Short-Term Shareholders
John Thanassoulis∗
Warwick Business School, University of Warwick†
July 17, 2014
Abstract
This paper studies the effect of corporate investors with short investment horizons
on Board business model choice; the price of key inputs under general equilibrium; and
CEO incentives. When investors have imperfect information as to the skills of the firm,
business model choice sends a signal. Pooling on business models which will only succeed
for the best management raises short run equity values. This pooling effect leads to the
mis-allocation of too many firms to risky technologies, an increase in the cost of equity
capital, and a bubble in the price of key inputs which is pushed above fundamentals. The
business-model distortion effect grows with the elasticity of input supply. A market signal
as to the true ability of management can both increase and reduce the distortion. CEO
incentives are robustly biased towards short-run bonuses, and weaken incentives for effort
on any actions not immediately priced by the market.
Keywords: investor time-horizons; short-term shareholders; CEO compensation; cost of
capital; short-termism; bonuses; shareholder register.
JEL Classification: G12, G34, L21, L25.
∗
email: john.thanassoulis@wbs.ac.uk. https://sites.google.com/site/thanassoulis/
I would like to thank Roberto Barontini, Vincent Crawford, Alexander Gumbel, James Malcolmson,
Joao Montez, Alan Morrison, Pasquale Schiraldi, Richard Taffler, Mungo Wilson, and Peyton Young for
helpful comments, as well as seminar audiences at Oxford University, London Business School, Cambridge
University, EFMA 2013, and at the Swiss IO day 2013. All errors remain my own.
†
Oxford-Man Institute, University of Oxford, Associate Member and Nuffield College, University of
Oxford, Associate Member.
1
Introduction
There is widespread public concern that some shareholders are not committed to the long
term success of the firms they own. Lack of appropriate shareholder oversight has been
blamed for many corporate failings in the US and UK economies. Short-term shareholders
are accused of distorting corporate investment decisions away from long run growth and
the true interests of owners and the economy. Such short-termism may, for example,
be the key theme behind the collapse of UK manufacturing since the second world war
(Mayer (2013)); and is an important difference between US/UK ownership structures
versus those in Germany and other Civil Law based countries (La Porta, Lopez-de-Silanes,
Shleifer, and Vishny (1998)). This long standing concern over short-term shareholders
has led to persistent calls for regulatory intervention to try to encourage long-term share
ownership. For example, in the US the Aspen Institute (2009) allege short-termism in the
US is ‘system-wide.’ They propose, inter alia, that shareholders should be able to vote
only after a minimum holding period to try to ensure only long-term owners influence
corporate decisions.1 This paper rigorously studies these fears using theoretical Finance
and Industrial Organization techniques to explore the effect of corporate investors with
short investment horizons on Board business model choice; the price of key inputs under
general equilibrium; and CEO incentives.
I build a tractable general equilibrium model in which firm business-model choices,
resultant input purchases, and shareholders interact. There are two key assumptions
which underpin the analysis. The first is that there is an information gap between the
firm and investors. The Board of a firm have superior information as to their management
skill and so the risks and rewards which attach to different business model choices. This
asymmetric information assumption is not controversial.2 The second assumption of this
work is that the Board of a firm seeks to maximise the aggregate expected value of the
shareholders on their register at the time a business decision is taken. This is one of
two standard paradigms used in the Finance literature. For example, the Pecking Order
theory of capital structure uses this assumption. Specifically, the seminal work of Myers
and Majluf (1984) has the firm maximising the value of the old shareholders as opposed to
those who might buy the stock in the future, and this distinction gives rise to the negative
signalling effects of issuing equity. The second paradigm is to posit that firms maximise
net present value. With the presence of shareholders this approach of npv maximisation
is delivered by the Fisher Separation Theorem (Fisher (1930, p141)). The Separation
1
In the UK the Kay review (2012) also concluded that ‘short-termism is a problem (Executive Summary, para ii)’. They proposed, inter alia, that CEO remuneration should be altered to forcibly reduce
the weighting on current performance. In the EU the Commission are consulting on increasing the voting
weight of shareholders who are long-term holders of the stock. (See Brussels aims to reward investor
loyalty, Financial Times, Jan 23, 2013.)
2
However this is not to say that management cannot learn anything from the market; Foucault and
Laurent (forthcoming).
1
Theorem notes that npv maximisation optimises every owner’s consumption opportunity
set and so would be unanimously supported. In capital markets in which risk-sharing
opportunities are not complete, or asymmetric information exists, the application of the
Fisher Separation Theorem is disputed (DeAngelo (1981)).
In the model studied the firms in an industry must decide between two competing
technologies. One is a business-as-usual technology and offers a known expected payoff.
The second is a risky technology. The expected payoff of this technology depends upon the
skills the firm has to profit from the opportunity. For some firms the expected payoff from
the risky technology will outweigh those expected from the business-as-usual technology.
As noted, the Board has better information as to the firm’s ability than investors. These
assumptions have broad applicability. For example, prior to the financial crisis a bank
could decide to pursue a business model of securitising mortgage backed securities, or
not. Not all banks would be equally adept at assessing the value and riskiness of the
underlying assets. Outside of Finance, the risky business-model might be outsourcing a
part of the supply chain offshore to a developing country. Not all firms will be equally
adept at managing this method of production.
If the firms were held solely by long-term investors, each firm’s Board could maximise
its value by developing the technology with the greatest expected long run payoff. However, suppose that the population of shareholders include a proportion who are subject
to liquidity shocks in which case they will need to sell their stake before payoffs are fully
realised. Or equivalently suppose the shareholder population contains a proportion of
owners who buy shares intending a short investment horizon. Such shareholders care
about the price of the shares at the point they sell. The Board, representing the totality
of the shareholder base, is therefore concerned for both the time-path of the share price
as well as the final payoff. An implication of management having better information as
to the firm’s abilities than outside investors is that the firm’s choice of technology sends
a signal to the market. Firms with the management most able to profit from the risky
technology would select it. However for other firms this effect creates a short-run value
to pooling with such firms. By choosing the risky technology there will be an increase in
the short-run market value due to the market inference that the firm type must be drawn
from a set which includes high ability firms. Firms in an economy containing short-term
shareholders will be willing to sacrifice some long run expected payoff for this short run
price increase.
Short-term shareholders and asymmetric market information therefore create a value
to pooling on the risky technology. It follows that the presence of short-term shareholders
increases the demand for the inputs required for the risky technology above the level
justified by fundamentals. This pushes the price of the inputs required for the risky
technology up. A bubble is created. This is a bubble in the technical sense that the input
price for the technology is divorced from fundamentals, however it is not a bubble in which
2
prices rise without limit in this model. The increase in the price of the inputs required
to develop the risky technology will imply that, ceteris paribus, firms will enter into the
risky technology at a smaller scale. Market clearing then implies that more firms will be
subject to the firm mis-allocation effect. On average therefore too many firms will choose
to develop the risky technology, and the inputs required to do so are more expensive.
Hence the cost of equity capital must rise as the equity is used ever less effectively as
the short-term pressures rise. If the input can be supplied elastically then the increased
demand will lead to increased supply, and a more modest input price rise. In this case
I show that the pooling value increases further, due to the reduction in the price of the
input asset, hence the mis-allocation effect is exacerbated.
Information asymmetry is key to the mechanism developed in this study. If there were
perfect information as to firm type then the liquidity preferences of investors would be
immaterial and the Fisher Separation Theorem would apply. Given this I explore the
effect of an informative signal on firm type on the business choice decisions. The effect
is ambiguous: even though the precision with which the market sees the firm’s type is
enhanced, this does not imply reduced business-model distortion. The decision to distort
or not the business model choice hinges on the expected value of the firm conditional
on being of a type which would select the risky technology. This is the statistical entity
which underpins the market’s short-term valuation of a firm. For example, if the signal
the market receives is poor but sufficiently precise, then the weight attached to high
types falls, but it falls least for the highest types. Hence the expected value conditional
on choosing the risky technology can rise, and so the distortion in firm behaviour can be
exacerbated.
The Board require the CEO to enact the business-model decisions, as well as to improve
firm type by exerting effort. Incentives can be provided by appropriate use of bonuses at
various time horizons, and these of course cost money. When the firm is owned in part
by short-term shareholders the balance of benefit and cost in the provision of managerial
incentives is altered. I show that greater short-term shareholder pressure leads robustly
to Boards under-weighting long-term CEO incentives (e.g. LTIPs), lowering the extent
to which the CEO is incentivised to raise the firm’s long-run potential. Short-term shareholders undervalue effort to improve long-term performance to the extent that such effort
is not factored into the early share price. Thus, as the horizon of the investors shrinks,
the Board structure CEO incentives to be based increasingly on the short-term so that
the CEO focuses on projects whose value is quickly apparent to the market, and not on
valuable but longer-term endeavours.
In the final part of this paper, I empirically demonstrate that short-termism in share
ownership differs significantly between the leading civil law countries (Germany/Switzerland)
and the leading common law one (US). Hence I conclude that understanding the channels
through which short-term ownership operates is relevant, and can potentially contribute
3
to the active policy debate.
