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Robust Portfolio Growth with Stochastic Factors and Drift Uncertainty

Article arXiv papers · Author: Balint Binkert et al.
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Summary

The document studies portfolio growth optimization when expected asset returns are uncertain. It considers an incomplete, high-dimensional market in which asset prices depend on stochastic factors. Rather than fixing the drift completely, the framework restricts admissible models through their shared volatility structure, long-run joint distribution, and specified factor dynamics, including an ergodicity condition.

The authors characterize the robust growth rate and worst-case admissible model, and derive the growth-optimal strategy from a partial differential equation. They argue that incorporating stochastic factors can improve robust growth, and illustrate the theory with numerical examples, including pairs trading where the spread is the modeled asset. The results depend on the chosen model class and its ergodicity and dynamics assumptions; the abstract does not provide the numerical size of the improvement or evidence from live trading.

Key ideas

  • The framework addresses sensitivity to uncertain asset-return drifts through robust growth optimization.
  • Admissible models constrain volatility, long-run joint density, and stochastic-factor dynamics.
  • The robust growth rate and worst-case model are characterized within this constrained model class.
  • A partial differential equation is used to characterize the robust growth-optimal strategy.
  • The authors report that using stochastic factors can improve robust growth, including in a pairs-trading example.

Tags

StatisticsRisk managementPortfolio constructionPairs trading
Full text
# Stochastic factors can matter: improving robust growth under ergodicity


# Stochastic factors can matter: improving robust growth under ergodicity









Drifts of asset returns are notoriously difficult to model accurately and, yet, trading strategies obtained from portfolio optimization are very sensitive to them. To mitigate this well-known phenomenon we study robust growth-optimization in a high-dimensional incomplete market under drift uncertainty of the asset price process $X$, under an additional ergodicity assumption, which constrains but does not fully specify the drift in general. The class of admissible models allows $X$ to depend on a multivariate stochastic factor $Y$ and fixes (a) their joint volatility structure, (b) their long-term joint ergodic density and (c) the dynamics of the stochastic factor process $Y$. A principal motivation of this framework comes from pairs trading, where $X$ is the spread process and models with the above characteristics are commonplace. Our main results determine the robust optimal growth rate, construct a worst-case admissible model and characterize the robust growth-optimal strategy via a solution to a certain partial differential equation (PDE). We demonstrate that utilizing the stochastic factor leads to improvement in robust growth complementing the conclusions of the previous study by Itkin et. al. (arXiv:2211.15628 [q-fin.MF], forthcoming in $\textit{Finance and Stochastics}$), which additionally robustified the dynamics of the stochastic factor leading to $Y$-independent optimal strategies. Our analysis leads to new financial insights, quantifying the improvement in growth the investor can achieve by optimally incorporating stochastic factors into their trading decisions. We illustrate our theoretical results on several numerical examples including an application to pairs trading.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.