Active and passive portfolio management with latent factors

Abstract

We address a portfolio selection problem that combines active (outperformance) and passive (tracking) objectives using techniques from convex analysis. We assume a general semimartingale market model where the assets' growth rate processes are driven by a latent factor. Using techniques from convex analysis we obtain a closed-form solution for the optimal portfolio and provide a theorem establishing its uniqueness. The motivation for incorporating latent factors is to achieve improved growth rate estimation, an otherwise notoriously difficult task. To this end, we focus on a model where growth rates are driven by an unobservable Markov chain. The solution in this case requires a filtering step to obtain posterior probabilities for the state of the Markov chain from asset price information, which are subsequently used to find the optimal allocation. We show the optimal strategy is the posterior average of the optimal strategies the investor would have held in each state assuming the Markov chain remains in that state. Finally, we implement a number of historical backtests to demonstrate the performance of the optimal portfolio.

Keywords:

• Portfolio choice
• Optimal control
• Convex analysis
• Growth optimal portfolio
• Hidden Markov models
• Partial information

JEL Classifications:

• G11
• C61

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under the funding reference numbers RGPIN-2018-05705 and RGPAS-2018-522715.