本論文研究美國股票市場風險與超額報酬間之關係，主要的風險衡量變數為傳統風險之已實現波動(Realized volatility, RV)與下方風險之風險值(Value-at-Risk, VaR)，並且比較何者風險變數較能適當捕捉與超額報酬間之抵換關係。其中風險值之估計異於一般採用Normal分配，本文所使用skew generalized t (SGT) 分配能捕捉一般金融性資產具有偏態、厚尾及高峽峰之特徵並且配合移動視窗法(rolling window)來估出風險值。另外，也考量金融海嘯期間之影響，探討風險與報酬間之關係有何變化。而樣本資料為美國股票市場2004年至2010年期間之日資料。由實證結果發現風險值之估計以SGT分配優於拔靴法，在愈嚴格的信賴水準下SGT分配愈能合理計算出風險值，而風險值與超額報酬間存在正向抵換關係，但已實現波動依天期有不同的見解，過短或太長天期之已實現波動對報酬不具解釋能力，唯有30、60及90天之已實現波動與超額報酬間呈正向相關。最後在考量金融海嘯期間之影響後，結果發現無論使用何種風險衡量變數，都難以解釋超額報酬之變化。

This paper examines the relationship between risk and excess returns in the U.S. stock market. The main risk measure variables are realized volatility (RV) of the traditional risk and Value-at-Risk (VaR) of downside risk. Moreover, comparing RV with VaR for the sake of finding a best explaining power of evaluating the risk-return tradeoff. In order to forecast VaR, we employ skewed generalized t (SGT) distribution, to capture skewness, fat-tails and leptokurtosis of financial assets, and rolling window method. Furthermore, we also investigate that whether the relationship between risk and returns changes during the period of global financial tsunami. The data period is from 2004 to 2010. Empirical results indicate that VaR of SGT distribution is superior to bootstrapping even at the strict level of confidence. Value-at-Risk has a positive and significant relationship between risk and excess returns. However, realized volatility only has a positive relationship with excess returns in 30, 60, and 90 days. Finally, we find that any risk measure variables is difficult to define the risk-return tradeoff during the period of global financial tsunami.

表目錄 V
圖目錄 VI
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與特色 5
第三節 研究架構 6
第二章 文獻回顧 8
第一節 風險值之簡介及文獻 8
第二節 風險與報酬之抵換關係文獻 15
第三章 研究設計 24
第一節 研究資料 24
第二節 風險衡量方法 24
第三節 線性迴歸模型	31
第四章 實證結果 34
第一節 基本統計分析 34
第二節 風險與報酬之抵換關係 48
第五章 結論與建議 56
參考文獻 58

表目錄
表4.1 日報酬基本敘述統計 36
表4.2 已實現波動基本敘述統計 38
表4.3 風險值(VaR) 基本敘述統計 42
表4.4 風險值(VaR) 檢定結果 43
表4.5 控制變數基本敘述統計 46
表4.6 已實現波動與報酬之抵換關係 49
表4.6 (續)已實現波動與報酬之抵換關係 50
表4.7 風險值(拔靴法)與報酬之抵換關係 52
表4.8 風險值(SGT分配)與報酬之抵換關係 54
表 4.9 已實現波動與風險值之比較 55

圖目錄
圖1.1 本文之研究流程圖 7
圖2.1 持有某資產在信賴水準 (1-α%)下之損益分配圖 8
圖4.1 每日股價走勢圖 (NYSE / NASDAQ / AMEX) 35
圖4.2 每日報酬走勢圖 (NYSE / NASDAQ / AMEX) 37
圖4.3 已實現波動圖 39
圖4.4 實際報酬率與風險值(拔靴法)比較圖 44
圖4.5 實際報酬率與風險值(SGT分配)比較圖 44
圖4.6 違約利差(DEF)圖 47

參考文獻
Andersen, T. and T. Bollerslev, (1998), “Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts” International Economic Review, 39, pp. 885-905.
Angelidis, T. and S. Degiannakis, (2008), “Forecasting One-day-ahead VaR and Intra-Day Realized Volatility in the Athens Stock Exchange Market”, Managerial Finance, 34(7), pp. 489-497.
