Mean Reverting Portfolios via Penalized OU-Likelihood Estimation
This addresses portfolio optimization for financial traders seeking statistical arbitrage opportunities, but it is incremental as it builds on existing Ornstein-Uhlenbeck process methods.
The paper tackles the problem of constructing mean-reverting portfolios by optimizing for high mean reversion, low variance, and parsimony, using a specialized algorithm and testing on simulated and empirical data.
We study an optimization-based approach to con- struct a mean-reverting portfolio of assets. Our objectives are threefold: (1) design a portfolio that is well-represented by an Ornstein-Uhlenbeck process with parameters estimated by maximum likelihood, (2) select portfolios with desirable characteristics of high mean reversion and low variance, and (3) select a parsimonious portfolio, i.e. find a small subset of a larger universe of assets that can be used for long and short positions. We present the full problem formulation, a specialized algorithm that exploits partial minimization, and numerical examples using both simulated and empirical price data.