Learning from Peers’Stock Prices and Corporate Investment
Laurent Frésard
University of Maryland
R.H. Smith School of Business
College Park, MD 20742
lfresard@rhsmith.umd.edu
Thierry Foucault
HEC, Paris
1 rue de la Liberation
78351 Jouy en Josas, France
foucault@hec.fr
July 2012
Abstract
There is a positive relationship between the investment of a …rm and the stock price of
its peers, de…ned as …rms selling related products. It is stronger when the level of informed
trading in a …rm’s stock is weak. Moreover, the link between the investment of a …rm and its
own stock price is weaker when the level of informed trading in its peers’ stocks is high, or
when the demand for its products is more correlated with the demand for its peers’products.
We show theoretically that these …ndings are expected when managers use peer stock prices
as a source of information but not otherwise. Overall, our results provide new insights on how
…nancial markets a¤ect the real economy.
JEL Classi…cation Numbers: G31, D21, D83
Keywords: Corporate investment, managerial learning, peers, informed trading
We thank Alexandre Jeanneret, Sebastien Michenaud, Nagpurnanand Prabhala, Philip Valta and seminar
participants at the University of Maryland for valuable discussions and suggestions. We also thank Jerry Hoberg
and Gordon Phillips for sharing their data with us.
1
Electronic copy available at: http://ssrn.com/abstract=2117150
1
Introduction
Security prices aggregate the private signals of a myriad of investors about …rms’ prospects
(e.g., Grossman (1976) and Hellwig (1980)) and, for this reason, convey information about the
implications of managers’decisions for …rm cash ‡ows. Does this information matter for …rms’
real decisions?
There are two opposite views on this long-standing question (see Morck, Shleifer and Vishny
(1990), Blanchard, Rhee, and Summers (1993), and Bond, Edmans, and Goldstein (2012) for a
survey). According to the …rst view, the …nancial market is just a “side show”: Security prices
re‡ect the consequences of managers’decisions for …rms’cash ‡ows but do not in‡uence them. In
this case, trading in secondary markets has no direct impact on …rms’decisions. The second view
(the “active informant hypothesis”) gives a more active role to security prices:1 They in‡uence
managers’ real decisions because some investors trade on private information not available to
managers, who therefore rely on stock prices a source of information.2
Evidence supporting the active informant hypothesis have been provided in recent research
(e.g., Durnev, Morck and Yeung (2004), Luo (2005), Chen, Goldstein, and Jiang (2007), Bakke
and Whited (2010), or Foucault and Fresard (2012)). Empirical tests in this literature typically
relate a …rm investment to its own stock price and the informativeness of this price. In this paper,
we push the logic underlying these tests one step further by studying whether managers also learn
information from the stock prices of their “peers”, that is, …rms selling related products.
A …rm and its peers are, by de…nition, exposed to common demand shocks for their products
(in addition to …rms’idiosyncratic shocks). The joint observation of a …rm’s stock price and the
stock prices of its peers should be a more precise signal about the future realizations of these
shocks than the …rm’s stock price alone (in any case, this cannot be a less precise signal).3 Hence,
1
The expression “Active Informant Hypothesis” has been coined by Morck, Shleifer and Vishny (1990). They
write (on page 164): “The active informant hypothesis [...] says that stock prices predicts investment because they
convey to managers information useful in making investment decisions.”
2
Bresnahan, Milgrom and Paul (1992), Dow and Gorton (1997), Subrahmanyam and Titman (1999), Goldstein
and Guëmbel (2007), Foucault and Gehrig (2008), Dow, Güembel and Goldstein (2011), among others, analyze
theoretical implications of this hypothesis. As shown by some of these models (e.g., Dow and Gorton (1997)),
informational e¢ ciency does not necessarily translate into more e¢ cient investment decisions (see Bond, Edmans,
and Goldstein (2012) for an in-depth discussion of this point).
3
This is the case, for instance, if the stock price of a …rm only incorporates with delay the information contained
2
Electronic copy available at: http://ssrn.com/abstract=2117150
if managers rely on the stock market as a source of information, they should rely both on their
own stock price and the stock price of their peers in making their decisions. In this case, one
expects a …rm’s investment to co-vary positively with its own stock price as well as with the stock
price of its peers.
However, evidence of such co-variation is not a su¢ cient test of the active informant hypothesis. Indeed, investment and stock prices can co-vary simply because managers’information and
investors’signals re‡ected into stock prices are correlated (henceforth, the “correlated information channel”). To isolate predictions speci…c to the active informant channel, we rely on a simple
model of corporate investment and stock price formation. In this model, a …rm sells a product
for which demand is uncertain and correlated with the demand for another …rm’s product (its
peer). The …rm manager must decide to expand production capacity or not. Expansion is a
positive net present value project only if future demand for the …rm’s product (about which the
manager is imperfectly informed) is strong enough. As investors trade on private information
about future demand, the …rm’s stock price and the stock price of a peer …rm are informative
about this demand. We compare the relation between the …rm’s investment and each stock price
in three di¤erent scenarios: (i) the manager uses the information contained in both stock prices;
(ii) the manager only relies on his own stock price (“narrow managerial learning”); and (iii) the
manager ignores stock market information (“no managerial learning”).
We obtain …ve predictions that uniquely arise when managers learn information from their
stock price and the prices of their peers. These predictions are based on a similar mechanism:
When a decision-maker learns information from multiple signals, his decision becomes less sensitive to one speci…c signal when other signals become relatively more informative. Accordingly
the sensitivity of a …rm’s investment to its peer stock price is inversely related to (i) the level of
informed trading in its own stock price and (ii) the precision of “managerial information” (i.e.,
information used by managers for their investment decisions unknown to investors). Symmetrically, the sensitivity of a …rm’s investment to its own stock price decreases when its peers’stock
in related …rms’ stock prices, as found in Cohen and Frazzini (2008) or Hou (2007), or if a …rm’s decision (e.g.
to enter or invest into a new product space) is still unknown to investors so that its stock price cannot contain
information about future demand for this new product.
3
price becomes more informative, that is, when the level of informed trading in its peers’ stock
market increases. Furthermore, the e¤ect of an increase in the precision of managerial information on this sensitivity is negative if the level of informed trading in the peer stock market is low
enough, and positive otherwise. Last, the sensitivity of a …rm’s investment to its own stock price
is weakly increasing in the correlation between the demands for its product and the product of
its peer.
None of these predictions are obtained if managers ignores stock market information or if
they rely only on their own stock price. Hence, we focus on these unique predictions to test the
hypothesis that managers use information from their own stock price and their peer stock prices
to make investment decisions. To this end, we use a large sample of …rms drawn from Compustat
over the period 1997 to 2008. In order to de…ne the peers of a given …rm, we use the Text-based
Network Industry Classi…cation (TNIC) developed by Hoberg and Phillips (2010), which is based
on the similarity of …rms’products description (from their annual 10Ks).
We …rst show that …rms’investment is positively and signi…cantly related to the stock price
of their peers after controlling for their own stock price and other characteristics. The economic
magnitude of this correlation is substantial: A one standard deviation increase in peer stock
prices is associated with a 5.6% increase in corporate investment, about 14.5% of the sample
average. The sensitivity of a …rm investment to its peer stock prices is about half the sensitivity
to its own stock price (a one standard deviation increase in a …rm’s stock price is associated with
a 12.80% increase in its investment in our sample).
One bene…t of the TNIC is that the set of peers for a given …rm changes over time as …rms
modify their product range, innovate, or enter new product markets. We document that the
sensitivity of a …rm’s investment to a peer stock price disappears once the …rm and its peer
stop operating in the same product space. Furthermore, the investment of a …rm turns out to be
sensitive to a peer stock price before the two …rms start operating in the same product space. This
…nding suggests that managers may decide to launch a new product after learning information
about its expected pro…tability from the stock prices of …rms already selling related products.
In a second step, we concentrate on the cross-sectional implications of our model that uniquely
4
arise if managers managers use information from their stock price and the stock prices of peers.
Overall we …nd support for this claim. First, using various proxies for the level of informed trading
in a stock, we …nd that a …rm’s investment is less sensitive to the stock price of its peers when the
level of informed trading in its own stock price is high.4 The economic magnitude of this e¤ect
is large. For instance, a one standard deviation increase in peer stock price is associated with
a 1.68% increase in a …rm’s investment when its own stock price is highly informative against a
7.30% increase when its stock price is uninformative. Symmetrically, a …rm’s investment is less
sensitive to its own stock price when its peer stock prices are more informative.
We also study the e¤ect of managerial information on investment-to-price sensitivities, using
the trading activity of the main insiders of the …rm (its top …ve executives) as a proxy for
managerial information. The investment of a …rm is more sensitive to its peer stock prices when its
managers appear less informed. In addition, the sensitivity of a …rm’s investment to its own stock
price is not signi…cantly related to the amount of managerial information, on average (as found in
Chen, Goldstein, and Jiang (2007)). Yet, consistent with our hypothesis, this unconditional e¤ect
depends on level of informed trading in peer stock markets. In particular, when peer stock prices
are not very informative, an increase in the amount of managerial information has a negative
e¤ect on the sensitivity of a …rm’s investment to its stock price. This e¤ect is reversed when peer
stock prices are highly informative.
We also …nd that the sensitivity of a …rm’s investment to its own stock price increases when its
product becomes less similar to that of its peer (they share fewer common words in the description
of their products or their sales are less correlated). In contrast, the sensitivity of its investment
to the stock price of its peers increases when the …rm is more similar to its peers or when its sales
are more correlated with those of its peers. Again these …ndings are consistent with the active
informant channel.
Our paper is related to several strands of research. First, it contributes to the literature on
4
We use three di¤erent proxies for the level of informed trading in a stock: (i) a measure of a …rms speci…c
return variation (as in Durnev, Morck and Yeung (2004), Chen, Goldstein and Jiang (2007), and Bakke and Whited
(2010)), (ii) a measure of the likelihood of informed trading in a given trade, P IN (Easley, Kiefer, and O’Hara
(1996)) and (iii) a measure based on the autocorrelation of returns (developed by Llorente, Michaely, Saar, and
Wang (2002)).
5
the real e¤ects of equity markets (see Bond, Edmans, and Goldstein (2012) for a survey). Several
empirical papers have shown that the information contained in a …rm’s stock price a¤ects its
real decisions in various ways.5 Our paper, however, is …rst to show that there is a link between
a …rm’s investment and the stock price of its peers. This link has far reaching implications as
it provides a source of learning externalities that could greatly magnify the e¤ect of the stock
market on the real economy. For instance, the prospect of learning from other stock prices could
induce …rms to cluster on similar investment projects and decrease product di¤erentiation. Also,
the informational e¢ ciency of the stock market can in‡uence the behavior private …rms’decisions
(e.g. stay private vs go public), as managers of privately held …rms can also glean information
from the stock prices of their public peers.
Second, our evidence add to the empirical literature showing the importance of peers in …rms’
decision making (e.g., Gilbert and Lieberman (1987) or Leary and Roberts (2011)). Our goal
is not to identify “peer e¤ects”, that is, the direct e¤ect of a …rm’s decision on its peers and
vice versa.6 However, our results con…rm that peers matter in shaping investment behavior.
While Fracassi (2012) and Dougal, Parsons, and Titman (2012) recently document that a …rm’s
investment is related to that of other …rms through social connections and geograohic proximity,
our results suggest that investment decisions are correlated across peers also because managers
can learn from each other stock prices.
According to the active informant channel, variations in stock prices have a causal e¤ect
on corporate investment because managers learn from the stock market. We do not claim to
have identi…ed such a causal e¤ect. This is very challenging since stock price variations are
endogenous and can be related to investment through various, non mutually exclusive, channels.
As in related studies, our approach is to show that cross-sectional variations in the sensitivity
of a …rm investment to its stock price and to the stock price of its peers are consistent with
implications of the active informant channel. In this respect, focusing on peer …rms is helpful for
5
See for instance Durnev, Morck and Yeung (2004), Luo (2005), Chen, Goldstein, and Jiang (2007), Fang, Noe
and Tice (2009), Bakke and Whited (2010), Ferreira, Ferreira, and Raposo (2011), Edmans, Goldstein and Jiang
(2012).
6
In the context of our paper, a peer e¤ ect (in the econometrics sense; see Manski (1993)) would be the tendency
of a …rm’s investment to directly a¤ect the investment of its peers and vice-versa. We discuss this point in more
details in Section 3.
6
two reasons. First, as shown by our model, the active informant channel has unique cross-sectional
predictions regarding the e¤ect of peer (respectively a …rm) stock prices informativeness on the
sensitivity of a …rm investment to its own stock price (respectively peer stock prices). Second,
previous research indicates that a positive correlation between a …rm investment and its stock
price may arise because of mispricings and …nancial constraints, as the overvaluation of a stock
could spur investment by relaxing …nancial constraints (Baker, Wurgler and Stein (2003), or
Graham and Campello (2011)). Yet, there is little reason to believe that such a channel can
explain the relation between a …rm investment and the stock price of its peers.
The paper is organized as follows. In the next section, we derive our main testable implications
using a simple model of investment in which managers learn information from their stock price,
the stock prices of their peers, and other sources. In Section 3 we describe the data and discuss
the methodology. In Section 4 we present the empirical …ndings and in Section 5 we conclude.
Proofs are collected in an appendix at the end of the paper. An Internet Appendix provides
additional theoretical and empirical results.
2
2.1
Hypotheses Development
Model
We consider two …rms A and B operating in related product markets.7 The timing of the model
is described in Figure 1.
