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Robust Estimation and Forecasting of the Capital Asset Pricing Model

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  • Bian, G.
  • McAleer, M.J.
  • Wong, W.-K.

Abstract

In this paper, we develop a modified maximum likelihood (MML) estimator for the multiple linear regression model with underlying student t distribution. We obtain the closed form of the estimators, derive the asymptotic properties, and demonstrate that the MML estimator is more appropriate for estimating the parameters of the Capital Asset Pricing Model by comparing its performance with least squares estimators (LSE) on the monthly returns of US portfolios. The empirical results reveal that the MML estimators are more efficient than LSE in terms of the relative efficiency of one-step-ahead forecast mean square error in small samples.

Suggested Citation

  • Bian, G. & McAleer, M.J. & Wong, W.-K., 2010. "Robust Estimation and Forecasting of the Capital Asset Pricing Model," Econometric Institute Research Papers EI 2010-62, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:21112
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    1. Wong, Wing-Keung & McAleer, Michael, 2009. "Mapping the Presidential Election Cycle in US stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3267-3277.
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    4. James J. Kung & Wing‐Keung Wong, 2009. "Efficiency Of The Taiwan Stock Market," The Japanese Economic Review, Japanese Economic Association, vol. 60(3), pages 389-394, September.
    5. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    6. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    7. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2010. "Market efficiency of oil spot and futures: A mean-variance and stochastic dominance approach," Energy Economics, Elsevier, vol. 32(5), pages 979-986, September.
    8. Wai Fong & Wing Wong, 2006. "The modified mixture of distributions model: a revisit," Annals of Finance, Springer, vol. 2(2), pages 167-178, March.
    9. Honore, Bo E. & Hu, Luojia, 2004. "Estimation of cross sectional and panel data censored regression models with endogeneity," Journal of Econometrics, Elsevier, vol. 122(2), pages 293-316, October.
    10. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
    11. Wing-Keung Wong & Meher Manzur & Boon-Kiat Chew, 2003. "How rewarding is technical analysis? Evidence from Singapore stock market," Applied Financial Economics, Taylor & Francis Journals, vol. 13(7), pages 543-551.
    12. Broll, Udo & Wahl, Jack E. & Wong, Wing-Keung, 2006. "Elasticity of risk aversion and international trade," Economics Letters, Elsevier, vol. 92(1), pages 126-130, July.
    13. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    14. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    15. Egozcue, Martin & Wong, Wing-Keung, 2010. "Gains from diversification on convex combinations: A majorization and stochastic dominance approach," European Journal of Operational Research, Elsevier, vol. 200(3), pages 893-900, February.
    16. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, vol. 13(1), pages 89-101.
    17. Wong, Wing-Keung & Phoon, Kok Fai & Lean, Hooi Hooi, 2008. "Stochastic dominance analysis of Asian hedge funds," Pacific-Basin Finance Journal, Elsevier, vol. 16(3), pages 204-223, June.
    18. Hsiao, Cheng, 1989. "Consistent estimation for some nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 41(1), pages 159-185, May.
    19. Wing-Keung Wong & Chenghu Ma, 2008. "Preferences over location-scale family," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 119-146, October.
    20. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    21. Qiao, Zhuo & Li, Yuming & Wong, Wing-Keung, 2008. "Policy change and lead-lag relations among China's segmented stock markets," Journal of Multinational Financial Management, Elsevier, vol. 18(3), pages 276-289, July.
    22. Ella Mae Matsumura & Kam†Wah Tsui & Wing†Keung Wong, 1990. "An extended multinomial†Dirichlet model for error bounds for dollar†unit sampling," Contemporary Accounting Research, John Wiley & Sons, vol. 6(2), pages 485-500, March.
    23. Zhidong Bai & Hua Li & Huixia Liu & Wing‐Keung Wong, 2011. "Test statistics for prospect and Markowitz stochastic dominances with applications," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 278-303, July.
    24. Wing-keung Wong & Raymond Chan, 2004. "On the estimation of cost of capital and its reliability," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 365-372.
    25. Bai, Zhidong & Wong, Wing-Keung & Zhang, Bingzhi, 2010. "Multivariate linear and nonlinear causality tests," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 5-17.
    26. Fong, Wai Mun & Lean, Hooi Hooi & Wong, Wing Keung, 2008. "Stochastic dominance and behavior towards risk: The market for Internet stocks," Journal of Economic Behavior & Organization, Elsevier, vol. 68(1), pages 194-208, October.
