Análisis de situación del caso de estudio

We now turn to the case where, instead of one firm, there are two firms, indexed by i ∈ {A, B}, that have correlated productivity shocks. We show that overinvestment resulting from the shareholders’ efforts to improve market monitoring increases the correlation between investments across firms. The reason is that both firms optimally invest in negative NPV projects at the same time, namely, when both stock prices are high.

We assume that the two firms are controlled by different managers who simultaneously make their investment decisions at time 1, after having observed the stock prices P1,A and

P1,B. As before, managers can improve the quality of investment projects by exerting effort. To allow for the possibility of industry-wide productivity shocks, we modify our basic model, presented in Section 2, as follows. By incurring a utility cost of Ψ, each manager can increase her firm’s probability of having a high-quality project from 0 to ˜ν, where ˜νis the same for both firms and is equally likely to be either (1 +ν)/2 or (1−ν)/2 withν ∈[0,1]. The value of ˜ν is

not known to the manager at time 0 when she makes her effort choice. Thus, this assumption does not change the ex ante expected increase in firm value through managerial effort. It only affects the correlation of the quality of the two projects, which (in an equilibrium with high effort) can be shown to beCorr(qA, qB) =ν2. For simplicity, we assume that there are no production externalities. The payoff of firm A’s investment project is independent of firm

B’s investment decision and vice versa.

As before, there are three types of traders active in the stock market at time 1: speculators, liquidity traders, and market makers. All of them have essentially the same characteristics as in Section 2. There are now two speculators, each able to produce information about one of the firms. That is, by incurring a costK, speculatorA(B) learnsqA(qB) with probabilityδ. The event of receiving an informative signal is assumed to be independent across speculators. Note that this implies that the occurrence of a liquidity shock in the two markets is independent as well.23 To keep the model tractable, we further assume that the correlation between qA and qB is sufficiently low and that the return premium required by speculators is sufficiently high, so that each speculator only trades shares of the firm for which she has observed an informative signal. With these simplifying assumptions, the speculators’ trading strategy in this extended version of the model is identical to that specified in Section 3.1. As before, stock prices are determined by a perfectly competitive market-making sector. Each market maker observes the demand for both stocks before quoting her prices. Depending on the order flow (dA, dB)∈ {−α, α}2, there are now four possible prices for each stock, denoted by

P++

1,i =P1,i(di =α, dj =α),P1+,i−=P1,i(di =α, dj =−α), etc. Thus, the positive correlation between qA and qB makes price P1,i more informative about project quality qi. The details of the stock market equilibrium are given in the Appendix. Each firm’s investment policy is then characterized by the vector λi = λ++_i,h, λ+_i,h−, λ−_i,h+, λ−−_i,h, λ++_i,l , λ+_i,l−, λ−_i,l+, λ−−_i,l

, whereλ++

i,h =

λi h, P₁++_,i

denotes the probability that firm i invests in a high-quality project when the demand for both stocks is high (the other probabilities are defined analogously).

23

The increased price informativeness enables shareholders to design a more efficient man- agerial contract. For simplicity, we assume that each manager’s compensation can only be contingent on her own firm’s stock prices P1,i and P2,i. Using the same techniques as in Section 3.2, it is straightforward to show that the optimal managerial contract is given by mi P₁++_,i ,1 = 8Ψ/ (δ+θ)(1 +δ ν2) and mi P₁++_,i,1₂ = l mi P₁++_,i,1

. All other state- contingent payments are zero. As before, the manager receives compensation only in the state of nature that is most informative about the fact that she has exerted a high effort. The manager’s expected compensation is given by:

CI,i=

1 +δ θ+δ(δ+θ)ν2

(δ+θ)(1 +δ ν2₎ Ψ. (28)

Not surprisingly, CI,i is decreasing in ν. The stronger the correlation between qA and qB, the more informative is the demand for stock j about the project quality of firm i. It is important to note that this contract can be used to induce the manager to exert a high effort and to implement any investment policy λi withλ++_i,h = 1 at minimum cost.