[Insert Figure 1 about here]
At date 1, the stock market opens and investors can trade shares of …rms A and B. At date
2, …rm A has the option to expand its production capacity. Capacity expansion requires to make
an irreversible investment K at date 2 before demand for …rms As’and Bs’products are known.
At date 3, the demand for the products of each …rms and their cash ‡ows are observed. We now
describe the actions of the participants at each stage and their payo¤s in more details.
7
Note that …rms A and B can be, but do not need to be competing …rms. The demand for the product of two
…rms can be correlated because of vertical relationships or product complementarity. For instance, if the demand
for computer hardware is strong, the demand for softwares is likely to be strong as well.
7
Firms’cash ‡ows. At date 3, the demand dj for the product of …rm j can be High (H) or
Low (L) with equal probabilities. The state of the demand for the product of a …rm determines
H
B
whether its cash ‡ow is high or low. Speci…cally, the cash ‡ow of …rm B at date 3 is
demand for its product is high and
L
B
(<
H
B)
if the
otherwise.
At date 2, …rm A has the option to expand capacity. Expansion costs K and generates an
uncertain cash ‡ow. The net present value of …rm A’s investment decision at date 2 is:
A
The cash ‡ow of …rm A is
=
H
A+
8
>
>
>
>
>
<
>
>
>
>
>
:
I (
K (> 0) if dA = H;
(1)
K
if dA = L:
K) if the demand for its product is high and
L
A
I K
if the demand for its product is low, where I is a variable equals to 1 if …rm A invests (“expands
capacity”) at date 2 and zero otherwise.8
As …rms A and B sell related products, we assume that the demand for their product share
a common factor. Speci…cally:
Pr(dA = H jdB = H ) = Pr(dB = H jdA = H ) =
1
> .
2
(2)
That is, the demand for the product of one …rm is more likely to be high if the demand for the
product of the other …rm is also high. As we shall see below, this correlation implies that the
manager of …rm A can learn about the strength of the demand for its product from the stock
price of …rm B.
The manager of …rm A. The manager of …rm A has two sources of information when
he makes his investment decision at date 2: (i) he observes stock prices realized at date 1 and
(ii), with probability , he privately observes a perfect signal smA 2 fH; Lg on the demand for
its product at date 3. We refer to this signal as “direct managerial information” and
8
is the
For simplicity, we assume that the incremental production capacity is worthless if demand is low. The idea
is that in this case the existing capacity of the …rm is su¢ cient to serve all consumers at market prices. It is
straigtforward to extend the model to the more general case in which the investment generates a cash-‡ow even
when demand is low. The important point is that expanding capacity has a negative NPV in this case.
8
precision of direct managerial information. If he does not receive direct managerial information,
the only source of information for the manager is the stock market.
For a given investment decision, I, the expected value of …rm A at date 2 is:
VA (I) = E(
A jsmA ; pA ; pB )
+I
where pj is the stock price of …rm j at date 1 and
E(
A
A jsmA ; pA ; pB );
(3)
the cash ‡ow of …rm A at date 3 that is
independent from the investment decision. The manager of …rm A makes his investment decision
to maximize …rm value and the …rm faces no …nancing constraints.
We assume that in the absence of any information, the expected NPV of capacity expansion
is negative. That is:
A.1 : E(
where RH =
K.
A)
= K(
RH
2
1)
0,
(4)
Hence, if the manager had no information, he would never invest at date 2.
Moreover, for the moment, we assume that the correlation in the demands of both …rms is high
enough, so that if the manager of …rm A learns that the demand for the product of …rm B is
high then he invests. That is:
A.2: E(
or
>
1
RH .
A jdB
= H ) = K( RH
1) > 0;
(5)
We relax this assumption in Section 2.4.
The Stock Market. At date 1, investors can trade the stock of each …rm. There are three
types of investors in the stock market: (i) a continuum of risk-neutral speculators, (ii) liquidity
traders with an aggregate demand, zj , for …rm j, and (iii) risk neutral dealers. Liquidity traders’
aggregate demand is uniformly distributed over [ 1; 1].
A fraction
j
of speculators receive a perfect signal sbj 2 fH; Lg on the state of demand for
the product of …rm j 2 fA; Bg. After receiving her information on stock j, a speculator decides
to buy or to sell one share of this stock, or to stay put. We denote by xij (b
sj ) 2 f 1; 0; +1g
the size of the order submitted by speculator i when she has received signal sbj . For tractability,
9
we assume that a speculator only trades the stock for which she has acquired information. This
assumption simpli…es the analysis and it is indeed optimal for speculators to only trade a stock
in which they have information if there is a …xed cost of trading per asset or if
is not too high
(see Section A.5 in the Internet Appendix).9
Let fj be the sum of speculators and liquidity traders’net demand for stock j:
fj = zj +
Z
1
xij (b
sj )di
(6)
0
This net demand is absorbed by dealers in stock j at a price such that they just break even (as
in Kyle (1985) or Glosten and Milgrom (1985)) given the information contained in investors’net
demand. Thus, stock prices for each …rm are given by
pA (fA ) = E(VA (I) j fA ),
(7)
and
pB (fB ) = E(
where
2.2
B
B
j fB ),
(8)
is the cash ‡ow of …rm B at date 3.
Investment decisions and stock prices
We now solve for equilibrium prices at date 1 and the manager’s optimal investment decision at
date 2. Our main interest is to understand how this decision depends on stock prices realized at
date 1. We …rst consider the equilibrium of the stock market for …rm B. Let
B
=E(
B)
be the
mean cash ‡ow of stock B, which can be seen as the price of stock B at date 0, before trading
occurs.
Lemma 1 : The stock market equilibrium for …rm B is as follows:
1. A speculator: (i) buys when she knows that demand for …rm B’s product is high (xiB (H) =
9
In the Internet Appendix (Section A.4), we also endogenize the fraction of speculators in each stock by assuming
that speculators must pay a cost c to receive a signal. Variations in j across stocks are then driven by variations
in the cost of information, c, and the volatility of …rm cash ‡ows.
10
+1) and (ii) sells when she knows that demand for …rm B’s product is low (xiB (L) =
1).
2. The stock price of …rm B is an increasing step function of investors’ net demand for this
stock:
pB (fB ) =
8
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
:
H
B
B
when fB > 1
when
L
B
1+
B
when fB <
B;
fB
1
1+
B:
B;
The stock price of …rm B at date 1 depends on investors’ net demand for the stock (fB )
because this demand re‡ects speculators’orders, which are informative. If investors’net demand
is relatively strong (fB
1
B ),
dealers infer that speculators have received a good signal
to
H
B.
If
about the demand for …rm B’s product and the price of stock B increases from
B
instead, investors’ net demand for stock B is su¢ ciently low (fB
dealers infer
1+
B ),
that speculators have received a bad signal and the price of stock B decreases. Intermediate
realizations for investors’net demand are not informative and therefore do not a¤ect the price of
stock B.
Thus, if
B
> 0, the price of stock B is a source of information for the manager of …rm A, in
addition to his private managerial information and the information that the manager can obtain
from the stock price of his …rm. To see this more formally, let rB = pB E(
B)
be the change in
the price of stock B from date t = 0 to date t = 1. It is immediate from Lemma 1 that:
Pr(rB
Pr(rB
As
>
1
2,
0 jdA = H )
+ (1
=
0 jdA = H )
(1
)(1
B ) + (1
B)
)
=
1
(1
1
)
B
.
(9)
B
this likelihood ratio is strictly greater than 1 and increases in
B.
That is, as
B
increases, a high stock price for B at date t = 1 is more likely to occur when the demand for the
product of …rm A is high than a low stock price (and vice versa when the demand for …rm A
is low). In other words, the stock price of …rm B is informative about the demand for …rm A’s
product and even more so when
B
increases.
11
Hence, the optimal investment decision of the manager of …rm A at date 2, I (smA , pA , pB ),
should depend on his managerial information, the stock price of his …rm, and the stock price of
his peer …rm, i.e., B at date 1. It solves
I (smj ; pA ; pB ) 2 ArgmaxI2f0;1g VA (I);
(10)
where VA (I) is given in (3).
The stock price of …rm A depends on the manager’s investment decision, which itself depends
on the stock price of …rm A. In equilibrium, speculators and dealers in stock A take this feedback
into account. Formally, a stock market equilibrium for …rm A is a set fxA ( ),pA ( ); I ( ))g such
that (i) the trading strategy xA ( ) maximizes the expected pro…t for each speculator, (ii) the
investment policy I ( ) maximizes the expected value of …rm A at date 2 (solves (10)), and (iii)
the pricing rule pA ( ) solves (7) given that speculators use the trading strategy xA ( ), and the
manager of …rm A follows the investment policy I ( ).
Let
A
=E(
A ),
pH
A =
H
A
+(
K), pM
A =
A
+
1
2
( + (1
)
K), and pL
A =
B) (
L
A.
M
L
Note that pH
A > pA > pA . We obtain the following result.
Proposition 1 : There is a stock market equilibrium for …rm A in which:
1. A speculator: (i) buys when she knows that demand for …rm A’s product is high (xiA (H) =
+1) and (ii) sells when she knows that demand for …rm A’s product is low (xiA (L) =
1).
2. The stock price of …rm A is an increasing step function of investors’ net demand for this
stock:
8
>
>
pH
>
A
>
>
>
>
>
>
>
>
>
<
pA (fA ) =
pM
A
>
>
>
>
>
>
>
>
>
>
>
>
: pL
A
when fA > 1
when
1+
A
when fA <
12
A
fA
1
1+
A
A
3. The optimal investment policy for the manager of …rm A is as follows:
I (smA ; pA ; pB ) =
8
>
>
1
>
>
>
>
>
>
>
>
>
>
>
>
>
>
0
>
>
>
>
>
>
>
>
>
>
<
if smA = H, 8pA , 8pB
if smA = L, 8pA , 8pB
:
1
if smA = ? and pA = pH
A , 8pB
>
>
>
>
>
>
>
>
>
>
>
>
H
>
1 if smA = ?, pM
pA < pH
>
A
A and pB = pB
>
>
>
>
>
>
>
>
>
>
>
>
: 0
H
if smA = ?, pA < pH
A and pB < pB
(11)
Investors’ net demand for stock A, fA , a¤ects its stock price because this demand is informative about the future demand for …rm A’s product, as previously explained for stock B.
Moreover, as the level of informed trading (
A)
in stock A increases, investors’demand for this
stock becomes more informative. Hence, the stock price of …rm A also contains information for
the manager of this …rm and its informativeness increases with
A.
The last part of the proposition (equation (11)) is the most important for our purpose. It
shows that in equilibrium the investment decision of the manager of …rm A depends on its own
stock price and the stock price …rm B.10 In particular, when the manager has received no
managerial information (smA = ?), his investment decision is in‡uenced by (i.e., contingent on)
its stock price and the stock price of …rm B. To analyze this point further, let pA0 be the stock
price of …rm A before trading at date 1. Using equation (7) and Proposition 1, we obtain:
pA0 = E(E(VA (I) j fA )) = E(pA (fA )) =
A
+
10
1
(
2
K) ( + (1
)(
A
+
B )).
(12)
Equation (11) speci…es the manager’s optimal decision for all possible prices for stocks A and B, even those that
cannot be observed in equilibrium (prices that are out of the equilibrium path). For these prices, the manager’s
beliefs regarding future demand cannot be computed by Bayes law. We choose these beliefs so that they are
identical to those that the manager would have if he could directly observe investors’ demand in each stock (see
the proof of the proposition). In this way the equilibrium described in Proposition 1 is identical to the equilibrium
that would be obtained if the manager could observe investors’demand (fA and fB ).
13
L
Thus, the value of …rm A at date 0 (before trading) is higher than pM
A and pA . Now suppose that
at date 1, investors’demand in stock A is moderate so that pA = pM
A . In this case, the change in
the price of stock A (from date 0 to date 1) is moderately negative. Despite this drop in his stock
price, the manager will choose to invest if the price of stock B increases during the same period,
as shown by equation (11). The reason is that, as noticed previously, the stock price of …rm B
is informative about the cash ‡ows for …rm A since the cash ‡ows of …rm A and B are exposed
to correlated demand shocks. Hence, a high stock price for …rm B is a good signal about future
demand for the product sold by …rm A, that compensates the bad signal sent by a low price of
stock A (because
2.3
is assumed high enough; see assumption A.2).
Empirical implications
If managers learn information from their own stock price and the stock price of their peers, their
investment should be positively correlated with these stock prices. This correlation, however,
can arise even in the absence of managerial learning from stock prices, simply because managers’
signals (smA in our model) are correlated with informed investors’ information. Hence, the
existence of a correlation between a …rm’s investment and stock prices is a pre-requisite but
is per se insu¢ cient to establish that managers use information from stock prices in making
their real decision. To isolate predictions that only arise when managers learn from peers’prices
we study three di¤erent scenarios: (i) managers ignore stock market information; (ii) managers
learn solely from their own stock price; and (iii) managers learn from their stock price and that
of their peers. The reader can refer to Table 5 in Section 4.3 (where we test the cross-sectional
implications of the model) for a synoptic view of the predictions derived below.