Angelidis, T., A. Benos and S. Degiannakis, (2004), ‘‘The Use of GARCH Models in VaR Estimation’’, Statistical Methodology, 1(2), pp. 105-28.
Angelidis, T. and S. Degiannakis, (2005), “Modeling Risk for Long and Short Trading Positions.” The Journal of Risk Finance, 6, pp. 226-38.
Baillie, R. T. and R. P. DeGennaro, (1990), “Stock Returns and Volatility.” Journal of Financial and Quantitative Analysis, 25(2), pp. 203-214.
Bali, T. G., (2007), “Modeling the Dynamics of Interest Rate Volatility with Skewed Fat-tailed Distributions.” Annals of Operations Research, 151, pp. 151-178.
Bali, T. G., (2008), “The Intertemporal Relation between Expected Returns and Risk.” Journal of Financial Economics, 87, pp. 101-131.
Bali, T. G. and N. Cakici, (2004), “Value at Risk and Expected Stock Returns.” Financial Analysts Journal, 60(2), pp. 57-73.
Bali, T. G. and L. Peng, (2006), “Is There A Risk–Return Trade‐off? Evidence from High‐Frequency Data.” Journal of Applied Econometrics, 21(8), pp. 1169-1198.
Bali, T. G. and P. Theodossiou, (2007), “A Conditional-SGTVaR Approach with Alternative GARCH Models.” Annals of Operations Research, 151(1), pp. 241-267.
Bali, T. G., H. Mo, and Y. Tang, (2008), “The Role of Autoregressive Conditional Skewness and Kurtosis in the Estimation of Conditional VaR.” Journal of Banking & Finance, 32, pp. 269-282.
Bali, T. G., K. O. Demirtas, and H. Levy, (2009), “Is There an Intertemporal Relation between Downside Risk and Expected Returns?” Journal of Financial and Quantitative Analysis, 44(4), pp. 883-909.
Bekaert, G. and G. Wu, (2000), “Asymmetric Volatility and Risk in Equity Markets.” Review of Financial Studies, 13(1), pp. 1-42.
Black, F., (1976), “Studies of Stock Price Volatility Changes.” Proceedings of the 1976 Meeting of Business and Economics Statistics Section of the American Statistical Association, 27, pp. 399– 418.
Bollerslev, T., (1986), “Generalized Autoregressive Conditional Heteroscedasiticity.” Journal of Econometrics, 31, pp. 307-327.
Bollerslev, T. and H. Zhou, (2006), “Volatility Puzzles: A Simple Framework for Gauging Return-Volatility Regressions.” Journal of Econometrics, 131, pp. 123-150.
Brandt, M. W. and Q. Kang, (2004), “On the Relationship between the Conditional Mean and Volatility of Stock Returns: A Latent VAR Approach.” Journal of Financial Economics, 72, pp. 217–257.
Campbell, J. Y., M. Lettau, B. G. Malkiel, and Y. Xu, (2001), “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk.” Journal of Finance, 56, pp. 1–44.
Cecchetti, S. G., (2008), “Crisis and Responses: The Federal Reserve and The Financial Crisis of 2007-2008.” National Bureau of Economic Research. NBER Working Paper No. 14134. http://www.nber.org/papers/w14134.
Chen, D. H., C. D. Chen, and J. Chen, (2009), “Downside Risk Measures and Equity Returns in the NYSE.” Applied Economics, 41, pp. 1055-1070.
Christoffersen, P. F., (1998), “Evaluating Interval Forecasts.” International Economic Review, 39, pp. 841-862.
Cox, J. and S. Ross, (1976), “The Valuation of Options for Alternative Stochastic Process.” Journal of Financial Economics, 3, pp. 145-166.
Dowd, K., (1998), “Beyond Value at Risk.” John Wiley & Son.
Efron, B., (1979), “Bootstrap Methods: Another Look at the Jackknife.” The Annals of Statistics, 7, pp. 1-26.