We are particularly interested in how correlated productivity shocks across firms affect the manager’s optimal investment strategy. To this end, we again compare the effects of overinvestment on the speculator’s profit and on the initial shareholders’ wealth in different states of nature, in order to determine the most efficient way to compensate the speculator for her costly monitoring service. We begin our analysis by calculating the expected trading profit (loss) per share of speculators (liquidity traders), Li, and the ex ante value of the firm gross of managerial compensation payments, V0,i:

Li(λi) = ₁₆1 δ(1−δ) 1−δ2ν4θ 1 +δ2ν2−1 λ++ i,h +λ −− i,h +λ ++ i,l +λ −− i,l + 1−δ2ν2−1 λ+− i,h +λ −+ i,h +λ +− i,l +λ −+ i,l , (29)

V0,i(λi) = 1₂ +₁₆1 θ (1 +δ ν2) (1 +δ) λ++ i,h −λ −− i,l + (1−δ) λ−+ i,h −λ +− i,l + (1−δ ν2)(1 +δ) λ+− i,h −λ −+ i,l + (1−δ) λ−− i,h −λ ++ i,l . (30)

From the discussion in Section 3.3, it follows that underinvestment is never optimal, because it lowers the firm value as well as the speculator’s trading profit. Further, overinvestment is a more efficient way to boost the speculator’s profit when the order flowdi indicates a high- quality project. This can also be seen from equations (29) and (30). A marginal increase in λ++

i,l (λ

+−

i,l ) has the same effect on Li as a marginal increase inλ−−i,l (λ

−+

i,l ), but it causes a smaller decline in firm valueV0,i. The only remaining question is how the demand for stockj influences the optimal investment strategy of firmi. Is it more effective (in terms of inducing information production) to invest in negative NPV projects when stock prices of other firms are high as well? The answer to this question follows immediately from equations (29) and (30). In terms of their effects on the speculator’s expected profit, increasing λ+−

i,l by is equivalent to increasing λ++

i,l by (1 +δ2ν2)/(1−δ2ν2)> . However, a marginal increase in

λ+−

i,l reduces the value of the firm by

1

16θ(1−δ) 1 +δ ν 2

, whereas a marginal increase in

λ++

i,l reduces it only by

1 16θ(1−δ) 1−δ ν 2 . Because: 1 +δ ν2 > 1 +δ 2_ν2 1−δ2_ν2 1−δ ν 2 , (31)

overinvestment is therefore less costly for shareholders of firm iwhen the stock price of firm

j is up as well. This, in fact, establishes the following proposition.

Proposition 5. For any ν >0, the most efficient way for inside owners of firm i∈ {A, B}

to increase the speculator’s expected profit by deviating from the first-best investment policy is to increase λ++

i,l , i.e., to increase the probability of investing in a low-quality project when

the demand for shares of both firms is high.

Proposition 5 has several interesting implications. First, it shows that investments are more strongly correlated across firms than the correlation between fundamentals would sug-

gest. This is in stark contrast to models which attribute the overinvestment problem to the manager’s desire to control more assets. In these models, investment decisions become stochastically independent across firms when the correlation between fundamentals goes to zero.

Proposition 5 further suggests that the correlation between stock returns is state-dependent. If the stock market is down, the manager’s decision to invest clearly indicates a high-quality project. However, if the market is up, the manager’s investment decision becomes a less reliable predictor of the firm’s prospects. Thus, controlling for the firms’ investment deci- sions, we would expect stock returns to be more strongly correlated when the stock market is declining.

Finally, proposition 5 implies that overinvestment poses a systematic risk to investors that cannot simply be diversified away. For any arbitrarily small ν > 0, firms optimally choose to undertake negative NPV projects “at the same time” (i.e., in the same state of nature), namely, when the stock market as a whole is booming.24 Thus, in a more complex model where prices are not determined by risk neutral arbitrageurs, investors would demand higher expected returns for holding shares of firms that are prone to this kind of investment distortion.