A Dynamic Mean-Variance Analysis for Log Returns

We propose a dynamic portfolio choice model with the mean-variance criterion for log-returns. The model yields time-consistent portfolio policies and is analytically tractable even under some incomplete market settings. The portfolio policies conform with conventional investment wisdom (e.g. richer people should invest more absolute amount of money in risky assets; the longer investment time horizon, the more proportional amount of money should be invested in risky assets; and for long-term investment, people should not short sell major stock indices whose returns are higher than the risk-free rate), and the model provides a direct link with the CRRA utility maximization in a complete market.