Portfolio Optimization with Latent Mean-Reversion and Momentum Drift

Summary

The paper studies portfolio choice when the drift of a risky asset is not directly observed and depends on two hidden stochastic factors evolving at different speeds. It derives a filtered estimate of the latent mean-reversion level from the difference between fast and slow exponential moving average processes applied to trailing prices, together with a deterministic Volterra correction. The resulting estimator has a MACD-like form, connecting a familiar technical signal to inference about hidden drift.

For logarithmic, power, and exponential utility, the authors derive candidate optimal strategies in explicit feedback form and report admissibility and verification results. These are mathematical results for a partial-information model; the description does not give empirical tests, asset-specific evidence, or comparisons of realized portfolio performance. The proposed connection explains how MACD-type signals can arise within an optimization framework, but it does not by itself establish that the signal is profitable in practice.

Key ideas

• The model assumes risky-asset drift depends on two latent factors with distinct time scales.
• A filtered estimate of latent mean reversion combines fast and slow price averages with a Volterra correction.
• The estimate has a MACD-like structure and is interpreted as information about hidden drift.
• Candidate feedback strategies are derived for three utility families, with mathematical admissibility and verification results.

Tags

# Portfolio Optimization under Fast and Slow Latent Mean-Reverting and Momentum Drift


# Portfolio Optimization under Fast and Slow Latent Mean-Reverting and Momentum Drift









We consider a class of partial-information portfolio optimization problems in which the drift of a risky asset is driven by two latent stochastic factors evolving at distinct time scales. We show that the filtered estimate of the latent mean-reversion level is driven by the difference between fast and slow exponential moving average (EMA)-type processes of the trailing price history, yielding a Moving Average Convergence Divergence (MACD)-type signal, along with a deterministic Volterra correction. Under logarithmic, power, and exponential utility, we derive candidate optimal strategies in explicit feedback form and establish admissibility and verification results. In particular, the results provide a mathematical foundation for the endogenous emergence of MACD-type trading signals as estimators of latent drift information contained in observed price paths.

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