2
Review Of The Literature
The objective of this study is to explore how corporate investors with short investment
horizons affect business model choice; the price of key inputs in general equilibrium; and
CEO incentives. There is a large literature on managerial myopia in which CEOs exogenously have the current share price as part of their remuneration, but the economy wide
implications of corporate investors with short investment horizons has, I believe, rarely
been analysed theoretically. Two salient papers in this regard are Bolton, Scheinkman
and Xiong (2006) and Albagli, Hellwig, and Tsyvinski (2013). Bolton et al. study a setting in which some investors are rational while others, and in particular would-be buyers,
are over-optimistic and so incorrectly value some projects. The authors show that the
optimal CEO compensation in this setting is one which encourages the CEO to pursue the
projects which potential investors will over-value the most. This study is complementary
to Bolton, Scheinkman and Xiong (2006) as, firstly, there is no bounded rationality just
differences in the realisation of individual liquidity shocks, and secondly we conduct a
general equilibrium analysis of business model choice. Albagli et al. (2013) develop a
rational expectations model of information aggregation in asset markets and demonstrate
that this can lead to corporate distortions. Their model is fundamentally different in
that the firm has no control over the information environment whereas here the Board
do, allowing us to explore how improvements in the information environment alter the
incentives for firms to invest so as to change further the information available to the asset
market.
The relative paucity of theoretical studies of investor time horizons on firm behaviour
has not held back a fruitful empirical research agenda which seeks to make the link
between the two. An early contribution to this endeavour is Gaspar, Massa, and Matos
(2005) who construct an index of investor time-horizon for a population of investors and
show that firms with short-term owners do less well in acquisition situations. Since this
work others have also demonstrated empirically that short investor time horizons are
correlated with firms being less responsive to investment opportunities (Derrien, Kecskes,
and Thesmar (2013), Polk and Sapienza (2009)). Graham, Harvey, and Rajgopal (2005)
offer evidence that publicly owned firms, which are argued to have owners with short
investment horizons, cause management to forego valuable investment opportunities if
needed to lower the volatility of current announced results. Brochet, Loumioti, and
Serafeim (2012) offer evidence that the cost of equity capital declines with the time horizon
of investors.
A full and influential theoretical literature exists which explores managerial myopia
induced by having a CEO incentivised on the short-term share price when there is asym4
metric information between the market and the manager. Stein (1989) shows that if the
market cannot observe investment decisions then the short-run motivated manager will
under-invest. Bebchuk and Stole (1993) note that if however the market can observe
the investment decision, as is the case here, then the short-run motivated manager will
over-invest. In both cases the market draws inferences on the extent of investment from
the earnings which are announced. The mechanism and analysis here are both different.
The market here draws inferences in a general equilibrium setting on the ability of management by looking at the business-model choice across firms; I do not study the volume
of investment as these papers do. Further these analyses are silent on the relationship
between ownership liquidity, input price distortions, cross-sectional mis-allocation, and
the link between information precision and business-model choice.
The literature linking the time profile of executive compensation to management myopia has seen numerous recent contributions, though the implications owner liquidity has
on the incentives have remained unexplored. Thanassoulis (2013) links optimal CEO incentives with industry structure. Edmans et al. (2012) and He (2012) derive the optimal
contract in a principal-agent setting if an executive can save and take myopic actions. All
of these models demonstrate that deferral of pay is part of the optimal contract, but they
remain silent on the effect of short term shareholders on corporate outcomes.
This work is also related to the rich literature on bubbles in asset markets. Allen and
Gale (2000) offer a model of asset bubbles in which investors borrow from a banking sector
which cannot observe their investments. Due to assumed limited liability the investors
seek to risk-shift and move the funds into the risky asset, thus pushing the price of
the risky asset above fundamental levels. A related mechanism is at work in Allen and
Gorton (1993).3 Unlike these works, there is no risk-shifting rationale in the framework
here. Rather maximisation of shareholder value is linked to firms’ technology choices, and
hence to the equilibrium price of input assets. Further this prior work on bubbles is silent
on the optimal incentive contracts for the CEOs of firms subject to these effects.
3
The Model
Consider a continuum of firms indexed by type variable: τ ∈ [0, 1] . The types of firms in
the population are distributed according to the commonly known cumulative distribution
function G (τ ) with probability density g (τ ) . The Board of the firm privately knows its
type. Thus management are more informed about their firm’s capabilities than investors.
The Board publicly selects and announces a business activity choice at time t = 1. There
are two possible technologies to select from. The Board can choose to develop a businessas-usual technology. This technology requires an input priced at the numeraire of 1 and
yields an expected payoff at t = 2 of r > 1. Alternatively the Board can choose to develop
3
For a review of the broader literature on bubbles see Camerer (1989).
5
a risky technology. In this case the firm must buy a different input labelled the input
asset. It has a price per unit of P . The t = 2 expected payoff from investing a unit in the
risky technology is R̄ · τ. This simple formulation captures that for some firms the risky
technology generates a higher expected payoff. However for others the risky technology is
dominated in that the firm’s skills are better adapted to profit from the business-as-usual
technology. One can interpret the risky technology as a true new business model, or as a
fad or fashion. What is key in the model is that the new technology is not self-evidently
a good idea for all firms in the industry. For example, firms might not be equally adept
at managing overseas factories and long distance supply chains; or financial institutions
might not be equally adept at trading and managing a portfolio of loans to a given sector.
Each firm is assumed to have a unit of capital, and the input asset is assumed to be
in restricted supply of b. I assume that
R̄b < r < R̄
(1)
This guarantees that we remain within an interior solution so that an intermediate proportion of firms will develop the risky technology. The price, P, of the input asset will be
determined in equilibrium by the balance of supply and demand. The input asset captures
the specific input needed to access the risky business line. For example in finance, the
input asset may be sub-prime mortgages which can be securitized and so used to create
tranches of Mortgage Backed Securities (MBSs). The type τ captures that firms differ in
their ability to value and/or harness these assets.
The firms are assumed to be entirely equity owned. The shareholders however will not
all be long-term owners, and so will not necessarily hold their shares until after all profits
are realised. Shareholders are ex ante identical, but have a probability L of suffering a
liquidity shock. This liquidity shock assumption is standard in the banking literature
for example (Allen and Gale (2009)). Those who suffer a liquidity shock will sell their
holding at the end of t = 1, after the Board make their technology choice, but before
the profits are realised. The sale price at the end of t = 1 will be the fair market value
which is the expected t = 2 payoff conditional on all public information. The remaining
shareholders, proportion 1 − L, hold their shares until the payoffs are realised at t = 2.4
Hence L measures the time horizon of shareholders in the industry.
The probability L ∈ [0, 1) of short-term ownership is common knowledge. In practice
chairmen claim to develop an insight for the likely time horizon of shareholders through
extensive discussion with owners and experience of the prior behaviour of given investors.5
4
The model however has a second equivalent interpretation that every firm in the economy/industry
contains a proportion L of shareholders who intentionally have a short time horizon and will sell before
results are realised, with the remainder being buy-and-hold investors.
5
For example, the Chairman of Cadbury, the main UK confectionery company until its purchase by
Kraft, claimed to be very aware of the time horizon of his investors, and how it changed during the
takeover process. See ‘The inside story of the Cadbury Takeover.’ Financial Times, March 12, 2010.
6
The academic empirical literature demonstrates that by analysing the breadth of investors’
portfolios and their stock turnover rate, investor time horizons can be deduced.6 The
objective function of the Board is to seek to maximise the expected value generated for
the shareholders who own the firm at the time the business decision is made.
The timeline of the entire model is depicted graphically in Figure 1. I restrict attention
in the analysis to pure strategy Nash equilibria.
t=1
Start of period
t=2
End of period
-
Buy a unit of
input, cost 1
-
-
Buy 1/P units of
input asset
-
Develop business as
usual technology
Expected payoff
r
Board of firm type τ
decides and announces
business activity.
Develop fad /
risky technology
Short-term
shareholders sell.
Expected payoff
Rτ /P
All profits returned
to shareholders.
Figure 1: Time line of the model.
Notes: The Board select the technology the firm develops so as to maximise the expected value of the
shareholders who own the firm at the point the decision is made. Short-term shareholders (e.g. because of
liquidity shocks) sell after the business decision, but before payoffs are realised. Long term shareholders
hold their shares until the payoffs are realised. Firms are endowed with a unit of capital which they use to
buy the required input for the technology chosen. All payoffs are returned to shareholders at the end of
t = 2. The firm type is private information, the choice of technology and the probability L of short-term
ownership are both public information.
6
Bushee (1998), Gaspar, Massa, and Matos (2005), and Derrien, Kecskes, and Thesmar (2013).
7
4
Shareholder and Technology Choice Analysis
In this section we solve the model to explore the relationship between short-term shareholders, the price of the input to the risky technology, and the allocation of firms to
different technologies.
4.1
Input Asset Fundamental Value
The fundamental value of an asset is the market price established when agents are obliged
to subsequently maintain their holdings for ever (Allen, Morris, and Postlewaite (1993)).
The fundamental value of the input asset can therefore be found when all firms are longterm value maximisers.
If a firm of type τ invests in the business-as-usual technology then it generates an
expected long-run payoff of r. If instead it invests in the risky technology then it invests
at a scale of 1/P and so its expected payoff is R̄τ /P . It is immediate that if a firm of type
τ would invest in the risky technology, so would all firms of higher type. Market clearing
at the fundamental price P f requires that the total supply of the input asset is bought.
Define the function q (y) as the type for which there exists a mass y of higher type firms.
Thus G [q (y)] := 1 − y. The market clearing condition is then that firms τ ∈ [τ̂ , 1] invest
in the risky technology where
Z
1
τ =τ̂
1
g (τ ) dτ = b ⇒ τ̂ = q bP f
f
P
(2)
Market clearing requires the borderline firm τ̂ to be indifferent between developing the
risky and the safe technology. Hence the fundamental price P f is defined implicitly by
the relation
R̄q bP f P f = r
(3)
Lemma 1 The fundamental price for the input asset (equation (3)) exists and is unique.
