Bian, Guorui and McAleer, Michael and Wong, WingKeung (2012) Robust Estimation and Forecasting of the Capital Asset Pricing Model. [ Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE); nº 09, 2012, ] (Unpublished)

PDF
Creative Commons Attribution Noncommercial. 175kB 
Official URL: http://eprints.ucm.es/15059/
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 onestepahead forecast mean square error in small samples.
Item Type:  Working Paper or Technical Report 

Additional Information:  The third author would like to thank Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. For financial support, the first author is grateful to East China Normal University, the second author acknowledges the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science, and the third author wishes to acknowledge Hong Kong Baptist University. 
Uncontrolled Keywords:  Maximum likelihood estimators; Modified maximum likelihood estimators; Student family; Capital asset pricing model; Robustness. 
Subjects:  Social sciences > Economics > Econometrics 
JEL:  C1, C2, G1 
Series Name:  Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE) 
Volume:  2012 
Number:  09 
ID Code:  15059 
References: 
Amemiya, Y., 1985. Instrumental variable estimator for the nonlinear errorsinvariables model. Journal of Econometrics 28, 273–290. Bai, Z.D., Lui, Y.C., Wong, W.K., Zitikis, R., 2012. Evaluating Prospect Performance: Making a Case for a NonAsymptotic UMPU Test, Journal of Financial Econometrics, (forthcoming). Bai, Z.D., Li, H., Liu, H.X., Wong, W.K., 2011. Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications, Econometrics Journal 14(2), 278303. Bai, Z.D., Liu, H.X., Wong, W.K., 2009. Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory. Mathematical Finance 19(4), 639667. Bai, Z.D., Liu, H.X., Wong, W.K., 2011. Asymptotic properties of eigenmatrices of a large sample covariance matrix. Annals of Applied Probability 21(5), 1994–2015. Bai, Z.D., Wong, W.K., Zhang, B. 2010. Multivariate linear and nonlinear causality tests. Mathematics and Computers in Simulation 81, 5–17. Barnett, V.D., 1966a. Evaluation of the maximum likelihood estimator where the likelihood equation has multiple roots. Biometrika 53, 151165. Barnett, V.D. 1966b. Order statistics estimators of the location of the Cauchy distribution. Journal of the American Statistical Association 61, 12051218. Bhattacharyya, G.K., 1985. The asymptotics of maximum likelihood and related estimators based on Type II censored data. Journal of the American Statistical Association 80, 398404. Bian, G., Tiku, L.M., 1997. Bayesian inference based on robust priors and MML estimators: Part I, symmetric locationscale distributions. Statistics 29, 317345. Bian, G., Wong, W.K., 1997. An alternative approach to estimate regression coefficients. Journal of Applied Statistical Science 6, 2144. Blattberg, R.C., Gonedes, N.J., 1974. A comparison of stable and student distribution as statistical models for stock prices. Journal of Business 47, 244280. Blume, M.E., 1975. Betas and their regressions tendencies. Journal of Finance 30, 785795. Breeden, D.T., Gibbons M., Litzenberger, R.H., 1989. Empirical tests of the consumption based on CAPM. Journal of Finance 44, 231262. Broll, U., Egozcue, M., Wong, W.K., Zitikis, R., 2010. Prospect theory, indifference curves, and hedging risks. Applied Mathematics Research Express 2010(2), 142–153. Broll, U., Wahl, J.E., Wong, W.K.. 2006. Elasticity of risk aversion and international trade. Economics Letters 91(1), 126130. Chan, C.Y., de Peretti, C., Qiao, Z., Wong, W.K., 2012. Empirical Test of the Efficiency of UK Covered Warrants Market: Stochastic Dominance and Likelihood Ratio Test Approach, Journal of Empirical Finance 19(1), 162174. Chiang, T.C., Qiao, Z., Wong, W.K., 2009. New evidence on the relation between return volatility and trading volume. Journal of Forecasting 29(5), 502 – 515. Clark, P.K., 1973. A subordinated stochastic process model with finite variance for speculative prices. Econometrica 37, 135155. Clements, M.P., Hendry, D.F., 1997. An empirical study of seasonal unit roots in forecasting. International Journal of Forecasting 13, 341355. Drost, F.C., Nijman, T.E., 1995. Temporal aggregation of GARCH processes, in Engle, R.F., ed. ARCH: Selected Readings, Oxford University Press. Egozcue, M., Wong, W.K., 2010. Gains from diversification: A majorization and stochastic dominance