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<p>This paper considers dynamic portfolio selection models where uncertainty in the financial market is characterized by business cycles. We consider that the financial market is defined by factors and present a regime switching autoregressive model for macro-economic factors to reflect financial cycles. It is assumed that the regime dynamics are Markovian and the parameters in the autoregressive model depend on regime dynamics. We then define a factor model for asset returns, with returns depending on regimes through the factors. The joint distribution of regimes and asset returns is the input to optimal portfolio selection models. Contrasting approaches to risk measurement of returns on investment are variance and exponential Rényi entropy (Rényi, 1960). We compare portfolio models with minimum variance and minimum entropy objectives. In the empirical analysis, we use the select sector ETFs to test the asset pricing model and examine the portfolio performance. Weekly financial data from 04-March-2016 to 26-June-2020 is employed for the estimation of the hidden Markov model including the asset return parameters, while the out-of-sample period from 26-June-2020 and 14-July-2023 is used for portfolio performance testing. It is found that, under both the empirical Sharpe and excess return to entropy ratios, the dynamic portfolio strategy with the entropy objective is an improvement on mean-variance models.</p>

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Comparisons of mean-variance analysis and entropy-based approaches to portfolio selection under asymmetric returns in bear and bull markets

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Leonard MacLean,
  • Yonggan Zhao,
  • Huajian Miao

摘要

This paper considers dynamic portfolio selection models where uncertainty in the financial market is characterized by business cycles. We consider that the financial market is defined by factors and present a regime switching autoregressive model for macro-economic factors to reflect financial cycles. It is assumed that the regime dynamics are Markovian and the parameters in the autoregressive model depend on regime dynamics. We then define a factor model for asset returns, with returns depending on regimes through the factors. The joint distribution of regimes and asset returns is the input to optimal portfolio selection models. Contrasting approaches to risk measurement of returns on investment are variance and exponential Rényi entropy (Rényi, 1960). We compare portfolio models with minimum variance and minimum entropy objectives. In the empirical analysis, we use the select sector ETFs to test the asset pricing model and examine the portfolio performance. Weekly financial data from 04-March-2016 to 26-June-2020 is employed for the estimation of the hidden Markov model including the asset return parameters, while the out-of-sample period from 26-June-2020 and 14-July-2023 is used for portfolio performance testing. It is found that, under both the empirical Sharpe and excess return to entropy ratios, the dynamic portfolio strategy with the entropy objective is an improvement on mean-variance models.