Proof. All proofs are in the appendix.
4.2
Short-term Shareholder Analysis
We now analyse the general model in which firms are owned by shareholders with a
probability L of a liquidity shock and so early sale. A strategy for the Board of each firm
is a decision function which maps the privately known firm type and the publicly known
shareholder time horizon to a choice between developing the risky or the business-as-usual
technology. It follows that, observing the business model chosen, the market can make
inferences as to the set of types from which the firm must be drawn. This will affect the
price shareholders will receive if they sell early.
8
The Board seeks to maximise the aggregate expected value of the shareholders. The
proportion 1 − L of the shareholders will be long-term holders of the stock and see the
realised payoffs. The expectation of this payoff is R̄τ /P as the Board are aware of the
true type τ of their firm. The proportion L of shareholders will be short-term owners
and sell their holding before the business results are realised. Thus what matters to these
shareholders is the market price they receive for their stock. The value of the equity at the
point of sale (end t = 1) will be the expected payoff at t = 2 conditional on all publicly
available information. Hence if a firm of type τ develops the risky technology then the
Board’s objective function at t = 1 takes value V risk (τ, L) given by:
V risk (τ, L) = (1 − L) ·
+L
R̄τ /P
| {z }
Expected t=2 payoff
R̄
· E (τ | risky chosen)
|P
{z
}
(4)
Equity value at end t=1
The objective function (4) follows from the assumption that the Board maximises the
expected value of the shareholders who own the firm at the point of taking a business
decision. The market’s inference as to expected firm payoff depends upon the equilibrium
strategy of the Board:
Lemma 2 The Board’s strategy takes a cut-off form: if firm type is above some level
τ ∗ (L) then the Board decides to develop the risky technology; otherwise it develops the
safe technology.
The proof of Lemma 2 follows by noting that firms of higher type τ create greater
expected value for their long-term shareholders from developing the risky technology
than firms with lower type. Short-term shareholders are indifferent between all firm types
which select the same technology. This is because firm type is private information and so
not priced in until payoffs are realised. The partition of the type space then follows.
This brings us to the first main result of this analysis:
Proposition 1 In an economy/industry with a probability L of short term shareholder
ownership:
1. Short term shareholders create a bubble in the price of the input asset: P (L) > P f .
This bubble becomes more severe the larger is the probability of short-term ownership
(dP (L) /dL > 0) .
2. Inefficiently many firms develop the risky technology. This mis-allocation grows in
the probability of short-term ownership, L.
3. The input asset price is uniquely defined by:
R̄
R̄
r = q (bP ) + L 2
P
bP
9
Z
1
1 − G (τ ) dτ
τ =q(bP )
(5)
4. The ex ante cost of equity capital for a representative firm is increasing in the
probability of short-term ownership, L.
The Board of a firm are assumed in this study to seek to maximise the value of the
shareholders who own the firm at the time a business decision is being taken. Therefore,
in assessing whether to pursue a new risky technology, or adopt the business-as-usual
technology, the Board are concerned with the path of their share price as well as the net
present value maximising decision, (4). If an action can be taken which increases the
market value of the firm’s equity in the short term then this is desirable as it will increase
the payoff of short-term shareholders. As investors have asymmetric information as to the
type of the firm, the short-run share price can be increased by pooling with high quality
firms. Here this means developing the risky technology so as to alter the information
available to investors – even at the cost of some long-term value. Proposition 1 shows
that across the industry or market such behaviour has general equilibrium effects: it leads
to cross-sectional distortions in technology choices; bubbles in input asset markets; and
increases in the cost of capital.
That shareholders with short time horizons, should lead to bubbles, that is to distortions in the price of real assets, is, I believe, a new insight. This is a bubble in the technical
sense (Allen, Morris and Postlewaite (1993), and Allen and Gale (2000)), but perhaps not
in the common use of the term as this is not a repeated game in which the asset price rises
indefinitely. To understand the result suppose that there was no bubble in the price of
the input asset (e.g. sub-prime mortgages, or IT skills in a developing country) which is
therefore at its fundamental level, P f (3). Each firm which pursues the risky technology
will do so at a scale of 1/P f . Market clearing would then guarantee that the marginal
firm which develops the risky technology extracts the same expected net present value as
it would do from the business-as-usual technology. Now consider the incentives for the
Board of a firm of type just below this cut-off level. At the fundamental price P f for the
input asset the net present value of the risky technology is below that from the business
as usual option. Thus long term-shareholders would lose out slightly from a decision to
invest in the risky technology. The net present value would fall in a continuous way as
the firm type fell further from the cut-off level. However, if the firm did invest in the risky
technology, then the market would infer, mistakenly, that the firm was drawn from the
top portion of the type distribution. Hence the market value of the equity at the end of
t = 1 would jump up discontinuously. This would represent a discontinuous gain for any
shareholders who suffered a liquidity shock and sold early, and so would outweigh the loss
to the long-term shareholders.7
7
The t = 1 share price is not raised here by the absence of short-sellers (Lamont (2004)). Neither long
nor short term shareholders have privileged information at t = 1 as to whether the firm is at the top or
bottom end of the ability range which self-selects the risky technology. The share price is the expected
firm value over this firm ability range.
10
This implies that firms below the efficient cut-off type would buy the input asset at
its fundamental price. This extra demand at the fundamental price will force the price
of the input asset up. Hence a bubble is created in the input asset. As the probability
of short-term ownership in the economy grows, so the Board is willing to sacrifice more
long-run value in return for the short-run boost provided to the t = 1 market value of the
equity from pooling with the best management firms and developing the risky technology.
This increase in demand pushes the price of the input asset up yet further. So we have
the first result of Proposition 1.
The increasing mis-allocation of firms to the risky technology is then an implication of
market clearing, and only becomes apparent due to the general equilibrium nature of the
analysis. As the probability of short-term ownership grows, so the price of the input asset
rises. Other things equal therefore, the firms which invest in the risky technology now
use less of the more expensive input asset, and enter the risky technology at a smaller
scale. Market clearing for the risky asset then requires that more firms invest in the
risky technology. Thus the proportion of firms which develop the risky technology grows,
moving further away from the first-best, in the probability of short-term ownership in the
economy or industry.
The mis-allocation effect has an immediate and important further consequence on the
cost of equity capital. All investors realise that as the probability of short-term ownership
in an industry or economy increases, so more firms will be drawn into developing the
risky technology at the expense of long-run value. Hence, ex ante at the investment stage
(t = 0) , there is a greater probability that a firm will choose a business line not in its
long term interests. This is a cross-sectional mis-allocation effect which lowers the t = 0
expected value of firms. Further, there is also a second general equilibrium effect. An
increase in the probability of short-term ownership raises the price of the input asset, and
this also lowers the expected value of any firm developing the risky technology. Hence
through this channel also the representative firm sees its value decline at the financing
stage. Both of these effects lower the value of firms at t = 0. Therefore entrepreneurs must
sell a larger proportion of their firms to raise the desired dollar investment. Hence the
cost of equity capital rises with the probability of short-term ownership. This result offers
support for the policy objective suggested in both the UK and the US that shareholders
should be encouraged to be long term holders of a stock.8
Figure 2 demonstrates the input asset price bubble and cost of capital increases resulting from short-term shareholders for the case of uniformly distributed firm types. The
calculations for this numerical simulation are contained in Appendix B.
8
See footnote 1 and the discussion which refers to it.
11
Figure 2: Numerical Simulation Depicting Proposition 1
Notes: The left hand graph depicts the critical firm type, τ , for any given probability of short-term
ownership in the industry/economy. Types above the critical level develop the risky technology. The
mis-allocation of firms to technologies grows as the probability of short-term ownership increases. The
right hand panel depicts the magnitude of the growth in the price of the input asset, and in the cost of
equity capital, as a function of the probability of short-term ownership, L. The greater the probability
of short-term ownership, the greater the distortions engendered in these related markets. Calculations
underlying these simulations are contained in Appendix B.
5
Robustness to Elasticity of Supply of the Input Asset
The presence of short-term shareholders in the economy causes too many firms to invest
in the high risk technology and it causes bubbles to form in the price of inputs, distorting
input prices. In this section we explore the robustness of these effects to the elasticity of
supply of the input asset required for the high risk technology. In particular if the input
asset should be perfectly elastically supplied, its price cannot rise and so the bubble effect
cannot exist in this extreme case. This section asks whether the distortionary effect of too
many firms entering the risky technology applies irrespective of the elasticity of supply
of the input asset, and it asks whether the distortion in the price for the input asset also
always exists except in the polar case of perfect supply elasticity.
Suppose that the supply S (P ) of the input asset responds to price according to:
S (P ) := b ·
P
Pf
ζ
(6)
The supply function has a constant elasticity ζ with respect to price to facilitate the
empirical interpretation of the results. The benchmark example had inelastic supply
(ζ = 0) . The supply function (6) is normalised so that absent short-term shareholders,
and for any elasticity of supply ζ, the fundamental price of the input asset is invariant at
the level P f given by (3). To see this note that at P = P f , the supply is b. At the price P f
the critical firm type is therefore τ̂ , given by (2). Hence absent short-term shareholders,
12
and for any supply elasticity, the first best situation would have types [τ̂ , 1] entering the
risky technology. I augment (1) and restrict attention to parameters such that
b<
r r f ζ
·
P
R̄
R̄
(7)
This is sufficient to ensure existence of the equilibrium price for any given elasticity of
supply, ζ.
