Parameter uncertainty in multiperiod portfolio optimization with transaction costs

We study the impact of parameter uncertainty in multiperiod portfolio selection with trading costs. We analytically characterize the expected loss of a multiperiod investor, and we find that it is equal to the product of two terms. The first term corresponds with the single-period utility loss in the absence of transaction costs, as characterized by Kan and Zhou (2007), whereas the second term captures the multiperiod effects on the overall utility loss. To mitigate the impact of parameter uncertainty, we propose two multiperiod shrinkage portfolios. The first multiperiod shrinkage portfolio combines the Markowitz portfolio with a target portfolio. This method diversifies the effects of parameter uncertainty and reduces the risk of taking inefficient positions. The second multiperiod portfolio shrinks the investor's trading rate. This novel technique smooths the investor trading activity and it also may help to considerably reduce the impact of parameter uncertainty. Finally, we test the out-of-sample performance of our considered portfolio strategies with simulated and empirical datasets, and we find that ignoring transaction costs, parameter uncertainty, or both, results into large losses in the investor's performance