This research examined the alternatives of Jensen’s alpha (α) estimation models in the Capital Asset Pricing Model, discussed by Treynor (1961), Sharpe (1964), and Lintner (1965), using the robust maximum likelihood type m-estimator (MM estimator) and Bayes estimator with conjugate prior. According to finance literature and practices, alpha has often been estimated using ordinary least square (OLS) regression method and monthly return data set. A sample of 50 securities is randomly selected from the list of the S&P 500 index. Their daily and monthly returns were collected over a period of the last five years. This research showed that the robust MM estimator performed well better than the OLS and Bayes estimators in terms of efficiency. The Bayes estimator did not perform better than the OLS estimator as expected. Interestingly, we also found that daily return data set would give more accurate alpha estimation than monthly return data set in all three MM, OLS, and Bayes estimators. We also proposed an alternative market efficiency test with the hypothesis testing Ho: α = 0 and was able to prove the S&P 500 index is efficient, but not perfect. More important, those findings above are checked with and validated by Jackknife resampling results.

Abstract
 1. Introduction
 2. Literature Review
 3. Data Description and Empirical Results
  3.1. The Kolmogorov-Smirnov Goodness-of-FitTests
  3.2. The Daily versus Monthly Alpha Estimateand Standard Deviation with OLS, MM, andBayes Estimators.
  3.3. Daily Alpha Estimate and Standard Deviationwith the Three OLS, MM, and BayesEstimators
  3.4. The Market Efficiency Test
  3.5. The Jackknife Resampling MethodologyResults
 4. Conclusions
 References

• Le Tan Phuoc(Becamex Business School, Eastern International University) Corresponding Author