金融資產中常見的波動度群聚現象（volatility clustering）與利用樣本變異數（sample variance）作為風險衡量指標的缺陷，使得採用傳統的期望值－變異數法則（mean-variance rule）的投資組合選擇（portfolio selection）方式，已不能滿足現在的投資人從事投資組合管理的需求。本研究旨在探討如何透過殘差（innovation）為厚尾分配（fat-tailed distribution）的GARCH模型與期望值－風險值（Value-at-Risk，VaR）最佳化的應用，建構能達成風險與報酬間平衡的投資組合管理策略。本文以數個預先選定的資產形成投資組合，並假設各資產的報酬率符合殘差項為厚尾分配的ARMA-GARCH模型。接著以混合常態分配（mixture of normal distribution）對各資產報酬率的時間序列做近似，形成投資組合機率模型。最後透過移動窗格（rolling window）的方式建構本文的投資組合管理策略。在以臺灣股票市場中五間大型公司股票作為樣本的回測結果中，本文所建構的策略可以在不嚴重影響獲利能力的情形下，進行準確的風險控制，幫助投資人達成有效率的投資組合管理。同時，本文的策略也能在與多個不同的benchmarks的投資效率評比中勝出。

The well-known behavior of volatility clustering in financial time series and the weakness of using sample variance as a measure of risk make the traditional mean–variance framework for portfolio selection no longer an appropriate way for investors to manage their portfolios. The GARCH model and the mean-VaR optimization provide a reasonable solution to these problems. The aim of this study is to construct a portfolio management strategy based on a framework of mean-VaR optimization and a GARCH model with fat-tailed innovations. We assume that all assets in a portfolio follow an ARMA-GARCH model with fat-tailed innovations. To derive the probability distribution of portfolios with different weights, we introduce a mixture of normal distribution approximation so that the VaR of the portfolio can be estimated. Finally, we establish an optimal portfolio under a mean-VaR framework and construct a portfolio management strategy by estimating optimal portfolio weights in each time period. In our empirical analysis, we apply our strategy to an asset pool consisting of five large cap stocks in Taiwan stock market. We show that our strategy maintains a nice balance in the tradeoff between risk management and profitability with strength in managing the portfolio risk. Although the performance may be sensitive to the choice of components, our strategy outperforms several benchmarks in terms of four different risk-adjusted return ratios.

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