Multiperiod portfolio optimization with multiple risky assets and general transaction costs. AbstractWe analyze the optimal portfolio policy for a multiperiod mean-variance investor facing multiple risky assets in the presence of general transaction costs. For proportional transaction costs, we give a closed-form expression for a no-trade region, shaped as a multi-dimensional parallelogram, and show how the optimal portfolio policy can be efficiently computed for many risky assets by solving a single quadratic program. For market impact costs, we show that at each period it is optimal to trade to the boundary of a state-dependent rebalancing region. Finally, we show empirically that the losses associated with ignoring transaction costs and behaving myopically may be large.

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We consider the portfolio optimization problem for a multiperiod investor who seeks to maximize her utility of consumption facing multiple risky assets and proportional transaction costs in the presence of return predictability. Due to the curse of dimensionality, this problem is very difficult to solve even numerically. In this paper, we propose several feasible policies that are based on optimizing quadratic programs. These proposed feasible policies can be easily computed even for many risky assets. We show how to compute upper bounds and use them to study how the losses associated with using the approximate policies depend on different problem parameters. Portfolio Selection with Proportional Transaction Costs and Predictability Xiaoling MeiJavier Nogales AbstractWe consider the portfolio optimization problem for a multiperiod investor who seeks to maximize her utility of consumption facing multiple risky assets and proportional transaction costs in the presence of return predictability. Due to the curse of dimensionality, this problem is very di cult to solve even numerically. In this paper, we propose several feasible policies that are based on optimizing quadratic programs. These proposed feasible policies can be easily computed even for many risky assets. We show how to compute upper bounds and use them to study how the losses associated with using the approximate policies depend on di↵erent problem parameters.

In this section, we evaluate the performance of our proposals for Models 2-4. Tables 1-19 provide the results. We observe that the proposed covariance matrices provide robust results compared to standard approaches based on the sample covariance matrix and Ledoit-Wolf covariance estimator when the sample data is contaminated.However, as it was expected, sample covariance matrix provides better performance under the absence of contamination. In general, the obtained results are similar to those for Model 1. We observe that Spearman correlation performs better than Kendall correlation for both estimators GLasso and DTrace in terms of statistical losses. In terms of the GGM prediction measures, we obtain mixed results. The precision matrix estimators based on Kendall coecient mostly provide higher MCC than the estimators based on Spearman coecient for most of the experiments. We can also see that MAD performs better than Qn and Sn under high contamination level, whereas Qn and Sn perform better under low level of contamination.