KELLY TRADING AND MARKET EQUILIBRIUM

The Kelly framework is the natural multi-period extension of one-period mean-variance model Markowitz in sense that efficient frontier characterized by trading strategies having maximal instantaneous Sharpe ratio. We show traders naturally trade such a way as to induce an equilibrium for covariance matrix. This equilibrium, arising from alone, has property correlation can be described saddle point stochastic differential game. However, because game not necessarily zero-sum volatility shown lower than what predicted fully specified rate logarithmic return, interest and aggregate willingness leverage seen market.