approach. European Journal of Operational Research 200, 893–900. Fama, E.F., 1963. Mandelbrot and the stable Paretian hypothesis. Journal of Business 36, 420429. Fama, E.F., 1965a. The behaviour of stock market prices. Journal of Business 38, 34105. Fama, E.F., 1965b. Portfolio analysis in a stable Paretian market. Management Science 11, 401419. Fielitz, B.D., Rozelle, J.P., 1983. Stable distributions and mixtures of distributions hypotheses for common stock return. Journal of the American Statistical Association 78, 2836. Fong, W.M., Lean, H.H., Wong, W.K., 2008. Stochastic dominance and behavior towards risk: the market for internet stocks. Journal of Economic Behavior and Organization 68(1), 194208. Fong, W.M., Wong, W.K., 2006. The modified mixture of distributions model: A revisit. Annals of Finance 2(2), 167 – 178. Fong, W.M., Wong, W.K., Lean, H.H., 2005. Stochastic dominance and the rationality of the momentum effect across markets. Journal of Financial Markets 8, 89109. Gasbarro, D., Wong, W.K., Zumwalt, J.K., 2007. Stochastic dominance analysis of iShares. European Journal of Finance 13, 89–101. Gasbarro, D., Wong, W.K., Zumwalt, J.K., 2012. Stochastic Dominance and Behavior towards Risk: The Market for iShares, Annals of Financial Economics 7(1), (forthcoming). Gibbons, M.R., Ross, S.A., Shanken, J., 1989. A test of efficiency of a given portfolio. Econometrica 57, 11211152. Harvey, M.C., Zhou, G., 1993. International asset pricing with alternative distributional specifications. Journal of Empirical Finance 1, 107131. Hausman, J.A., Abrevaya, J., ScottMorton, F.M., 1998. Misclassification of the dependent variable in a discreteresponse setting. Journal of Econometrics 87, 237269. Honor, B.E., Hu, L.J., 2004. Estimation of cross sectional and panel data censored regression models with endogeneity. Journal of Econometrics 122, 293316. Hsiao, C., 1989. Consistent estimation for some nonlinear errorsinvariables models. Journal of Econometrics 41, 159–185. Huber, P.J., 1981. Robust Statistics. Wiley, New York. Islam, M.Q., Tiku, M.L., 2005. Multiple linear regression model under nonnormality. Communications in Statistics  Theory and Methods 33(10), 24432467. Islam, M.Q., Tiku, M.L. 2010. Multiple linear regression model with stochastic design variables. Journal of Applied Statistics 37(6), 923  943. Kendall, M.G. Stuart, A., 1979. The Advanced Theory of Statistics. Charles Gri.n, London. Kon, S.J., 1984. Models of stock returns  a comparison. Journal of Finance 39, 147165. Lam, K., Liu, T., Wong, W.K. 2010. A pseudoBayesian model in financial decision making with implications to market volatility, under and overreaction. European Journal of Operational Research 203(1), 166175. Lam, K., Liu, T., Wong, W.K. 2012. A New Pseudo Bayesian Model with Implications to Financial Anomalies and Investors’ Behaviors, Journal of Behavioral Finance, (forthcoming). Lawrence, K.D., Arthur, J.L., 1990. Robust Regression. Marcel Dekker, New York. Leavy, R.A., 1971. On the short term stationarity of Beta coefficient. Financial Analysis Journal 27, 5562. Lean, H.H., McAleer, M., Wong, W.K., 2010. Market efficiency of oil spot and futures: A meanvariance and stochastic dominance approach. Energy Economics 32, 979–986. Lee, K.R., Kapadia, C.H., Dwight, B.B., 1980. On estimating the scale parameters of the Rayleigh distribution from doubly censored samples. Statistical Papers 21(1), 1429. Leung, P.L., Wong, W.K., 2008. On testing the equality of the multiple Sharpe ratios, with application on the evaluation of IShares. Journal of Risk 10(3), 116. Li, C.K., Wong, W.K., 1999. Extension of stochastic dominance theory to random variables. RAIRO Recherche Opérationnelle 33(4), 509524. Li, T., Hsiao, C., 2004. Robust estimation of generalized linear models with measurement errors. Journal of Econometrics 118, 51–65. Lintner, J., 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47, 1337. Ma, C., Wong, W.K., 2010. Stochastic dominance and risk measure: A decisiontheoretic foundation for VaR and CVaR. European Journal of Operational Research 207, 927935. Matsumura, E.M., Tsui, K.W., Wong, W.K., 1990. An extended multinomialDirichlet model for error bounds for dollarunit sampling. Contemporary Accounting Research 6(2I), 485500. Pearson, E.S., Hartley, H.O, 1972. Biometrika Tables for Statisticians, Vol II: University Press, Cambridge. Pettit, R.R., Westerfield, R., 1974. Using the capital asset