Dynamic Functionally Generated Portfolios for Statistical Arbitrage

Summary

This paper extends functionally generated portfolios, a framework within continuous-time stochastic portfolio theory. In the standard formulation, a generating function describes a portfolio’s return relative to a passive benchmark through a pathwise master equation that avoids stochastic integrals. The paper broadens the framework in two ways: the reference numéraire can be any strictly positive wealth process, and the generating function can change dynamically in response to an auxiliary continuous-path, finite-variation process.

The authors state that these extensions retain the master equation’s tractability. They discuss applications to scenario analysis, statistical arbitrage, portfolio risk immunization, and mirror portfolios. The document presents theoretical generalizations and application areas, but provides no specific trading rules, empirical results, or performance comparisons. Consequently, it explains a portfolio-construction framework that may support further analysis rather than establishing that a particular strategy will outperform a benchmark.

Key ideas

• Functionally generated portfolios use a master equation to describe returns relative to a chosen numéraire.
• The numéraire can be generalized to any strictly positive wealth process.
• Generating functions can adapt dynamically through an auxiliary finite-variation process.
• The proposed extensions retain the pathwise tractability of the master equation.
• Potential applications include statistical arbitrage, scenario analysis, risk immunization, and mirror portfolios.

Tags

# Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage


# Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage









The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the numéraire. This description has proven to be analytically very useful, as it is both pathwise and free of stochastic integrals. Here we generalize the class of FGPs in several ways: (1) the numéraire may be any strictly positive wealth process, not necessarily the market portfolio or even a passive portfolio; (2) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation. These generalizations do not forfeit the important tractability properties of the associated master equation. We show how these generalizations can be usefully applied to scenario analysis, statistical arbitrage, portfolio risk immunization, and the theory of mirror portfolios.

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