We can establish the price of the input asset, P, and the critical firm type, τ̃ , above
which the Board will pursue the risky technology.
Lemma 3 In an industry with elasticity of supply ζ and with L short-term shareholders,
the critical firm type, τ̃ , which just selects the risky technology satisfies
r
R̄
"
Pf
b
ζ
1
# 1+ζ
(1 − G (τ̃ ))
L
= τ̃ +
1 − G (τ̃ )
Z
1
1 − G (τ ) dτ
(8)
τ =τ̃
The critical firm type is uniquely defined and the price of input asset, P , is given implicitly
by
ζ !
P
τ̃ = q b · P
(9)
Pf
Lemma 3 allows us to establish the robustness of the mis-allocation and price distortion
results in Proposition 1 to an elastically supplied input asset:
Proposition 2 When the input asset is elastically supplied:
1. For anything less than perfectly elastic supply, ζ < ∞, the price of the input asset
grows in the proportion of short-term shareholders.
2. The extent of mis-allocation to the risky technology in any industry grows with the
elasticity of supply of the input asset: ∂ τ̃ /∂ζ < 0; and the mis-allocation grows with
the proportion of short-term shareholders, ∂ τ̃ /∂L < 0.
Irrespective of the elasticity of supply of the input asset, the input asset sees its price
distorted upwards from its fundamental level. The logic outlined in Section 4 continues
to apply: firms seek to increase their short run value by following a pooling strategy and
are willing to sacrifice some long run value to benefit shareholders who need to sell early.
The existence of a price distortion is therefore robust, though its magnitude falls as the
elasticity of supply increases.
Part 2 demonstrates that the mis-allocation result that short-term shareholder pressure
causes an excessive proportion of the firms to choose the risky technology is entirely robust
to the introduction of elastic input supply. Holding the proportion L > 0 of short-term
13
shareholders in the economy fixed, the mis-allocation of firms to the risky technology will
grow with the elasticity of supply. To see why, consider the marginal firm type which just
elects to develop the risky technology, and consider the thought experiment of increasing
the elasticity of supply of the input asset. The increased elasticity of supply must increase
the volume of the input asset on the market. If there were no change in the identity of
the marginal firm, the price of the input asset would fall to allow the extra supply to be
absorbed. The marginal firm will now however benefit from a lower input price and so
strictly benefit from developing the risky technology. This is a contradiction to the firm
being marginal, and so more firms will find it profitable to develop the risky technology
for the short run pooling value increase. Hence the mis-allocation effect is exacerbated.
6
Market Learning From Signals As To Firm Type
The information asymmetry between the firm and investors has played a key role in this
analysis. The Board see value in pooling on business-model choice with high ability firms
as this alters the information environment of investors and so the near-term share price.
In this section we explore the effect of an informative signal on firm type. We will see
that this can actually exacerbate the distortion.
Let us suppose that the firm types in the population are distribution according to
a normal distribution τ ∼ N (µ, 1/hµ ) . I ignore the restriction that τ ∈ [0, 1] and so
implicitly assume that the precision hµ is high enough that the mass outside of the unit
interval is deminimis. At the general equilibrium the introduction of some short-term
shareholders, L > 0, causes a distortion as too many firms opt for the risky technology to
benefit in the short-term from pooling. Hence firms τ ∈ [τ̃ , 1] enter the risky technology
with τ̃ < τ̂ the first best level ((2), Proposition 1). The cut-off type τ̃ is indifferent
between entering the risky technology and not implying that (4):
r−
R̄
R̄τ̃
(1 − L) = L E (τ | τ ≥ τ̃ )
P
P
(10)
Now suppose that before any investment decisions (t = 0) a signal zi is generated as
to the type of an individual firm τi , where the subscript i denotes the firm. This signal is
centered on τi but is generated with normal noise so that zi ∼ N (τi , 1/hε ) . The market
14
will update their beliefs as to the type of firm i. Bayesian updating will deliver that9
τi ∼ N
zi hε + µhµ
1
,
hε + hµ hε + hµ
(11)
The presence of the signal will alter the critical firm i type, τ̃i , which will just be indifferent
between the two technologies. The critical firm type will satisfy the analogue of (10)
using the posterior distribution of firm i types, (11). If E (τi | τi ≥ τ̃ ) is greater than
E (τ | τ ≥ τ̃ ) , then as the left hand side of (10) is strictly declining in τ̃ , we must have
τ̃i < τ̃ . In words, if the signal increases the market’s estimation of firm i’s type conditional
on that type lying above τ̃ , then a firm of type τ̃ would strictly prefer to develop the risky
technology. Hence the critical firm type falls further below the first best cut-off.
However as a signal alters both the mean and the precision of the posterior distribution,
there is no simple relationship between the signal received and the expected mean of the
posterior distribution conditional on the type lying above a given level τ̃ . To proceed
further we note that the moments of the truncated normal distribution have an explicit
characterisation (Greene (2003), Theorem 24.2):
1
ϕ (α)
zi hε + µhµ
+p
E (τi | τi ≥ τ̃ ) =
µ )−(zi hε +µhµ )
hε + hµ
hε + hµ 1 − Φ (α) α= τ̃ (hε +h√
(12)
hε +hµ
where ϕ (·) and Φ (·) are the standard normal density and cumulative distribution. The
second term is known as the inverse Mills ratio. To allow analytical analysis I borrow
from the statistics literature and use Shore (1982) to closely approximate this ratio as
ϕ (α)
=
1 − Φ (α)
(
1.4184 [Φ (α)]0.8632
α≤0
−0.1368
1.4184 [1 − Φ (α)]
Φ (α) α ≥ 0
(13)
Of particular interest is the effect that a positive signal as to the type of firm i has
on the actions of this firm. This signal may or may not be justified due to the noise. A
positive signal is one such that zi ≥ µ.
Proposition 3 Suppose that there is a positive measure of short-term shareholders, L >
0. Consider a positive signal for firm i as regards the risky technology: zi ≥ µ.
1. If the market expects most firms to invest in the risky technology, τ̃ ≤ µ, then:
(a) The existence of a weak positive signal, zi ≈ µ, reduces the distortion in firm
i’s technology choice behaviour;
9
To see this note that through Bayes’ rule:
1
1
2
2
Pr ( τi | zi ) ∝ Pr ( zi | τi ) Pr (τi ) ∝ exp − hε (zi − τi ) · exp − hµ (τi − µ)
2
2
Completing the square of this expression in τi generates the result.
15
(b) The distortion in firm i’s technology choice behaviour increases in the strength
of the signal: τ̃i falls as the signal zi increases.
2. If the market expects most firms to invest in the safe technology, µ < τ̃ then:
(a) The existence of a weak positive signal, zi ≈ µ < τ̃ can increases the distortion
in firm i’s technology choice, and will do so if the precision of the signal is
great enough;
(b) The distortion in firm i’s technology choice behaviour is not monotonic with
increases in the strength of the signal. The distortion can be increased by better
strong signals, and reduced by better weak signals.
The proof of Proposition 3 uses the statistical approximation offered by Shore (1982)
to balance the change in both the mean and the precision of the posterior distribution
from given signals. There are two basic cases studied. The first is when the market
expects most firms to invest in the risky technology. This would be the case if the safe
returns r were relatively small compared to the returns from the risky technology (R̄). In
this case a positive signal is going to move the untruncated density of firm i’s type to the
right, and increase its precision. If however the signal is weak so that zi is close to the ex
ante expected value µ, then the truncated distribution does not change its expectation a
+µhµ
. The loss of
great deal, but the precision increases pulling mass to the new mean zihhεε+h
µ
mass from the right tail of the distribution lowers the market’s expectation of the firm’s
value conditional on choosing the risky technology. Hence the benefit of pooling is less and
so the distortion created by short-term shareholders is reduced. However, as the signal
grows in strength, more mass is moved in the truncated posterior to higher values and so
the market will assign higher expected types to firm i if indeed the firm does develop the
risky technology. Hence the benefits of pooling grow, and so firm i will deviate at even
lower type values.
The second part of Proposition 3 considers the case in which the market expects the
majority of firms not to invest in the risky technology; the returns are only good enough
for the few firms most suited to it. Now the existence of a signal which is only just positive,
and certainly below the cut-off type, can increase the distortion in firm i’s behaviour. The
signal will barely raise the expected value of the untruncated ex post distribution, but it
will increase the precision of the distribution and so reduce the mass in the tails. If the
increase in the precision assigned to firm i is great enough then the reduction in tail mass
causes the density function to be flatter over the whole region of types above the cut-off
τ̃ . This implies that the reduction is relatively larger at lower types above the cut-off
than higher types, causing the expected value conditional on being above the cut-off to
rise. This therefore increases the distortion in firm i’s behaviour. However, as the signal
16
improves the expected type of the firm conditional on being above the cut-off can be
dragged down or up depending on the parameter values.
7
Shareholder Time Horizons and Pay Structure
We now explicitly consider the CEO within the firm. The Board face a standard PrincipalAgent problem. They wish the CEO to exert effort to improve the firm, and can provide
incentives to do this by giving the CEO an equity stake and so exposing him or her to
improvements in the firm’s equity value. However a tension is now created with the second
objective of respecting the interests of the proportion L of short-term shareholders who
will sell early by guaranteeing a high early share price. All shareholders contribute to the
costs of providing incentives, but if the fruits of the CEO’s efforts are not fully priced
into the early share price, not all shareholders will benefit. This section will study the
outcome of this dilemma on the structure of CEO pay.
To pursue this analysis consider a single firm of type τi , and consider a contracting
stage at t = 0 between the Board (principal) and CEO (agent). Both the CEO and
Board are aware of the firm type τi . To study contracting with a risk-averse agent I use
the standard approach of normal payoffs and CEO mean-variance utility. If the CEO’s
payment is given by the random value W then the expected utility, gross of the effort cost
is:
E (U (W )) = E (W ) − (ρ/2) var (W )
(14)
The parameter ρ is the CEO’s coefficient of absolute risk aversion. The CEO’s outside
option is normalised to utility u.
Let us suppose that at t = 0 the Board can offer a contract to the CEO with three
parameters. The Board can offer a fixed wage payment f which I allow to take positive
or negative values.10 In addition the Board can use a bonus b as a proportion of market
value of the firm at t = 1, or a deferred (vested) bonus at t = 2 as a proportion v
of realised value, or any combination. These remuneration tools are all standard. The
bonus elements agreed between the Board and the CEO at t = 0 are private information
to the contracting parties. This assumption captures that in reality the Board is not
bound by publicly stated bonus rates.11 Normalise discounting to zero. Thus if the equity
value at time t ∈ {1, 2} is denoted Xt , then the CEO receives remuneration f +bX1 +vX2 .
I assume that the CEO makes the technology decision.
In the standard effort model, the CEO can raise the expected t = 2 payoff from either
10
A negative fixed fee, f, captures settings in which the CEO must first make a payment to the firm
in return for being hired with the incentive pay schedule.
11
One case study example is provided by the CEO of BP in 2010. The share price performance over
the period 07-09 would have led to no share award according to the publicly published criteria. In the
event the CEO was awarded a substantial bonus of shares regardless. See “BP’s Hayward Given 41%
Increase,” Financial Times, March 5, 2010.
17
strategy by an amount η at a personal effort cost of κη 2 /2. Thus the t = 2 expected
payoff from the risky technology would be η + R̄τ /P while that from the business-asusual technology would be η + r. The effort component, η, is privately chosen by the CEO
and not directly observable to others. The realised returns are observed at t = 2, and I
assume they are normally distributed around their expected values η + r, η + R̄τ /P .
Define the payoff variance of the business-as-usual technology as σs2 , and that of the risky
technology as σr2 .
As in the benchmark model, outside investors do not observe the firm’s type τi , they
are aware only of its distribution: G (τi ). The probability L of short-term ownership
continues to be common knowledge. As I consider one firm, suppose the price of the
input asset is constant at P.
7.1
The Equilibrium Incentive Contract
The market at t = 1 does not observe the remuneration contract and so must infer the
likely impact of CEO effort on firm type. The expected utility of the CEO from the risky
choice is denoted U risk (η, τ ) and is given, using the mean-variance assumption, by
U
risk
(η, τ ) = f +
bX1risk
R̄τ
κ
ρ
+v η+
− η 2 − v 2 σr2
P
2
2
(15)
The expected utility to the CEO from the business-as-usual (or safe) technology choice is
U safe (η, τ ) and is given by
ρ
κ
U safe (η, τ ) = f + bX1safe + v (η + r) − η 2 − v 2 σs2
2
2
(16)
Lemma 4 The CEO will improve the firm type by an amount η ∗ :
η∗ =
v
κ
(17)
Proof. Direct optimisation of CEO utility, (15) and (16), with respect to the effort level
η.
Lemma 4 demonstrates that the CEO’s effort choice depends upon the deferred bonus,
v, but not the short-run bonus b. This is because in the model studied, before the
realisation of results at t = 2, private effort exerted to raise the expected payoffs of the
business cannot be verified by the market, and so is not fully reflected in the early share
price. This is therefore a model of long-term projects which the CEO can undertake.
These are projects where success is not immediately apparent and so is not immediately
priced into the firm’s equity value. Early bonuses do not incentivise CEO effort on such
projects concerning the long run capabilities of the firm. The utility of the contract to
the CEO will depend on the business-model choice he is incentivised to make:
18
Lemma 5 The CEO will prefer the risky to the safe technology if:
b
h
|
X1risk
−
{z
X1safe
(i)
ρ R̄τ
+ v 2 σr2 − σs2
≥v r−
P
2
}
| {z }
i
(18)
(ii)
If (18) is satisfied, the CEO will accept the contract if
f+
bX1risk
R̄τ
v2 1
2
+v
+
− ρσr ≥ u
P
2 κ
(19)
Otherwise the CEO will accept the contract if
f+
bX1safe
v2 1
2
− ρσs ≥ u
+ vr +
2 κ
(20)
Lemma 5 determines the restrictions on the contract the Board can offer which ensures
that the CEO both accepts the contract, and then selects a given technology. Equation
(18) is the CEO’s incentive compatibility constraint. If the CEO implements the risky
technology, then the share price of the firm will increase due to the pooling effect which
places the firm with high type firms. This effect is captured in bracket (i) . The CEO
internalises this jump in short-run value via his short-term bonus, b. If b is made sufficiently
large then the CEO is incentivised to select the risky technology. For high types of
firm, long term bonus alone will be sufficient to incentivise the firm to select the risky
technology. But if the firm type is low enough ((ii) positive) then a large enough short-run
bonus is required to ensure that the CEO pursues the risky technology.
Equations (19) and (20) are the participation constraint. They measure the CEO’s
utility from developing the risky and safe technology respectively. If the utility from the
contract exceeds the outside option, then it is acceptable to the CEO.
7.2
Shareholders and Endogenous Incentives
We are now in a position to explore how the Board will manage the competing pressures
of incentivising the CEO and also ensuring the share price is high for those shareholders
who need to sell early. Short-term shareholders sell at a price of X1risk if the CEO is
incentivised to pursue the risky project. This price is not affected by private changes to
the CEO contract, unless the contract should incentivise the CEO to alter technology
choice. Assuming the Board incentivise the risky technology then the objective function
is:
R̄τ
R̄τ
risk
∗
risk
risk
∗
− f + bX1 + v η +
V
(τ ) = LX1 + (1 − L) η +
P
P
subject to (18) and (19).
(21)
19
A similar objective function for the Board exists if the Board targets the business-as-usual
technology. These objective functions can be solved to yield:
Proposition 4 Consider a firm of type τ with a probability L of short-term ownership.
The optimal CEO deferred bonus rate is declining in L and given by:
(
v=
1
(1 − L) 1+κρσ
2
If Board targets risky technology
r
1
If Board targets business-as-usual technology
(1 − L) 1+κρσ
2
(22)
s
The CEO is incentivised to improve firm type by an expected amount which is declining
in L and given by:
(
∗
η =
1
(1 − L) κ(1+κρσ
2)
r
(1 − L)
1
κ(1+κρσs2 )
If Board targets risky technology
If Board targets business-as-usual technology
(23)
Proposition 4 delivers the result that the Board translate the shareholder pressure
coming from the proportion L who will sell early into reduced long term incentives, and
so a lower expected level of firm type improvement. This is irrespective of whether the
other parameters of the contract are structured to incentivise one technology choice or
another.
Deferred pay incentivises the CEO to improve the long run capabilities of the firm
(Lemma 4). But the benefits of these sorts of improvements are not fully reflected in the
short-run share price. To the extent that the Board internalise the sale price of shares at
t = 1 through the L who will suffer a liquidity shock, the Board undervalue these benefits.
This leads to the lowering of deferred payments. As deferred payments are reduced, the
CEO is less incentivised to improve the long run capabilities of the firm, and so the firm
will improve its type by less the greater the probability of short-term ownership. In the
extreme of only having short-term shareholders on the register, the CEO will receive no
long-term deferred bonus payments, and will not be incentivised to improve the long-run
capabilities of the firm at all if such efforts are not immediately priced into the short term
share price.
8
Model Robustness to Further Extensions
The model of firms selecting between competing technologies is designed to be tractable
and allow the key market pooling and profit maximisation forces which contribute to the
cost of equity and the equilibrium price of inputs to be explained. In this section we
explore a number of further extensions to the analysis undertaken.
Short-termism Differing Across Firms The model has assumed that all firms have
the same probability of short-term ownership. This simplification allows the insights
20
to be developed in a setting where firms differ only in one dimension: their type.
The results of the analysis are then immediately applicable to a comparison between
different economies or industries. It would be possible to extend the analysis to the
case of an exogenous distribution of shareholder time horizons across firms. For
any given probability of short-term ownership, L, one would have a conditional
distribution of firm types: f (L, ·) . For this conditional distribution the results of
this analysis apply: the highest types opt for the risky technology, and this set is
enlarged beyond the optimum by the presence of the L short-term shareholders.
However endogenising the shareholder time horizon is beyond the scope of this
model. This would require the relative asset prices of the firms to be endogenised
in the context of shareholders who differ in the value they attach to a given firm.12
Informed Trading In the analysis above all buyers and sellers of shares at the interim
date are uninformed as to the true type of the firm. Shareholders can only make
inferences based upon the signalling value contained within the technology choice.
The Board however are aware of the firm type, and they are also owners of some
of the shares. Let us suppose that Board members can decide to sell early to profit
from their privileged information, or that they might also be subject to liquidity
shocks requiring sale at t = 1 with some probability. Stock market rules require
Boards to disclose any sales to the market, therefore the relevant case to consider
is one in which Board members have the opportunity to publicly sell their shares
in advance of the other liquidity shock shareholders. Board members will only sell
in the absence of a liquidity shock if the sale price they receive is in excess of the
true long-run value of the firm. Hence, observing a Board member’s sale the market
will infer that a firm might be over-valued and mark down the stock price. The less
the probability of a liquidity shock for Board members, the greater the information
content of the signal in the Boards’ sale, and so the stronger is this price effect.