pricing model and returns. Journal of Financial and Quantitative Analysis 9, 579605. Qiao, Z., McAleer, M., Wong, W.K., 2 009. Linear and nonlinear causality between changes in consumption and consumer attitudes. Economics Letters 102(3), 161–164. Qiao, Z., Smyth, R., Wong, W.K., 2008. Volatility switching and regime interdependence between information technology stocks 19952005. Global Finance Journal 19, 139156. Schneider, H., 1986. Truncated and censored samples from normal populations. New York Marcel Dekker. Sharpe, W., 1963. A simplified model for portfolio analysis. Management Science 9, 277293. Sharpe, W., 1982. Factors in New York Stock Exchange security returns, 19311979. Journal of Portfolio Management 8, 519. Smith, W.B., Zeis, C.D., Syler, G.W., 1973. Three parameter lognormal estimation from censored data. Journal of Indian Statistical Association 11, 1531. Tan, W.Y., 1985. On Tiku's robust procedure  a Bayesian insight. Journal of Statistical Planning and Inference 11, 329340. Thompson, H E, Wong, W.K., 1991. On the unavoidability of ‘unscientific’ judgment in estimating the cost of capital. Managerial and Decision Economics 12, 2742. Thompson, H E, Wong, W.K., 1996. Revisiting ‘dividend yield plus growth’ and its applicability. Engineering Economist 41(2), 123147. Tiku, M.L., 1968. Estimating the parameters of lognormal distribution from censored samples. Journal of the American Statistical Association 63, 134140. Tiku, M.L., 1970. Monte Carlo study of some simple estimators in censored normal samples. Biometrika 57, 207211. Tiku, M.L., Islam, M.Q., Selcuk, A.S., 2001. Nonnormal regression, II: Symmetric distributions. Communications in Statistics: Theory and Methods 30, 10211045. Tiku, M.L., Suresh, R.D., 1992. A new method of estimation for location and scale parameters. Journal of Statistical Planning and Inference 30, 281292. Tiku, M.L., Tan, W.Y., Balakrishnan, N., 1986. Robust Inference. Marcel Dekker, New York. Tiku, M.L., Wong, W.K., Bian, G., 1999. Estimating parameters in autoregressive models in nonnormal situations: Symmetric innovations. Communications in Statistics: Theory and Methods 28(2), 315341. Tiku, M.L., Wong, W.K., Vaughan, D.C., Bian, G., 2000. Time series models with nonnormal innovations: Symmetric locationscale distributions. Journal of Time Series Analysis 21(5), 571596. Tse, Y.K., 1991. Price and volume in the Tokyo stock exchange: An exploratory study, in Ziemba, W., Bailey, T., Hamao, W., (eds.). Japanese Financial Market Research, 91119. Vaughan, D.C., 1992. On the TikuSuresh method of estimation. Communications in Statistics: Theory and Methods 21, 451469. Vaughan, D.C., 1994. The exact values of the expected values, variances, and covariances of order statistics from the Cauchy distribution. Journal of Statistical Computation and Simulation 49, 2132. Wong, W.K., 2007. Stochastic dominance and meanvariance measures of profit and loss for business planning and investment. European Journal of Operational Research 182, 829843. Wong, W.K., Bian, G., 2000. Robust Bayesian inference in asset pricing estimation, Journal of Applied Mathematics and Decision Sciences 4(1), 6582. Wong, W.K., Bian, G., 2005. Estimating parameters in autoregressive models with asymmetric innovations. Statistics and Probability Letters 71, 6170. Wong, W.K., Chan, R., 2004. The estimation of the cost of capital and its reliability. Quantitative Finance 4(3), 365372. Wong, W.K., Chan, R., 2008. Markowitz and prospect stochastic dominances. Annals of Finance 4(1), 105129. Wong, W.K., Chew, B.K., Sikorski, D., 2001. Can P/E ratio and bond yield be used to beat stock markets? Multinational Finance Journal 5(1), 5986. Wong, W.K., Li, C.K., 1999. A note on convex stochastic dominance theory. Economics Letters 62, 293300. Wong, W.K., Ma, C., 2008. Preferences over Meyer’s locationscale family. Economic Theory 37(1), 119146. Wong, W.K., McAleer, M., 2009. Mapping the presidential election cycle in US stock markets. Mathematics and Computers in Simulation 79(11), 32673277. Wong, W.K., Miller, R.B., 1990. Analysis of ARIMAnoise models with repeated time series. Journal of Business and Economic Statistics 8(2), 243250. Wong, W.K., Phoon, K.F., Lean, H.H., 2008. Stochastic dominance analysis of Asian hedge funds. PacificBasin Finance Journal 16(3), 204223. 
Deposited On:  27 Apr 2012 12:15 
Last Modified:  17 Jun 2016 09:28 
Repository Staff Only: item control page