Portfolio Optimisation Under Parameter Instability: An Empirical Evaluation of Regime-Switching Models and the CAPM

Abstract

This thesis examines the potential of regime-switching models to enhance portfolio optimisation for U.S. equities. The study utilises daily data from 20 S&P 500 stocks across eight sectors between 2013 and 2024. A three-state Hidden Markov Model is employed for regime identification, combined with the Capital Asset Pricing Model (CAPM) for expected return estimation. The regime-conditional portfolio is evaluated against four benchmarks in a nine-year out-of-sample backtest. Findings indicate substantial instability in CAPM parameters, with an average rolling beta variation of 117.5%. The equity risk premium ranges from +24.31% in Bull markets to −27.19% in Bear markets, representing a spread of 5,150 basis points. Despite these variations, the regime-conditional strategy fails to deliver portfolio gains; its annual turnover of 405.3% diminishes returns and results in the lowest bear-market Sharpe ratio among the five strategies assessed. The most significant improvement is achieved by substituting historical means with CAPM equilibrium expected returns, which increases the Sharpe ratio from 0.942 to 1.037, a 10.1% improvement, without regime conditioning. This outcome suggests that reducing estimation error, rather than regime detection, is the primary factor for enhancing mean-variance portfolios in practice.