(302a) Optimal Portfolio Selection Under Uncertainty

A key element of supply chain management is the oversight of a company's funds and the investment of these assets. In order to guard against industry-wide losses, a company must diversify itself in sectors outside of its realm of influence. The investment in other companies by means of purchasing stock is one way to attain a level of diversification. Markowitz [1] provides an overview of the general portfolio selection problem under consideration. A novel nonlinear and mixed-integer optimization framework for the portfolio selection of stocks under uncertainty which utilizes Conditional Value-at-Risk theory based upon the work of Rockafellar and Uryasev [2] has been developed in order to address the aforementioned objective of managing a company's financial assets for the purposes of diversification.

The framework eliminates much of the guesswork in portfolio selection and replaces it with rigorous mathematical modeling, combinatorial and nonlinear continuous optimization techniques. The novel portfolio selection under uncertainty framework simultaneously takes into account thousands of large-cap stocks and makes a determination not only regarding what stocks to purchase or sell but also the number of shares of each individual stock which should be purchased or sold. The framework has the ability to quickly generate several different types of portfolios. By quantifying risk levels and diversification requirements, the framework can explicitly take into account changing risk preferences, as well as desired diversification levels. It can adapt efficiently and effectively to changing investor preferences. Also, the framework works well for both large and small portfolios since it makes no implicit assumptions regarding the size of the funds available for investment. If the company imposes a restriction on the turnover of the portfolio from one time period to the next, a bound on the amount of shares which can be sold both for an individual stock and overall is enforced. A case study has been conducted which indicates that the given framework has the ability to consistently outperform standard stock market indicators, making it an attractive addition to any supply chain management strategy.

[1] Markowitz, H.M. Portfolio Selection. Journal of Finance. 1952, 37, 77.

[2] Rockafellar, R.; Uryasev, S. Optimization of Conditional Value-at-Risk. Journal of Risk. 2000, 2, 21.