A Kalman filter control technique in mean-variance portfolio management

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Abstract

This article develops and tests a methodology for rebalancing the mean-variance optimized portfolio through the use of a Kalman filter. The approach combines information from a mean-variance (MV) optimization technique along with a three factor regression model that includes market capitalization, book to market ratio, and the market index. We demonstrate empirically using 46 years of daily returns from 17 industrial sectors that a Kalman filter model can be an effective approach under the conditions of minimum variance and low expected risk-to-return for both a constrained and unconstrained MV technique. Enhancements to returns are largely due to the ability to reduce turnover for the unconstrained case, and the ability to maintain portfolio exposure to cap and value weighted positions in the constrained case. Statistical significance is demonstrated to show return improvements of the Kalman filter model over a comparable MV technique, where the greatest statistical benefit at the 0.05 and 0.10 level is shown under the minimum variance objective. Additionally, the KF applied to the constrained optimization case always provides a Sharpe ratio higher than the Naïve portfolio, after transactions costs are taken into account.