2.3.1
No managerial learning
We …rst consider the benchmark case in which managers ignore the information contained in stock
prices, either because managers are fully informed ( = 1), or because managers fail to realize that
stock prices contain information. The second case (the “inattentive managers scenario”) is more
general since it encompasses the …rst as a special case when
14
= 1. Furthermore, by considering
the inattentive managers’ scenario, we can contrast the e¤ect of an increase in the precision of
managerial information ( ) when there is no managerial learning and when there is. Hence, as a
benchmark, we characterize the co-variation between investment and stock prices when managers
are inattentive, i.e. when they ignore the information contained in stock prices even though …rm
value would be higher if they accounted for this information.11 Let
j
=
H
j
L
j
=2.12
Corollary 1 (benchmark 1: no managerial learning) In the absence of managerial learning, the
covariance between the price of stock B and the investment of …rm A is positive and equal to:
cov(KI ; pB ) = [
B (2
1)]
B
K
2
0:
(13)
Hence, this covariance increases with (i) the precision of managerial information ( ), (ii) the
fraction of informed speculators in stock B (
B ),
and (iii) the correlation in the demands for the
products of …rms A and B ( ). Moreover the covariance between the price of stock A and the
investment of …rm A is also positive and equal to:
cov(KI ; pA ) =
A( A
+
2
(
K))
K
2
0:
(14)
Hence, this covariance increases with (i) the precision of managerial information ( ), (ii) the
fraction of informed speculators in stock A (
informed speculators in …rm B(
A ),
and (iii) is independent of the fraction of
B ).
Thus, even in the absence of managerial learning, the investment of a …rm should be positively
correlated with its peers’ stock price and its own stock price. We refer to this channel as the
“correlated information” channel. When investment and stock prices are related only through
this channel, cov(KI ; pj ) increases with
because the correlation between speculators’and the
11
As the manager of …rm A ignores the information in stock prices, he never invests (Assumption A.1). Hence,
the value of the …rm in this case is A , which is less than the value of the …rm when the manager optimally uses
the information from stock prices (see Equation (12)).
12
In the absence of managerial learning, the stock price of …rm B at date 1 is unchanged. The stock price of
…rm A is di¤erent because this price depends on the investment policy followed by the manager at date 2, which
depends on whether the manager of …rm A relies or not on stock prices as a source of information. We account for
this in deriving Corollary 1.
15
manager’s signals becomes stronger.
2.3.2
Narrow managerial learning
Another possibility is that the manager uses his stock price as a source of information, but ignores
that of his peers. This scenario (“narrow managerial learning”) is another useful benchmark to
better understand the predictions that are unique to our hypothesis that managers also learn
from their peer stock prices.
Corollary 2 (benchmark 2: narrow managerial learning). When the manager of …rm A only
uses the information contained in the price of his stock, the covariance between the price of stock
B and the investment of …rm A is positive and equal to:
cov(KI ; pB ) = [( + (1
)
A )(2
1)
B]
B
K
2
0:
(15)
Hence, it increases with the fraction of informed speculators in …rm A and the e¤ ects of the other
parameters ( ,
B
and ) are as in Corollary 1. Moreover the covariance between the price of
stock A and the investment of …rm A is also positive and equal to:
2
6
cov(KI ; pA ) = 6
4
|
A( A
+ (
{z2
K)) + A (1
} |
Correlated information
)(
A
+(
K
2{z
)((2
(1
Managerial learning from stock A
)
3
7K
7 :
} 2
A ))5
(16)
Hence, it decreases with the precision of managerial information ( ) while the e¤ ects of the other
parameters ( ,
A
and ) are as in Corollary 1.
With narrow managerial learning, the manager obtains an informative signal (either directly
or from the stock market) with probability
future demand when either
or
A
+ (1
)
A.
Hence, he is better informed about
increases. In either case, his decision (investment) becomes
more correlated with the actual state of demand for …rm B and therefore with its peer stock price.
In any case, the model implies that a change in the level of informed trading in a …rm’s stock
(here
A)
should a¤ect the sensitivity of its investment to its peer stock price when managers
16
learn information from stock prices (in a narrow sense as here or in a broader sense as in Corollary
3). This is not the case in the absence of managerial learning.
With narrow managerial learning, the covariance between the investment of …rm A and its
stock price is higher than in the absence of managerial learning because a high stock price for A
induces the manager to invest when he has no information. This e¤ect is captured by the second
component in the expression for cov(KI ; pA ). This component decreases with : the manager
puts less weight on the signal conveyed by his stock price when direct managerial information is
more precise. As a result, the net e¤ect of an increase the precision of managerial information on
the covariance between the investment of …rm A and its stock price is now negative. The opposite
prediction holds in the absence of managerial learning (Corollary 1).
2.3.3
Learning from peers’stock prices
Now, we turn to the more general case in which both the stock price of …rm A and the stock price
of …rm B in‡uence the investment decision of the manager of …rm A, as described in Proposition
1.
Corollary 3 In equilibrium, for
>
1
RH
> 12 , the covariance between the investment of …rm A
and the stock price of …rm B is positive and equal to:
0
B
cov(KI ; pB ) = @( + (1
|
)
A )(2
{z
1)
Correlated information
B
}
+
(1
|
)
B (1
{z
1
A)
}
Managerial learning from stocks A and B
This covariance increases in the fraction of informed speculators in stock B (
C
A
B ).
BK
2
Moreover, it
decreases in (i) the likelihood that the manager of …rm A receives managerial information,
(ii) the fraction of informed speculators in stock A (
A)
if
. (17)
and
< 1.
Equation (17) splits the co-variation between the investment of …rm A and the stock price of
…rm B in two components. The …rst component is the contribution of the correlated information
channel: this contribution is just equal to the covariance between the investment of …rm A and
the price of its peer with narrow managerial learning. The second component is the incremental
17
contribution of the active informant channel. It is positive because an increase in the stock price
of …rm B conveys a positive signal about future demand for …rm A’s product and can thereby
induce the manager of …rm A to scale up capacity at date 2.
When the manager learns from his peer stock price and his own stock price, the covariance
between the price of stock B and the investment of …rm A decreases with the fraction of informed speculators in …rm A,
A
and the precision of direct managerial information. The same
mechanism is at work in both cases. The manager has three sources of information: (i) direct
managerial information, (ii) his stock price, (iii) the stock price of its peer. As
or
A
increase,
the informativeness of the two …rst sources of information becomes relatively higher relative to the
third. Hence, the manager relies relatively less on the third source of information and as a result
its investment becomes less correlated with the stock price of …rm B. This substitution e¤ect
does not arise when the manager ignores the information contained in stock prices (benchmark
1) or when he only uses the information contained in his own stock price (benchmark 2).
Corollary 4 For
>
1
RH
>
1
2
(assumptions A.1 and A.2), the covariance between the investment
of …rm A and the stock price of …rm A is given by:
0
B
B
B
B
B
cov(KI ; pA ) = B
B
B
B
B
@
|
|
A (1
)(
A
+(
A( A
K))
}
Correlated information
+
K
2
+ (
{z2
1
)((2
B
(1
)(
{z
A (1
Managerial learning from stocks A and B
C
C
C
C
CK
C . (18)
C 2
C
C
C
)
+
))
B
B
A
}
For all values of , the covariance between the investment of …rm A and the stock price of …rm A
is positive. This covariance increases in (i) the fraction of informed speculators in stock A (
and (ii) it decreases in the fraction of informed speculators in stock B (
B ),
if
< 1. Moreover,
it decreases in the likelihood that the manager of …rm A receives managerial information,
B
< bB and increases in this likelihood if
B
> bB where bB =
2(1 )(1
1+2(1 )(1
A)
A)
A ),
if
.
Hence, the co-variation between the investment of …rm A and its own stock price is equal to
a baseline component, due to the correlated information channel, plus an additional component
18
due to the active informant channel. The covariance between the investment of …rm A and its
stock price increases in the fraction of informed speculators in stock A because this fraction has
a positive e¤ect on both components.
We obtain two additional predictions that are speci…c to the case in which both the stock
price of …rm A and the stock price of …rm B in‡uence the investment decision of the manager of
…rm A. First, the covariance between the investment of …rm A and its stock price should decline
when the level of informed trading in stock B increases. Indeed, such an increase strengthens
the informativeness of the price of stock B, which leads the manager of …rm A to rely more on
this price as a source of information.
Second, the precision of direct managerial information,
, has an ambiguous e¤ect on the
covariance between the investment of …rm A and its stock price: it is negative if
B
is small and
positive otherwise. Indeed, on the one hand, an increase in the precision of direct managerial
information strengthens the correlated information channel (the …rst component in Equation
(18)) and weakens the active informant channel (the second component in Equation (18)). When
the manager ignores the information in the stock price of …rm B (e.g.,
dominates (Corollary 2). As
B
B
= 0), the second e¤ect
increases, the size of this second e¤ect becomes smaller because
the manager of …rm A relies relatively less on his stock price. Hence, when
…rst e¤ect dominates and cov(KI ; pA ) starts increasing with
B
is high enough, the
(as with no managerial learning).
Chen, Goldstein, and Jiang (2007) …nd that the sensitivity of a …rm’investment to its stock
price is negatively related with a proxy for managerial information (see their Table 3). However,
this relationship is not statistically signi…cant in their sample. Corollary 4 suggests a possible
explanation. The e¤ect of managerial information on the investment-to-price sensitivity of a …rm
depends on the level of informed trading in its peers. Hence, the unconditional e¤ect (i.e., the
average e¤ect across …rms with di¤erent
B s)
may well be indistinguishable from zero. A stronger
test can be obtained by allowing the e¤ect of managerial information on the investment-to-price
sensitivity to di¤er according to
B,
the level of informed trading in peer …rms for each …rm. We
implement such a test in Section 4.3.2.
19
2.4
The role of correlation in …rm demands ( )
We now study the implications of the active informant channel for the e¤ect of a change in
the correlation between the demand for both …rms’ products ( ) on the co-variation between
investment and stock prices. So far we have assumed that
1=RH (Assumption A.2). To
obtain predictions that cover all possible values for the correlation in products demand (from
zero correlation to 1, that is,
1
2
=
1
2
to 1), we must extend the model to consider the case in which
< 1=RH .
When
1
2
< 1=RH , the informativeness of the price of stock B about the demand for …rm
A’s product is too small to in‡uence the manager’s investment decision. Hence, this decision
only depends on his own signal and his own stock price, as in the narrow managerial learning
channel. The only di¤erence is that when
stock price is rational. Hence, when
e¤ects of parameters
A,
B,
and
1
2
1
2
< 1=RH , manager’s inattention to its peer
< 1=RH , the predictions of the model regarding the
are given in Corollary 2. In addition, we obtain the following
implication regarding the e¤ect of .
Corollary 5 The covariance between the investment of …rm A and the stock price of …rm B
(cov(KI ; pB ) increases in
whether or not the manager of …rm A learns from the stock price of
…rm B. Moreover, the covariance between his investment and his own stock price (cov(KI ; pA )
weakly declines in
if and only if the manager of …rm A uses peer stock prices as a source of
information. Otherwise this covariance does not depend on .
An increase in the correlation between the demand for the products of …rms A and B increase
both the correlated information and the active informant components in the covariance between
…rm A investment and the stock price of B. This explains the …rst part of the corollary.
When
> 1=RH , the manager of …rm A uses information contained in the stock price of …rm
B. As a result his investment is relatively less driven by his own stock price than when he does
not use the information contained in his peer stock price (second part of Corollary 5). Hence,
we expect the covariance between a …rm investment and its own stock price to be smaller when
the correlation between the demand for the …rm product and the demand for its peer products
20
is higher. As this prediction is speci…c to the case in which managers learn both from their stock
price and their peer stock price, it o¤ers another way to test whether managers learn information
from their peer stock prices.
2.5
Timing
In the model, the markets for stocks A and B clear simultaneously. As a result, at date 1, the
price of stock A does not re‡ect the speci…c information contained in the price of stock B when
the manager makes his investment decision (at time t = 2). Suppose instead that dealers in stock
A adjust their date 1 valuation after observing the price of stock B, at some date . If date
is
posterior to the date at which the investment decision is made, the model is obviously unchanged.
If instead date
occurs between dates 1 and 2 (the investment date), we have:
pA = E(VA (I ) j pA ; pB );
where pA is dealers’valuation for stock A at date
(19)
given stock prices realized at date 1. Given
our assumptions, the manager of …rm A makes exactly the same investment decisions whether he
only conditions his investment policy on pA or on fpA ; pB g (see the Internet Appendix) because
the price of stock A at date
is a su¢ cient statistic for the information contained in fpA ; pB g
about the future demand for …rm A.
This case, however, is quite special for several reasons. First, in the model, the stock price
of A at date
is a su¢ cient statistic for fpA ; pB g because it is equal to dealers’forecast of the
value of the …rm in our model (a consequence of dealers’risk neutrality). In reality, at any point
in time, the price of a stock is likely to deviate randomly from this forecast, even if on average it
is equal to the latter (see Black (1988)). In this case, managers will obtain more precise signals
by watching their stock price and the stock price of their peers rather than only their own stock
price, as in our static model.13
13
For instance, Cespa and Foucault (2012) consider a model of trading with two assets A and B. In this model,
dealers in each asset can condition their price on the price of the other asset. The joint observation of the price
of both assets is more informative about the payo¤ of an asset than simply the price of this asset. Indeed, each
dealers require a compensation to buy or sell the asset relative to their expectation of its payo¤. This compensation
21
In addition, it takes time for the price of a stock to incorporate the information contained in
the price of other stocks. For instance, Cohen and Frazzini (2008) analyze empirically the speed
at which …rms’stock prices adjust to good or bad news regarding the stock price of other related
…rms (e.g., their customers). They show (see their Figure 2) that this adjustment may take up
to one year on average for the …rms in their sample.14 In this scenario as well managers obtain
more precise information by conditioning their investment policy on their stock price and the
stock price of their peers, as in the baseline model.