In the extreme case of the Board members having exactly zero probability of a
liquidity shock, then we have a ‘lemons market.’ If there is any positive probability
of a liquidity shock for Board members, then the economics described above would
apply. If Board members sell early then this contains some bad news, lowering the
share price and mitigating the ex ante reason to distort technology choice. But a
share premium would remain from the risky technology as the Board member might
be selling for exogenous (liquidity shock) reasons. Hence the economics described
remains robust to Board members trading for their own profit.
Shareholder Activism In the model presented, shareholders purely invest in the firms.
Shareholders do not actively monitor and correct management failings in the Board
12
Albagli, Hellwig and Tsyvinski (2013) develop such an asset pricing model without exploring differences in shareholders’ realised liquidity shocks.
21
(or senior management team). Consider now if some of the shareholders are activists
who can have a material impact on the behaviour of the firm. The presence of such
activist investors on a firm’s shareholder register would, in theory, alter the results
that short-term shareholders raise the cost of capital in an ambiguous way. Any
monitoring by such shareholders which improved management’s focus on the long
run would act to increase ex ante firm value and lower the cost of capital. However, if
an activist investor had a short-term focus and could alter management’s behaviour
to maximise the early path of the share price, then this would act against the
value improvements from monitoring, and so lead to negative effects on firm value.
Bebchuk, Brav and Jiang (forthcoming) offer evidence that activist shareholders
improve the long-term profitability of firms they own suggesting that the primary
effect is dominant.
9
Empirical Discussion
In this section I offer some empirical evidence that short-term ownership differs significantly between countries, and I document the empirical predictions afforded by the analysis and their relationship to the existing empirical evidence.
9.1
Evidence Of Short-Term Shareholders
Measuring the extent and indeed existence of short-termism amongst shareholders is an
ongoing topic of research. Holderness (2009) notes that most of the empirical research
on ownership focuses on blockholders and inside ownership – relatively little looks at the
full spectrum of owners. We have noted that recently, empirical research has constructed
indices of owner time-horizons, see for example Gaspar, Massa, and Matos (2005). The
study presented here considers general equilibrium effects of short-term shareholders. It
is therefore tempting to ask whether there is evidence of owner liquidity differing across
jurisdictions, as La Porta et al. (1998) suggest is likely. Gaspar et al. (2005) do not
consider such cross-sectional comparisons. The easiest data to acquire on this question
involve share turnover rates, however the existence of short-termism cannot be inferred
from a high share turnover rate. Froot, Perold and Stein (1992) note that a firm can have
a high turnover rate if a small percentage of the firm is repeatedly bought and sold, whilst
the vast majority of the firm remains under stable ownership. To address differences in the
likelihood of stable ownership, and so justify the assumptions underlying this theoretical
model, I therefore construct a bespoke dataset. I collected the shareholder register data
at multiple time periods for the largest 20 firms by market capitalization in the Germanic
civil law countries of Germany, Austria and Switzerland. In addition I constructed a
matched sample of 20 US firms which were in identical 3-digit SIC codes as their primary
22
business, and whose size was as near to the Germanic firms as possible.13 The identity
of the 20 German owned firms and their US match are provided in Appendix C. I then
derive a lower bound for the short-termism of ownership over two, four, six and eight
quarters using the following construction:


 



Percentage of
%
common
Minimum
%
stock


X



 

 Short-termism  =
 stock owned by  −  held by j over 




j named
over z quarters
j at Sep 2012
prior z quarters.
on shareholder

register at
Sep 2012
(24)
The database (CapitalIQ) lists the ownership data of all common stock owners with
a stake in excess of 0.1% of the firm. Definition (24) is a conservative measure of shorttermism. First (24) assumes that all unnamed owners (i.e. owners of less than 0.1 % of
the equity) are long-term as they do not count towards the short-termism measure. In
fact one would expect a proportion of these individuals to be liable to liquidity shocks.
Second, if an owner of shares should sell part of their stake over the z quarters, only
the part which is sold counts towards the short-termism measure. The remainder which
has been held over the entire z quarters finishing in Q3 2012 is assumed to be long-term
held.14
I compare civil law countries to the leading common law country as the legal differences
in shareholder protection, it is argued, might lead to differences in ownership patterns and
corporate behaviour (see La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998)). Using
the matched sample we can interrogate to what extent short-termism in share ownership
differs between Germanic civil law countries as compared to the US. Figure 3 demonstrates
that the Germanic firms enjoy lower levels of short-termism than their matched US firms.
Over 2 quarters the top 20 Germanic firms have 5.5% of short-term held common stock,
whereas the matched US sample over 2 quarters faces 9.7% of short-term held common
stock, almost double the amount. That is, over six months, 10% of the matched US firms’
equity changed hands on average, while only 5% of the equity moved over the period in the
Germanic firms. This difference has a p value of 0.011 and so is almost significant at the
1% level, and easily so at the 5% level. The significant difference remains in the extent of
short-termism over 4 quarters. The difference in short-termism remains constant at longer
time horizons, though loses significance in this small sample. The proportion of shorttermism grows as the time horizon grows: If a firm is contemplating an investment with a
two year payback period, they can expect to see around 20% of the equity change hands
before the results are fully realised. Thus there is reason to explore the effect of differing
13
This process of matching firms by industry and then market value is a standard approach. For an
early example consider Spiess and Affleck-Graves (1995).
14
Note that if owner k sells shares to j over the prior z quarters, then these shares count towards the
short-termism measure. These shares are captured exactly once in equation (24) by the increase in owner
j’s holding.
23
Figure 3: Comparison of Shareholder Short-Termism Between Germanic Civil Law countries and US (Common Law)
Notes: The graph depicts the mean short-termism amongst the top 20 firms in the Germanic civil
law countries of Germany, Switzerland and Austria. This is compared against the mean short-termism
amongst the matched panel of firms in the leading common law country (United States). Short-termism
is measured using construction (24). The data is drawn from CapitalIQ and measures short-termism
in the period ending with Q3 2012. The matching is done by 3-digit SIC, followed by firm size. **, *,
denotes that the difference in mean is significant at the 5%, 10% level; p values in parentheses. The
difference in means is plotted on the right hand axis.
investor time-horizons across economies, and indeed across industries. In particular this
analysis would suggest a stronger pressure on US firms, as opposed to Germanic ones, to
follow a new technology to benefit from the pooling effect we describe. Further, Figure 3
provides evidence consistent with the suspicion of many commentators that short-termism
is greater in the US (common law jurisdiction) than in countries such as Germany and
Switzerland (civil law).15
9.2
Empirical Predictions
The analysis of short-term shareholders yields the following three main empirical predictions:
1. Economies/industries/firms whose shareholders have shorter time horizons are sub15
See Franks, Mayer, and Rossi (2009).
24
ject to pressure to choose risky business-models only suitable for the most exceptional management teams; and prone to upwards price distortions from fundamentals (technically bubbles) in the cost of the required inputs.
This prediction follows from Proposition 1. This prediction of the model makes rigorous a great deal of anecdotal evidence and policy maker suspicion referred to in the
Introduction. As noted in the Literature Review (Section 2), there is a great deal of
empirical work which links short investor time-horizons with poor corporate performance:
Gaspar, Massa, and Matos (2005), Derrien, Kecskes, and Thesmar (2013), Polk and
Sapienza (2009), Graham, Harvey, and Rajgopal (2005). The assumptions underlying
the pressure to pool mechanism we explore here explicitly finds support in Graham et al.
(2005) who document the aversion that management have to actions which lower current
share prices, even at the cost of long term value creation.
2. In perfect capital markets, economies/industries/firms whose shareholders have short
expected time horizons face higher costs of equity capital.
This prediction follows from Proposition 1 and is robust to elastically supplied inputs
(Proposition 2). Using conference call transcripts, Brochet, Loumioti and Serafeim (2012)
document that firms with a short-term oriented investor base acquire higher betas, and
so pay higher costs of capital. Further, Attig, Guedhami and Mishra (2008) find that the
implied cost of equity capital decreases with the presence of large shareholders who are
banks, the state, or family, beyond the controlling owner. It seems likely that such blockholders are in the main long-term shareholders. Both analyses are therefore supportive
of this prediction. Cella (2012) finds that long-term investors improve firms’ investment
performance which would typically imply reduced costs of capital.
3. Economies/industries/firms whose shareholders have short time horizons have CEOs
with reduced long-term incentives.
This prediction follows from Proposition 4. Dong and Ozkan (2008) document that
long-term institutional investors lower short-term CEO pay as proxied by base salary and
cash bonus. Further, they document that long-term investors increase the sensitivity of
overall pay to realised firm performance.16 Cadman and Sunder (2010) also report that
CEO contracts when a firm is backed by a venture capital fund have short-term incentives
corresponding to the time of anticipated exit of the VC – an outcome naturally explained
by this model.
16
Dikolli, Kulp and Sedatole (2009) also argue that transient shareholders lead CEOs to be under
pressure to increase current earnings, however they report some evidence that boards try to compensate
for this with contracts which underweight quarterly earnings in favour of yearly returns.
