臺灣博碩士論文加值系統

本文提出非線性分量異質變異數資本資產定價模型，此模型包含非線性市場貝他係數，非線性異常交易量因子，與非線性異質變異數。文獻指出，交易量與股票報酬有關聯，而且此關聯可使我們瞭解金融市場結構與反應投資者偏好。因此，我們採用HP-過濾器將對數交易量時間序列分離成隨機成長趨勢的交易量與異常交易量時間序列。我們將延遲的異常交易量，加進資本資產定價模型，以描述非理性交易行為，提供預測資訊，並增進增本資產定價模型之解釋能力。我們採用分量迴歸分析，去檢驗延遲異常交易量對股票報酬之影響，以避免此影響被普通迴歸分析所忽略。本論文採用貝氏馬可夫鍊蒙地卡羅法與非對稱Laplace分配對參數做推論。我們用提出之模型分析六檔道瓊指數股票，結果顯示，在低分量的情況下，異常交易量對股票報酬有顯著的負影響，然而，在高分量的情況下，異常交易量對股票報酬呈現顯著正影響。市場貝他係數會隨分量不同而改變，反映股票市場的系統風險波動。我們也觀察到，在極端的分量條件下，延遲的股票超額報酬與異常交易量在市場壞消息與好消息的不同影響下，呈現不對稱現象。從這些結論可證實極端的交易量隱含未來股價變化的訊息。更重要的是，考慮異常交易量，可增進資本資產定價模型之解釋能力並涵蓋財務行為學之考量。綜合以上發現，相對於傳統的資本資產定價模型而言，本文所提出之模型可提供基金經理人或投資者更彈性而廣泛的投資策略。

In this paper, we develop a nonlinear quantile CAPM with heteroskedasticity, nonlinear market betas, nonlinear lagged abnormal volume factor, and nonlinear volatility dynamics. It’s widely reported that volume is related to return and such volume-return relationship provides insight into financial market structures and reflects investors’ preferences. Hence, we employ HP-filter to separate the log-volume time series into a stochastic growth trend of volume and the abnormal volume time series. We add the lagged abnormal volume factor in CAPM to capture irrational behavior, to provide predicting information, and to enhance the explanatory power of CAPM. Quantile regression is employed to examine the dependence of lagged volume on return which is uncovered by mean regression. To efficiently estimate the coefficients, Bayesian MCMC methods with asymmetric Laplace distribution are utilized. We analyze six Dow Jones Industrial stocks to demonstrate our proposed models. The results exhibit significantly negative effects of abnormal volume on stock excess return under low quantile levels while there are significantly positive effects under high quantile levels. Each Market beta varies with different quantile levels, representing fluctuations of systematic risk in the stock market. We observe that the coefficients of lag-one stock excess return and abnormal volume are asymmetric between lower regime and upper regime under extreme quantile levels. This work confirms that extreme trading volume contains information about the future evolution of stock prices. More importantly, considering abnormal volume factor could enhance the explanatory power of CAPM and provide considerations in behavioral finance. Adopting these findings, fund managers and investors could have more flexible strategies than using the traditional CAPM.

1. Introduction.......................1
2. CAPM Family........................5
2.1 Basic CAPM........................5
2.2 Modified CAPMs....................6
3. The Extended Quantile Threshold CAPM with GARCH Errors and Abnormal Volume Factor.............................9
3.1 HP-Filter........................10
3.2 Abnormal Volume..................11
3.3 Quantile Regression..............12
3.4 The Proposed Model...............14
4. Bayesian Inference................16
5. Empirical Study...................19
6. Concluding Remarks and Future Works ..................................53
References...........................55
Appendix A: MCMC Sampling Scheme.....59
Appendix B: RW-MH Algorithm and IK-MH Algorithm................60
Appendix C: ACF and Trace Plots......61

Acharya, V. V. and Pedersen, L. H. (2005) Asset pricing with liquidity risk. Journal of Financial Economics, 77, 375-410.

Adrian, T. and Franzoni, F. (2009) Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM. Journal of Empirical Finance, 16, 537-556.

Ahumada, H. and Garehnani M. L. (1999) Hodrick-Prescott filter in practice. Economica, 45, 61-76.