Engle, R., (1982), “Autoregressive Conditional Heteroskedasticity with Estimates of Variance of UK Inflation.” Econometrica, 50(4), pp. 987-1007.
Engle, R., D. M. Lilien and R. P. Robins, (1987), “Estimating Time Varying Risk Premia in the Term Structure the ARCH-M Model.” Econometrica, 55, pp. 391-407.
Fama, E. F. and J. D. MacBeth, (1973), “Risk Return and Equilibrium: Empirical Test.” Journal of Political Economy, 81, pp. 607-636.
Fama, E. F. and K. R. French, (1993), “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33, pp. 3-56.
Fama, E. F. and K. R. French, (2006), “The Value Premium and the CAPM.” Journal of Finance, 61, pp. 2163-2185.
French, K. R., W. Schwert, and R. F., Stambaugh, (1987), “Expected Stock Returns and Volatility.” Journal of Financial Economics, 19(1), pp. 3-29.
Christie, A. A., (1982), “The Stochastic Behavior of Common Stock Variances-Value, Leverage and Interest Rate Effects.” Journal of Financial Economics, 10, pp. 407-432.
Ghysels, E., P. Santa-Clara, and R. Valkanov, (2005), “There is a Risk-Return Trade-Off After All.” Journal of Financial Economics, 76, pp. 509-548.
Giot, P., (2000), “Intraday Value-At-Risk.” CORE DP 2045, Maastricht University METEOR RM/00/030.
Giot, P. and S. Laurent, (2003a), “Market Risk in Commodity Markets: A VaR Approach.” Energy Economics, 25 (5), pp. 435-457.
Giot, P. and S. Laurent, (2003b), “Value-at-Risk for Long and Short Trading Positions.” Journal of Applied Econometrics, 18, pp. 641-664.
Glosten, L. R., R. Jagannathan, and D. E. Runkle, (1993), “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48(5), pp. 1779-1801.
Goyal, A. and P. Santa-Clara, (2003), “Idiosyncratic Risk Matters!” Journal of Finance, 58, pp. 975-1007.
Guo, H. and R. F. Whitelaw, (2006), “Uncovering the Risk-Return Relation in the Stock Market.” The Journal of Finance, 61(3), pp. 1433-1463.
Hansen, B. E., (1994) “Autoregressive Conditional Density Estimation.” International Economic Review, 35, pp. 705-730.
Harrison, P. and H. H. Zhang, (1999), “An Investigation of the Risk and Return Relation at Long Horizons.” Review of Economics and Statistics, 81, pp. 399-408.
Harvey, C. R., (2001), “The Specification of Conditional Expectations.” Journal of Empirical Finance, 8(5), pp. 573-638.
Huang, Y.C. and B. J. Lin, (2004), “Value-at-Risk Analysis for Taiwan Stock Index Futures: Fat Tails and Conditional Asymmetries in Return Innovations.” Review of Quantitative Finance and Accounting, 22, pp. 79-95.
Huffman, S. P. and C. Moll, (2008), “Value-at-Risk: An Analysis of January and Non-January Returns.” Quarterly Journal of Finance and Accounting, 47(1), pp. 97-107.
Hung, J. C., M. C. Lee, and H. C. Liu, (2008), “Estimation of Value-at-Risk for Energy Commodities via Fat-tailed GARCH Models”, Energy Economics, 30, pp. 1173-1191.
Jarque, C. M. and A. K. Bera, (1980), “Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residual.”  Economics Letters, 6, pp. 255-259.
Jondeau, E. and M. Rockinger, (2003), “Conditional Volatility, Skewness, and Kurtosis: Existence, Persistence, and Comovements.” Journal of Economic Dynamics and Control, 27(10), pp. 1699-1737.
Jorion, P., (2001), “Value at Risk: The New Benchmark for Managing Financial Risk.” Second Edition, New York: McGraw-Hill.
Lee, M. C., J. B. Su, and H. C. Liu, (2008), “Value-at-Risk in US Stock Indices with Skewed Generalized Error Distribution”, Applied Financial Economics Letters, 4, pp. 425-431.
