firms

simultaneously, and firm-specific shocks affecting only firm i. Let Iit be the investment

for date t, then Kitþ1¼Iit. Investment entails quadratic adjustment costs,

a/2ðÞIit/Kit

ðÞ

2Kit, in which a>0 is a constant parameter.

Firm iuses its operating profits at date tto pay inve stment and adjustment costs. If

the free cash flow, Dit XitKit Iit a/2

ðÞ

Iit/Kit

ðÞ

2Kit, is positive, the firm

distributes it back to the ho usehold. A negative Dit means externa l equity raised by

the firm from the household. At date tþ1, firm iuses capital, Kitþ1, to obtain

operating profits, which are in turn distributed as dividen ds, Ditþ1Xitþ1Kitþ1.With

only two dates, firm idoes not invest i n date tþ1, Iitþ1¼0, and the ex-dividend

equity value, Pitþ1, is zero.

Taking the household’s stochastic discount factor, Mtþ1, as given, firm ichooses Iit to

maximise the cum-dividend equity value at the beginning of date t:

Pit þDit ¼max

Iit

fg XitKit Iit a

2

Iit

Kit



2

Kit þEtMtþ1Xitþ1Kitþ1

½

"#

:ð3Þ

The first principle of investment for firm isays that:

1þaIit

Kit

¼EtMtþ1Xitþ1

½:ð4Þ

Intuitively, the marginal co sts of investment, consisting of the purchasing pric e (unity)

and the marginal adjustment co sts, aI

it/Kit

ðÞ, must equal marginal q, which is th e

© 2017 John Wiley & Sons, Ltd.

546 Lu Zhang

present value of the marginal ben efits of investment given by the marginal

product of capital, Xitþ1.

The first principle of investme nt can be rewritten without the sto chastic

discount factor, Mtþ1(Cochrane, 1991). Equation (3 ), when combined

with Dit XitKit Iit a/2ðÞIit /Kit

ðÞ

2Kit, implies tha t the ex-dividend equity value

at the optimum is:

Pit ¼EtMtþ1Xitþ1Kitþ1

½:ð5Þ

The stock return can then be rewritten as:

rS

itþ1¼Pitþ1þDitþ1

Pit

¼Xitþ1Kitþ1

EtMtþ1Xitþ1Kitþ1

½

¼Xitþ1

EtMtþ1Xitþ1

½

:ð6Þ

Combining equations (4) and (6) yields the investment CAPM:

rS

itþ1¼Xitþ1

1þaI

it/Kit

ðÞ

:ð7Þ

Intuitively, firm ikeeps investing until the date tmarginal costs of investment,

1þaI

it/Kit

ðÞ, equal the marginal benefits of investment at tþ1, Xitþ1, discounted to

date twith the stock return, rS

itþ1, as the discount rate. Equivalently, the ratio of the

marginal benefits of investment at tþ1 divided by the marginal costs of investment at

tequals the discount rate, rS

itþ1.

Most important, the investment CAPM, as asset pricing theory, gives rise to

cross-sectionally varying expected returns. The model predicts that, all else equal, high

investment stocks should earn lower expected returns than low investment stocks, and

that stocks with high expected profitability should earn higher expected returns than

stocks with low expected profitability. When expected returns vary cross- sectionally in

equilibrium, stock prices will adjust in a way that connects expected returns to

characteristics. Stock prices will not conform to a cross-sectionally constant discount

rate, meaning that characteristics do not predict returns. A cross-sectionally constant

discount rate is equivalent to saying that all stocks are equally risky.

The intuition behind the invest ment CAPM is just the net present value rul e in

capital budgeting, which is a f undamental principle in corporat e finance. Investment

predicts returns because given expected profitability, high cos ts of capital imply low

net present values of new capi tal and low investment, and low costs of capital imply

high net present values of new capital and high investment. Profitability predicts

returns because high expec ted profitability relative to low in vestment must imply high

discount rates. The high disc ount rates are necessary to offse t the high expected

profitability to induce low net present va lues of new capital and low investment . If the

discount rates were not high enough, firms would observe high net present values of

new capital and invest more. Conversely, low expected pr ofitability relative to high

investment must imply low dis count rates. If the discount rates were not low enough to

counteract the low expected profitability, firms would observe low net present values

of new capital and invest le ss.

© 2017 John Wiley & Sons, Ltd.

The Investment CAPM 547