Information Aggregation and Investment Decisions by Elias Albagi, Christian Hellwig, and Aleh Tsyvinnski Comment: Frank Heinemann Technical University Berlin Asset Prices, Credit and Macroeconomic Policy International Conference Marseilles - March 25 -26, 2011 1
The Market • A firm‘s dividends depend on a normally distributed state variable θ. • Risk neutral shareholders (traders) get private signals about the state xi ~ N(θ, 1/β). Call those whose signal is higher than θ „optimistic“. • They may hold or sell their asset. • There is exogenous asset demand determined by a random variable u. • Market price is common knowledge. • There are no other traders (arbitrageurs/speculators). 2
Equilibrium • A trader sells iff her signal is below a threshold x*. • Price reveals a compound of θ (=> dividends) and u (=> demand). If price is high, traders partially attribute this to a high state and expect higher dividends. The higher demand, the more traders must sell. The marginal trader is changing and becomes more optimistic. => price rises above expected dividends (conditional on z). Since individual trader does not know her position in the distribution of private signals, she cannot correct this. Low demand => price < expected dividends. => excess volatility! 3
Why can‘t a shareholder offset her „mistake“ by taking the expected wedge into account? Marginal trader has a signal that leads her to belief that z is higher than it actually is. She is too optimistic. 4
Equilibrium The higher demand, the more traders must sell. Whenever u > 0, the marginal trader is an optimist. The posterior belief of the marginal trader is biased from public information z towards a state with higher expected dividends. This bias increases in u. Positive demand shocks increase optimism and overvaluation w. r. t. exp‘d dividends. Negative demand shocks => undervaluation Note that demand also reflects some market value. 5
Firm‘s investment and convexity • Firm‘s manager decides on investment, observing share price P(z) and a private signal y on investment costs. • RE => Decision rule is foreseen by shareholders. • Profitability of investment depends (positively) on θ. => Firm is more likely to invest in good expected states, i. e. for high z(θ, u). acceleration of expected dividends. => Expected dividends are a convex function of z. => Ex ante expected difference between price and fundamental value, E(P(z)) – E(V(z)), is positive. 6
Firm‘s investment and convexity • With a positive demand shock, the marginal trader („the market“) gets more optimistic and she is willing to pay a higher premium on an investment by the firm than an unbiased risk neutral trader would do. => If manager‘s compensation rises in the share price, he has an incentive to invest, even if the expected reward is below costs. => overinvestment for positive demand shocks underinvestment for negative demand shocks => higher volatility! 7
Firm‘s investment overinvestment for positive demand shocks underinvestment for negative demand shocks • This reduces ex-ante expected prices and dividends in comparison to a firm with the right investment decisions. This is a bit like Barro/Gordon: a commitment to invest efficiently, given available information, would raise the average price. But since costs are private info of the manager, a commitment is not credible. Hence, manager follows beliefs of „the market“ (= posterior of an optimistic or pessimistic trader). 8
An outside observer • knows distribution and observes price. • Since price function is invertible, he can calculate summary statistic z • Wedge P(z) – V(z) depends on z. • Outside observer (speculator) should buy, whenever P(z) < V(z), and sell (short), if P(z) > V(z). QUESTION 1: Is it reasonable to exclude speculation? Q 2: Does a trader who neglects her private signal make higher expected profits than a shareholder with additional private information? Is this a „curse of knowledge“? Q 3: Could arbitrageurs/speculators be included and results still hold, if one applies „cursed equilibrium“? 9
Other questions • • Role of belief heterogeneity (p. 20): what would results be, if beliefs are identical but noisy? (or distributed around a noisy mean) Introducing arbitrage traders: - what is the optimal trading strategy of an informed trader w/o limits to buy and sell? - what is the optimal trading strategy of an outsider who just observes P(z)? 10
Ex-ante perspective Suppose, setting up the firm costs S. These costs are sunk at the time of our game. • • A rational investor should invest in the firm if E(P) > S. For E(P) > S > E(V) expected returns are below these costs. => A rational investor may setup a firm although its expected return is below the setup-costs. => Overinvestment / bubble / Tobin‘s q. • Under which conditions do these phenomena arise here? Macroeconomic consequences? • Optimal regulation? Note: Exogenous demand also reflects some welfare components. 11
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