Economics and Finance

Transcription

1 Economics and Finance Lecture 17: Information efficiency and governance role of capital markets Luca Deidda DiSEA-Uniss 2014 Luca Deidda (DiSEA-Uniss) / 12

2 Plan Model of capital market with information acquisition and revelation Governance role of capital markets (and speculation) References: Tirole, The Theory of Corporate Finance, Ch 8, sections 1, 2, 3 Luca Deidda (DiSEA-Uniss) / 12

3 The model Let us consider our standard MH framework, and add the following assumptions Each firm issues shares to be exchanged in an official stock market Each share entitles to a share of the cash flow R Ex ante, conditional on insiders putting effort, the value of the share is ph R Financial investors buy shares in the primary market and can then sell them in the secondary market Before the realization of uncertainty, financial investors can acquire a signal about the prospects of the firm incurring a cost c > 0 We call speculator an investor who acquires information about firms prospects Luca Deidda (DiSEA-Uniss) / 12

4 Structure of the signal: Posterior and prior probabilities of success The signal, j can take two values, H, or L The probability of a signal j is σ ij, which depends on effort i H, L Conditional on a signal j, the probability of success is v j, with v H > v L The prior probability of success conditional on high or low effort are: p H = σ HH v H + σ HL v L (1) p L = σ LH v H + σ LL v L (2) We assume σ HH > σ LH : exerting effort increases the probability of a H signal Luca Deidda (DiSEA-Uniss) / 12

5 Grossman-Stiglitz Paradox: Impossibility of efficient markets Before the realization of the signal, conditional on the fact that firms insiders are putting effort in managing the firm, the market value of the equity capital of the firm is p H R/(1 + r), which is also the price of a share if the number of share is normalized to one Let us assume that a speculator incurs the cost c and observes a high signal. Observing a high signal, he re-estimates the probability of success, assigning a posterior probability of success equal to v H > p H. Accordingly, since the price is p H R he wants to buy to earn an extra-profit v H R p H R > 0 The question is: will uninformed investors sell at p H R? Investors are uninformed. Yet, they are rational. The speculator s willingness to buy reveals that he must have observed a high signal. Hence, they won t sell at a price lower than v H R. Hence, the speculator will end up making a loss equal to c There is no equilibrium where speculators produce information Things change, however, if there are other motives for trading, such as liquidity reasons for instance (which happens to be the case in reality) Luca Deidda (DiSEA-Uniss) / 12

6 Liquidity trading In order for speculators to have incentives to acquire information, it must be the case that share market prices do not react always in the way described above In order for the share prices not to react "too much" or "so promptly" to speculators order flows, the market must be deep Deep market: there must be many investors who trade for different reasons, which implies that the amount of supply of securities in each moment is unknown (or not perfectly forecastable) If supply of securities is unknown, order flows of speculators are not necessarily revealed We assume the following A fraction s of investors are "liquidity traders": with probability λ they will all trade their shares (sell their shares) before the realization of uncertainty (the liquidity shock is perfectly correlated across liquidity traders) The rest, 1 s, are long-term investors who don t experience any liquidity shock Anonymous trading: We assume that the speculator can split his order in a way that the long-term investors or any new investor cannot tell his order apart from those of the liquidity traders Luca Deidda (DiSEA-Uniss) / 12

7 Order flows and stock prices Define y and z the demand of shares by speculators and liquidity traders, respectively As we shall see, firms probability of success will in general depend on y + z, so that the price of share will be generally given by P = Pr(success y + z)r (3) where Pr(success y + z) is the probability of success conditional on the order flow Demand by liquidity traders is s if there is a liquidity shock, and 0 otherwise Luca Deidda (DiSEA-Uniss) / 12

8 Speculators behavior Assume that a speculator incurs the information cost c Then, speculators willingness to buy is as follows Buy z = 0 if the signal is low Buy as much as possible if the signal is high Note however, that if the speculator buys more than s shares, his order will be disclosed Hence, optimal strategy is Buy z = 0 if the signal is low Buy z = s if the signal is high Luca Deidda (DiSEA-Uniss) / 12

9 Equilibrium characterization: Net order flows and information revelation and prices Conditional on speculators incurring the cost c, given their optimal behavior we have the following possible cases 1. With probability (1 λ)σ HH : High signal and no liquidity shock: z + y = s > 0 P = v H R 2. With probability λσ HH : High signal and liquidity shock: z + y = 0 P = P 1, where P 1 is to be determined 3. With probability λσ HL : Low signal and liquidity shock: z + y = s < 0 P = v L R, 4. With probability (1 λ)σ HL :Low signal and no liquidity shock: z + y = 0 P = P 1, where P 1 is to be determined The value of P 1 is determined as follows: P 1 = λσ HH (1 λ)σ HL v H R + v L R (4) λσ HH + λσ HL λσ HH + (1 λ)σ HL Luca Deidda (DiSEA-Uniss) / 12

10 Speculator s profits and Existence of equilibrium with information production Expected revenues for the speculator are: Expected profits are, sλσ HH (v H R P 1 ) (5) sλσ HH (v H R P 1 ) c (6) For information production to occur in equilibrium it is necessary that c is not too large Luca Deidda (DiSEA-Uniss) / 12

11 Managerial compensation through stock options Due to MH, in order for the firm to be financed, the manager should be given the right incentives This can be obtained by paying the manager conditional on success or offering him a compensation that is related to the early signal j about firms prospects In the latter case this can take the form of a stock option The manager is paid with the right to buy x shares at the ex ante price P = p H R after the realization of the signal Let us assume that P 1 < p H R = P 0 Then, if we are in an equilibrium in which the speculators produce information, the manager earns 1. With probability (1 λ)σ HH : R b = x(v H R p H R) 2. With probability (1 λ)σ HL : R b = 0 3. With probability λσ HH : R b = 0 4. With probability λσ HL : R b = 0 with probability σ ih, where i = L, H depending on whether he exerts effort or not. Incentive compatibility requires (1 λ)σ HH R b (1 λ)σ LH R b + B R b B (1 λ)(σ HH σ LH ) (7) Luca Deidda (DiSEA-Uniss) / 12

12 Stock option as incentive mechanism Accordingly, the stock option program implies offering the manager the right to buy at a price p H R, after the realization of the signal an amount x, of shares such that: x (v H R p H R) = B (1 λ)(σ HH σ LH ) (8) Luca Deidda (DiSEA-Uniss) / 12