Real economy effects of short-term equity ownership

Abstract

Investor time horizon varies by company, industry and economic system. In this article we explore the importance of this variation by studying the impact of shareholder time horizon on the investment decisions of the firms they own, and externalities on the wider market. We demonstrate theoretically that short-term shareholders cause Boards to care about the path of the stock price, rationalising firms’ pursuit of investments for signalling reasons at the expense of long-term value. We demonstrate that short-termism has spillover effects, leading to higher costs of equity capital; bubbles in the price of input assets; and predictable excess returns. We build testable cross-country hypotheses and evaluate these using existing evidence coupled with a new dataset on owner duration of US and Germanic firms.

Abstract

L’horizon temporel des investisseurs varie suivant les entreprises, le secteur d’activité et le système économique. Dans cet article, nous explorons l'importance de cette variation en étudiant l’impact de l’horizon temporel des actionnaires sur les décisions d’investissement des entreprises qu’ils possèdent, ainsi que les externalités sur un marché plus large. Nous démontrons, d’un point de vue théorique, que les actionnaires ayant une vision à court terme incitent les comités exécutifs à considérer l’évolution du prix de l’action, en rationalisant la poursuite des investissements pour des raisons de signalisation aux dépens de la valeur à long terme. Nous démontrons qu’une vision à court terme a des retombées qui entraînent des coûts plus élevés concernant les fonds propres; des bulles dans le prix des actifs entrants; et des rendements prévisionnels excessifs. Nous émettons des hypothèses qui peuvent être testées au niveau des pays et nous les évaluons en utilisant les preuves existantes combinées avec une nouvelle base de données portant sur la durée de propriété des entreprises américaines et germaniques.

Abstract

El horizonte del tiempo del inversionista varía según la empresa, la industria y el sistema económico. En este artículo exploramos la importancia de esta variación a través de estudiar el impacto del horizonte de tiempo de los agentes de interés en las decisiones de inversión de las empresas de su propiedad, y las externalidades del mercado ampliado. Teoréticamente demostramos que los agentes de interés de corto plazo causan que la Junta Directiva cuide la trayectoria del precio de las acciones, racionalizando la búsqueda de inversiones mediante indicar razones a costa del valor a largo plazo. Demostramos que el cortoplacismo tiene efectos indirectos , llevando a altos costos de capital patrimonial; burbujas en el precio de los activos; y exagerados retornos previsibles. Construimos una hipótesis probable entre países, y evaluamos estas usando la evidencia existencia paralelamente con una nueva base de datos de duración de propiedad de firmas Estadounidenses y Germánicas.

Abstract

O horizonte de tempo de um investidor varia de acordo com a empresa, a indústria e o sistema econômico. Neste artigo exploramos a importância dessa variação ao estudar o impacto do horizonte de tempo do acionista sobre as decisões de investimento das empresas de sua propriedade, e nas externalidades no mercado amplo. Nós demonstramos teoricamente que acionistas de curto prazo fazem o conselho se preocupar com a evolução do preço das ações, limitando a busca da empresa por investimentos a sinalizações, às custas do valor a longo prazo. Nós demonstramos que a visão de curto prazo tem efeitos colaterais, levando a maiores custos de capital próprio; bolhas no preço dos ativos de entrada; e retornos excessivos e previsíveis. Nós construímos hipóteses testáveis interpaíses e as avaliamos usando evidências existentes juntamente com um novo conjunto de dados sobre a duração do dono em empresas americanas e germânicas.

Abstract

投资者的投资期随公司、行业和经济系统而变。在这篇文章中, 我们通过研究股东投资期对他们所拥有公司的投资决策的影响, 探索了这一变化的重要性及更广泛的市场外部性。我们从理论上证明 : 短期股东引发董事会关心股票价格路径, 使公司以长远价值为代价的意在给出信号的投资追求合理化。我们证明短期主义有溢出效应, 导致更高的股权资本成本; 输入资产价格泡沫; 及可预测的超额回报。我们构建了可验证的跨国家的假设, 并使用现有证据加上新数据集在美国和日耳曼公司所有者持续期间评价这些假设。

Appendices

APPENDIX A

Proofs from the Section “Shareholder and technology choice analysis”

Proof of Lemma 1:

• The market clearing condition is that firms invest in the risky technology where the “first-best” cut-off type, , is determined by the fundamental price and given by

Market clearing requires the borderline firm to be indifferent between develo** the risky and the safe technology. Hence the fundamental price is defined implicitly by the relation in (2).

Rewrite (2) as The left-hand side is increasing in The right-hand side is declining in Hence any solution to (2) must be unique. We have and , 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 such that a firm of type would strictly prefer to develop the risky technology, while the firm with higher type would strictly prefer to develop the business-as-usual technology. Hence we would have

However, from (3), as A contradiction to (A9). □

Proof of Proposition 1:

• We first determine the equilibrium input asset price in part 3. Using the cut-off property of Lemma 2, market clearing (A8) implies firms with type will develop the risky technology. Each firm will buy 1/P units of the input asset. Applying Bayes rule, the expected type at end of a firm that develops the risky technology is

using an integration by parts. Market clearing requires that, in equilibrium, firm type be indifferent between develo** the risky technology and the business-as-usual technology. Hence, substituting (A10) into (3) and evaluating at type we require:

This can be simplified to yield (4). Existence and uniqueness follow by multiplying (4) through by P, noting the right-hand side is declining in P, and applying the Intermediate Value Theorem on prices in conjunction with assumption (1). This yields part 3.

Now consider part 1. Define the function equal to the right-hand side of (4), so at equilibrium The sensitivity of the market price to the probability of short-term ownership is By inspection we see that For the denominator we explicitly find

The inequality follows as Hence , and we have the first result.

For part 2 note that firms of type develop the risky technology, and as this range expands with the probability of short-term ownership.

For part 4 at the market value of the equity of a randomly drawn firm is given as

This follows as firms of type will develop the risky technology. To raise $1 from equity investors at an entrepreneur must offer a proportion 1/V of his firm. The cost of equity capital therefore moves inversely to V. Implicit differentiation of expected firm value yields:

We have shown and so from (2) as Given , we have as required. Hence a greater probability of short-term ownership raises the firm cost of equity capital. □

Proof of Claim 1:

• In equilibrium at we must have indifference in valuation between both technologies. Hence from (3) Now consider lowering L. We have from Proposition 1 part 1 so the denominator shrinks as L falls. The claim follows if . We have

as from Proposition 1 part 2, completing the proof. □

APPENDIX B

Manifestations of Short-Termism: Further Details

Elasticity of supply of the input asset

We first develop the study of an elastically supplied input asset and prove Lemma 3. This then allows us to build up to the proof of Proposition 2.

Suppose that the supply, S(P), of the input asset responds to price according to the constant elasticity of supply function:

The supply function (A12) is normalised so that absent short-term shareholders, the fundamental price of the input asset is invariant at the level given by (2) for any elasticity, .²³ Therefore, absent short-term shareholders, the first best situation would have types investing in the risky technology. We augment (1) and restrict attention to parameters such that:

This is sufficient to ensure existence of the equilibrium price for any given elasticity of supply, .

Lemma 3:

• In an industry with elasticity of supply and with L short-term shareholders, the critical firm type, that just selects the risky technology satisfies

Proof of Lemma 3:

• If the price of the input is P then market clearing with supply function (A12) implies that the critical firm type satisfies

The critical firm type, given L, is indifferent between the risky and safe payoffs and so satisfies, using (3):

From (A15) we have Using this to substitute for P yields (A14).

The critical type exists by applying the Intermediate Value Theorem to (A14) at and using (A13). For uniqueness note that the left-hand side of (A14) is decreasing in . Differentiation confirms that the right-hand side is increasing in □

Lemma 3 allows us to establish Proposition 2 demonstrating that the mis-allocation described in Proposition 1 is robust to an elastically supplied input asset.

Proof of Proposition 2:

• We first confirm the misallocation to the risky-technology: given in (A8). Evaluating (A14) at yields:

As the left-hand side of (A14) is decreasing in while the right-hand side is increasing, we must have . Next note that as the price is given in (A15), so

Now we show the result. The critical firm type is given by (A14). Differentiating with respect to

It follows that

As we have already shown . □

Imperfect capital markets

Here we develop the machinery to study mis-estimation by capital markets of the short-term pressure on firms, and build up to the proof of Proposition 3 below.

