臺灣博碩士論文加值系統

隨著衍生性商品蓬勃發展，而金融市場上重大事件頻傳，漸漸喚起金融機構對有效風險管理的重視。風險值擁有量化風險的優點，是金融市場波動的新興風險管理工具，它的定義為持有某資產一段期間，在一定的信賴水準下，所可能遭受的最大損失。金融機構為了內部控管及調整，已經將風險值視為衡量市場風險的標準。
美國第一檔交易所買賣基金（Exchange Traded Fund）-「SPDR」 ，於1993年在美國證券交易所掛牌，短短十年間，ETFs在美國資產增長超過1,000億美元，成為美國金融史上成長速度最快的金融商品。近年來，ETFs熱潮吹向全球各大證交所，在全球投資一片低迷氣氛中，ETFs卻逆勢上揚，受到投資人歡迎。台灣股票市場上第一檔ETF -「台灣50」於2003年6月30日問市，受限於歷史資料樣本數不足，故本研究是以其追蹤標的台灣五十指數為實證對象，評估不同模型估計出的風險值與預測績效。模型分為有母數模型與無母數模型兩大類。有母數模型假設資產報酬率為隨機、獨立之常態分配且序列不相關，分別包含了均等加權移動平均法、RiskMetric的指數加權移動平均法及含有異質變異的GARCH（1,1）模型；而無母數模型對於資產報酬並不假設任何分配，主要是透過歷史資料模擬而得，分別包含了歷史模擬法及蒙地卡羅模擬法；同時，本研究更進一步的加入了Engle and Manganelli（2000）提出的條件自我相關風險值模型－CAVaR，用以探討風險值間具有自我相關（Autocorrelated）的特性，將傳統衡量出風險值具有跳躍的情況予以平滑化（Smoothly），以符合資產報酬真實情況。
根據上述的實證結果分析，隨著歷史資料視窗長度的增加，或提高信賴區間對於風險值的估計不一定會降低RMSE值或提高估計的成功率，也就是說，不一定會帶來較好的估計結果。故本研究建議投資人若要進行台灣五十指數的投資，基於計算成本及效率的考量，以一年（250天）的歷史資料期間為最適估計期間及5%的顯著水準，利用歷史模擬法或加權指數平均法來衡量風險值即可；若考量風險值也有自我相關的特性，可以Engle and Manganelli（2000）提出的CAVaR模型來衡量。

Value at Risk （VaR）is an emerging tool of risk management which is designed to meet the trend of various derivatives and more volatile financial markets. VaR is defined as the value that portfolio will lose with a given probability, over a certain time horizon. It is a better way of quantifying risk. It has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Recently, financial disasters have emphasized the importance of effective risk management for financial institutions.
The first Exchange Traded Fund（ETFs）, SPDR, was listed in American Stock Exchange in 1993. During lately decade, ETFs increasing over 100 billion dollars in American become the fastest growing up financial goods in U.S.A.''s financial history. In recent years, ETFs upsurge blows to every large stock exchange in the world despite a depressing atmosphere of investing of the whole world. First ETF, Taiwan 50, on Taiwan stock market was listed on June 30 2003. Limited to not enough historical samples, this study uses the behavior of daily Taiwan 50 Index as our empirical data. It compares the VaR and predicting effectiveness for different models. There are two types of models. One is parametric model. It is constructed under the assumptions that return is iid and normally distributed, but most return of financial assets is non-normally distributed. Parametric models include equally weighted moving average approaches, exponentially weighted moving average approaches and generalized autoregressive conditional heteroskedastic. The other is non-parametric model that requires no assumptions on distribution of returns. It comes mainly from the simulation on historical data. Non-parametric models include historical simulation method and Monte Carlo simulation method. Besides, this study attempts to address a conditional autoregressive specification on VaR, which is called Conditional Autoregressive Value at Risk - CAVaR (Engle and Manganelli, 2000). CAVaR model that is different from traditional VaR model is the value of quantitative risk changes “smoothly” over time.
According to results of this study, it will not reduce RMSE value or improve the success rate on estimation of value at risk with the increase of the historical length of materials window or improve confidence interval. That is to say, it will not bring better estimation result. When investors are going to make investment on Taiwan 50 Index, using historical simulation method or exponentially weighted moving average approaches to estimate the Value at Risk in 5% significant level and 250 days-holding period is suggested by this study. Considering risk has characteristic of heteroscedasticity, investors can use CAVaR Model mentioned by Engle and Manganelli (2000 ) to measure Value at Risk .

