考慮近似尾端分佈條件下風險控制投資組合最佳化之研究

The Study of Safety-First Portfolio Optimization Problem under Approximated Tail Distribution

江昱霖(Yu-Lin Chiang)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2007年)

https://doi.org/10.6840/cycu200700399

摘要

近年來，投資者在追求最大化報酬的同時，也逐漸重視風險管理。在風險管理上，目前各財金公司均利用風險值（Value-at-Risk）作為管理風險的重要工具。但是風險值不具備一致性風險測度的性質，因此在利用風險值衡量投資組合風險時，無法獲得最佳化的投資組合，只能以窮舉法進行求解，不符合實務上的需要。風險值最主要是在衡量下方風險，也就是投資者所重視的損失風險。為了避免在常態分配假設下低估了下方風險，本研究將利用尾端分佈估計風險。由於歷史資料的不足，因此本研究目的是在考慮近似尾端分佈的條件下，應用Safety-First模式及Mean-Variance模式建立出穩定且優於市場之最佳化投資組合。由於資產之間常存在尾部相關性，因此本研究應用了Pair-Copula模擬資產未來報酬的分佈情形，藉由篩選後的資料建立近似尾端分佈，再利用近似尾端分佈建立投資組合。
在本研究中，為了反應市場變化，我們選取摩根台灣股價指數（MSCI Taiwan Index）成份股之中的20支股票，作為投資標的，並和大盤指數比較其績效。最後驗證結果證實，考慮尾端分佈條件下，Safety-First投資組合以及Mean-Variance模式所建立之投資組合其績效均優於市場。

關鍵字

Mean-Absolute Deviation ； Mean-Variance模式 ； Safety-First投資組合 ； 近似尾端分佈 ； Pair-Copula ； 下方風險

並列摘要

Recently, investors respect the risk management gradually when they seek the maximum return. In risk management, Value-at-Risk is a very important tool for financial enterprises. Unfortunely, Value-at-Risk can not find the optimal portfolio because Value-at-Risk doesn’t comform the characteristic of coherent risk measure. People measure the downside risk by Value-at-Risk. In order to avoid the underestimates of downside risk under normal distribution, we estimate the risk by using the tail distribution. But the history data is not enough and we want establish the approximated tail distribution. The purpose of this thesis is to establish portfolio whose performance is more stable than market by applying the Safety-First portfolio and the Mean-Variance model in the approximated tail distribution. In addition, there often exists some tail dependence between assets. Thus, we specially consider the Pair-Copula dependence structure when simulating the future return. Finally, we establish the portfolio by using the data of approximated tail distribution.
In this thesis, we choose the combination of MSCI Taiwan Index and compare its performance with the Taiwan-Weighted Stock Index. We establish the combination by the Telser’s and Kataoka’s criteria of the safety-first portfolio and the mean-variance model. The results verify that the performances of these models are more stable than the performance of Taiwan-Weighted Stock Index.

並列關鍵字

Safety-First portfolio ； Pair-Copula ； Approximated Tail Distribution ； Mean-Absolute Deviation ； Mean-Variance model ； Downside Risk

參考文獻

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