We use a partial equilibrium analysis, fixing the price of the input asset at P. Given the financial markets’ belief about the probability of short-term ownership, , the critical firm type, , that would choose the risky technology would be given implicitly, using (3), by:

The term is the market’s valuation of a firm that has chosen the risky technology. Equation (A16) captures the market’s awareness that short-term shareholders cause the Board to weight the path of the share price as well as the long-run net present value. The term is given by:

Substituting (A17) into (A16) gives the critical firm type, , expressed implicitly in terms of fundamental parameters and the market’s belief, We can therefore calculate the ex ante equity value of a randomly drawn firm as:

We are now in a position to prove Proposition 3 above.

Proof of Proposition 3:

• Given market beliefs, the critical firm type for the firm is given by , where

The market value of a firm at time will be if the firm is drawn from and r otherwise. Hence the average market value is

The excess return between and is given by the difference between (A20) and (A18). The value of the firm at can be written Hence the excess return is

Now note from (A17) that Therefore if then (A16) would yield a contradiction. It follows that and so (A16) implies that Also from (A19)

And so as we have Hence we have shown that Differentiating we have

yielding the excess returns result.

Now consider the realised values produced at The market’s beliefs will now be irrelevant as the payoffs can be observed. Firms with types in the range will have developed the risky technology. On average the payoffs realised will be

Compared to the excess return is given by the difference between (A22) and (A18). Using that this is:

where the inequality follows as we noted Hence the excess return is negative. Differentiating we have

From (A21), Given (A19) implies that and so as required. □

Market learning from signals as to firm type

Here we develop a tractable model of the signal of firm type before building up to the proof of Proposition 4.

Recall that in the benchmark model the critical type indifferent between choosing the risky technology and the risk-free technology is given implicitly by:

Now suppose that before any investment decisions are made shareholders receive a signal about firm i’s type, . We assume that this signal gives the true firm type, , with probability s, otherwise it contains no information. The market will use Bayes’ rule to update their beliefs as to firm i’s type:

The presence of the signal will alter the posterior distribution of and so alter the critical value of for firm i to choose the risky technology, to If and the firm selects the risky technology regardless then the market knows for sure that is not true, and therefore ignores the signal. If and the risky technology is chosen the market’s expectation of firm i’s type is:

Now we are able to prove Proposition 4.

Proof of Proposition 4:

• First we show that for sufficiently positive signals, firm misallocation to the risky technology is greater than without a signal. That is The post signal cut-off is determined implicitly as:

Assume the signal is sufficiently strong that . Evaluate (A26) at

where the inequality follows as we assumed . Therefore as both sides of (A26) are monotonic with respect to we must have that as claimed.

Next we show that the misallocation to the risky technology is increasing in the quality of the signal received. Differentiating (A26) with respect to and using (A25) yields:

demonstrating the result. □

APPENDIX C

Index of Short-Termism

Figure C1 explains the short-termism measure constructed in equation (5). The examples presented consider ownership stakes over four consecutive quarters for fictitious owners A, B and C who are assumed to own of the shareholder equity of a given company. Panel (a) demonstrates that volatile share ownership leads to stable short-term measures with no double counting. Panel (b) demonstrates that divestments are captured by equation (5) via the purchasing investor.

Figure C1

Graphical explanation of short-termism measure.

(a) Volatile shareholder ownership example.

Notes: Only the 20% of the shares that are oscillated between investors B and C are captured as short-term over the 4 quarters. Using equation (5):

(b) Shareholder B selling early example. Notes: At the end of Q4 the firm is owned solely by A and C. The full 50% bought by C is captured as short-term owned over the 4 quarters. Using equation (5):

Summary statistics for the dataset created by this index of short-termism are presented in Table C1.

Table C1 Summary statistics for firm and ownership data

APPENDIX D

Proofs from the Section “Empirical predictions and evidence”

Proof of Proposition 5:

• Let be the density of firm types that announce a merger bid at Using the cut-off property of Lemma 2, market clearing implies firms with type will develop the risky technology and so will complete the acquisition. The market value of the equity of a firm at announcement is therefore given by V in (A11). The cumulative abnormal return to the bid announcement is therefore which gives (6).

Part 1 follows as (Proposition 1 part 4). For part 2 we use Claim 1:

□

Proof of Proposition 6:

• Conditional on the risky business model, the market believes the firm’s type lies in Hence the value is given by However types choose the risky business model, and so the expected value conditional on the risky business model is in reality Subtracting one from the other yields (7). Proposition 3 demonstrates so part 1 follows. Proposition 3 demonstrates that given the assumption that Hence part 2 follows. □