25
10
Conclusions
A firm seeks to maximise the expected wealth of its shareholder owners at the time
a business decision is taken. As shareholders may have short expected time horizons,
because of the chance of liquidity shocks or because some shareholders only intend a
short-term investment, this implies that the Board of a firm must be concerned with the
path of the share price through time as well as with its final value. So firms will see value
in taking actions which pool them with firms of high ability and so high value. Thus a
firm which decides on a risky business model which only high ability management can
make a success of will send a signal that the management may indeed be high quality.
This pressure to choose business models so as to manipulate the market’s information
drives up the price of the input needed for the risky technology to above its fundamental
level. A bubble is created. Market clearing then implies that too many firms enter this
technology. This distortion in business-model choice results in an increased cost of equity
capital, no matter what the elasticity of supply is of the input asset. And this distortion
is not necessarily mitigated by a more precise signal of the type of any given firm. Finally
a Board will respond to the apparent interests of shareholders with short expected time
horizons by underweighting long term incentives. Doing so reduces effort on tasks which
do not have short-term price impact.
In principle, if a firm was unable to determine the time-horizon of its owners then the
negative outcomes described here would be avoided. Thus, if investors all channeled their
funds through a third party, such as a bank, then the effects described here would not
occur. Though the providers of capital may be subject to liquidity shocks, by pooling
resources into a bank those liquidity shocks would not impact corporate decision making.
The bank could structure its portfolio so as to allow the firm to invest for the long run
while also owning other short-term assets to manage the liquidity requirements of the
fundamental investors. Such a model of ownership is similar to the German and Japanese
models of corporate control (see, for example, Breally, Myers and Allen (2011)). It is well
known however that such an approach has its own disadvantages. In particular set against
the study here must be the implications of having an overly powerful group of long-term
shareholders who might be tempted to exploit the firm to the detriment of the wider
population of shareholders. Such broader issues of the perils of shareholder influence and
the implications for technology choice and CEO contracting are left to future scholarly
study.
A
Omitted Proofs
Proof of Lemma 1. Rewrite (3) as rP f = R̄q bP f . The left hand side is increasing
in P f . The right hand side is declining in P f . Hence any solution to (3) must be unique.
26
We have limP f →0 R̄q bP f = R̄ > rP f P f =0 and limP f →1/b R̄q bP f = 0 < rP f P f =1/b
hence a fundamental price exists by the Intermediate Value Theorem.
Proof of Lemma 2. Suppose otherwise that the Board’s strategy was not a cut-off
type of this form. Then there must exist two firm types τ1 < τ2 such that a firm of type
τ1 would strictly prefer to develop the risky technology whilst the firm with higher type
τ2 would strictly prefer to develop the business-as-usual technology. Hence we would have
V risk (τ1 , L) > r > V risk (τ2 , L)
(25)
∂
V risk (τ, L) = (1 − L) R̄/P > 0 as L < 1. A contradiction to (25).
However, from (4), ∂τ
Therefore if τ1 develops the risky technology so must higher type firms.
Proof of Proposition 1. I first determine the equilibrium input asset price in part
3. Using the cut-off property of Lemma 2, market clearing (2) implies firms with type
τ ∈ [q (bP ) , 1] will develop the risky technology. Each firm will buy 1/P units of the
input asset. Applying Bayes rule, the expected type at end t = 1 of a firm which develops
the risky technology is
1
E (τ | τ ∈ [q (bP ) , 1]) =
bP
Z
1
1
τ g (τ ) dτ =
bP
τ =q(bP )
Z
q (bP ) bP +
1
1 − G (τ ) dτ
τ =q(bP )
(26)
Using an integration by parts. Market clearing requires that the firm of type τ = q (bP ) be
indifferent between developing the risky technology and the business-as-usual technology.
Hence, using (4) and (26) we require:
Z 1
R̄
R̄τ
r = (1 − L)
1 − G (τ ) dτ
+ L 2 q (bP ) bP +
P
bP
τ =q(bP )
τ =q(bP )
This can be simplified to yield (5). Existence and uniqueness follow by multiplying (5)
through by P, noting the right hand side is declining in P, and applying the Intermediate
Value Theorem on prices P ∈ {0, 1/b} in conjunction with assumption (1). This yields
part 3.
Now consider part 1. Define the function W (P ) equal to the right hand side of (5),
so at equilibrium r = W (P ) . The sensitivity of the market price to the probability of
short-term ownership is dP/dL = − (∂W/∂L) / (∂W/∂P ) . By inspection we see that
∂W/∂L > 0. For the denominator we explicitly find
∂W
R̄
q (bP )
R̄
− 2L 3
= q 0 (bP ) b (1 − L) − R̄
2
∂P
P
P
bP
Z
1
1 − G (τ ) dτ < 0
τ =q(bP )
The inequality follows as q 0 (·) < 0. Hence dP/dL > 0, and we have the first result.
For part 2 note that firms of type τ ∈ [q (bP ) , 1] develop the risky technology, and as
27
dP/dL > 0, this range expands with the probability of short-term ownership.
For part 4 at t = 0 the market value of the equity of a randomly drawn firm is given as
R q(bP )
R1
V = τ =0 rg (τ ) dτ + τ =q(bP ) PR̄ τ g (τ ) dτ. This follows as firms of type τ ∈ [q (bP ) , 1] will
develop the risky technology. To raise one dollar from equity investors an entrepreneur
must offer a proportion 1/V of his firm. The cost of equity capital therefore moves
inversely to V. Implicit differentiation of firm expected value yields:
Z 1
dV
R̄
dP
R̄
0
=
· q (bP ) bg (q (bP )) r − q (bP ) −
τ g (τ ) dτ
2
dL
dL
P
τ =q(bP ) P
We have shown P > P f , and so from (3) r > R̄q (bP ) /P. As q 0 (·) < 0 and dP/dL > 0, we
have dV /dL < 0 as required. Hence a greater probability of short-term ownership raises
the firm cost of equity capital.
Proof of Lemma 3. If the price of the input is P then market clearing with supply
function (6) implies that the critical firm type satisfies
1
Z
τ̃
1
g (τ ) dτ = S (P ) ⇒ τ̃ = q (P · S (P )) = q bP
P
P
Pf
ζ !
(27)
Yielding (9). The critical firm type, given L, is indifferent between the risky and safe
payoffs and so satisfies, using (4):
R̄τ̃
R̄
r = (1 − L)
+L
P (τ̃ )
P (τ̃ )
R1
τ g (τ ) dτ
1 − G (τ̃ )
τ =τ̃
h
i
R1
R̄ τ̃ − τ̃ G (τ̃ ) + τ̃ 1 − G (τ ) dτ
R̄τ̃
+L
= (1 − L)
P (τ̃ )
P (τ̃ )
1 − G (τ̃ )
ζ
From (27) we have G (τ̃ ) = 1 − bP P/P f . Using this to substitute for P yields (8).
The critical type τ̃ exists by applying the intermediate value theorem to (8) at τ̃ ∈
{0, 1} and using (7). For uniqueness note that the left hand side of (8) is decreasing in τ̃ .
Differentiation confirms that the right hand side is increasing in τ̃ .
Proof of Proposition 2. I first confirm that a bubble exists: τ̃ < τ̂ given in (2).
Evaluating (8) at τ̂ yields:
r
LHS =
R̄
"
Pf
b
ζ
bP
1
# 1+ζ
f
rP f
L
=
=(3) τ̂ < τ̂ +
bP f
R̄
Z
1
1 − G (τ ) dτ = RHS
τ =q (bP f )
As the left hand side of (8) is decreasing in τ̃ , while the right hand side is increasing, we
must have τ̃ < τ̂ . Next note that as the price is given by (9), so P > P f .
Now initially we show part 2. The critical firm type τ̃ (ζ, L) is given by (8). Differen-
28
tiating with respect to ζ:
1
# 1+ζ
ζ
Pf
1
1 − G (τ̃ )
ln
(1 − G (τ̃ ))
b
bP f
(1 + ζ)2


i 1
h

r 1
f 1−G(τ̃ ) 1+ζ g(τ̃ )
∂ τ̃ (ζ, L)
P
+ (1 − L) 
1−G(τ̃ )
bP f
R̄ 1+ζ
=
R1
g(τ̃ )


∂ζ
1 − G (τ ) dτ
+L [1−G(τ̃
2
τ =τ̃
)]
r
−
R̄
"
It follows that
" #
ζ+1
∂ τ̃ (ζ, L)
1 − G (τ̃ )
P
=sign − ln
=
−
ln
<0
(27)
∂ζ
bP f
Pf
As we have already shown P > P f . Similar working yields ∂ τ̃ (ζ, L) /∂L < 0 to complete
part 2.
ζ
For part 1 express the price condition (9) as 1 − G (τ̃ ) = b · P PPf and differentiate
with respect to the proportion of short-term shareholders to yield:
∂P
∂ τ̃
=
· b (ζ + 1)
−g (τ̃ )
∂L
∂L
|{z}
P
Pf
ζ
<0
giving that ∂P/∂L > 0.
