Multiperiod Dynamic Portfolio Choice: When High Dimensionality Meets Return Predictability

Multiperiod portfolio choice is the central problem in active asset management. Multi- period dynamic portfolios are notoriously difficult to solve, especially when there are hundreds of tradable assets as well as a large number of state variables. In this paper, we develop a novel two-step methodology to solve the multiperiod dynamic portfolio choice problem with high dimensional assets in the presence of return predictability conditional on a large number of state predictors. Specifically, in the first step, we propose the new Risk-Premium Projected- PCA (RP-PPCA) method to reduce the dimension of tradable assets. This method achieves Dimension Reduction (DR) by estimating latent factors with explanatory power in both time series variation and expected return in high-dimension-low-sample-size data. In the second step, we use dynamic programming to solve the multiperiod portfolio choice problem, and in each recursive step, we adopt an Adjusted semiparametric Model Averaging (AMA) method to avoid the curse of dimensionality associated with a large set of state variables while re- maining computationally efficient. Thus, we name this two-step approach DRAMA, which stands for a combination of a new dimension reduction method and an adjusted semipara- metric model averaging method. Analytically, we show that the portfolios constructed by the DRAMA are approximately optimal under mild assumptions. Moreover, our numerical results based on empirical data from US stock markets show that the proposed portfolios have both excellent in-sample and out-of-sample performances.