Bullish Bearish Strategies of Trading a Nonlinear Equilibrium
45 Pages Posted: 21 Feb 2001
Date Written: January 2000
In this paper, we study a financial market where risk neutral traders are endowed with a signal which is perfectly revealing of the direction (but not the exact amount) of the liquidation value of a normally distributed risky asset. This type of information is known as bullish or bearish and has been shown to have a great impact on prices. When the signal is positive (negative) the traders buy (sell) the asset. Trading recommendations issued by financial institutions fall into this category of information. At the equilibrium, the optimal strategy consists of buying (selling) when bullish (bearish) a fixed quantity of the asset. The market makers observe the aggregated volume submitted by the informed traders and the noise traders. In this model, since the optimal trading strategy is not linear, the pricing schedule is also a non-linear function of the volumes. We show i) that the price function is a non-linear Sigmoid-shaped function. ii) that price pressure is a regular bell-shaped curve of the volumes. iii) A monopolistic bullish-bearish type trader makes nearly thirty six percent of the profits she would have made with a perfect signal in a linear model a la Kyle (1985). iv) In the presence of competition, the market reveals his private information quicker than in a noisy informed strategic oligopoly and where the level of noise is chosen such that the monopoly bullish bearish expected profit is equal to the monopoly noisy informed expected profit with linearity. Moreover, the liquidity is no longer a monotonic increasing function of the number of competitors. This is true only for sufficiently large order imbalance leading to cross-liquidity-points for different size of the insider trading.
Keywords: Nonlinear equilibrium, recommendations of trading, asymmetric information, investment banks
JEL Classification: D43, D82, G14, G24
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