Portfolio Selection by Joint Estimation-Robustness Optimization with the Return and Risk Constraints

In answering the main criticism of the classical robust optimization that the size of the uncertainty set has to be determined beforehand, a recently proposed JERO (Joint Estimation and Robustness Optimization) framework treats the size of the uncertainty set as a variable and maximizes it subject to some robust conditions over the uncertainty set. This paper studies its effect on portfolio selection when both the robust return and risk constraints are built in JERO. Although JERO does not directly pursuit any optimality of portfolio return or risk, we report a surprising result that JERO actually selects efficient portfolios. This is proved by reformulating the robust risk constraint as a tractable form through the S-procedure. Moreover, a closed-form formula was derived when there is only the budget constraint. An efficient algorithm is proposed when more constraints are added. Numerical experiments illustrate the validity of the reported results. This research paves the way for JERO to be applied to the portfolio selection problem with return and risk related robust constraints.