    27. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2010. "Market Efficiency of Oil Spot and Futures: A Stochastic Dominance Approach," CARF F-Series CARF-F-201, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    28. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    29. Harvey, Campbell R. & Zhou, Guofu, 1993. "International asset pricing with alternative distributional specifications," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 107-131, June.
    30. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    31. Chan, Chia-Ying & de Peretti, Christian & Qiao, Zhuo & Wong, Wing-Keung, 2012. "Empirical test of the efficiency of the UK covered warrants market: Stochastic dominance and likelihood ratio test approach," Journal of Empirical Finance, Elsevier, vol. 19(1), pages 162-174.
    32. Broll, Udo & Egozcue, Martín & Wong, Wing-Keung & Zitikis, Ričardas, 2010. "Prospect theory and hedging risks," Dresden Discussion Paper Series in Economics 05/10, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    33. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    34. Ma, Chenghu & Wong, Wing-Keung, 2010. "Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR," European Journal of Operational Research, Elsevier, vol. 207(2), pages 927-935, December.
    35. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, vol. 13(1), pages 89-101.
    36. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    37. Pettit, R. Richardson & Westerfield, Randolph, 1974. "Using the Capital Asset Pricing Model and the Market Model to Predict Security Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(4), pages 579-605, September.
    38. Qiao, Zhuo & Smyth, Russell & Wong, Wing-Keung, 2008. "Volatility switching and regime interdependence between information technology stocks 1995-2005," Global Finance Journal, Elsevier, vol. 19(2), pages 139-156.
    39. Li, Tong & Hsiao, Cheng, 2004. "Robust estimation of generalized linear models with measurement errors," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 51-65.
    40. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    41. Wong, Wing-Keung & Li, Chi-Kwong, 1999. "A note on convex stochastic dominance," Economics Letters, Elsevier, vol. 62(3), pages 293-300, March.
    42. Zhidong Bai & Yongchang Hui & Wing-Keung Wong & Ričardas Zitikis, 2012. "Prospect Performance Evaluation: Making a Case for a Non-asymptotic UMPU Test," Journal of Financial Econometrics, Oxford University Press, vol. 10(4), pages 703-732, September.
    43. Blume, Marshall E, 1975. "Betas and Their Regression Tendencies," Journal of Finance, American Finance Association, vol. 30(3), pages 785-795, June.
    44. Wong, Wing-Keung & Bian, Guorui, 2005. "Estimating parameters in autoregressive models with asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 61-70, January.
    45. Qiao, Zhuo & McAleer, Michael & Wong, Wing-Keung, 2009. "Linear and nonlinear causality between changes in consumption and consumer attitudes," Economics Letters, Elsevier, vol. 102(3), pages 161-164, March.
    46. Thomas C. Chiang & Zhuo Qiao & Wing-Keung Wong, 2010. "New evidence on the relation between return volatility and trading volume," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(5), pages 502-515.
    47. Clements, Michael P. & Hendry, David F., 1997. "An empirical study of seasonal unit roots in forecasting," International Journal of Forecasting, Elsevier, vol. 13(3), pages 341-355, September.
    48. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2012. "Stochastic Dominance And Behavior Towards Risk: The Market For Ishares," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-20.
    49. Wong, Wing-keung & Miller, Robert B, 1990. "Repeated Time Series Analysis of ARIMA-Noise Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 243-250, April.
    50. Lam, Kin & Liu, Taisheng & Wong, Wing-Keung, 2010. "A pseudo-Bayesian model in financial decision making with implications to market volatility, under- and overreaction," European Journal of Operational Research, Elsevier, vol. 203(1), pages 166-175, May.
    51. M. Qamarul Islam & Moti Tiku, 2010. "Multiple linear regression model with stochastic design variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 923-943.
    52. Qiao, Zhuo & Chiang, Thomas C. & Wong, Wing-Keung, 2008. "Long-run equilibrium, short-term adjustment, and spillover effects across Chinese segmented stock markets and the Hong Kong stock market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(5), pages 425-437, December.
    53. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
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    More about this item

    Keywords

    G1; capital asset pricing model; maximum likelihood estimators; modified maximum likelihood estimators; robustness; student t family;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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