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題名：擺脫對VaR的迷戀：以極值方法估計DaR
作者：陳尚武
作者(外文)：Sun-wu Chen
校院名稱：國立高雄第一科技大學
系所名稱：管理研究所
指導教授：周賢榮
學位類別：博士
出版日期：2006
主題關鍵詞：風險值；極值理論；一般柏拉圖分配；Drawdown；Drawdown-at-risk；Extreme value theory；Generalized Pareto Distribution
原始連結：連回原系統網址new window
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傳統的下方風險衡量系統如風險值(VaR)是以單期的損失為風險因子，因此忽略了連續價跌對財務投資所可能造成的巨大損失。反觀drawdown是以連續損失做為風險因子，因而能從更保守的角度來探討極端損失的可能性，而不是僅以VaR為極端風險衡量的絕對標準。雖然如此，相對於其他傳統的風險衡量指標，學術上對drawdown的研究卻是非常有限；台灣的財務學界與實務界對drawdown的研究更是付諸闕如。因此，藉由drawdown相關的先驅研究或野i以進而吸引學術界與實務界對drawdown的理論與應用做更廣泛與深入的探討。
本研究旨在探討金融資產的實證DaR值相對於其實證VaR值是否更具保守性，並進而探討drawdown風險因子的分配模型配適及其DaR門檻值的估計。由於並無先前的實證顯示，財務drawdown的機率分配究竟為常態、瘦尾、或胖尾，面對這樣的不確定性，極值理論提供了彈性的模型配適與DaR的估計方法。本研究提出以極值理論為基礎的ㄧ般柏拉圖分配(GPD)之兩種估計方法操作來探討50種國際股價指數與匯率的drawdown分配模型配適及其DaR門檻值。第一個方法藉由全部的drawdown樣本資料進行GPD模型配適，並進而估計其尾部的臨界值來求得DaR。第二個方法則是依照傳統的極值理論架構，選定一個尾部高門檻值，並僅以超越此門檻值的極端值樣本估計drawdown尾部的極限分配，並進而反推求得其DaR值。最後，本研究再透過四種統計檢測R2、TIC、HMAE、及HRMSE來評判上述兩種估計方法的準確性。
本研究的資料分析與實證研究結果顯示，所有的國際股價指數樣本及多數的國際匯率樣本其DaR值明顯地低於VaR值，說明了相對於VaR而言，DaR的確更具極端風險估計的保守性。再者，於DaR估計的準確性比較，上述的方法一在估計尾部5% DaR上，其準確性顯著優於方法二；然而在估計尾部1% DaR時，方法二的準確性則略佔上風，雖然優於方法一的程度有限。本研究之結果可供金融機構及投資經理人建構其DaR風險衡量系統的參考依據。
Traditional downside risk measures such as value-at-risk (VaR) rely on using one-period loss as the target risk factor, and therefore fail to recognize the devastating severity of consecutive price drops of a portfolio. A drawdown measures the consecutive losses as a whole from a local peak to trough, and highlights the territory of extreme risk from an alternative angle, rather than persists in following VaR as the absolute benchmark. However, drawdown as a measure of risk has failed to attract the same kind of academic research and attention that are devoted to other traditional measures. Research deficiency of drawdown is even worse in Taiwan’s financial community. Some pioneering studies are, therefore, expected to fill this research gap and attract more attentions from researchers and practitioners on drawdown applications.
This study intends to explore the model fitting of drawdowns distributions and precise estimation of drawdown-at-risk (DaR��), which, similar to the unconditional VaR��, is basically the (1-��)-quantile of the fitted drawdown distribution. Since there are no previous evidences that financial drawdowns are normal, thin-tailed, or thick-tailed distributions, the extreme value theory (EVT) provides flexible approaches to modeling the drawdowns of major international stock indices and currencies, and estimating their threshold values of DaR. Our proposed competing approaches consider two arrangements on using the generalized Pareto distribution (GPD). Firstly, fit the aggregate drawdowns data by the GPD, and then derive DaR thresholds from the specified percentiles of the fitted model. Secondly, following traditional EVT frameworks, we concentrate on fitting the GPD with drawdown-tail excesses over a specified high threshold to shape the asymptotical distribution of excesses, which can be also employed to solve the corresponding DaR thresholds. In addition, four statistical tests, the R2, TIC, HMAE, and HRMSE, will be implemented to examine the accuracy performances of these two competing approaches.
Our data analysis and empirical study show that all sample stock indexes and most currencies provide significantly lower empirical values of DaR than those of VaR at various tail confidence levels. These results recognize that the estimating performances of DaR are in general more conservative than those of VaR as an extreme risk measure. In addition, among our fifty sample indexes and currencies, most have more precise 5% DaR estimates by using the GPD approach fitting with aggregate drawdowns data. However, for estimating 1% DaR thresholds, the traditional EVT-based approach dominates the estimating performance to a small extent but not substantially. The study findings hence conclude that DaR can act as a more conservative extreme risk measure than VaR, and the EVT model applications on DaR estimation presented here provide useful insights into the measurement of financial extreme risk.
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