考慮近似尾端分佈條件下最佳化投資組合之研究

Portfolio Optimization Considering Conditional Value-at-Risk under Approximated Tail Distribution

魏銘寬(Ming-Kuan Wei)

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/cycu200700430

摘要

在金融產品創新的潮流下，風險管理逐漸受到投資者的重視，在實務上，風險值（Value-at-Risk）已是財金機構管理資產風險時的重要工具。但是由於風險值不具備一致性的特性，使得它在用來衡量資產組合風險時有許多限制。而條件風險值（Conditional Value-at-Risk）的提出正好解決了風險值在投資組合方面的問題。
由於投資者所關注的是下方風險，因此本研究將考慮在近似尾端分佈下，以條件風險值作為風險的限制，建立優於市場的投資組合。本研究應用了Pair-copula方法建立了近似尾端分佈，在此分佈之下，分別以投資組合的偏態以及三階隨機優勢的方式建立其投資組合。
在本研究中，為了反應市場變化，我們選取了摩根台灣股價指數（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，以條件風險值作為風險控制的方法確實能建立波動穩定且優於市場的投資組合。

關鍵字

偏態 ； 條件風險值 ； 近似尾端分佈 ； Pair-copula ； 下方風險 ； 三階隨機優勢

並列摘要

Recently, Risk management is more and more important for investors. Value-at-Risk has become the important tools for financial institution when managing the risk of asset. Because the Value-at-Risk is not the coherent measure, it has some restriction on measuring risk of portfolio. The conditional Value-at-Risk is the coherent measure and it can solve the optimization of portfolio.
The investors usually concern about the downside risk. In this thesis, we take the conditional Value-at-Risk to be the constraint of the risk by using the approximated tail distribution. We consider the Pair-copula dependence structure when simulating the future return. Finally, we establish the portfolio by the skewness of the portfolio and third-order stochastic dominance.
In this thesis, we choose the combination of MSCI Taiwan Index and compare its performance with the Taiwan-Weighted Stock Index. We denote the combination as model 1、model 2 and model 3. The results verify that the performance of these model is better than the performance of the Taiwan-Weighted Stock Index by using conditional Value-at-Risk.

並列關鍵字

Pair-copula ； conditional Value-at-Risk ； third –order stochastic dominance ； approximated tail distribution ； downside risk ； skewness

參考文獻

[1] Arditti, F.D., and H. Levy, (1975) ”Portfolio Efficiency Analysis in Three Moments: The Multi-period case”, Journal of Finance, Vol. 30, No. 3, 797-809.

[3] Bawa, V. S. and E. B. Lindenberg (1977), “Capital Market Equilibrium in a Mean-Lower Partial Moment Framework”, Journal of Financial Economics, Vol. 5, 189-200.

[6] Bedford, T. and Cooke, R. M., 2002, "Vines – a New Graphical model for Dependent Random Variables", Annals of Statistics, Vol. 30, No.4, pp.1031-1068.

[7] Bradley, B., Taqqu, M., 2004, "Asset Allocation when Guarding against Catastrophic Losses: Univariant verse Multivariate Approaches", Quantitative Finance, Vol.7, No.6, pp.619-636.

[9] Dentcheva, D. and A., Ruszczy´nski (2006) ”Portfolio Optimization with Stochastic Dominance Constraints”, Journal of Banking & Finance, Vol. 30, No. 2, 433-451.