Before revision: This note poses the problem of developing a non-stochastic version of Fernholz's stochastic portfolio theory and discusses a possible approach to it. In particular, it gives a non-stochastic interpretation of the tension between market efficiency and market diversity that is a key finding of stochastic portfolio theory  .
After revision: This note poses the problem of developing a non-stochastic version of Fernholz's stochastic portfolio theory for a simple model of stock markets with continuous price paths. It establishes non-stochastic interpretation of the tension between market efficiency and market diversity that is a key finding of stochastic portfolio theory .