摘要......................................................i
Abstract............................................... iii
第一章　緒論..............................................1
第一節　研究背景及動機..................................1
第二節　研究目的及方法..................................3
第三節　研究流程及架構..................................5
第二章　文獻回顧..........................................7
第一節　風險值介紹......................................7
第二節　風險值之不同估計方法............................8
第三節 風險值之實證研究...............................12
第三章　理論模型與研究方法...............................17
第一節　風險值之理論模型...............................17
第二節　有母數模型.....................................18
第三節　無母數模型.....................................22
第四節　CAVaR模型（conditional autoregressive value at risk by autoregressive method）...............................24
第五節　風險值績效之檢測...............................27
第六節　評估各模型之考量...............................28
第四章　模型設計與實證結果分析...........................29
第一節　資料說明與選取.................................29
第二節　報酬之敘述統計.................................30
第三節　報酬率之實證步驟...............................32
第四節　實證結果分析...................................43
第五節　對投資人在實際應用時之建議.....................47
第五章　結論與未來研究方向...............................49
第一節　結論...........................................49
第二節　研究限制及未來研究方向...........................50
參考文獻.................................................52
附錄一　台灣五十指數之AR模型.............................55
附錄二　台灣五十指數之ARCH及GARCH模型....................56

一、中文部份
1、李進生、謝文良、林允永、蔣炤坪、陳達新、盧陽正合著，民國90年，「風險管理－風險值（VaR）理論與應用」，清蔚科技
2、沈大白、周大慶、張大成、敬永康、柯瓊鳳合著，民國91年，「風險管理新標竿－風險值理論與應用」，智勝
3、吳欣桐，（2000），風險值（Value at Risk）在台灣股市的應用－股票與認購權證投資組合，中正大學國際經濟研究所碩士論文
4、卓訓方，（2000），美國高科技類股風險值估計模型之實證研究，文化大學經濟學研究所碩士論文
5、胡為善、宋文仁，（1999），「以三種風險價值法衡量在亞洲金融風暴期間台灣及香港股價指數與外匯的投資組合」，中原學報，27卷2期，頁33~48
6、黃達業譯（Philippe Jorion著），民國90年，「風險值：市場風險控管之新基準」，台灣金融研訓院
7、蔡維溢，（1997），以VaR風險計量模型衡量衍生性金融商品之市場風險，中原大學企業管理學系碩士
8、蒲建亨，（2000），整合VaR法之衡量與驗證－以台灣金融市場投資組合為例，政治大學國際貿易學系碩士論文
9、謝振耀，（2000），台灣債券投資組合風險值之評估，政治大學國際貿易學系碩士論文
二、英文部份
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3、Dowd, K., (1997), “Beyond Value at Risk : The New Science of Risk Management”.
4、Duffie, D. and J. Pan, （1997）, “An Overview of Value at Risk.” The Journal of Derivatives, Vol. 4, pp. 7-49.
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7、Engle, R. F. and S. Manganelli,（2000）, “CAVaR：Conditional Autoregressive Value at Risk by Regression Quantiles,” Working paper, NBER.
8、Hendricks, D.,（1996）, “Evaluation of Value-at-risk Models Using Historical Data,” Economic Policy Review, Federal Reserve Bank of New York, Vol. 2, pp. 39-69.
9、Jackson Patricia, David J. Maude, William Perraudin ,（1997）,“Bank Capital and Value at Risk,”The Journal of Derivatives, Spring, pp.73~89.
10、Jorion, P.,（1996）, “Risk：measuring the risk in Value at Risk,” Financial Analysts Journal, November/December, pp. 47-56.
11、Jorion, P., （2000）, Value at Risk：The New Benchmark for Controlling Market Risk, McGraw-Hill, New York.
12、J.P. Morgan （1996）, “RiskMetrics Technical Document” Fourth Edition, http://www.jpmorgan.com.
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14、Venkataraman, S. ,（1997）,“Value at Risk for a Mixture of Normal Distribution: The Use of Quasi-Bayesian Estimation Techniques,” Economic Perspectives, Federal Reserve Bank of Chicago, March-April, pp.2-13.