Do Short Sale Constraints Impede the Diffusion of Negative Information?

I model the process of information diffusion through trading decisions of informed agents and the rational response of risk-neutral market makers (arbitrageurs).I find that in a model where the probability distribution of the asset's payoff is modeled as a Bernoulli random variable (following Glosten and Milgrom (1985) and Diamond and Verrecchia (1987)), the short sale constraints inhibit the information diffusion to the same degree in cases of positive information and negative information. Put another way, after fixed number of trades, the positive news have a positive expected price impact of the same magnitude as the negative price impact of negative news.I consider also a more complex specification following Kyle (1985). The payoff of the asset is modeled as a normal random variable and the behavior of the informed agents and the market makers is determined by the non-linear Nash equilibrium where informed agents make portfolio choices so as to maximize their expected profits (one of them subject to selling constraint) while market makers set the price equal to the conditional expectation of the payoff given the public information about the order flow. In this setting, the price impact of the private information about the true payoff depends not only of the direction of the private information (whether the true payoff is higher or lower than the expected payoff) but also on the magnitude of the private signal. In the equilibrium, I find that (i) the price impact in the model where some of the informed agents are constrained has typically lower magnitude than in the model where all the agents can sell the asset, (ii) in the model where some agents cannot sell, the price impact of extreme positive news is higher in magnitude than the price impact of the equally sizable negative news, (iii) in the model where some agents cannot sell, the price impact of moderate positive news is lower in magnitude than the price impact of the equally small negative news.In conclusion, in the model with Bernoulli-distributed payoff, “Bad News Travels Slowly” does not hold because they travel as slowly as good news. In the model with normally-distributed payoff “Bad News Travels Slowly” holds only for sizable bad news as compared to commensurate good news. For the news of moderate magnitude however, the very reverse is the case