The Investment CAPM
| DOI | http://doi.org/10.1111/eufm.12129 |
| Author | Lu Zhang |
| 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
itþ1Pitþ1þDitþ1
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
½is the real interest rate, bM
it Cov rS
itþ1;Mtþ1
/Var Mtþ1
ðÞ
is the consumption beta, and lMt Var Mtþ1
ðÞ/EtMtþ1
½is 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, Ditþ1Xitþ1Kitþ1.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
To continue reading
Request your trial