Finally, and maybe most important, a …rm stock price re‡ects the value of its portfolio of
products rather than the contribution of each product line to this value. Hence, the stock price
of a …rm can be a poor guide about the incremental value of a growth opportunity in one speci…c
product, especially if the latter contributes little to its total cash ‡ow.15 In this case, a …rm
manager has an incentive to use stock prices of …rms with cash ‡ows highly correlated with the
cash ‡ows of his incremental project as a source of information. We provide a simple model of
this scenario in the Internet Appendix (see Section A.6 in this appendix) and show that in this
case pA is not a su¢ cient statistic for fpA ; pB g.
One version of this scenario is when a manager considers investing in a new product line. As
long as the manager does not make investments required for this product line, the …rm stock
price is unlikely to convey any information about the performance of this investment. Yet, the
…rm manager can learn information from stock prices of …rms already active in this product line.
One implication is that a …rm investment should become sensitive to the stock price of a peer
…rm before the …rm actually becomes a peer. We provide evidence supporting this possibility in
Section 4.2.
is random as it depends on the realization of noise traders’demands.
14
See also Hou (2007), who …nds that, within a given industry, small stocks react more slowly to common
information than large stocks. His evidence suggest that the process of adjustment may be as long as one month.
15
Bresnahan, Milgrom, and Paul (1992) make a similar point. However, they do not consider the possibility for
a manager to learn information from the price of other …rms, more focused on the investment projects on which
they need to learn.
22
3
3.1
Data and Methodology
Sample construction and de…nition of peer …rms
Our empirical analysis is based on a sample of U.S. …rms. To test the main predictions of
the model (Corollaries 3 and 4), we must pair each …rm in our sample with another …rm (the
empirical counterpart of …rm B in our model) selling similar products. To this end, we use
the new Text-based Network Industry Classi…cation (TNIC) developed by Hoberg and Phillips
(2010).16
This classi…cation is based on text-based analysis of product descriptions from …rms’ 10-K
statements …led yearly with the Securities and Exchange Commission (SEC). Speci…cally, Hoberg
and Phillips (2010) calculate …rm-by-…rm similarity measures by parsing the product descriptions
from the …rm 10-Ks and forming word vectors for each …rm to compute a measure of product
similarity for every pair of …rms in each year. The similarity measure is based on the (relative)
number of words that two …rms’ product description have in common. It ranges between 0%
and 100%. Intuitively, the more …rms use common words in their business description, the more
similar are their products (that is, the higher is
in the model). Using this similarity measure,
Hoberg and Phillips (2010) construct TNIC industries using a minimum similarity threshold.
They de…ne each …rm i’s industry to include all …rms j with pairwise similarities relative to i
above a pre-speci…ed minimum similarity threshold chosen to generate industries with the same
fraction of industry pairs as 3-digit SIC industries (equals to 21.32%). We de…ne as “peers” all
the …rms that belong to the same TNIC industry in a given year. Because TNIC industries are
based on the availability of 10-K annual …lings in electronically readable format, the classi…cation
covers the 1997 to 2008 period.
Hoberg and Phillips (2010)’s TNIC industries have three important features. First, unlike
industries based on the Standard Industry Classi…cation (SIC) or the North American Industry
Classi…cation System (NAICS), they are dynamic as they change over time as …rms’ products
evolve. In particular, when a …rm modi…es its product range, innovate, or enter a new product
16
The data can be found at: http://www.rhsmith.umd.edu/industrydata/industryclass.htm
23
market, the set of peer …rms change accordingly. Second, in line with the model, TNIC industries
are based on the products that …rms supply to the market, rather than its production processes
as, for instance, is the case for NAICS. Third, unlike SIC and NAICS industries, TNIC industries
do not require relations between …rms to be transitive. Indeed, as industry members are de…ned
relative to each …rm in the product space, each …rm has its own distinct set of similar …rms. This
provides a richer de…nition of similarity and product market relatedness.
For the set of …rms with available TNIC industries, we gather …rms’stock price and return
information from the Center for Research in Securities Prices (CRSP), investment and other
accounting data from Compustat. We exclude …rms in the …nancial industries (SIC code 60006999) and utility industries (SIC code 4000-4999). We also exclude …rm-year observations with
negative sales, missing information on total assets, capital expenditure, …xed asset (property,
plant and equipment), and (end of year) prices. We detail the construction of all the variables in
Table 1. To reduce the e¤ect of outliers all ratios are winsorized at 1% in each tail.
[Insert Table 1 about here]
Table 2 presents descriptive statistics on the sample. The sample includes 40,893 …rm-year
observations (6,997 distinct …rms). For a given …rm, the average number of peers is 65 (#peers),
while the median is 29. The minimum is 1 and the maximum is 554. Summary statistics for
the main variables used in the analysis resembles those reported in related studies. The average
(median) rate of investment (capital expenditures divided by lagged PPE) is 38.4% (23.9%).
Following other studies on the sensitivity of investment to stock price, we use Tobin’s Q as a
proxy for its (normalized) stock price. Q is de…ned as a …rm’s stock price times the number of
shares outstanding plus the book value of assets minus the book value of equity, scaled by book
assets. There is a large heterogeneity in Q in our sample: It ranges from 0.55 to 13.79 with a
mean of 2.17 and a median of 1.53. Also, the average …rm has a total assets of $1.8 billion, while
the median sample size is $183 million. We also report the summary statistics for the peers’
variables, computed as the average across all peers for each …rm-year. They are very close from
24
their own …rm counterpart, although aggregation lowers their standard variation.
[Insert Table 2 about here]
3.2
Empirical methodology
To empirically measure the co-variation between a …rm’s investment and the stock prices of its
peers (cov(KI ; pB )) and between its investment and its own stock price (cov(KI ; pA )) we adapt
a standard linear investment equation. Speci…cally, we estimate (several versions of) the following
equation:
Ii;t =
i
+
t
+ Qi;t
1
+ Q
i;t 1
+ Xi;t
1
+ 'X
i;t 1
+ "i;t ;
(20)
where the subscripts i and t represent respectively …rm i (…rm A in the model) and the year,
while the subscript
i represents a (equally-weighted) portfolio of peer …rms based on the TNIC
industries (…rm B in the model). The dependent variable Ii;t is a measure of corporate investment
in year t, which in the baseline speci…cation, is the ratio of capital expenditure in that year scaled
by lagged …xed assets (property, plant and equipment). The variable Qi;t
stock price of …rm i in year t
1 (as de…ned above). The variable, Q
1
is the normalized
i;t 1 ,
is the (average)
normalized stock price of …rm i’s peers, computed as the average Q across all the …rms included
1, except …rm i.17
in the same TNIC industry as …rm i in year t
In the baseline speci…cation, the vector Xi;t
1
includes control variables known to correlate
with investment decisions. Following previous research, we include the natural logarithm of
assets (ln(T Ai;t
1 ))
to control for the impact of size on corporate investment. Moreover, to
account for the well documented relationship between cash ‡ows and investment, we include cash
‡ows (CFi;t
1)
as an additional control variable. We also include the characteristics of peers
(their average size, ln(T A
i;t 1 ),
and cash ‡ows, CF
i;t 1 )
to further control for product market
characteristics. In addition, we account for time-invariant …rm heterogeneity by including …rm
17
Following common practice, we impose a lag of one year between the measurement of investment and the
measurement of Q (e.g., Chen, Goldstein, and Jiang (2007)). This timing also matches that of the model. In the
Internet Appendix (Table C1), we show that the …ndings holds when we consider no lag between investment and
Q.
25
…xed e¤ects ( i ) and time-speci…c e¤ects by including year …xed e¤ects ( t ).18 We allow the error
term ("i;t ) to be correlated within …rms and correct the standard errors as in Petersen (2009).19
Coe¢ cients
and
in equation (20) measure respectively the co-variation between the in-
vestment of …rm i and its stock price and the co-variation between the investment of …rm i and
the (average) stock price of its peers, holding other variables a¤ecting investment constant. We
use estimates of these coe¢ cients to test the main implications of the model. We proceed in
two steps. First, we establish that estimates for
and
are both positive and robust in our
sample. This is indeed a necessary condition for the active informant channel to play a role (see
Corollaries 3 and 4). This condition is, however, not su¢ cient, as shown by Corollary 1. Hence,
in a second step, we test whether the cross-sectional variation of
and
is explained by measures
of informed trading or proxies for managerial information as predicted by Corollaries 3 and 4,
with a special focus on the predictions of the model speci…c to the scenario in which a manager
learns from his own stock price and its peer stock price (see Section 2.3).
Although we use the characteristics of peers to explain …rms’ investment (Q
i
and X i ),
our goal is not to identify endogenous peer e¤ects. A peer e¤ect is de…ned as the impact of an
average characteristic of a group (e.g. the average investment of product market peers) on the
characteristic of an individual member of the group (e.g. the investment of a …rm). As explained
by Manski (1993), and discussed in Leary and Roberts (2011), the identi…cation of peer e¤ects
is challenging because of the the so-called re‡ection problem. Our focus is instead on the e¤ect
of an average characteristic of a group on a di¤ erent characteristic of an individual member of
the group. Because the stock prices of peers can be reasonably assumed to be exogenous to the
actions of a given …rm, the coe¢ cients
and
in equation (20) really capture so called contextual
e¤ects. Nevertheless, to make sure that our results are not a¤ected by unspeci…ed peer e¤ects, we
estimate speci…cations where we include the average investment of peers as an additional control
variable. Our main conclusions remain una¤ected (see Table C4 of the Internet Appendix).
18
As a result, the coe¢ cient measures how, over time, the average …rm’s investment is tied to its peers’stock
price.
19
In Table C2 of the Internet Appendix we show that our inference is robust the various forms of clustering.
26
4
4.1
Empirical Findings
Corporate investment and stock market prices
Table 3 presents estimates for various speci…cations of the baseline investment equation (20). We
start by estimating equation (20) with …rm and year …xed e¤ects, without including the stock
price and characteristics of peers as independent variables. As found in many other studies (e.g.
Baker, Stein, and Wurgler (2003), Chen, Goldstein, and Jiang (2007), or Campello and Graham
(2011)), the …rst column reveals a positive and signi…cant relation between a …rm’s stock price
(Qi;t
1)
and its investment (Ii;t ). On average, the estimated investment-to-price sensitivity,
,
is 0.073 with a t-statistic of 24.54. The control variables (…rm’s size and cash ‡ows) have the
expected sign (negative and positive respectively), and their magnitude is similar to that found
in related studies.
The second column reports the estimate of the sensitivity of a …rm investment to its peers’
stock price, , as proxied by their average price (Q
i;t 1 ).
On average,
is positive (equal to
0.050) and is highly signi…cant with a t-statistic of 10.42.20 The economic magnitude of the
relationship between the investment of a …rm and the stock price of its peers is substantial. To
see this, consider a one standard deviation increase in the stock price of peers (1:12). This shock
is associated with a 5:6% increase in investment on average, about 14.5% of the sample average
ratio of capital expenditures on …xed capital (
sd(Q i )=0.050 1.12=5.6%). The estimates in
column 2 reveals that, in terms of magnitude, the e¤ect of peers’price on a …rm investment is
about half that of its own stock price. Indeed, a one standard deviation increase in the …rm own
price (1.94) is associated with a 12.8% increase in investment (
sd(Qi )=0.066 1.94=12.8%).
We also observe that the coe¢ cients on the size and cash ‡ows of peers are signi…cant.21
[Insert Table 3 about here]
20
The estimated coe¢ cients on Qi;t and CFi;t do not change signi…cantly when we include Q i as a control in
our baseline regression. Hence, although the correlation between Qi and Q i is 0.40 in the sample, the coe¢ cient
on Q i captures an information distinct from the information in Qi .
21
In the Internet Appendix we show that the estimates for and are positive and signi…cant in each of the
year between 1997 and 2008 (see Figure C1).
27
We check the robustness of these …ndings to several changes in the baseline speci…cation.
First, we change the measurement of peers’ stock prices. In column 3 of Table 3, we modify
the proxy for peers’ stock price and characteristics (size and cash ‡ow) by using their median
values instead of their average values. The estimates of
and
are virtually una¤ected. In
the fourth and …fth column of Table 3, we use di¤erent de…nitions of peers. More speci…cally,
we identify peers as the set of …rms within the same 3-digit SIC (column 4) or 4-digit NAICS
(column 5) instead of the TNIC industries. With both de…nitions, we continue to observe that
the investment of a …rm co-varies positively with the stock price of its peers. Yet, the estimates
for
are slightly smaller (0.048 for SIC and 0.037 for NAICS). As pointed out by Hoberg and
Phillips (2011) …rms within the same 3-digit SIC or 4-digit NAICS can operate in very di¤erent
product space. Hence, we expect the correlation in the cash ‡ows of these …rms ( in the model)
to be smaller than the correlation between …rms within the same TNIC industry.
We perform additional robustness tests that we report in the Internet Appendix. We show
that our inference is robust to various estimation methodologies (e.g. industry and industry-year
…xed e¤ects), di¤erent forms of clustering, and di¤erent de…nitions of corporate investment. Also,
our conclusions remain identical if we use the price-to-earning ratio (PE) or (idiosyncratic) stock
returns as alternative proxies for stock prices. We have also checked that the investment of a
…rm is not sensitive to the stock price of unrelated …rms (…rms for which a priori
= 0 in the
model). To this end, we generated 100 random samples of pseudo peers (a randomly picked set of
…rms outside …rms’TNIC industries) and estimated equation (20) using the average stock price
(and characteristics) of pseudo peers (instead of true TNIC peers). Also, the internet Appendix
presents additional speci…cations where we include a larger set of control variables (leverage, cash
holdings, asset tangibility, sale growth, lagged capital expenditures, and future (3 years) returns
of …rms and their peers). The main results remain una¤ected.
