應用模擬資料之風險控制投資組合最佳化

The Study of Safety-First Portfolio Optimization Problem on Simulated Data Set

10.6840/CYCU.2010.00301

林玉媚

極值理論 ； Safety-First 投資組合 ； Pair-Copula ； Safety-First ； Extreme Value Theory(EVT) ； Pair-Copula

中原大學工業與系統工程研究所學位論文

2010年

碩士

張國華

英文

美國次級房貸以及雷曼兄弟風暴席捲全球，次級房貸風暴連鎖效應波及，導 致雷曼兄弟在財務方面受到重大打擊而虧損，2008 年9 月雷曼兄弟破產揭開了 金融風暴的序幕，歐美多家銀行陸續爆發財務危機，信貸緊縮加劇，造成全球股 價大跌，這使得投資者更加關心損失下端風險。因此，投資者在追求最大化報酬 率的同時，更重視風險管理。風險值是目前最廣為使用的風險管理工具，傳統上 利用常態分配分析整體分配，缺點在於容易低估下端風險。 為了能夠精確地估計報酬分佈的下端風險，我們利用極值理論來估計下端風 險，由於極端值理論要估計的是尾部分配，所以樣本中必須有足夠數目的極端 值，才能提供可靠的估計，這也代表使用極端值理論所需要的樣本數目，會比一 般方法多許多，如果樣本數不足，會有使用上的困難。因此，在本研究中，使用 極值理論來估計下端風險，並利用Pair-Copula 可以求得資產報酬率分佈的之間 相關性的特質來模擬資產的未來報酬，藉由safety-first 模式所求出的投資組合最 佳解篩選出近似尾端分佈的數據作為下週投資組合的資料來源，以此建構本研究 的研究方法。 本研究中，以摩根台灣股價指數（MSCI Taiwan Index）成份股權重排行前 二十支股票作為投資標的，並和使用Pair-Copula 篩選出全為負報酬作為資料來 源的safety-first 模式比較其績效,經實證結果顯示，我們的研究優於市場以及傳統 safety-first 模式。

As the subprime mortgage and Lehman Brothers crises swept through the world in 2008, a number of banks erupted into financial crisis in Europe and the United States. It caused the price of the stock to fall globally. The investors cared about the risk more than the maximum return. Therefore, the investors more concerned about the management of risk than pursue the maximum rate of return. Value-at-Risk is the most common tool to calculate the risk. Traditionally, normal distribution is used to fit the whole data, but the study says it would be easy to underestimate the downside risk. In order to estimate the downside risk of the return rate precisely, we use the extreme value theory (EVT) to estimate the downside risk, it needs a sufficient number of extreme values to provide a credible estimation. Due to the lack of historical data, we used pair-copula which considers the dependency structure between stocks to simulate the future return distribution of stocks, and then use the portfolio result obtained from the safety-first model to select the data and use the selected data to obtain the portfolio for the current week. In this study, we choose the first 20 stocks at the MSCI Taiwan Index to be investment targets. Also, compared with the traditional safety-first model that use all the negative return to find the optimal portfolio. The results verified that the performances of our model are more stable than the traditional safety-first model and market.

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1. 侯嘉彥(2014)。考慮極值分布之行為投資組合最佳化。中原大學工業與系統工程研究所學位論文。2014。1-99。