應用狀態空間模型與風險值建立投資組合之風險預警模式

Implementation of State-Space Method and VaR Applied to Risk Alert Model

黃啟宗(Chi-Tsung Huang)

指導教授 ： 陳雲岫

元智大學/工程學院/工業工程與管理學系/碩士(2006年)

摘要

本研究所建立的風險預警模式分成三個區塊：監控指標、預測模式與修正策略。如同品質管制圖監控品質特性般，本預警模式即對投資組合進行監控。由於投資組合可能過於複雜，因此就借重風險值（VaR）之整合投資組合概念的指標來作為監控的觀察值，並且設定門檻值，如同管制界限一樣，當發生超出管制範圍時，即必須從事下一步的修正步驟。從過去文獻中發現，狀態空間法（State Space Method）對於預測的準確度上有一定的水準，預測能力越強，則預警能力亦越強，因此將狀態空間法加入此模式中，透過對未來資產價格的先行預測，強化在修正上的有效性。在修正方法上，引入投資組合理論的效率前緣概念，使用最低風險投資組合（Minimum Variance Portfolio）來調整投資組合權重，期望能藉此修正原先超出監控門檻值的風險值。
透過案例的實際操作，我們發現隨著所設定的門檻值越小，投資組合在經過權重的調整之後，期望的損失值的確有越來越小的趨勢。另外比較最低風險修正情形與非最低風險修正情形，發現以最低風險修正的結果較佳。最後透過夏普比率的計算，找出以5%的門檻設定，最低風險的修正情形下，修正的效果是所有假設情境中最好的。

關鍵字

風險值 ； 狀態空間法 ； 最低風險投資組合 ； 風險預警

並列摘要

In this thesis, a new risk alert model is proposed. This model mainly has three parts. First, Value at Risk (VaR) is taken to be the monitoring benchmark because VaR can represent what risk level is the whole portfolio involved in. Second, state-space method is added to increase the whole model’s effectiveness owing to the high performance in forecasting. Third, some actions should be taken when VaR is over the set threshold value. And, minimum variance portfolio is the way to solve weighted combination of investments.
The proposed model is verified by real data. In the case, we assume three thresholds, 5%, 10%, and 15%, separately. The testing result shows that 5% threshold has a better result. Besides, we compare the result of adjusted by minimum variance portfolio and non- minimum variance portfolio. It shows that minimum variance portfolio indeed gets a better result. Finally, we use sharp-ratio to evaluate every situation we set. 5% threshold and adjusted by minimum variance portfolio are the better action.

並列關鍵字

VaR ； State-Space Method ； Minimum Variance Portfolio ； Risk Alert

參考文獻

[1]Alexander. C. O and Leigh. C. T, On the Covariance Matrices Used in Value at Risk Models, Journal of Derivative, pp. 50-62, 1997.

[2]Bender. T. S, VAR: Seductive but Dangerous, Financial Analysts Journal, pp. 12-24, 1995.

[5]Havenner. A and Leng. Z, Improved Estimates of the Parameters of State Space Time Series Models, Journal of economic dynamics and control, vol. 20, pp. 767-789, 1996.

[6]Johnston. J, Econometric Methods, 3rd edition, McGraw-Hill, New York, 1984.

[7]Jorion, Value at Risk: The New Benchmark for Controlling Market Risk, McGraw-Hill, New York, 1997.