考慮條件風險值下投資組合最佳化之 二階段隨機規劃模式

Two-Stage Stochastic Linear Programming Model for Portfolio Optimization under Conditional Value at Risk

吳忠哲(CHUNG-CHE WU)

指導教授 ： 張國華

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2008年)

https://doi.org/10.6840/cycu200900636

摘要

隨著社會的快速變遷與民生物價的高漲，投資者在追求最大化報酬的同時， 更重視投資風險之管理。在風險管理上，風險值( Value-at-Risk )主要為財經領域 上廣為被應用來衡量風險的一個風險衡量指標。儘管風險值是一個如此廣受歡迎 的風險衡量指標，在性質上仍有著不符合次可加性( Sub-additivity ) 的缺點存 在。也就是說，風險值在新增投資資產到投資組合時，無法有效達到分散風險的 目的。另一個具有較佳性質的風險衡量指標已經被提出，也就是條件風險值 ( Conditional Value-at-Risk )。條件風險值已經被學者証明可以藉由線性規劃 ( Linear Programming )來求解最佳化問題。 本論文中，主要以條件風險值作為衡量風險的指標，並考慮投資組合最佳化 之問題。首先，我們以二階段隨機線性規劃( Two-Stage Stochastic Linear Programming )作為主要模式，資料數據為考慮尾端分佈下所模擬之報酬率情境。 在本論文中，主要從摩根台灣股價指數( MSCI Taiwan Index )選取其成份股中之 50 支股票，並將投資組合之績效與大盤指數及Safety-First 模式相比較。最後驗 證結果證實模式之績效較大盤指數要來的佳。

關鍵字

條件風險值 ； 二階段隨機線性規劃 ； Pair-Copula ； Safety-First

並列摘要

With the depression of the society and the rise of prices of commodities, investors
put much emphasis on risk management when they are pursuing higher return rates
simultaneously. In risk management, Value-at-Risk (VaR) is a widely used index for
measuring risk in the financial field. Notwithstanding VaR is a very popular measure
of risk, it still has undesirable properties such as lack of sub-additivity. That is to say,
VaR does not conform to the property of decentralizing risk by adding new assets to
portfolio. Regarding to the shortcomings of VaR we described above, an alternative
measurement of losses with more attractive properties is proposed. This method of
risk management is called Conditional Value-at-Risk (CVaR). It is already shown
that the calculating CVaR can be modeled as a linear program.
In this thesis, we consider a portfolio optimization problem, in which CVaR is
used as the risk measure. We model it as a two-stage stochastic linear programming
(two-stage SLP) in which scenario is generated by sampled tail distribution. In this
thesis, we select fifty stocks from combinations of MSCI Taiwan Index and compare
its performance with the Taiwan-Weighted Stock Index and Safety-First model. The
results verify that the performance of the Model is better than the performance of
the Taiwan-Weighted Stock Index.

並列關鍵字

Conditional value-at-risk ； Two-stage stochastic linear programming ； Safety-First ； Paircopula

參考文獻

[2] Pflug, G. Ch. ,(2000): Some Remarks on the Value-at-Risk and the Conditional

Value-at-Risk. In. Uryasev S. (Ed.) Probabilistic Constrained Optimization:

(1997): Evaluating Value at Risk Methodologies, Journal of Financial Services

Research, 12:2/3, 201-242.

[3] Rockafellar, R.T. and S. Uryasev., (1999), ”Optimization of Conditional Valueat-