Heterogeneous beliefs and short selling taxes: A note

Short selling is widespread in financial markets but regulators can ban short positions. The intermediate policy of taxing short sellers has been studied in an asset pricing model with evolutionary competition of two belief types (Anufriev and Tuinstra, 2013). We extend this approach to an arbitrary number of belief types H, giving $3^H-2^H$ cases to check each period in the worst-case scenario. We provide analytic expressions for asset prices along with conditions on beliefs (optimism) that determine which types take long, short or zero asset positions at the market-clearing price. We use these results to construct a fast solution algorithm (quadratic in H) which can solve models with hundreds or thousands of types in a matter of seconds. A numerical example with a short-selling tax and many heterogeneous beliefs in evolutionary competition shows that price dynamics can differ substantially relative to the benchmark of few types.