An Analysis of Linear Portfolio Optimization Theoretic on Empirical Data

Open Access
Author:
Rowles, Benjamin Austin
Area of Honors:
Finance
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Christoph Hinkelmann, Thesis Supervisor
  • Brian Spangler Davis, Honors Advisor
Keywords:
  • Portfolio Management
  • Optimization
  • Portfolio Optimization
  • Sharpe Ratio
  • Sortino Ratio
  • Conditional Value at Risk
  • Value at Risk
  • Risk
  • Semivariance
Abstract:
In the portfolio management world, numerous methodologies of optimizing on risk-adjusted returns exist with the definition of risk being the primary differentiating factor within the frameworks. The multitude of established theory that exists however has little to no robust analysis of performance on empirical data, with concrete examples of the theory presented in these papers being performed on an insubstantial amount of different investment universes, and only on single periods. Furthermore, they tend to focus on differing asset class returns, in which correlations are more concrete and return profiles of assets are tightly distributed. This paper focuses on the analysis of empirical performance of portfolio optimization techniques. Specifically, the three optimizations techniques defining risk as standard deviation, semideviation, and conditional value at risk (CVaR). Furthermore, the optimization is done on the domestic equity universe only, utilizing consensus sell-side analyst price targets as expected return estimates. Domestic equities were chosen due to the varying nature of correlations in individual equity investments, combined with the broader expected returns and risk profiles of the varying names. In order to analyze the effectiveness of the techniques, random groups of single name equities were iteratively chosen and optimized on repeatedly for two different time periods. The two periods represent a bull-market and side-ways market so as to see if different market trends lead to different results. Through generating multiple baskets of assets and optimizations for each period, a large enough sample was collected so as to derive empirical results with little to no single iteration skew as in previous papers. Ultimate results showed that in both periods, optimization frameworks with risk defined as CVaR performed best on risk adjusted and absolute return metrics. Interestingly, semivariance based optimization techniques saw little advantage relative to standard deviation based optimizations with the two ranking fairly similar.