Overall, the investment of a …rm is positively and signi…cantly correlated with its stock price
and the stock prices of its peers. The …rst empirical …nding is well known. The second is new to
our paper.
28
4.2
Dynamic peers classi…cation
By using TNIC industries, the set of peers for each …rm is changing over time. So we can identify
past, present, and future peers and gauge how the investment of a …rm is related to the stock
price of each set of peers. Consider a …rm B which until date t is not a peer of …rm A but becomes
a peer of …rm A at date t. This entry of …rm B in the set of peers is like a positive shock on
in
the model. Hence, we should observe an increase in the sensitivity of …rm A investment to the
stock price of …rm B. Symmetrically, the investment of …rm A should become less sensitive to
the stock price of a peer when this …rm exits its set of peers (e.g., because it exits the product
space and therefore its price becomes uninformative). These e¤ects should hold whether or not
managers learn information from stock prices (see Corollary 5) as long as the price of a peer (new
or old) contains information correlated with the cash ‡ows of …rm A’s incremental investment
projects.
Now consider the case in which a …rm B is not yet a peer of …rm A at date t but will become
one at some point in the future, say date t + 2. This case is particularly interesting for us as it
may capture cases in which the manager of …rm A decides to enter the product space of …rm B at
date t + 1, after learning information from …rm B’s stock price (and other sources of information)
at date t (see the discussion at the end of Section 2.5). In this case, the investment of …rm A
should co-vary with the stock price of …rm B before …rm B becomes a peer of …rm A.
To test these implications, we construct for each …rm-year four distinct sets of peers: (i) new
peers, (ii) old peers, (iii) past peers, and (iv) future peers. For …rm i and year t, we de…ne new
peers as …rms in the same TNIC industry as …rm i in year t but not in year t
1. Following the
same logic, past peers are …rms that were in the TNIC industry in year t
1 but are not anymore
in year t, old peers are …rms that were in the TNIC industry in year t
1 and continue to be
in year t. Finally f uture peers are …rms that are not in the TNIC industry in year t but will
be in year t + 1 (or t + 2). Then, to examine whether investment is di¤erently sensitive to the
stock prices of each type of peers, we compute the average price (market-to-book ratio) for each
set of peers and use this price instead of the average stock price of all current peers (Q
29
i;t 1 )
in
equation (20).
[Insert Table 4 about here]
Table 4, present the results. In columns 1, 2, and 3, we focus on the new, past and old peers,
respectively. We observe a positive and signi…cant relation between …rms’ investment and the
stock price of their new peers. The estimated coe¢ cient is 0.021 with a t-statistic of 6.83.22 In
contrast, column 2 shows that the investment of …rms stop being sensitive to the stock price
of …rms that exit their set of peers (the sensitivity of investment to the price of past peers is
0.004 with a a t-statistic of 1.37). Finally, results regarding old peers largely mirror the baseline
results (presented in Table 2) with a large coe¢ cient on the stock price of old peers (0.034 with
a t-statistic of 6.65).
In columns 4 and 5, we consider the e¤ect of the stock price of f uture peers (one year or
two years ahead) on …rms’ investment. We …nd that the stock prices of f uture peers matter.
Indeed, the sensitivity of …rms’ investment to the prices of their one year ahead (respectively
two years ahead) future peers is equal to 0:018 (0:014) and is statistically signi…cant.23 These
empirical …ndings …t well with the scenario in which …rms’managers look at the stock price of
other …rms to learn information about the pro…tability of new investment projects (for example
the development of a new product line).
4.3
Cross-sectional tests
We now focus on the cross-sectional implications that are unique to the active informant hypothesis. We examine how the co-variation between investment and stock prices varies cross-sectionally
with (i) measures of informed trading (
A
and
B ),
(ii) measures of managerial information other
than stock prices ( ), and (iii) measures of the correlation in demand shocks between a …rm and
its peers ( ).
[Insert Table 5 about here]
22
The sample size is smaller than that used in previous tests because we exclude from the analysis …rms that
keep the same peers over the entire sample period.
23
We obtain virtually the same results if we include the …ve sets of peers in the same regression (see Internet
Appendix).
30
Table 5 summarizes the cross-sectional predictions of the model. We highlight with an “ ”
the predictions that enable us to distinguish the scenario (“learning from peers”) in which …rms’
investment decisions are in‡uenced by their own stock price and the price of their peer …rms from
the two alternative scenarios considered in the model ("no managerial learning", and "narrow
managerial learning").
4.3.1
Informed trading (
j)
and investment-to-price sensitivity
We …rst examine how investment-to-price sensitivities ( and ) varies with the level of informed
trading in the stock market of a …rm (
di¤erent types of proxies for
…rm i is increasing in
i.
j.
A)
and the stock markets of its peers (
B ).
We use three
In the model the informativeness of the stock price of a given
Hence, we use measures of price informativeness as proxies for the level
of informed trading in a stock.
First, as in many other papers (e.g., Durnev, Morck, and Yeung (2004), or Chen, Goldstein,
and Jiang (2007)), we measure the informativeness of a …rm stock price with a measure of …rmspeci…c return variation (or price non-synchronicity), de…ned as
i;t
2 )=R2 ), where
Ri;t
i;t
= ln((1
2 is the R2 from the regression in year t of …rm i’s weekly returns on the returns on the
Ri;t
(value-weighted) market and a (value-weighted) portfolio of peers (using the TNIC industries).
The idea, due to Roll (1988), is that trading on …rm-speci…c information makes stock returns
less correlated and thereby increases the fraction of total volatility that is due to idiosyncratic
returns. The level of informed trading in a stock is higher when
In our sample, the correlation between
i
and
i
is high.
(the average …rm-speci…c return variation
of the peers for stock i) is equal to 0:421. To test the model’s predictions, we need to measure
the e¤ect of
i
i
on the co-variation between investment and stock prices, while holding constant
(and vice versa). To do so, we …rst regress
residuals as
+
i.
Similarly, we regress
as
+
i .
of
and . As the variation of
i
on
i
In our tests, we analyze how a change in
+
i
on
i
(respectively
i
each year and de…ne the regression
each year and de…ne the regression residuals
+
i
(respectively
+
i )
+
i )
a¤ects the estimates of
is independent of
i
(respectively
i)
by construction, this amounts to varying the level of informed trading in the peers of stock i
31
(respectively in stock i) while keeping the level of informed trading in stock i
To gauge the e¤ect of informed trading in peers’stock prices (using
+
i
i
…xed.
as a proxy for
B)
on
the co-variation between a …rm’s investment and stock prices, we assign (each year) observations
that are in the bottom and top quintiles of the distribution of
+
i
into low and high groups. Then,
we estimate our baseline regression (equation (20)) for each group and compare the coe¢ cient
estimates of
and
across groups.24 Panel A of Table 6 presents the results. For brevity, we
only display the estimated coe¢ cients for
well as the average values of
i
and
i
and , their statistical and economic signi…cance, as
(bottom two lines).25 A prediction speci…c to the active
informant channel is that the sensitivity of a …rm’s investment to its own stock price should be
lower when the level of informed trading in its peers is high. This is indeed what we …nd in Panel
A: the estimate of
is lower in the high group than in the low group (0.062 versus 0.068). The
di¤erence in these estimates for
between the two groups is not statistically signi…cant (p-value
of 0:140). However, in economic terms, the di¤erence is not small: a one standard deviation
increase in a …rm’s stock price is associated with a 13.14% increase in investment when the level
of informed trading in peers’ stocks is low while the same shock raises investment by 11.06%
when the level of informed trading in peers’stocks is high.
Moreover, a …rm’s investment turns out to be more sensitive to the stock prices of its peers
when peers’ markets have a higher level of informed trading, as implied by both the learning
channel and the correlated information channel (Corollaries 1 and 2). The estimate for
is
0.034 in the low group while it is 0.058 in the high group (the di¤erence is signi…cant at a 1%
con…dence level). All else equal (i.e., keeping
i
…xed), these results show that …rms rely less on
their own stock price and more on the stock prices of their peers when peers’ stock prices are
more informative.
[Insert Table 6 about here]
24
We partition …rms based on the informativeness variables measured at date t 1, i.e., contemporanously to the
stock price (Q) in equation (20). Moreover, we focus on only the lowest and highest quintile to limit the impact of
measurement errors in the price informativeness proxies (see Greene (2008)). The Internet Appendix also report
speci…cations with interactive variables (9 additional variables). For ease of presentation, we favor the sample-split
approach.
25
By construction the average i is similar across the low and high groups (2.480 vs. 2.476), but the average
i is not. It amounts to 1.259 in the low group vs. 3.540 in the high group.
32
In Panel B, we study how changes in the level of informed trading in a …rm’s own price (
A)
a¤ects the sensitivity of its investment to its own stock price and the stock price of its peers
(holding
B
constant). The …rst row con…rms the results of Chen, Goldstein, and Jiang (2007)
and Bakke and Whited (2010): a …rm’s investment is markedly more sensitive to its own stock
price when its market displays a higher level of informed trading. The coe¢ cient estimate for
is 0.045 in the low group and 0.076 in the high group (the di¤erence is highly signi…cant). As
shown by the model, this observation is consistent both with the correlated information channel
and the active informant channel.The second row shows that the co-variation between a …rm’s
investment and the stock price of its peers decreases in the amount of informed trading in its
own market. Indeed, the coe¢ cient on
is large and signi…cant in the low group (0.067 with a
t-statistic of 10.56), but only marginally signi…cant in the high group (0.015 with a t-statistic of
1.64). The di¤erence is statistically signi…cant and economically large. A one standard increase
in peers’ stock prices generates a modest 1.68% increase in a …rm’s investment when its own
market has a high level of informed trading. In contrast, the same shock is associated with a
7.30% increase in a …rm’s investment when the level of informed trading in its own stock is low.
As explained in Section 2.3, the correlated information channel does not predict this …nding, but
the active informant channel does.
In the rest of Table 6 (Panels C to F), we check the robustness of these …ndings using two
other proxies for the level of informed trading in a stock. First, in Panels C and D, we use
the measure of trading based on private information in a stock developed by Llorente, Michaely,
Saar, and Wang (2002). To obtain it, we regress every year …rm i’s weekly returns on its lagged
weekly return, the value-weighted contemporaneous market return, and the interaction between
the …rm lagged return and the logarithm of …rm i’s weekly turnover (detrended by substracting
its 26-week moving average).26 The coe¢ cient on the interaction term (that we call LM SW ) is
a proxy for the level of informed trading in stock i, as shown theoretically and empirically by
Llorente, Michaely, Saar, and Wang (2002). Intuitively, the returns on stocks with a high level
of informed trading are more likely to be positively autocorrelated conditional on volume being
26
See equation (15) in Llorente, Michaely, Saar, and Wang (2002). In contrast to them, we use weekly returns
rather than daily returns.
33
high.27 In Panels E and F, we use the P IN measure developed by Easley, Kiefer, and O’Hara
(1996) as another proxy for the likelihood of informed trading in a stock. It is used in a context
related to ours by Chen, Goldstein, and Jiang (2007) and Bakke and Whited (2010). In our tests,
we use an adjusted measure of P IN (AP IN ), developed by Duarte and Young (2007), which
better captures the informational component of P IN .28
We conduct our tests with these two proxies for the level of informed trading in a stock
using exactly the same methodology that we have followed with
of a regression of LM SWi (respectively P INi ) on LM SW
variations in the level of informed trading in a stock,
i,
i
. That is, we use the residuals
(respectively P IN i ) to generate
while holding the level of informed
trading in its peers constant (or vice versa). Reassuringly, the results are qualitatively similar
with these two proxies, with two exceptions. First, when we use LM SW , we obtain that a …rm’s
investment is more sensitive to the stock prices of its peers when peers’ markets have a higher
level of informed trading (see second row of Panel C), as implied by Corollaries 1 and 2. However,
the di¤erence in sensitivity between the high and the low groups is not statistically signi…cant
(while it is with
). Second, when we use AP IN …rms’ investment is more sensitive to their
stock price when the stock price of their peer is more informative (…rst row in Panel E). However,
the di¤erence is again no statistically signi…cant.
The general picture that emerges from Table 6 supports the hypothesis that managerial
learning explains part of the positive correlation between corporate investment and stock prices.
In particular, two results that are unique to the scenario in which managers learn from the stock
market stand out. First, a …rm’s investment appears to be less correlated with its stock price
when the level of informed trading in its peers’stock markets is high. Second, a …rm’s investment
is markedly more correlated with the stock prices of its peers when the level of informed trading
in its own stock market is low.
27
Fernandes and Ferreira (2008, 2009) or Fresard (2011) also use this measure as a proxy for informed trading
in a stock.
28
We thank Je¤erson Duarte for making the AP IN data publicly available.
Due to data availability, the tests using AP IN are restricted on the period 1997-2004.
The data can be found at:
http://www.owlnet.rice.edu/~jd10/publications.htm
34
4.3.2
Managerial information ( )
In the presence of managerial learning, an increase in the precision of managerial information ( )
should decrease the sensitivity of a …rm’s investment to the stock price of its peers. Moreover, the
e¤ect of a higher
on the sensitivity of a …rm’s investment to its own stock price should depend
on the level of informed trading in its peers’stock markets. If this level is high, the e¤ect should
be positive while if this level is low, this e¤ect should be negative. None of these predictions are
obtained when the co-variation between investment and stock prices is only due to the correlated
information channel.
