Optimal Portfolio Rules Under Predictable Returns and Transaction Costs

This paper solves the optimal portfolio and consumption rules of an investor, who observes a dynamic signal that can forecast future stock returns and who faces both fixed and propor-tional transaction costs. We find that the value of the signal is determined by its expected Sharpe ratio, as well as the speed of mean reversion of the signal. For a monthly decay signal, transaction costs can reduce the expected utility associated with the predictability of the signal by more than 50%. For a weekly signal, the optimal trading can even be buy-and-hold. In other words, a fast mean reverting signal may not have any value in the presence of transaction costs. We also show that the higher Sharpe ratio of a signal leads to more aggressive trading and a larger net value, whereas a faster mean reversion (after controlling for the Sharpe ratio) also leads to more aggressive trading but a smaller net value. Therefore, the relationship between net performance and turnover can be either positive or negative. We further find that transaction costs naturally lead to a positive autocorrelation in the investor’s order flows