考慮期望風險值及下端風險之投資組合最佳化模式：以二階段隨機線性規劃為模型

Portfolio Optimization Under Conditional Value at Risk and Tail isk: Based on Two-Stage Stochastic Linear Programming Model

盧俞任(Yu-Ren Lu)

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(2009年)

https://doi.org/10.6840/cycu200901045

摘要

因應金融市場的高度不確定性，投資者於追求最大化報酬的同時，如何估計投資組合中可能產生的損失，是投資者最關心的議題。
由於股票的報酬和風險皆充滿不確定性，在本研究中，應用修正後的條件風險值模型作為不確定性的指標，進而選擇較低風險的投資組合，雖然條件風險值廣泛的受到應用，但其所選擇的投資組合仍然有著高度風險，為了降低風險之波動，我們利用safety-first模型控管其下端風險。
本研究選取摩根台灣股價指數（MSCI Taiwan Index）中的50支股票作為投資標的，並考慮了一個隨機線性規劃模型求解投資組合之選擇問題，此模型利用極小化條件風險值作為目標函數，佐以Safety-first 模型之限制式控制其尾端風險，進而求得優於大盤獲利與相對較低風險之最適投資組合。

關鍵字

投資組合 ； 控制尾端風險 ； 條件風險值 ； 二階段隨機線性規劃

並列摘要

In response to the high degree uncertainty of financial market, how to estimate the potential loss of portfolio is the most important topic concerned by investors when they are pursuing the maximum of reward.
Due to the return rate and risk of asset in stock are full of uncertainty, investors will face more complex investment problems than usual. In this thesis, we apply the modified Conditional Value-at-Risk (CVaR) model to be uncertainty to select the portfolio with riskless. Although CVaR be used in finance perform well, the portfolio that select by it is still risky. Therefore, in order to avoid any intensity fluctuates of risk, we structure our model based on safety-first model to control downside risk.
In this thesis we compare two relative linear programming models for solving the single period portfolio selection problem. The first model is considered a stochastic linear programming (SLP) model by using minimization of Conditional Value-at-Risk as objective function, and constrain is structured by safety-first model. The second is based on safety-first model using original data. However, test results of ours performances are better than market and the safety-first model with original data.

並列關鍵字

Conditional value at risk ； Portfolio selection problem ； Safety-first model ； Two-stage stochastic linear programming

參考文獻

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[6] Chung-Che Wu, (2008), “Two-Stage Stochastic Linear Programming Model for Portfolio Optimization under Conditional Value at Risk.”

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