We test these two predictions using the trading activity of corporate insiders as a proxy
for managerial information, following Chen, Goldstein, and Jiang (2007). The intuition is that
managers are more likely to trade their own stock if they possess more private information. We
measure the intensity of managers’ insider trading activity (Insideri;t ) in a given year as the
total number of insider transactions for that year divided by the total year’s transactions. We
obtain the trades of corporate insiders from the Thomson Financial Insider Trading database and
the total number of trades (turnover) from CRSP.29 We follow previous studies (e.g. Beneish
and Vargus (2002), or Peress (2010)) and limit insider trades to open market stock transactions
initiated by the top …ve executives (CEO, CFO, COO, President, and Chairman of the Board).
Table 7 reports the results from the estimation of equation (20) where observations in the
bottom and top quintiles of the distribution of Insideri are assigned into low and high groups
respectively.30 In the second row, we observe that the investment of a …rm is signi…cantly more
sensitive to the stock prices of its peers when managers have little private information. The
estimated coe¢ cient for
is 0.054 in the low group, and 0.032 in the high group. The di¤er-
ence between these estimates is highly signi…cant (p-value of 0.026). This …nding supports the
hypothesis that managers learn information from stock prices since, in the absence of managerial
learning, we should observe a positive relation between
and the amount of private information
29
The Thomson Financial Insider Filing database compiles all insider activity reported the the SEC. Corporate
insiders include those that have "access to non-public, material, insider information" and required to …le SEC form
3, 4, and 5 when they trade in their …rms stock.
30
The last row of Table 7 indicates that the average fraction of insider trading is 0% in the low group, while it
amounts to 9.85% in the high group. The sample average is 1.85%.
35
managers possess (see Corollary 1).
[Insert Table 7 about here]
The estimates for
are not signi…cantly di¤erent between the low and the high group (0.063
vs. 0.067; see …rst row in Table 9). Chen, Goldstein, and Jiang (2009) also …nd that the sensitivity
of a …rm’s investment to its own stock price is not signi…cantly related to the extent of insider
trading. Yet, remember that our model predicts that, in the presence of managerial learning, the
relation between managerial information and the co-variation between a …rm’s investment and
its stock price is non-monotonic and depends on the level of informed trading in its peers’stock
markets (Corollary 4). To test whether the data uphold this prediction and to better understand
the role of managerial information in explaining investment-to-price sensitivities, we double-sort
…rm-year observations based on (i) the level of informed trading (measured by
+
i;
see Section
4.3.1) in peers and (ii) managerial information for each …rm. More speci…cally, as we did in
section 4.3.1, in each year, we keep the …rms that are in the lowest and highest quintiles of the
distribution of
+
i
and, in each of these two groups, we further separate …rms in two groups
based on the median value of Insideri (in each initial group). We then estimate
and
for each
of the four subgroups separately.
[Insert Table 8 about here]
Panel A of Table 8 displays the results. For low level of informativeness in peers’stock prices
(low
+
i ),
…rms’investment is less sensitive to their own price when managers enjoy more private
information. The coe¢ cient on Qi is 0.073 when the value of Insider is below the median (column
1), and 0.064 when the value of Insider is above the median (column 2). The di¤erence is not
signi…cant at conventional levels (p-value of 0.188). In contrast, when the level of informativeness
in peers’ stock prices is high (high
+
i ),
the e¤ect is reversed. A …rms’ investment is more
sensitive to its own price when managers enjoy more private information. The di¤erence between
groups is again not signi…cant (p-value of 0.317). Although not signi…cant (maybe due to lack
36
of power inherent in these smaller sub-samples), the direction of the e¤ects is consistent with
our predictions when managers learn information both from their own stock price and their peer
stock prices. Moreover, the coe¢ cients on Q
i
are as expected: Corporate investment co-varies
more with peer stock prices when managers have less private information (columns 1 and 3), and
even more so when peer stock prices are highly informative.
In Panels B and C , we perform the same tests but with LM SW and AP IN as proxies for
the level of informed trading in peers. Generally, the results are less clear-cut with these proxies,
in particular when we focus on cases where the level of informed trading in peers’stock markets
is high.
4.3.3
Correlated demand for products ( )
Finally we study how the correlation between the demand for a …rm’s products and that of its
peers ( ) is related to the co-variation between investment and stock market prices. In all cases
(that is, with no managerial learning, narrow managerial learning, or managerial learning from
peer stock prices), theory implies that the sensitivity of a …rm investment to its peer stock prices
should increase in this correlation (see Section 2.3). Moreover, only if …rms learn from their peer
stock prices, we should observe an inverse relationship between this correlation and the sensitivity
of a …rm investment to its own stock price (Corollary 5).
We use three di¤erent variables to proxy for the correlation between the demands for …rms’
products. First, we use the correlation between a …rm’s sales and its peers’sales (Sales correlation).
Similarly, we rely on the correlation between a …rm’s and its peers’cash ‡ow (CF correlation).
We compute these correlations for each …rm-year using quarterly sales and cash ‡ows over the
previous three years. In addition, we use a direct measure of product similarity based on …rms’
product description. As explained in section 3.1, the TNIC industries developed by Hoberg and
Phillips (2011) are constructed based on similarity scores (ranging from 0% to 100%) for each
pair of …rms that are above a minimum similarity threshold (of 21.32%). As we have access to
the exact scores between each …rm and its peers (i.e. all the …rms above the minimum threshold),
37
we can compute the average similarity score of a …rm with its peers in a given year.31 We use this
average similarity score (denoted similarity) for each …rm-year observation as another proxy for
.
[Insert Table 9 about here]
For each proxy for , we observe in Table 9 that the investment of …rms in the lowest quintile
is less sensitive to their peer stock price than the investment of …rms in the highest quintile (the
e¤ect is not always statistically signi…cant). For instance, the estimate for
is 0.047 (with a
t-statistic of 5.74) when the correlation between a …rm’s sales and that of its peers is high (the
high partition) and 0.018 (with a t-statistic of 2.27) when this correlation is low. As predicted by
Corollary 5, the ranking of the estimate for
between the high and the low quintiles is reversed.
For each proxy for , the investment of …rms in the low quintile is signi…cantly more sensitive to
their stock price. For instance, the estimate for
is 0.063 (with a t-statistic of 16.7) when the
average similarity between a …rm and its peers is low and 0.046 (with a t-statistic of 11.55) when
this average similarity is high. This is predicted by our model when managers learn from their
stock price and their peer stock price but not otherwise.
5
Conclusion
In this article, we document that a …rm’s investment is positively related to the stock prices of
peer …rms that sell related products. We argue and provide evidence that this connection arises
because managers can learn information from observing the stock price of their peers. Overall,
our results constitute a new piece of evidence in favor of the hypothesis that …nancial markets
in‡uence …rms’real decisions by conveying useful information to their managers.
The possibility for a …rm to learn from the stock prices of other …rms implies the presence
of learning externalities. These externalities can markedly magnify the real e¤ects of the stock
market on the allocation of resources in the economy. For instance, the prospect of learning
from peers’ stock prices might induce …rms to develop products that are close to other …rms’
31
We are especially grateful to Jerry Hoberg and Gordon Phillips for sharing the data required for this test with
us.
38
products rather than di¤erentiating their products. Eventually, this could lead to a relatively
high correlation of …rms’cash ‡ows and over-specialization in economies in which stock markets
are well developed and informationally e¢ cient.
From a di¤erent perspective, learning externalities could a¤ect the behavior of privately held
…rms. The precision and nature of the information they can gather from the stock prices of
publicly-listed peers could impact their willingness to go public, the type of securities issued,
their listing location, and the type of investors they want to attract.
If managers learn from each other stock prices, their behavior (e.g., investment) will appear
correlated. This mechanism could provide an alternative explanation for why managers may
rationally herd in their investment decisions (see Scharfstein and Stein (1990), or Devenow and
Welch (1996)). Ultimately, it would be interesting to better understand what charateristics (…rm,
product, or stock markets) determine the extent to which …rms can learn from each other stock
prices and the consequences of such learning. We plan to investigate some of these aspects in
future research.
39
A
Appendix
Proof of Lemma 1. We show that the strategies described in the lemma form an equilibrium.
(xiB ; sbB ) be the expected pro…t of a speculator who trades xiB 2 f 1; 0; +1g shares of …rm
Let
B when his signal is sbB and let
B
H
B
=
L
B
=
=
H
B
L
B
2
.
First, consider an informed speculator who observes sbB = H. If he buys the asset, his expected
pro…t is:
(+1; H) = E(
= Pr(
1+
B
< fB < 1
B
B
pB (fB ) jb
sB = H; xiB = 1 )
jb
sB = H; xiB = 1 )(
B)
+ Pr(fB <
1+
B
jb
sB = H; xiB = 1 )(2
When sbB = H, the informed speculator expects other informed speculators to buy the asset and
uninformed speculators to stay put . Hence, using equation (6), he expects:
fB = zB +
B
when sbB = H:
(21)
We deduce that
Pr(
1+
B
< fB < 1
B
jb
sB = H; xiB = 1 ) = Pr(
1 < zB < 1
2
and
Pr(fB <
1+
B
jb
s = H; xiB = 1 ) = Pr(zB <
Thus,
(+1; H) = (1
40
B) B
> 0:
1) = 0.
B )=(1
B ).
B ):
If instead, the speculator sells, his expected pro…t is:
( 1; H) = E(
pB (fB ) jb
sB = H; xiB =
B
1) =
(1
B) B
< 0,
where we have used the fact that each speculator’s demand has no impact on the aggregate
speculators’demand since each speculator is in…nitesimal. Thus, the speculator optimally buys
the asset when he knows that demand for …rm B is strong at date 3. A symmetric reasoning
shows that the the speculator optimally sells the asset when he knows that this demand is low
at date 3.
Now we consider dealers’prices at date t = 1. Remember that p(fB ) =E( B jfB ). If sbB = L,
R
then 0 B xiB (b
sB )di =
bB = L.
B . Thus, equation (6) implies that fB > 1
B is impossible if s
R B
In contrast, if sbB = H, then 0 xiB (b
sB )di = B . Thus, equation (6) implies that fB > 1
B
happens when zB > 1
2
B.
As a result, when dealers observe fB > 1
B,
they deduce that
sbB = H. This implies:
p(fB ) = E(
B
jfB ) = E(
B
jb
sB = H ) =
H
B
for fB > 1
B:
A symmetric reasoning implies:
p(fB ) = E(
Finally, for
p(fB ) = E(
1+
B
fB
B
j 1+
B
B
jfB ) = E(
1
fB
B,
1
B
jb
sB = L ) =
L
B
for fB <
1+
B:
we have:
B)
=
B
+ (2Pr(dB = H j 1 +
41
B
< fB < 1
B)
1)
B.
Now:
Pr(dB = H j 1 +
=
=
Pr(
1
B
< fB < 1
B
)
Pr( 1 + B < fB < 1
1 + B < fB < 1
B jdB = H ) + Pr(
1
1
B
= .
+
1
2
B
B
jdB = H )
1 + B < fB < 1
B
B
jdB = L )
Hence,
p(fB ) =
B
for
1+
B
fB
1
B:
Proof of Proposition 1.
Speculators’ optimal trading strategy. It can be shown that speculators’order placement
strategy is optimal following the same steps as in the proof of Lemma 1. Hence, we skip this step
for brevity.
The manager’s optimal investment policy. Now consider the investment policy for the
manager of …rm A given the equilibrium price function pA ( ). If the manager receives managerial
information, he just follows his signal since this signal is perfect. Hence, in this case, he invest if
smA = H and does not invest if smA = L. If he receives no managerial information (smA = ?),
the manager relies on stock prices. If he observes that pA = pH
A , the manager deduces that
fA > 1
A.
In this case, investors’net demand in stock A reveals that demand for product A is
strong, i.e., dA = H (the reasoning is the same as that followed for …rm B when fB > (1
B );
see the proof of Lemma 1). Thus the manager optimally invests. If instead the manager observes
that pA = pL
A then the manager deduces that fA <
1+
A
and he infers that the demand for
the product sold by …rm A will be low at date 3. In this case, the manager optimally abstains
from investing at date t = 2.
Finally if he observes pA = pM
A then the manager infers that
1+
A
fA
case, investors’demand in stock A is uninformative (that is, Pr(dA = H j 1 +
1
2 ).
A
1
A.
< fA < 1
In this
A )=
Hence, the manager of …rm A relies on the price of stock B as a source of information. If
42
pB =
H
B,
he deduces that fB > 1
B
and that the demand for product B will be high. We
deduce that
E(
A
pB =
H
B,
pA = pM
A ) = E(
A jdB
= H ) > 0;
where the last inequality follows from Assumption A.2. If pB <
fB
1
B,
H
B,
(22)
the manager deduces that
in which case either investors’ demand in stock B is uninformative or it signals
that the demand for product B will be low. Hence, when pB <
…rm A assigns a probability less than or equal to
1
2
H
B
and pA = pM
A , the manager of
to demand for product A being high at date
3. Using Assumption A.1, we deduce that the manager of …rm A does not invest in this case.
We have considered the manager’s optimal decision for the prices that can be observed on
M
L
the equilibrium path, that is, pH
j , pj , pj for j 2 fA; Bg. Other prices for stocks A and B are
out-of the equilibrium path and the manager’s belief about the demand for product A cannot
be computed by bayes rule. Consider the following speci…cation of the manager’s belief about
investors’demand for prices out of the equilibrium path: (i) if he observes pM
A
pA < p H
A , the
manager of …rm A believes investors’demand for stock A to be
1
1+
A
fA
A,
(ii) if
he observes pA < pM
A , the manager of …rm A believes investors’ demand for stock A to be less
than
1+
A,
and (iii) if he observes pB <
H
B,
the manager believes that fB
1
B.
