風險矩陣波動修正之風險值估計

Estimation of VaR with Revised Volatility of RiskMetrics

張簡彰程(Chang-Cheng Changchien) ； 林楚雄(Chu-Hsiung Lin) ； 曾正杰(Cheng-Chieh Tseng)

《輔仁管理評論》 15卷2期 (2008/05) Pp. 61-82

https://doi.org/10.29698/FJMR.200805.0004

摘要

風險矩陣(RiskMetrics)模型於計算風險值時，須假設資產的報酬爲常態分配，並以EWMA模型估計條件波動。然而，許多實證研究指出，即使是考慮條件機率分配的狀況，短天期的資產報酬仍非服從常態分配，並且具有尾部較常態分配爲厚之高狹峰(Leptokurtic)特性(Baillie & DeGennaro, 1990; Bollerslev, Chou & Kroner, 1992)，因此以EWMA 估計式來衡量波動將會有所偏誤。
本研究使用移動廻歸方式(rolling regression)來估計修正偏誤後的波動以預測風險值。本研究以包含台灣股票加權股價指數(TAIEX)及美元兌台幣(USD/TWD)等10種標的爲研究對象，經失敗率分析及Kupiec(1995)統計檢定結果，證實本研究波動修正之風險值估計方式，確可提升風險矩陣估算風險值的準確性。此外，藉由本研究之實證結果，可提供國內證券商應用風險矩陣模型時解決波動偏誤的問題，進而提高估算風險值之準確性，並依據其本身的偏好與需求，設定更有效率及較佳的風險值預測模型。

關鍵字

風險矩陣 ； EWMA ； 波動性

並列摘要

The RiskMetrics method to the calculation of Value-at -Risk assumes the daily returns are conditionally normal and uses an EWMA model to forecast conditional volatility. The conditional distribution of short horizon financial assets returns is leptokurtic, with tails fatter than those of normal distribution in literature. So EWMA estimator will generate biased forecasts of the true conditional volatility.
This study uses a rolling regression method to evaluate the conditional bias in the RiskMetrics approach to the estimation of VaR. In the light of results of the failure rates and Kupiec test, the empirical result shows that the method can considerably enhance the estimation accuracy of Value-at -Risk. This study hopes to shed light on building up risk prediction models and brings constructive implications for risk managers to effectively manage their port folios.

並列關鍵字

RiskMetrics ； EWMA ； volatility

參考文獻

Alexander, C.O.,C.T. Leigh(1997).On the Covariance Matrices Used in Value at Risk Models.Journal of Derivatives.spring,50-62.

Baillie, R.,R. DeGennaro(1990).Stock returns and Volatility.Journal of Financial and Quantitative Analysis.25,203-214.

Billio, M.,L. Pelizzon(2000).Value-at-Risk: A Multivariate Switching Regime Approach.Journal of Empirical Finance.7,531-554.

Bollerslev, T.,Chou, R.,K. Kroner(1992).ARCH Modeling in Finance.Journal of Econometrics.52,5-59.

Boudoukh, J.,Richardson, M.,R. Whitelaw(1997).Investigation of a Class of Volatility Estimators.Journal of Derivatives.14,63-71.