The price-volume relationship caused by asset allocation based on Kelly criterion

It is noticed that there is a relation between assets' return and trade volume in financial markets, but existing theory could not explain how exactly they are connected or what the relation is in a general scenario. Based on the hypothesis that investors who adopt a Kelly trading strategy will adjust their position periodically, we present a model describing the explicit price-volume relation. The model shows that factors related with the volume of trade are: (1) the total volume of the risk asset; (2) the optimal proportion of the risk asset implied by the Kelly criterion; and (3) the accumulated absolute deviation of the risk asset's return from the risk-free rate. In a multi-asset scenario, the factor (2) and (3) of one asset could partly explain other assets' trading volume. Empirical test with data from the Chinese and the U.S. stock markets verifies such relation.