Extreme Returns and Intensity of Trading

Asymmetric information models of market microstructure claim that variables like trading intensity are proxies for latent information on the value of financial assets. We consider the intervalvalued time series (ITS) of low/high returns and explore the relationship between these extreme returns and the intensity of trading. We assume that the returns (or prices) are generated by a latent process with some unknown conditional density. At each period of time, from this density, we have some random draws (trades) and the lowest and highest returns are the realized extreme observations of the latent process over the sample of draws. In this context, we propose a semiparametric model of extreme returns that exploits the results provided by extreme value theory. If properly centered and standardized extremes have well defined limiting distributions, the conditional mean of extreme returns is a nonlinear function of conditional moments of the latent process and of the conditional intensity of the process that governs the number of draws. We implement a two-step estimation procedure. First, we estimate parametrically the regressors that will enter into the nonlinear function, and in a second step, given the generated regressors, we estimate nonparametrically the conditional mean of extreme returns. Unlike current models for ITS, the proposed semiparametric model is robust to misspecification of the conditional density of the latent process. We fit several nonlinear and linear models to the 5-min low/high returns to three major bank stocks, Wells Fargo, Bank of America, and J.P. Morgan, and find that, either in-sample or out-of-sample, the nonlinear specification is superior to the current linear models and that the conditional standard deviation of the latent process and the conditional intensity of the trading process are major drivers of the dynamics of extreme returns. We find that there is an asymmetric relationship between extreme returns and trading intensity. While the lowest returns are sensitive to any large or small volume of trading (the largest the volume, the lower the lowest returns), the highest returns are responding mostly to extremely large trading volumes.