It is
straightforward, using the same reasoning as in the previous paragraph that this speci…cation
of the manager’s out-of-equilibrium beliefs leads to the optimal investment policy prescribed by
Proposition 1 for out-of-equilibrium prices.
Collecting these observations, we deduce that I (smA ; pA ; pB ) is as given in equation (11).
Equilibrium prices. Now consider the stock price of …rm A. We must check that the following
equilibrium condition is satis…ed:
p(fA ) = E(VA (I ) jfA );
(23)
where I is given by equation (11). We check that the price function given in the second part of
Proposition 1 satis…es this condition.
Suppose …rst that fA
(1
A ).
In this case, investors’net demand in stock A reveals that
43
demand for product A is strong, i.e., dA = H (the reasoning is the same as that followed for …rm
B when fB > (1
B );
see the proof of Lemma 1). Moreover, the stock price of …rm A is pH
A
according to the conjectured equilibrium. Hence, using equation (11), we deduce that:
H
A
E(VA (I ) jfA ) =
+(
which is equal to pH
A , so that for fA > (1
Now suppose that fA
1+
A.
K) for fA
A ),
(1
A );
Condition (23) is satis…ed.
In this case, investors’net demand in stock A reveals that
demand for product A is low, i.e., dA = L. Moreover, the stock price of …rm A is pL
A according
to the conjectured equilibrium. Hence, using equation (11), we deduce that:
E(VA (I ) jfA ) =
which is equal to pL
A . Hence, for fA
Last, consider the case in which
1+
1+
A
L
A
A,
for fA
1+
A;
Condition (23) is satis…ed.
fA
1
A.
In this case the investors’demand for
stock A is uninformative about the demand for product A, that is Pr(dA = H j 1 +
1
2
A
< fA < 1
(the reasoning is as for …rm B). Moreover, the stock price of …rm A is pM
A according to the
conjectured equilibrium. Hence, the manager of …rm A will invest if and only if pB =
H
B
or
smA = H. Using equation (11), we deduce that:
E(VA (I ) j 1 +
A
fA
1
A)
=
A
+ E(I (
K) j 1 +
A
fA
1
A ):
As the manager of …rm A will invest (I = 1) if and only if: (i) he receives a signal that demand
for product A is strong or (ii) he observes a high price for stock B, we deduce that:
E(I (
K) j 1 +
A
fA
1
A)
= Pr(smA = H j 1 +
+Pr(smA = ? \ fB > 1
44
B
A
< fA < 1
j 1+
A
A
< fA < 1
)(
K)
A
)(
K).
A )=
Now,
Pr(smA = H j 1 +
A
< fA < 1
)= ;
2
A
and
Pr(smA = ? \ fB > 1
= (1
=
B
j 1+
)Pr(fB > 1
(1
B
A
< fA < 1
A)
jdB = H )Pr(dB = H j 1 +
A
< fA < 1
A)
)
B
2
Hence,
E(VA (I ) j 1 +
fA
A
which is equal to pM
A , so that for
1
1+
A)
=
fA
A
A
1
+
2
A,
+
(1
)
B
(
2
K);
Condition (23) is satis…ed.
Proof of Corollary 1. When the manager of …rm A is inattentive, his investment policy, I b ( ),
is
I b (smA ) =
8
>
< 1 if smA = H
>
: 0 if smA 6= H
:
(24)
As this investment policy di¤ers from that obtained when the manager accounts for the information in stock prices (I b ( ) 6= I ( )), the equilibrium price of stock A in the benchmark case is
di¤erent from that given in Proposition 1. In the Internet appendix (Section A.1), we show that
this price is given by:
pbA (fA ) =
8
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
:
H
A
A
+ (
+ (
K)
when fA
K)=2 when
L
A
1+
when fA
A
1
A
< fA < 1
1+
A
(25)
A
By de…nition, the covariance between the price of stock A and the invesment of …rm A in the
45
benchmark case is:
h
cov(I b ; pbA ) = K E(I b pbA )
K
i
E(I b )E(pbA ) :
Using equations (24) and (25), we deduce that cov(KI ; pA ) =
A( A
K)) K2 , as
+ 2(
announced in the corollary.
The stock price of …rm B is given by Lemma 1 since the cash ‡ow for this …rm does not depend
on whether the manager of …rm A relies on stock prices or not as a source of information. Using
this observation, we can obtain the covariance between the price of stock B and the invesment
of …rm A in the benchmark case as we did for stock A.
Proof of Corollary 2. The result for cov(KI ; pA ) can be obtained by taking
B
to zero in
equation (18) in Corollary 3. Indeed, when learning from peer is possible, the manager of …rm A
ignores the information contained in the stock price of B if
B
= 0. For brevity, we derive the
expression for cov(KI ; pB ) in the internet appendix (Section A.2).
Proof of Corollary 3. The covariance between the price of stock B and the invesment of …rm
A in equilibrium is:
K
cov(I ; pB ) = K [E(I pB )
E(I )E(pB )] :
Using (11) and Lemma 1, calculations yield:
E(I pB ) =
Moreover, E(pB ) =
B
2
(
B
+
B (2
1)) +
(1
)
2
(
B A
+
B B (1
2
A
+
A
)):
and
E(I ) =
2
+
(1
)
2
(
A
+
B (1
A )):
(26)
Thus, after some algebra, we obtain
cov(KI ; pB ) = (( + (1
)
A )(2
1)
46
B
+ (1
)
B (1
A ))
BK
2
:
We deduce that:
@cov(I ; pB )
@ B
@cov(I ; pB )
@ A
@cov(I ; pB )
@
= ((2
1)( + (1
=
(1
)
B (1
=
(1
A ) B (1
)
A)
+ (1
) < 0; if
)
)(1
A ))
B =2
> 0;
< 1,
< 0.
B
This proves Corollary 3.
Proof of Corollary 4. The covariance between the price of stock A and the invesment of …rm
A is given by:
K
cov(I ; pA ) = K [E(I pA )
E(I )E(pA )] :
Equation (26) gives the expression for E(I ). By de…nition, pA0 = E(pA ). Hence, the expression
for E(pA ) is given by equation (12). Moreover, calculations yield:
E(I pA ) =
H
A pA
2
+ (1
M
A )pA
+(
1
2
)
H
A pA
M
A ) B pA
+ (1
.
Grouping terms together and simplifying we obtain equation (18). Using this equation, it is
straightfoward that
@cov(I ;pA )
@ B
< 0. Moreover, calculations yield:
@cov(I ; pA )
=
@
Clearly,
@cov(I ;pA )
@
increases in
K
A
B.
2
((1
Moreover, for
)(1
B
it is negative. Thus, there exists a value bB such that
B
< bB and
yield bB =
@cov(I ;pA )
@
2(1 )(1
1+2(1 )(1
@cov(I ; pA )
1
=
@ A
2
= 0 for
A)
A)
A
B
= 1,
A )(1
@cov(I ;pA )
@
@cov(I ;pA )
@
B
B)
2
).
is positive while for
> 0 if
B
> bB ,
B
@cov(I ;pA )
@
= 0,
< 0 if
= bB , as claimed in the last part of the corollary. Calculations
. Finally, calculations yield:
+(
K) ((1
)(1 +
A
+
B)
+1
2
A
+ (1
)2
B B)
> 0.
Proof of Corollary 5. For brevity we provide the proof of this result in the Internet Appendix
47
(Section A.3).
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51
Figure 1: Timing of the model Date 1 Date 2
1. Investors trade shares of firms A and B 2. Stock prices are realized 1. The manager of firm A
observes stock price pA, pB
and his private signal smA
2. The managers of firm A
decides to invest or not
Date 3 Demands and firms'
cash‐flows are realized Table 1: Variable definition Variable Capex PPE Q TA Size CF (cash flow) Sale Ψ LMSW APIN Insider Sales Correlation Similarity Definition Capital expenditures (capx) Property, Plant and Equipement (ppent)
[Book value of assets (at) – book value of equity (ceq) + market value of equity (csho*prcc_f)] / book value of assets (at) Book value of total assets (at)
Logarithm of the book value of assets (at)
Income before extraordinary items (ib) plus depreciation (dp) divided by total assets Total sales (sale) Firm specific return variation computed as ψi,t = ln[(1‐R2i,t)/ R2i,t], where R2i,t represents the R2 from a regression of firm i weekly returns on the returns on the (value‐weighted) market portfolio and a (value‐weighted) portfolio of peers, where peers are defined using the TNIC industries. Measure of trading based on private information developed by Llorente, Michaely, Saar, and Wang (2002) obtained by regressing (annually) firm i’s weekly return on its lagged return, the (value‐weighted) contemporaneous market return, and the interaction between firm i’s lagged returns and the logarithm of its weekly share turnover (de‐trended by subtracting its 26‐weeks moving average). LMSW is the estimated coefficient on this interaction Measure of the (adjusted) probability of informed trading in a stock (http://www.owlnet.rice.edu/~jd10/publications.htm) Total number of insider transactions in a given year divided by the total year’s transaction. We only consider open market stock transactions initiated by the top five executives (CEO,CFO, COO, President, and Chairman of the board) Correlation between firm i’s sales and the average sales of its peers (using quarterly observation over the past three years) Average similarity score across the peers of firm i. Similarity scores (ranging from 0% to 100%) are from the detailed text‐
based analysis of Hoberg and Phillips (2010) Source Compustat Compustat Compustat Compustat Compustat Compustat Compustat CRSP CRSP Jefferson Duarte’s website Thomson Financial Insider Trading Datavase and CRSP Compustat Hoberg ‐Phillips data library Table 2: Descriptive statistics This table reports the summary statistics of the main variables used in the analysis. We present the mean, median, 25th and 75th percentiles, standard deviation and the number of non‐missing observations. All variables are defined in the Appendix. In the upper panel, we present the statistics for firm‐level observations. In the lower panel, we present statistics for peers’ average (i.e. the average of peers for each firm‐year observation). Peers are defined using the TNIC industries developed by Hoberg and Phillips (2010). The sample period is from 1996 to 2008. Mean 25th Median 75th St. Dev. Obs. 0.464 1.948 0.319 4556.6 40,902 40,902 40,830 40,902 Own firm 0.385 2.179 ‐0.032 1882.9 Capital expenditures (Ii) Qi Cash Flow (CFi) Total assets (mio.) 0.128 1.111 ‐0.033 46.9 0.239 1.540 0.067 183.7 0.449 2.418 0.118 784.1 Average of peers # Peers Capital expenditures (I‐i) Q‐i Cash flow (CF‐i) Total assets (mio) 65.365 0.397 2.298 ‐0.037 1519.1 9 0.233 1.502 ‐0.094 416.9 29 0.359 1.938 0.030 900.1 89 0.510 2.807 0.083 1802.6 83.06914 0.226 1.123 0.173 2043.2 40,902 40,860 40,902 40,900 40,873 Table 3: Investment‐to‐price sensitivities: Baseline Results This table presents the results from estimations of equation (20). The dependent variable is investment, defined as capital expenditures divided by lagged property, plant and equipment (PPE). Qi is the market‐to‐book ratio of firm i, defined as the market value of equity plus the book value of debt minus the book value of assets, scaled by book assets. Q‐i is the average market‐to‐book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript –i refers to (the average across) firm i’s peers. The other explanatory variables are defined in Table 1. Columns (1) and (2) present the baseline estimations. In column (3) we use the median peers’ characteristics instead of the average. In column (4) the peers of firm i are all the firms that belong to firm i’s 3‐digit SIC industry. In column (5) the peers of firm i are all the firms that belong to firm i’s 4‐
digit NAICS industry. The sample period is from 1996 to 2008. The standard errors used to compute the t‐statistics (in squared brackets) are adjusted for heteroskedasticity and within‐firm clustering. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment (capex over lagged PPE) Baseline (1) Median (2) SIC‐3 (3) NAICS‐4 (4) Qi CFi Sizei 0.066** [22.41] 0.358** [18.11] ‐0.059** [7.24] 0.067** [22.73] 0.358** [18.10] ‐0.057** [6.98] 0.068** [23.11] 0.363** [18.37] ‐0.056** [6.83] 0.067** [22.05] 0.363** [18.36] ‐0.055** [6.74] Q‐i CF‐i Size‐i 0.050** [10.42] 0.141** [3.76] ‐0.004 [0.95] 0.054** [9.04] 0.128** [3.41] ‐0.006 [1.24] 0.048** [7.46] 0.120** [3.13] ‐0.008 [1.73] 0.037** [6.66] 0.123** [3.22] ‐0.007 [1.65] Firm FE Year FE Yes Yes Yes Yes Yes Yes Yes Yes Obs. Adj. R2 40,751 0.36 40,751 0.36 40,751 0.36 40,751 0.36 Table 4: Investment‐to‐price sensitivities: Dynamic peers’ classification This table presents the results from estimations of equation (20) where we change the definition of peers to include dynamic relationships. The dependent variable is investment, defined as capital expenditures divided by PPE. Qi is the market‐to‐book ratio of firm i. Q‐i is the average market‐to‐book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript –i refers to (the average across) firm i’s peers. The other explanatory variables are defined in Table 1. In column (1), peers are defined as firms in the same TNIC industry in year t that we not in year t‐1 (new peers). In column (2), peers are defined as firms that were in the same TNIC industry in year t‐1 but not in year t (past peers). In column (3), peers are defined as firms in the same TNIC industry in year t that we in year t‐1 (old peers). In columns (4) and (5) peers are defined as firms that are not in the same TNIC industry in year t but will be in year t+1 and t+2 respectively (future peers). The sample period is from 1996 to 2008. The standard errors used to compute the t‐statistics (in squared brackets) are adjusted for heteroskedasticity and within‐firm clustering. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment (capex over lagged PPE) New (1) Past (2) Still (3) Future (+1) (4) Future (+2) (5) Q‐i CF‐i Size‐i 0.021** [6.83] 0.157** [4.01] ‐0.007 [1.25] 0.004 [1.37] 0.137** [3.47] ‐0.004 [0.91] 0.034** [6.65] 0.155** [4.21] ‐0.006 [1.21] 0.018** [5.47] 0.132** [3.15] ‐0.007 [1.28] 0.014** [3.94] 0.153** [3.28] ‐0.009 [1.60] Qi CFi Sizei 0.070** [21.70] 0.350** [16.72] ‐0.041** [4.46] 0.061** [18.03] 0.324** [14.85] ‐0.036** [3.86] 0.057** [17.30] 0.317** [15.03] ‐0.038** [4.23] 0.071** [21.98] 0.353** [16.65] ‐0.038** [4.13] 0.073** [20.91] 0.349** [14.86] ‐0.033** [3.19] Firm FE Year FE Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Obs. Adj. R2 34,873 0.36 31,522 0.31 32,919 0.32 33,926 0.35 28,375 0.369 Table 5: Investment‐to‐price sensitivities: Cross‐sectional predictions This table summarizes the cross‐sectional predictions of the model as explained in Section 2.3. The model generates predictions for the co‐variation between a firm’s investment and its own stock price (β) and the co‐
