Active and Passive Portfolio Management with Latent Factors

41 Pages Posted: 7 May 2019

See all articles by Ali Al-Aradi

Ali Al-Aradi

University of Toronto - Department of Statistics

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: March 16, 2019

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: Active Portfolio Management, Convex Analysis, Stochastic Portfolio Theory, Growth Optimal Portfolio, Hidden Markov Models, Partial information, Machine Learning

Suggested Citation

Al-Aradi, Ali and Jaimungal, Sebastian, Active and Passive Portfolio Management with Latent Factors (March 16, 2019). Available at SSRN: https://ssrn.com/abstract=3355645 or http://dx.doi.org/10.2139/ssrn.3355645

Ali Al-Aradi

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

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