Equity factor timing framework using the Kalman Filter and Gaussian Hidden Markov Model

Abstract

Factor investment strategies aim to capture persistent risk premia, enhancing risk-adjusted returns over the long term. Traditional approaches, however, provide static exposure and fail to adapt to changing market conditions. Factor timing introduces dynamic adjustments to factor exposures based on expected market trends, with the goal of limiting risk, minimising losses and maximising returns by favouring outperforming factors and avoiding underperforming ones. Although factor timing presents opportunities to exploit market anomalies and inefficiencies, existing literature offers mixed evidence on its effectiveness due to several challenges that includes, knowing when to time factor adjustments during market fluctuations, creating reliable trading signals, accounting for transaction costs, evaluating diversification in dynamic portfolios and limiting the influence of manager’s skill when implementing a factor timing strategy.

This study addresses these challenges by using the Kalman filter, ARIMA forecasting, the Hidden Markov model, copula-based diversification analysis, and a hybrid fund of funds approach. The focus is mainly placed on the five most popular factors, namely momentum, value, growth, quality, and size. A momentum factor timing strategy entails a portfolio optimisation process for construct￾ing a large-capitalisation pure momentum portfolio. The process includes a dynamic portfolio construction criterion for selecting stocks, estimated from historical data of the United States of America (US) large-capitalisation stocks from January 2013 to June 2023 and South African (SA) large-capitalisation stocks from January 2013 to June 2024. The Kalman filter is applied to assess historical performance, while ARIMA forecasting estimates expected returns and confidence intervals. The mixture copula models are utilised to determine the dependence structure of a pure momentum portfolio. The portfolio is constructed from a population of large-capitalisation stocks, in which the top 20 stocks with the highest average momentum scores are selected. The value versus growth factor investing framework is assessed and analysed using the US exchange-traded funds (ETFs) from January 2013 to December 2024. A fund of funds is composed of the three largest exchange-traded funds ranked by assets under management, listed in the US. The HMM is used for factor timing.

The findings reveal that a dynamic, large-capitalisation momentum portfolio constructed using historical criteria and optimised using a Kalman filter and ARIMA performed well when trading costs were low. Copula analysis revealed that SA momentum portfolios were more diversified than US equivalents. HMM showed value factors recovered faster after market downturns. A combined value and growth fund of funds achieved higher returns than either alone. Comparing Kalman filter and HMM revealed that shorter rebalancing periods improve factor timing effectiveness, suiting active management styles. The HMM outperformed the Kalman filter. It turns out that factor timing can enhance returns by exploiting cyclical factor performance, but effectiveness is constrained by transaction costs and the need for frequent rebalancing. It is recommended that factor timing should complement, rather than replace, static multifactor portfolios. Empirical results show that HMM and Kalman filter methods can theoretically generate profitable trading signals, but practical success depends on cost control and disciplined execution.