Robust optimization for portfolio risk : a ravisit of worst-case risk management procedures after Basel III award.

The main purpose of this thesis is to develop methodological and practical improvements on robust portfolio optimization procedures. Firstly, the thesis discusses the drawbacks of classical mean-variance optimization models, and examines robust portfolio optimization procedures with CVaR and worst-case CVaR risk models by providing a clear presentation of derivation of robust optimization models from a basic VaR model. For practical purposes, the thesis introduces an open source software interface called “RobustRisk”, which is developed for producing empirical evidence for the robust portfolio optimization models. The software, which performs Monte-Carlo simulation and out-of-sample performance for the portfolio optimization, is introduced by using a hypothetical portfolio data from selected emerging markets. In addition, the performance of robust portfolio optimization procedures are discussed by providing empirical evidence in the crisis period from advanced markets. Empirical results show that robust optimization with worst-case CVaR model outperforms the nominal CVaR model in the crisis period. The empirical results encourage us to construct a forward-looking stress test procedure based on robust portfolio optimization under regime switches. For this purpose, the Markov chain process is embedded into robust optimization procedure in order to stress regime transition matrix. In addition, assets returns, volatilities, correlation matrix and covariance matrix can be stressed under pre-defined scenario expectations. An application is provided with a hypothetical portfolio representing an internationally diversified portfolio. The CVaR efficient frontier and corresponding optimized portfolio weights are achieved under regime switch scenarios. The research suggests that stressed-CVaR optimization provides a robust and forward-looking stress test procedure to comply with the regulatory requirements stated in Basel II and CRD regulations