Scenario Optimization Methods in Portfolio Analysis and Design

This chapter discusses techniques for analysis and optimization of portfolio statistics, based on direct use of samples of random data. For a given and fixed portfolio of financial assets, a classical approach for evaluating, say, the valueat- risk (V@R) of the portfolio is a model-based one, whereby one first assumes some stochastic model for the component returns (e.g., Normal), then estimates the parameters of this model from data, and finally computes the portfolio V@R. Such a process hinges upon critical assumptions (e.g., the elicited return distribution), and leaves unclear the effects of model estimation errors on the computed quantity of interest. Here, we propose an alternative direct route that bypasses the assumption and estimation of a model for the returns, and provides the estimated quantity of interest (together with its out-of-sample reliability tag) directly from data generated by a scenario generation oracle. This idea is then extended to the situation where one simultaneously optimizes over the portfolio composition, in order to achieve an optimal portfolio with a guaranteed level of expected shortfall probability. Such a scenario-based portfolio design approach is here developed for both single-period and multi-period allocation problems. The methodology underpinning the proposed computational method is that of random convex programming (RCP). Besides the described data-driven problems, we show in this chapter that the RCP paradigm can also be employed alongside more standard mean-variance portfolio optimization settings, in the presence of ambiguity in the statistical model of the returns, providing a viable technique to address robust portfolio optimization problems.