Akdeniz, L., Salih, A. A., and Caner, M. (2003) Time-varying betas help in asset pricing: The threshold CAPM. Studies in Nonlinear Dynamics and Econometrics, 6, 1-16.

Ang, A. and Chen, J. (2007) CAPM over the long run: 1926–2001. Journal of Empirical Finance, 14, 1-40.

Banz, R. W. (1981) The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3-18.

Bassett, G. and Koenker, R. (1982) An empirical quantile function for linear models with iid errors. Journal of the American Statistical Association, 77, 407-415.

Baur, D. G., Dimpfl, T., and Jung, R. C. (2012) Stock return autocorrelations revisited: A quantile regression approach. Journal of Empirical Finance, 19, 254-265.

Bekaert, G. and Wu, G. (2000) Asymmetric volatility and risk in equity markets. Review of Financial Studies, 13, 1-42.

Black, F. (1976) Studies of stock price volatility changes. Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Section, 177-181.

Bollerslev, T. (1986) Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307-327.

Bollerslev, T., Engle, R. F., and Wooldridge, J. M. (1988) A capital asset pricing model with time-varying covariances. Journal of Political Economy, 96, 116-131.

Bollerslev, T., Chou, R. Y., and Kroner, K. F. (1992) ARCH modeling in finance: a review of the theory and empirical evidence. Journal of Econometrics, 52, 5-59.

Brailsford, T. J. and Faff, R. W. (1997) Testing the conditional CAPM and the effect of intervaling: A note. Pacific-Basin Finance Journal, 5, 527-537.

Chan, L. K. C., Hamao, Y., and Lakonishok J. (1991) Fundamentals and stock returns in Japan. Journal of Finance, 46, 1739-1789.

Chen, C. W. S., Chiang, T. C., and So, M. K. P. (2003) Asymmetrical reaction to US stock-return news: evidence from major stock markets based on a double-threshold model. Journal of Economics and Business, 55, 487-502.

Chen, C. W. S. and So, M. K. P. (2006) On a threshold heteroscedastic model. International Journal of Forecasting, 22, 73-89.

Chen, C. W. S., Gerlach, R., and So, M. K. P. (2006) Comparison of non-nested asymmetric heteroscedastic models. Computational Statistics and Data Analysis, 51, 2164-2178.

Chen, C. W. S., Gerlach, R., and Wei, D. C. M. (2009) Bayesian causal effects in quantiles: accounting for heteroscedasticity. Computational Statistics and Data Analysis, a special issue on Computational Econometrics, 53, 1993-2007.

Chen, C. W. S., Gerlach, R. H., and Lin, M. H. (2011) Multi-regime nonlinear capital asset pricing models. Quantitative Finance, 11, 1421-1438.

Chen, C. W. S., Lin S., and Yu P. L. H. (2012) Smooth transition quantile capital asset pricing models with heteroskedasticity. Computational Economics, 40, 19-48.

Chen, C. W. S. and Gerlach, R. H. (2013) Semi-parametric quantile estimation for double threshold autoregressive models with heteroscedasticity. Computational Statistics, 28, 1103-1131.

Chen, S. S. (2012) Revisiting the empirical linkages between stock returns and trading volume. Journal of Banking and Finance, 36, 1781-1788.

Chiang, T. C. and Li, J. (2012) Stock returns and risk: Evidence from quantile regression analysis. Journal of Risk and Financial Management, 5, 20-58.

Christie, A. A. (1982) The stochastic behavior of common stock variance – value, leverage and interest rate effects. Journal of Financial Economics, 10, 407-432.

Chuang, C. C., Kuan, C. M., and Lin, H. Y. (2009) Causality in quantiles and dynamic stock return-volume relations. Journal of Banking and Finance, 33, 1351-1360.

Clark, P. K. (1973) A subordinated stochastic process model with finite variance for speculative prices. Econometrica, 41, 135-155.

Datar, V. T., Naik, N. Y., and Radcliffe, R. (1998) Liquidity and stock returns: an alternative test. Journal of Financial Markets, 1, 203-219.

Engle, R. F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987-1008.

Epps, T. W. and Epps, M. L. (1976) The stochastic dependence of security price changes and transaction volumes: implications for the mixture distributions hypothesis. Econometrica, 44, 305-321.