Lettau, M. and S. C. Ludvigson, (2002), “Measuring and Modeling Variation in the Risk-Return Rradeoff.” In: Ait-Sahalia, Y., Hansen, L.P. (Eds.), Handbook of Financial Econometrics. North-Holland, Holland.
Lehnert, T., (2003) “Explaining Smiles: GARCH Option Pricing with Conditional Leptokurtosis and Skewness.” The Journal of Derivatives, 10, pp. 27-39.
Leibowitz, M. L. and S. Kogelman, (1991), “Asset Allocation under Shortfall Constraints.” Journal of Portfolio Management. 17(1), pp. 18-23.
Linter, J., (1965), “The Valuation of Risky Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, 47, pp. 13-37.
Li, Q., C. Hsiao and Y. J. Chang, (2005), “The Relationship between Stock Returns and Volatility in International Stock Markets.” Journal of Empirical Finance, 12, pp. 650-665.
Lucas, A. and P. Klaassen, (1998), “Extreme Returns, Downside Risk, and Optimal Asset Allocation.” The Journal of Portfolio Management, 25(1), pp.71-79.
Ludvigson, S. C. and S. Ng, (2007), “The Empirical Risk-Return Relation: A Factor Analysis Approach.” Journal of Financial Economics, 83, pp. 171-222.
Markowitz, H., (1952), “Portfolio Selection.” Journal of Finance, 7(1), pp. 77-91.
McDonald, J. B. and W. K. Newey, (1988), “Partially Adaptive Estimation of Regression Models via the Generalized t Distribution.” Econometric Theory, 4, pp. 428-457.
McMillan, D. G. and A. E. H. Speight, (2007), “Value-at-Risk in Emerging Equity Markets: Comparative Evidence for Symmetric, Asymmetric, and Long Memory GARCH Models”, International Review of Finance, 7, pp. 1-19.
Merton, R. C., (1973), “An Intertemporal Capital Asset Pricing Model.” Econometrica, 41(5), pp. 867-887.
Mizen, P., (2008), “The Credit Crunch of 2007-2008: A Discussion of the Background, Market Reactions, and Policy Responses.” Federal Reserve Bank of St. Louis Review, 90(5), pp. 531-567.
Mossin, J., (1966), “Equilibrium in A Capital Asset Market.” Econometrica, 41, pp. 768– 783.
Nam, K. and J. Krausz, (2008), “Unexpected Volatility Shock, Volatility Feedback Effect, and Intertemporal Risk-Return Relation.” Working Paper.
Nelson, D. B., (1991), “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica, 59(2), pp. 347-370.
Newey, W. K., and K. D. West, (1987), “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, pp. 703-708.
Roy, A. D., (1952), “Safety First and the Holding of Assets.” Econometrica, 20(3), pp. 431-449.
Shao, X. D., Y. J. Lian, and L. Q. Yin, (2009), “Forecasting Value-at-Risk Using High Frequency Data: The Realized Range Model”, Global Finance Journal, 20, pp. 128-136.
Sharpe, W. F., (1964), “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19, pp. 425-442.
So, M. K. P. and P. L. H. Yu, (2006), “Empirical Analysis of GARCH Models in Value at Risk Estimation.” International Financial Markets, Institutions & Money,   16, pp. 180-197.
Subbotin, M. T., (1923), “On the Law of Frequency of Error.” Matematicheskii Sbornik, 31, pp. 296-301.
Su, E. and T. W. Knowles, (2006), “Asian Pacific Stock Market Volatility Modeling and Value at Risk Analysis.” Emerging Markets Finance and Trade, 42: 18-62.
Theodossiou, P., (1998), “Financial Data and the Skewed Generalized t Distribution.” Management Science, 44, pp. 1650-1661.
Theodossiou, P., (2001), “Skewed Generalized Error Distribution of Financial Assets and Option Pricing.” Working Paper, School of Business, Rutgers University.
van den Goorbergh, R. W. J. and P. J. G. Vlaar, (1999), “Value-at-Risk Analysis of Stock Returns: Historical Simulation, Variance Techniques or Tail Index Estimation?” De Nederlandsche Bank, DNB Staff Reports 40.