Skip to main content
Article thumbnail
Location of Repository

Robust Estimation and Forecasting of the Capital Asset Pricing Model

By Guorui Bian, Michael McAleer and Wing-Keung Wong


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.Maximum likelihood estimators; Modified maximum likelihood estimators; Student t family; Capital asset pricing model; Robustness

OAI identifier:

Suggested articles


  1. 1965b, Portfolio analysis in a stable Paretian market,
  2. (1992). A new method of estimation for location and scale parameters.
  3. A new pseudo Bayesian model with implications to financial anomalies and investors' behaviors,
  4. (1999). A note on convex stochastic dominance theory.
  5. A pseudo-Bayesian model in financial decision making with implications to market volatility, under- and overreaction,
  6. (1963). A simplified model for portfolio analysis.
  7. (1973). A subordinated stochastic process model with finite variance for speculative prices.
  8. (1989). A test of efficiency of a given portfolio,
  9. (1997). An alternative approach to estimate regression coefficients.
  10. (1997). An empirical study of seasonal unit roots in forecasting.
  11. (1990). An extended multinomial-Dirichlet model for error bounds for dollar-unit sampling,
  12. (1990). Analysis of ARIMA-noise models with repeated time series.
  13. (1997). Bayesian inference based on robust priors and MML estimators: Part I, symmetric location-scale distributions.
  14. (1975). Betas and their regressions tendencies.
  15. (1972). Biometrika Tables for Statisticians, Vol II:
  16. (2001). Can P/E ratio and bond yield be used to beat stock markets?,
  17. (1989). Consistent estimation for some nonlinear errors-in-variables models.
  18. (2006). Elasticity of risk aversion and international trade,
  19. (1989). Empirical tests of the consumption based on CAPM,
  20. (1999). Estimating parameters in autoregressive models in non-normal situations: Symmetric innovations.
  21. (2005). Estimating parameters in autoregressive models with asymmetric innovations.
  22. (1968). Estimating the parameters of log-normal distribution from censored samples.
  23. (2004). Estimation of cross sectional and panel data censored regression models with endogeneity.
  24. (1966). Evaluation of the maximum likelihood estimator where the likelihood equation has multiple roots.
  25. (1999). Extension of stochastic dominance theory to random variables.
  26. (1982). Factors in New York Stock Exchange security returns,
  27. (2010). Gains from diversification: A majorization and stochastic dominance approach.
  28. Gonedes, N.J.,1974. A comparison of stable and student distribution as statistical models for stock prices,
  29. (2003). How rewarding is technical analysis? Evidence from Singapore stock market,
  30. (1985). Instrumental variable estimator for the nonlinear errors-in-variables model.
  31. (1993). International asset pricing with alternative distributional specifications,
  32. (2009). Linear and nonlinear causality between changes in consumption and consumer attitudes,
  33. (2008). Long-run equilibrium, short-term adjustment, and spillover effects across Chinese segmented stock markets,
  34. (1963). Mandelbrot and the stable Paretian hypothesis.
  35. (2009). Mapping the Presidential Election Cycle
  36. (2010). Market efficiency of oil spot and futures: A mean-variance and stochastic dominance approach,
  37. (2008). Markowitz and prospect stochastic dominances.
  38. (1998). Misclassification of the dependent variable in a discrete-response setting.
  39. (1984). Models of stock returns - a comparison.
  40. (1970). Monte Carlo study of some simple estimators in censored normal samples.
  41. (2005). Multiple linear regression model under nonnormality,
  42. (2010). Multiple linear regression model with stochastic design variables,
  43. (2010). Multivariate linear and non-linear causality tests,
  44. (2009). New evidence on the relation between return volatility and trading volume,
  45. (2001). Non-normal regression, II: Symmetric distributions.
  46. (1980). On estimating the scale parameters of the Rayleigh distribution from doubly censored samples.
  47. (2008). On testing the equality of the multiple Sharpe ratios, with application on the evaluation of IShares,
  48. On the Markowitz mean-variance analysis of self-financing portfolios. Risk and Decision Analysis,
  49. (1971). On the short term stationarity of Beta coefficient.
  50. (1992). On the Tiku-Suresh method of estimation.
  51. (1991). On the unavoidability of ‘unscientific’ judgment in estimating the cost of capital,
  52. (1985). On Tiku's robust procedure - a Bayesian insight.
  53. (1966). Order statistics estimators of the location of the Cauchy distribution.
  54. (2008). Policy change and lead-lag relations among China’s segmented stock markets,
  55. (2008). Preferences over Meyer’s location-scale family.
  56. (1991). Price and volume in the Tokyo stock exchange: An exploratory study,
  57. (2010). Prospect theory, indifference curves, and hedging risks,
  58. (1996). Revisiting ‘dividend yield plus growth’ and its applicability,
  59. (2000). Robust Bayesian inference in asset pricing estimation,
  60. (2004). Robust estimation of generalized linear models with measurement errors.
  61. (1986). Robust Inference.
  62. (1990). Robust Regression.
  63. (1981). Robust Statistics.
  64. (1983). Stable distributions and mixtures of distributions hypotheses for common stock return,
  65. (2008). Stochastic dominance analysis of Asian hedge funds.
  66. (2007). Stochastic dominance analysis of iShares,
  67. (2009). Stochastic Dominance and Applications to Finance, Risk and Economics, Chapman and Hall/CRC, Taylor and Francis,
  68. (2008). Stochastic dominance and behavior towards risk: the market for internet stocks.
  69. (2007). Stochastic dominance and mean-variance measures of profit and loss for business planning and investment.
  70. (2010). Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR,
  71. (2005). Stochastic dominance and the rationality of the momentum effect across markets,
  72. (1995). Temporal aggregation of GARCH processes,
  73. (1979). The Advanced Theory of Statistics. Charles Gri.n,
  74. (1985). The asymptotics of maximum likelihood and related estimators based on Type II censored data.
  75. (1965). The behaviour of stock market prices,
  76. (2004). The estimation of the cost of capital and its reliability.
  77. (1994). The exact values of the expected values, variances, and covariances of order statistics from the Cauchy distribution.
  78. (2006). The modified mixture of distributions model: A revisit,
  79. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets.
  80. (1973). Three parameter lognormal estimation from censored data.
  81. (2000). Time series models with nonnormal innovations: Symmetric location-scale distributions.
  82. (1986). Truncated and censored samples from normal populations.
  83. (1974). Using the capital asset pricing model and returns.
  84. (2008). Volatility switching and regime interdependence between information technology stocks 1995-2005,
  85. Wong (2009a). Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.