本論文提出了一種具有雙重波動狀態的多變量馬可夫轉換模型，雙重波動性狀態可分別為牛市和熊市。按照Markowitz（1952）提出的平均數-變異數分析，我們提出了一種計算最優投資組合的權重的方法基於條件波動狀態下的平均數和變異數，並提供準似然估計（Quasi likelihood estimation）在馬可夫轉換模型中估計參數。 為了比較，我們考慮等權重投資組合、平均數-變異數投資組合以及馬可夫轉換模型的平均數-變異數組合實證研究使用台灣的六支指數型證券投資信託基金（ETF）和19個ETF在美國市場，將這些資料運用在不同的風險規避。資產重新分配的實驗顯示，平均數-變異數組合的多變量馬可夫轉換模型在各種策略方面優於其他組合。;This thesis proposes a multivariate Markov switching model with two regimes indicating the bull and bear market, respectively. Following the seminal mean-variance analysis framework \cite{Mark}, we propose a method to calculate the optimal portfolio weight based on the conditional means and variance under specific regimes, and provide a Quasi likelihood estimation for parameter estimation in the proposed Markov switching model. For comparison, we consider the equal-weighted portfolio, the standard mean-variance portfolio, and the mean-variance portfolio with the Markov switching model. Empirical studies are implemented using six exchange traded funds (ETFs) in Taiwan market and nineteen ETFs in the US market at various levels of risk aversion. Out of sample rebalancing experiments show that the mean-variance portfolio with the proposed multivariate Markov switching model outperforms the others in terms of various strategy summary statistics.
