Reliability-based portfolio optimization with conditional value at risk (CVaR)

Abstract

This paper builds on the work of Roman et al. [Quant. Finance, 2007, 7, 443–458], whereby we incorporate the concept of the reliability-based design optimization (RBDO) technique. We reformulate Roman et al.’s model by including both non-deterministic design variables as well as probabilistic parameter values of returns of assets, and solve it with a relevant probabilistic constraint. Apart from a similar set of conclusions as derived by Roman et al., we deduce a few other interesting observations, some of which are: (i) reliability forces diversification and hence reduces portfolio risk; (ii) an increase in the level of reliability aids in better portfolio management, as it aids diversification; and (iii) a decrease in the investor’s attitude with respect to how reliable the input data is, has an adverse effect on the optimal value of the portfolio risk/variance.

Keywords:

• Finance
• Linear programming
• Portfolio optimization
• Risk management

JEL Classification:

• C4
• C6
• C44
• C61

Acknowledgements

The first author would like to acknowledge the financial support and grants made available through the Indo–US Science and Technology Forum (IUSSTF) for a visit to Princeton University, USA, for one semester of research. The work of the second author forms part of his unpublished Masters in Technology (M. Tech) thesis done jointly in the IME and EE departments of IIT Kanpur, India. The authors would like to thank the Editor, Associate Editor and two anonymous referees for their individual critical and valuable comments/suggestions that helped us to improve the final version of this paper.

Notes

¹Note that, in our application to portfolio optimization, the portfolio weights of the stocks correspond to the set of uncertain design variables, while the estimates of expected returns of the stocks represent the vector of uncertain parameters.