Portfolio Optimization and Parameter Uncertainty Article
This post contains the latest version of the Portfolio Optimization and Parameter Uncertainty article by Laura Kristensen and Anton Vorobets.
Portfolio optimization is undoubtedly sensitive to the market model input, particularly the expected returns which are arguably also the hardest to estimate.
A common practical way of handling parameter uncertainty is by performing resampled portfolio optimization.
The article below analyzes the resampled approach and suggest a new method called Exposure Stacking that allows us to introduce fully general parameter uncertainty and even combine portfolios across different portfolio optimization methods like Conditional Value-at-Risk (CVaR) and Conditional Maximum Loss (CML).
Using the fundamental perspectives from this article, the more general Resampled Portfolio Stacking is introduced in Chapter 6 of the Portfolio Construction and Risk Management book and Lecture 10 in the Applied Quantitative Investment Management course.
Abstract: Portfolio optimization has a mixed reputation among investment managers, with some being so skeptical that they believe it is almost useless due to the inherent parameter uncertainty. It is undeniable that portfolio optimization problems are sensitive to parameter estimates, especially the expected returns that are arguably also the hardest parameters to estimate. However, most practitioners still attempt to build mean-risk optimal portfolios, albeit in implicit ways. Resampled optimization is a popular mathematical heuristic to tackle the parameter uncertainty issue. It computes optimal portfolios using sampled parameter estimates and calculates a simple average of the portfolio exposures across samples. The unsatisfactory aspect of the resampled approach is that there is no mathematical justification for using the average of portfolio exposures, it just works well in practice. This article provides perspectives for understanding the resampling approach by analyzing the portfolio exposure estimation process from a bias-variance trade-off. We show that the traditional resampled optimization corresponds to a naive version of stacked generalization. Finally, we introduce a stacked generalization approach that can be used to handle both parameter uncertainty and combine optimization methods in full generality. We coin the new method Exposure Stacking.
Keywords: Portfolio optimization, parameter uncertainty, Exposure Stacking, mean-CVaR, tail risk, mean-variance, efficient portfolio, efficient frontier, mean squared error, bias-variance trade-off, stacked generalization, quadratic programming, convex optimization, Python Programming Language.
Suggested Citation: Kristensen, L. and Vorobets, A., Portfolio Optimization and Parameter Uncertainty (January 30, 2024). Available at: https://antonvorobets.substack.com/p/portfolio-optimization-uncertainty
Video walkthrough
You can watch a video walkthrough of the Portfolio Optimization and Parameter Uncertainty article and its accompanying Python code below:
Lecture 10 in the Applied Quantitative Investment Management course provides a detailed walkthrough of the Resampled Portfolio Stacking generalization: