Derivatives Portfolio Optimization Parameter Uncertainty Article

As explained in the Portfolio Management Framework for Derivative Instruments article, elegant handling of derivative instruments is fairly straightforward for general portfolio management when we make a separation between relative market values and relative exposures.

However, if we want to optimize derivative portfolios with parameter uncertainty, using for example Resampled Portfolio Stacking, additional work is required to ensure that the parameter uncertainty we introduce in the underlying, and the derivative’s other risk factors, is consistent with the uncertainty that we introduce into the P&L of the derivative instrument.

Conveniently, Sequential Entropy Pooling (SeqEP) allows us to do this in an effective way. The article below formally describes how.

If you want to understand how all of the above fits into the larger Fully General Investment Framework (FGIF), you can read Section 6.4 of the Portfolio Construction and Risk Management book or watch Lecture 10: Resampled Portfolio Optimization from the Applied Quantitative Investment Management course.

Abstract: Portfolio optimization in practice almost always needs to account for market model uncertainty. Resampled portfolio optimization is a common heuristic to tackle the parameter uncertainty issue. The recently introduced Resampled Portfolio Stacking approach makes the resampled approach even more attractive. While resampled optimization of cash portfolios is straightforward and well known, resampled optimization of portfolios containing derivatives is a largely unexplored area. Derivatives introduce an additional layer of complexity, because there needs to be a logical consistency between the parameter uncertainty of the underlying and risk factors such as implied volatilities as well as the derivative instrument’s P&L. This article presents an elegant solution to the problem and introduces a new class of portfolio optimization with fully general risk factor parameter uncertainty.

Keywords: Portfolio optimization, parameter uncertainty, derivatives, risk factors, Exposure Stacking, Resampled Portfolio Stacking, mean-CVaR, tail risk, efficient portfolio, efficient frontier, mean squared error, bias-variance trade-off, stacked generalization, quadratic programming, convex optimization, Python Programming Language.

Suggested Citation: Vorobets, Anton, Derivatives Portfolio Optimization and Parameter Uncertainty (May 13, 2024). Available at: https://antonvorobets.substack.com/p/derivatives-parameter-uncertainty

The accompanying Python code for the Derivatives Portfolio Optimization and Parameter Uncertainty article is available here.

You can watch a video walkthrough of the Derivatives Portfolio Optimization and Parameter Uncertainty article and its accompanying Python code in the video below: