The Investment CAPM

DOIhttp://doi.org/10.1111/eufm.12129
AuthorLu Zhang
Publication Date01 September 2017
Date01 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@sher.osu.edu
Abstract
A new class of Capital Asset Pricing Models (CAPM) arises from the rst principle
of real investment for individual rms. Conceptually as causalas 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 nance and accounting with neoclassical
economics, the investment CAPM has succeeded in mounting an efcient markets
counterrevolution to behavioural nance 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
dening features of neoclassical economics: (i) agents have rational expectations; (ii)
consumers maximise utility, and rms 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 rms, indexed by i¼1, 2,...,N. The representative
household maximises its expected utility, UC
t
ðÞþrEtUC
tþ1
ðÞ½, in which ris the time
preference coefcient, and Ctand Ctþ1are consumption expenditures in tand tþ1,
respectively. Let Pit be the ex-dividend equity, and Dit the dividend of rm iat period t.
This article was prepared for my keynote speech at the European Financial Management
Symposium on Finance and Real Economyat 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, 545603
doi: 10.1111/eufm.12129
© 2017 John Wiley & Sons, Ltd.
The rst principle of consumption says that:
Pit ¼EtMtþ1Pitþ1þDitþ1
ðÞ½)EtMtþ1rS
itþ1

¼1;ð1Þ
in which rS
itþ1Pitþ1þDitþ1
ðÞ/Pit is rm is 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, rst 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, rms 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 protability, Xit , both of which are known at the
beginning of date t. The operating prots are given by Pit XitKit . Firm is protability
at date tþ1, Xitþ1, is stochastic, and is subject to aggregate shocks affecting all rms
simultaneously, and rm-specic shocks affecting only rm 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 prots at date tto pay inve stment and adjustment costs. If
the free cash ow, Dit XitKit Iit a/2
ðÞ
Iit/Kit
ðÞ
2Kit, is positive, the rm
distributes it back to the ho usehold. A negative Dit means externa l equity raised by
the rm from the household. At date tþ1, rm iuses capital, Kitþ1, to obtain
operating prots, which are in turn distributed as dividen ds, Ditþ1Xitþ1Kitþ1.With
only two dates, rm idoes not invest i n date tþ1, Iitþ1¼0, and the ex-dividend
equity value, Pitþ1, is zero.
Taking the households stochastic discount factor, Mtþ1, as given, rm 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 rst principle of investment for rm 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 ets of investment given by the marginal
product of capital, Xitþ1.
The rst 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, rm ikeeps investing until the date tmarginal costs of investment,
1þaI
it/Kit
ðÞ, equal the marginal benets of investment at tþ1, Xitþ1, discounted to
date twith the stock return, rS
itþ1, as the discount rate. Equivalently, the ratio of the
marginal benets 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 protability should earn higher expected returns than
stocks with low expected protability. 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 nance. Investment
predicts returns because given expected protability, 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. Protability predicts
returns because high expec ted protability relative to low in vestment must imply high
discount rates. The high disc ount rates are necessary to offse t the high expected
protability to induce low net present va lues of new capital and low investment . If the
discount rates were not high enough, rms would observe high net present values of
new capital and invest more. Conversely, low expected pr otability relative to high
investment must imply low dis count rates. If the discount rates were not low enough to
counteract the low expected protability, rms would observe low net present values
of new capital and invest le ss.
© 2017 John Wiley & Sons, Ltd.
The Investment CAPM 547

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