Worse-Case Conditional Value-at-Risk for Asymmetrically Distributed Asset Scenarios Returns

摘要

Many studies have reported empirical evidence of asymmetries in asset return distributions. Meanwhile, optimal solutions to the Conditional Value-at-Risk (CVaR) minimization are highly susceptible to estimation error of the risk measure because the estimate depends on only a small portion of sampled scenarios. In this paper, based on the robust optimization techniques Chen et al.(2007) [19], we propose a computationally tractable worst-case Conditional Value-at-Risk (CVaR). In the situation, the sampled scenario returns are generated by a factor model with some asymmetric affine uncertainty set. The remarkable characteristic of the new method is that the robust optimization model retains the complexity of original portfolio optimization problem, i.e., the robust counterpart problem is still a linear programming problem. Moreover, it takes into consideration asymmetries in the distributions of scenarios returns used for defining CVaR. We present some numerical experiments with simulated and real market data to illustrate the behavior of the robust optimization model.