Extended mean-conditional value-at-risk portfolio optimization with PADM and conditional scenario reduction technique

In this paper, we study mean-conditional value-at-risk portfolio optimization problem with short selling, cardinality constraints and transaction costs for large number of scenarios. To solve the large-scale mixed-integer model efficiently, conditional scenarios reduction technique and penalty alternating direction method are applied. The convergence of penalty alternating direction method is examined. Finally, experiments are conducted using the data set of the S &P index for 2020 to evaluate the proposed approaches in terms of CVaR values, CPU times and out-of-sample and in-sample Sharpe ratios. Results show that the proposed approaches significantly reduces the CPU times while keeping an acceptable degree of accuracy in terms of CVaR values. Also, out-of-sample and in-sample results show that the PADM and CS technique are reliable alternatives when the number of scenarios and stocks are large.