Fama, E. F. and French, K. R. (1992) The cross-section of expected stock returns. Journal of Finance, 47, 427-465.

Fama, E. F. and French, K. R. (1993) Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3-56.

Fama, E. F. and French, K. R. (1996) Multifactor explanations of asset pricing anomalies. Journal of Finance, 51, 55-84.

Fama, E. F. and French, K. R. (2004) The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18, 25-46.

Ferson, W. and Harvey, C. (1993) The risk and predictability of international equity returns. Review of Financial Studies, 6, 527-566.

Ferson, W. and Harvey, C. (1999) Conditioning variables and the cross-section of stock returns. Journal of Finance, 54, 1325-1360.

Gebka, B. and Wohar, M. E. (2013) Causality between trading volume and returns: Evidence from quantile regressions. International Review of Economics and Finance, 27, 144-159.

Ghysels, E. (1998) On stable factor structures in the pricing of risk: do time varying betas help or hurt? Journal of Finance, 53, 549-573.

Granger, C. W. J. and Silvapulle, P. (2001) Capital asset pricing model, bear, usual, and bull market conditions and beta instability: A value-at-risk approach. Working paper, University of California, San Diego.

Hansen, L. and Richard S. (1987) The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models. Econometrica, 55, 587-613.

Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.

Hodrick, R. J. and Prescott E. C. (1997) Postwar U.S. business cycle: An empirical investigation. Journal of Money, Credit, and Banking, 29, 1-16.

Jacoby, G., Fowler, D. J., and Gottesman, A. A. (2000) The capital asset pricing model and the liquidity effect: a theoretical approach. Journal of Financial Markets, 3, 69-81.

Jagganathan, R. and Wang, Z. (1996) The conditional CAPM and the cross-section of expected returns. Journal of Finance, 51, 3-53.

Jayakumar, K. and Kuttykrishnan, A. P. (2007) A time-series model using asymmetric Laplace distribution. Statistics and Probability Letters, 77, 1636-1640.

Karpoff, J. M. (1987) The relation between price changes and trading volume: A survey. Journal of Financial and Quantitative Analysis, 22, 109-126.

Koenker, R. and Bassett, G. (1978) Regression quantiles. Econometrica, 46, 33-50.

Koenker, R. and Machado, J. (1999) Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association, 94, 1296-1310.

Kotz, S., Kozubowski, T. J., and Podgorski, K. (2001) The Laplace Distribution and Generalizations: A Revisiting with Applications to Communications, Economics, Engineering, and Finance. Springer Science+Business Media, New York.

Lakonishok, J., Shleifer, A., and Vishny, R. W. (1994) Contrarian investment, extrapolation, and risk. Journal of Finance, 49, 1541-1578.

Lintner, J. (1965) The valuation of risky assets and the selection of risky investments in stock portfolio and capital budgets. The Review of Economics and Statistics, 47, 13-37.

Markowitz, H. M. (1959) Portfolio Selection. Journal of Finance, 7, 77-91.

Menzly, L., Santos, T., and Veronesi, P. (2004) Understanding predictability. Journal of Political Economy, 112, 1-47.

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953) Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1091.

Ng, L. (1991) Tests of the CAPM with time-varying covariances: A multivariate GARCH approach. Journal of Finance, 46, 1507-1521.

Perold, A. F. (2004) The capital asset pricing model. Journal of Economic Perspectives, 18, 3-24.

Ravn, M. O. and Uhlig, H. (2002) On adjusting the Hodrick-Prescott filter for the frequency of observations. The Review of Econometrics and Statistics, 84, 371-380.

Sharpe, W. F. (1964) Capital asset prices: A theory market equilibrium under conditions of risk. Journal of Finance, 19, 425-442.

Tierney, L. (1994) Markov chains for exploring posterior distribution. Annual of Statistics, 22, 1701-1762.

Wagner, N. and Marsh, T. A. (2005) Surprise volume and heteroskedasticity in equity market returns. Quantitative Finance, 5, 153-168.

Ying, C. C. (1966) Stock market prices and volumes of sales. Econometrica, 34, 676-685.

Yu, K. and Moyeed, R. A. (2001) Bayesian quantile regression. Statistics and Probability Letters, 54, 437-447.