variation between a firm’s investment and the price of its peers (ɳ) as a function of four parameters: the fraction of informed trading in a firm’s stock πown (πA in the model), the fraction of informed trading in the peer’s stock πpeer
(πB in the model), the private information of managers (γ), and the correlation between the demands for firms’ products. We present the predictions for three scenarios: (i) managers ignore stock market information: (ii) managers only rely on the information contained in their own stock price, and (iii) managers rely on their stock price and the stock price of their peers. We highlight with an “*” the predictions that are unique the scenario in which managers learn from the stock prices of their peers (iii). Sensitivity of Investment to: Own stock price (β) Peer stock price (ɳ) πown
πpeer
γ
ρ
πown
πpeer
γ
ρ
(i) No managerial learning + 0 + 0 0 + + + (ii) Narrow managerial learning + 0 ‐ 0 + + + + (iii) Learning from peers (ρ high enough) + ‐* +/‐* ‐* ‐* + ‐* + Effect of Table 6: Investment‐to‐price sensitivities: Stock price Informativeness (πA and πB) This table presents the results from estimations of equation (20) across different partitions based on price informativeness proxies. The dependent variable is investment, defined as capital expenditures divided by PPE. Qi is the market‐to‐book ratio of firm i. Q‐i is the average market‐to‐book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript –i refers to (the average across) firm i’s peers. The other explanatory variables (not reported) are defined in Table 1. The low (high) partition corresponds to the bottom (top) quintile of each partitioning variable (in year t‐1). In Panel A (B) the partitioning variable is peers’ average (firm) firm‐specific return variation Ψ‐i+ (Ψi+). In Panel C (D) the partitioning variable is peers’ average (firm) LMSW‐i+ (LMSW i+). In Panel E (F) the partitioning variable is peers’ average (firm) APIN‐i+ (APIN i+). All the partitioning variables are de‐correlated (superscript+) as explained in section 4.3.2. The sample period is from 1996 to 2008 (2004 with APIN). The standard errors used to compute the t‐statistics (in squared brackets) are adjusted for heteroskedasticity and within‐firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p‐values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Panel A : Investment‐to‐price sensitivities as a function of Ψ‐i+ (Low) (High) (p‐value) 0.068** [15.80] 13.14% 0.034** [4.59] 3.53% 0.062** [15.86] 11.06% 0.058** [4.84] 6.96% 0.140 Obs. Mean (Ψi) Mean (Ψ‐i) 7,872 2.480 1.259 7,859 2.476 3.540 Panel B : Investment‐to‐price sensitivities as a function of Ψi+ (Low) (High) (p‐value) 0.045** [15.83] 9.67% 0.067** [10.56] 7.30% 0.076** [13.71] 12.99% 0.015 [1.64] 1.68% 0.000** 7,881 ‐0.025 2.360 7,857 5.170 2.410 Qi (β) Q‐i (η) Qi (β) Q‐i (η) Obs. Mean (Ψi) Mean (Ψ‐i) 0.010** 0.000** Table 6: Investment‐to‐price sensitivities: Stock price Informativeness (πA and πB) – Continued Investment‐to‐price sensitivities as a function of LMSW‐i+ Panel C : Qi (β) Q‐i (η) (Low) (High) (p‐value) 0.068** [14.27] 0.062** [14.22] 0.163 12.21% 11.90% 0.031** 0.042** [4.52] [3.84] 3.59% 4.36% Obs. 7,625 7,643 Mean (LMSWi) 0.009 0.005 Mean (LMSW‐i) ‐0.031 0.018 0.204 Investment‐to‐price sensitivities as a function of LMSWi+ Panel D : Qi (β) Q‐i (η) (High) (p‐value) 0.052** 0.064** 0.013** [14.44] [15.79] 11.23% 12.73% 0.065** 0.041** [8.05] 10.46% [4.89] 4.59% Obs. 7,648 7,639 Mean (LMSWi) ‐0.123 0.135 Mean (LMSW‐i) 0.007 0.007 (Low) 0.021** Table 6: Investment‐to‐price sensitivities: Stock price Informativeness (πA and πB) – Continued Investment‐to‐price sensitivities as a function of APIN‐i+ Panel E : (Low) (High) (p‐value) 0.061** 0.073** 0.208 [11.51] [5.69] 9.88% 10.29% ‐0.020* 0.025 [2.35] [1.33] ‐2.04% 1.15% Obs. 2,001 2,010 Mean (APINi) 0.175 0.171 Mean (APIN‐i) 0.118 0.214 Qi (β) Q‐i (η) 0.014** Investment‐to‐price sensitivities as a function of APINi+ Panel F : Qi (β) (Low) (High) (p‐value) 0.034** 0.092** 0.000** [8.20] [7.53] 5.67% 11.77% 0.024** 0.003 [2.98] [0.15] 2.13% 0.23% Obs. 2,004 2,004 Mean (APINi) 0.089 0.292 Mean (APIN‐i) 0.168 0.164 Q‐i (η) 0.139 Table 7: Investment‐to‐price sensitivities: Managerial Information (γ) This table presents the results from estimations of equation (20) across different sample partitions based on a proxy for managerial information. The dependent variable is investment, defined as capital expenditures divided by PPE. Qi is the market‐to‐book ratio of firm i. Q‐i is the average market‐to‐book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript –i refers to (the average across) firm i’s peers. The other explanatory variables (not reported) are defined in Table 1. The low (high) partition corresponds to the bottom (top) quintile of insider trading (Insider) in year t‐1, defined as the number of insider transactions in year t divided by the total year t’s transactions. We limit insider trades to open market stock transactions initiated by the top five executives (CEO, CFO, COO, President, and Chairman of the board). The sample period is from 1996 to 2008. The standard errors used to compute the t‐statistics (in squared brackets) are adjusted for heteroskedasticity and within‐firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p‐values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment‐to‐price sensitivities as a function of Insider (γ) (Low) (High) (p‐value) 0.063** 0.067** 0.516 [15.58] [13.90] 14.04% 13.13% 0.054** 0.032** [6.76] [3.89] 6.80% 3.48% Obs. 9,006 8,124 Mean (Insider (%)) 0.000 9.857 Qi (β) Q‐i (η) 0.026** Table 8: Investment‐to‐price sensitivities: Peers’ stock price informativeness (πB) and Managerial Information (γ) This table presents the results from estimations of equation (20) across different sample partitions based on a proxy for managerial information and three proxies for price informativeness of peers. The dependent variable is investment, defined as capital expenditures divided by PPE. Qi is the market‐to‐book ratio of firm i. Q‐i is the average market‐to‐book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript –i refers to (the average across) firm i’s peers. The other explanatory variables (not reported) are defined in the Table 1. The sample is first partitioned into low and high groups based on the bottom and top quintiles of the (de‐correlated) peers’ average price informativeness in year t‐1 (Ψ‐i+, LRMV‐
+
+
i , and APIN‐i as defined in section 4.3.1). Then, we further partition the (low and high) groups in two sub‐groups based on whether the value of Insider is below or above the median. Insider corresponds to the number of insider transactions divided by the total number of transactions. The sample period is from 1996 to 2008 (2004 for APIN). The standard errors used to compute the t‐statistics (in squared brackets) are adjusted for heteroskedasticity and within‐firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p‐values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment‐to‐price sensitivities as a function of Ψ‐i+ and Insider (γ) Panel A: Low Ψ‐i+ Qi (β) High Ψ‐i+ Low Insider High Insider p‐value 0.073** 0.064** 0.188 [10.80] [8.63] Low Insider High Insider p‐value 0.053** 0.057** 0.317 [7.96] [9.00] 12.79% 11.07% 0.036** 0.030* [3.22] [2.41] 3.92% 3.00% 16.11% 1.06% Obs. 3,943 3,947 3,953 3,960 Mean (Ψi) 2.243 2.720 2.628 2.477 Mean (Ψ‐i) 1.239 1.281 2.858 2.837 Mean (Insideri) 0.043 5.140 0.036 3.634 Q‐i (η) 0.353 12.29% 13.73% 0.131** 0.009 [7.37] [0.40] 0.000** Table 8: Investment‐to‐price sensitivities: Price informativeness (πA and πB) and Managerial Information (γ) ‐ Continued Investment‐to‐price sensitivities as a function of LMSW‐i+and Insider (γ) Panel B : Low LMSW‐i+ High LMSW‐i+ Low Insider High Insider p‐value 0.085** 0.068** 0.068* [10.92] [8.35] 15.30% 12.44% 14.97% 10.30% 0.048** 0.040** 0.024 0.035 [3.89] [3.80] [1.31] [1.78] 5.60% 4.46% 2.56% 3.53% Obs. 3,816 3,823 3,823 3,835 Mean (LMSWi) 0.007 0.010 0.007 0.004 Mean (LMSW‐i) ‐0.032 ‐0.031 0.018 0.018 Mean (Insideri) 0.042 4.563 0.042 3.750 Qi (β) Q‐i (η) 0.318 Low Insider High Insider p‐value 0.076** 0.050** 0.005** [11.21] [6.51] 0.647 Table 8: Investment‐to‐price sensitivities: Price informativeness (πA and πB) and Managerial Information (γ) ‐ Continued Investment‐to‐price sensitivities as a function of APIN‐i+and Insider (γ) Panel C : Low APIN‐i+ Qi (β) Q‐i (η) High APIN‐i+ Low Insider High insider p‐value 0.057** 0.051** 0.322 [7.67] Low Insider High Insider p‐value 0.110** 0.059** 0.932 [5.27] [3.63] [3.95] 8.83% 8.61% 13.42% 9.26% ‐0.024* ‐0.023 ‐0.051 0.026 [2.13] [1.52] [1.29] [1.12] ‐2.47% ‐2.32% ‐3.97% 1.95% 0.503 Obs. 1,001 1,004 1,005 1,008 Mean (APINi) 0.156 0.194 0.116 0.177 Mean (APIN‐i) 0.117 0.119 0.215 0.213 Mean (Insideri) 0.046 6.467 0.064 5.988 0.046** Table 9: Investment‐to‐price sensitivities: Correlation between demands (q) This table presents the results from estimations of equation (20) across different sample partitions based on proxies for the correlation between the demands for firms’ products. The dependent variable is investment, defined as capital expenditures divided by PPE. Qi is the market‐to‐book ratio of firm i. Q‐i is the average market‐to‐book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript –i refers to (the average across) firm i’s peers. The other explanatory variables (not reported) are defined in Table 1. The low (high) partition corresponds to the bottom (top) quintile of each partitioning variable (in year t‐1). We use three proxies. Sales correlation is the correlation between a firm’s sales and the average sales of its peers (using quarterly information over the past three years). CF correlation is the correlation between a firm’s cash flows and the average cash flows of its peers (using quarterly information over the past three years). Similarity is the similarity score (based on firms’ description of their products) provided by Hoberg and Phillips (2010). The sample period is from 1996 to 2008 (2004 with APIN). The standard errors used to compute the t‐statistics (in squared brackets) are adjusted for heteroskedasticity and within‐firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p‐values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment‐to‐price sensitivities as a function product relatedness (q)
SalesCorrelation
Qi (β) Q‐i (η) Obs. SalesCorr.
Score
CFCorr.
(Low) (High) 0.057** [12.90] 11.85% 0.018* [2.27] 2.08% 0.054** [13.90] 9.61% 0.047** [5.74] 4.70% 7,284 ‐0.382 7,274 0.694 ‐ ‐ ‐ ‐ CFCorrelation
(p‐value) 0.279 0.006** (Low) (High) 0.058** [14.42] 11.94% 0.024** [2.92] 2.71% 6,987 0.047** [9.73] 8.13% 0.053** [5.48] 5.56% 6,987 ‐ ‐ ‐0.451 0.597 ‐ ‐ Similarity
(p‐value) 0.031** 0.011** (Low) (High) (p‐value) 0.063** [16.71] 11.90% 0.034** [5.89] 4.01% 8,138 0.046** [11.55] 10.35% 0.049** [3.96] 6.02% 8,101 ‐ ‐ ‐ ‐ 0.000** 0.132 0.011 0.057