本文探討隱藏式馬可夫狀態轉換模型是否能夠使投資組合績效上升。基於隱藏式馬可夫模型對台灣加權指數進行狀態分類後，得到兩種狀態：高波動低報酬狀態與低波動高報酬狀態。本文建立逆變異數加權、分層式風險評價與二次規劃最小化變異數三個投資組合，並採用 2007 年 1 月 4 日至 2021 年 12 月 31 日的台灣股市資料與美債報酬進行回測。實證發現，狀態轉換下的動態資產配置能使投資組合的夏普比率、索提諾比率與最大策略虧損報酬上升，其中又以加入狀態轉換模型的逆變異數加權投資組合表現最佳。

This paper explores whether a hidden Markov regime-switching model can improve portfolio performance. After we classify the Taiwan Weighted Index based on the Hidden Markov Model, two states are obtained: the state of high volatility and low return, and the state of low volatility and high return. This paper constructs three portfolios: inverse variance weighting, hierarchical risk parity and quadratic programming minimizing variance. We conduct backtests based on Taiwan stock market and U.S. bond data from January 4, 2007 to December 31, 2021. We find that the dynamic asset allocation under the regime-switching model can increase the Sharpe ratio, Sortino ratio and maximum drawdown return of the portfolio. The inverse variance weighted portfolio under the regime-switching model performs the best.

Ang, A., & Bekaert, G. (2002). International asset allocation with regime shifts. The review of financial studies, 15(4), 1137-1187.
Bailey, D. H., & Lopez de Prado, M. (2012). The Sharpe ratio efficient frontier. Journal of Risk, 15(2), 13.
Bulla, J., Mergner, S., Bulla, I., Sesboüé, A., & Chesneau, C. (2011). Markov-switching asset allocation: Do profitable strategies exist?. Journal of Asset Management, 12(5), 310-321.
Cajas, D. (2022). Riskfolio-lib (3.0.0). Retrieved from https://github.com/dcajasn/Riskfolio-Lib
Costa, G., & Kwon, R. (2020). A Regime-Switching Factor Model for Mean-Variance Optimization. Journal of Risk.
De Prado, M. L. (2016). Building diversified portfolios that outperform out of sample. The Journal of Portfolio Management, 42(4), 59-69.
Konstantinov, G., Chorus, A., & Rebmann, J. (2020). A network and machine learning approach to factor, asset, and blended allocation. The Journal of Portfolio Management, 46(6), 54-71.
Kritzman, M., Page, S., & Turkington, D. (2012). Regime shifts: Implications for dynamic strategies (corrected). Financial Analysts Journal, 68(3), 22-39.
Lo, A. W. (2002). The statistics of Sharpe ratios. Financial analysts journal, 58(4), 36-52.
Meucci, A. (2009). Managing diversification. Risk, 74-79.
Nystrup, P. (2014). Regime-based asset allocation. Do profitable strategies exist. Master's thesis, Technical University of Denmark.
Nystrup, P., Madsen, H., & Lindström, E. (2017). Long memory of financial time series 39 and hidden Markov models with time‐varying parameters. Journal of Forecasting, 36(8), 989-1002.
Papenbrock, J. (2011). Asset Clusters and Asset Networks in Financial Risk Management and Portfolio Optimization (Doctoral dissertation, Dissertation, Karlsruhe, Karlsruher Institut für Technologie (KIT), 2011).
Pfitzinger, J., & Katzke, N. (2019). A constrained hierarchical risk parity algorithm with cluster-based capital allocation. Stellenbosch University, Department of Economics.
Prajogo, A. U. (2011). Analyzing patterns in the equity market: ETF investor sentiment and corporate cash holding. Princeton University.
Visser, I., Raijmakers, M. E., & Molenaar, P. C. (2000). Confidence intervals for hidden Markov model parameters. British journal of mathematical and statistical psychology, 53(2), 317-327.
Wang, M., Lin, Y. H., & Mikhelson, I. (2020). Regime-switching factor investing with hidden Markov models. Journal of Risk and Financial Management, 13(12), 311.
Yue, S., Wang, X., & Wei, M. (2008). Application of two-order difference to gap statistic. Transactions of Tianjin University, 14(3), 217-221.