Proof of Proposition 3. For the first part, we sign dzd i E (τi | τi ≥ τ̃ ) . We consider a
positive signal: zi ≥ µ. As by assumption τ̃ ≤ µ we have from (12) that α ≤ 0. Hence
substituting (13) into (12) and differentiating with respect to zi yields
hε d
E (τi | τi ≥ τ̃ ) =
1 − 1.2244 [Φ (α)]−0.1368 ϕ (α)
τ̃ (hε +hµ )−(zi hε +µhµ )
√
α=
dzi
hε + hµ
hε +hµ
Now Shore (1982, equation 6) provides the underlying approximation for the density
function as, for α < 0 :
ϕ (α) = ϕ (−α) = 1.4184 (1 − Φ (−α))0.8632 Φ (−α) = 1.4184 (Φ (α))0.8632 (1 − Φ (α))
And so
d
hε E (τi | τi ≥ τ̃ ) =
1 − 1.7366 (Φ (α))0.7264 (1 − Φ (α))
τ̃ (hε +hµ )−(zi hε +µhµ )
√
α=
dzi
hε + hµ
hε +hµ
0.7264
Now note that (Φ (α))0.7264 (1 − Φ (α)) < [Φ (α) (1 − Φ (α))]0.7264 < 12 1 − 21
=
d
0.3653. Hence dzi E (τi | τi ≥ τ̃ ) > 0. Thus by the logic above Proposition 3 the distortion
grows in the strength of the signal, yielding part 1b.
29
To complete the proof of the first part suppose that the signal was at the weakest
possible positive level so that zi = µ. In this case only the precision has increased. From
(12) and using (13):
[E (τi | τi ≥ τ̃ )]zi =µ
1.4184
[Φ (α)]0.8632 = µ+ p
hε + hµ
Now differentiating with respect to
√
α=
hε +hµ (τ̃ −µ)
p
hε + hµ we have
d
[E (τi | τi ≥ τ̃ )]zi =µ =sign 0.8632 [Φ (α)]−0.1368 ϕ (α) α − [Φ (α)]0.8632 α=√hε +hµ (τ̃ −µ) < 0
dhε
The inequality follows as α < 0. Hence if the signal is just at zi = µ then the conditional
expectation is reduced. Thus the distortion in firm i’s behaviour is reduced in this case.
Note that there must always be a distortion by the logic of Proposition 1.
Now we turn to part 2 and suppose that µ < τ̃ . In this case we begin our analysis
with the signal at the weakest possible positive level so that zi = µ. From (12) and using
(13), recalling that now α > 0 by assumption:
1.4184 [1 − Φ (α)]−0.1368 Φ (α) α=√hε +hµ (τ̃ −µ)
[E (τi | τi ≥ τ̃ )]zi =µ = µ + p
hε + hµ
Now differentiating with respect to
p
hε + hµ we have
d
[E (τi | τi ≥ τ̃ )]zi =µ
dhε
d = sign α
[1 − Φ (α)]−0.1368 Φ (α) − [1 − Φ (α)]−0.1368 Φ (α)
dα
= α 0.1368 [1 − Φ (α)]−1.1368 Φ (α) ϕ (a) + [1 − Φ (α)]−0.1368 ϕ (a) − [1 − Φ (α)]−0.1368 Φ (α)
Now this expression is negative for α = 0, however we also have
d
[E (τi | τi ≥ τ̃ )]zi =µ >
dhε
=
−0.1368
sign
[1 − Φ (α)]
sign 0.1368α1.4184 [1
αϕ (a)
Φ (α) 0.1368
−1
1 − Φ (α)
− Φ (α)]−0.1368 Φ (α) − 1
And this is positive if α is large enough. Hence the existence of the signal can increase
p
the firm distortion if hε + hµ (τ̃ − µ) is large enough.
We now consider progressively better signals. Analogously to above, substituting (13)
30
(with α > 0) into (12) and differentiating with respect to zi yields
d
E (τi | τi ≥ τ̃ )
dzi

=


hε 
−1.1368
Φ (α) + [1 − Φ (α)]−0.1368 
1 − 1.4184ϕ (a) 0.1368 [1 − Φ (α)]
hε + hµ |
{z
}
(i)
α=
τ̃ (hε +hµ )−(zi hε +µhµ )
√
hε +hµ
Using Shore (1982, equation 6) the square bracket, (i) is equal to
(i) = 1 − (1.4184)2 [1 − Φ (α)]0.8632 Φ (α) 0.1368 [1 − Φ (α)]−1.1368 Φ (α) + [1 − Φ (α)]−0.1368
= 1 − (1.4184)2 [1 − Φ (α)]−0.2736 Φ (α) [0.1368Φ (α) + [1 − Φ (α)]]
= 1 − (1.4184)2 [1 − Φ (α)]−0.2736 Φ (α) [1 − 0.8632Φ (α)]
(28)
This has ambiguous sign depending on the specific value of α. For most intermediate
ranges, e.g. a signal strong enough that α = 0 ⇒ Φ (α) = 1/2, expression (i) is positive.
However for Φ (α) close enough to 1, achieved if τ̃ >> µ and the signal is positive but
weak, expression (i) is negative. Combined with the logic above Proposition 3 we have
the required result.
Proof of Lemma 5. Substituting (17) into (15) delivers the CEO’s utility from pursuing
the risky technology as
U risk (f, b, v) = f + bX1risk + v
R̄τ
1 v2 ρ 2 2
+
− v σr
P
2κ
2
(29)
And the utility from the safe technology is
U safe (f, b, v) = f + bX1safe + vr +
1 v2 ρ 2 2
− v σs
2κ
2
(30)
Comparing (29) to (30) yields (18).
risk
R̄τ
ρ safe
b X1 − X1
>v r−
+ v 2 σr2 − σs2
P
2
The participation constraint for the CEO is that the expected utility, (29) or (30),
exceeds u. This delivers (19) and (20).
Proof of Proposition 4. The fixed fee can be lowered until (19) or (20) is satisfied
with equality. Using (17) and substituting into the Board’s objective function (21) yields
v
R̄τ
v2 1
2
V
(τ ) =
+ (1 − L) + (1 − L)
−
+ ρσr − u
κ
P
2 κ
v
v2 1
safe
safe
2
or V
(τ ) = LX1 + (1 − L) + (1 − L) r −
+ ρσs − u
κ
2 κ
risk
LX1risk
31
(31)
Equation (31) is a negative quadratic in v and is independent of b in either case. Optimising for v yields (22). Combining (22) with (18) yields (23).
B
Numerical Simulation
In this Appendix I develop the calculations for Figure 2. Suppose firm types are uniformly
distributed on [0, 1] . This implies that q (y) = 1 − y. With probability L of short-term
ownership (5) yields:
R̄
R̄
r = (1 − bP ) + L 2
P
bP
Z
1
(1 − τ ) dτ
τ =1−bP
Solving implies that P (L) = R̄ r + (1 − L/2) bR̄ . The critical firm type is then τ̃ (L) =
1 − bP (L) .
The bubble can be found by calculating the ratio P (L) /P (0) . The t = 0 ex ante
average value of a firm with probability L of short-term ownership is:
Z
1−bP (L)
V (L) =
Z
1
rdτ +
τ =0
τ =1−bP (L)
R̄b
R̄
τ dτ = r (1 − bP (L)) +
[2 − bP (L)]
P (L)
2
Hence the proportion of the firm required to secure a unit of capital is 1/V (L) . The
increase in the cost of capital can be found as [1/V (L)] / [1/V (0)] = V (0) /V (L) .
The parameters used in the numerical example depicted in Figure 2 are R̄ = 1.15,
r = 1.02 and b = 0.75.
C
Matched Sample Data
The following firms, listed in order of their market capitalization, are the 20 Germanic
firms studied in Section 9. Their US match follows in parentheses:
1. Nestle S.A. (SWX:NESN) [ The Coca-Cola Company (NYSE:KO) ];
2. Roche Holding AG (SWX:ROG) [ Pfizer Inc. (NYSE:PFE) ];
3. Novartis AG (SWX:NOVN) [ Merck & Co. Inc. (NYSE:MRK) ];
4. Volkswagen AG (DB:VOW) [ Ford Motor Co. (NYSE:F) ];
5. Siemens AG (DB:SIE) [ General Electric Company (NYSE:GE) ];
6. SAP AG (DB:SAP) [ Oracle Corporation (NasdaqGS:ORCL) ];
7. BASF SE (DB:BAS) [ Amgen Inc. (NasdaqGS:AMGN) ];
32
8. Bayer AG (DB:BAYN) [ Eli Lilly and Company (NYSE:LLY) ];
9. Allianz SE (DB:ALV) [ UnitedHealth Group Incorporated (NYSE:UNH) ];
10. Daimler AG (XTRA:DAI) [ General Motors Company (NYSE:GM) ];
11. Bayerische Motoren Werke Aktiengesellschaft (DB:BMW) [ PACCAR Inc. (NasdaqGS:PCAR) ];
12. Xstrata plc (LSE:XTA) [ Southern Copper Corp. (NYSE:SCCO) ];
13. Deutsche Telekom AG (DB:DTE) [ CenturyLink, Inc. (NYSE:CTL) ];
14. ABB Ltd. (SWX:ABBN) [ Littelfuse Inc. (NasdaqGS:LFUS) ];
15. Compagnie Financiere Richemont SA (SWX:CFR) [ Tiffany & Co. (NYSE:TIF) ];
16. Deutsche Bank AG (DB:DBK) [ U.S. Bancorp (NYSE:USB) ];
17. Glencore International plc (LSE:GLEN) [ ConocoPhillips (NYSE:COP) ];
18. Zurich Insurance Group AG (SWX:ZURN) [ Markel Corp. (NYSE:MKL) ];
19. Syngenta AG (SWX:SYNN) [ The Mosaic Company (NYSE:MOS) ];
20. Credit Suisse Group (SWX:CSGN) [ Annaly Capital Management, Inc. (NYSE:NLY)
].
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