This research examines the alternative ways of estimating the coefficient of non-diversifiable risk, namely beta coefficient, in Capital Asset Pricing Model (CAPM) introduced by Sharpe (1964) that is an essential element of assessing the value of diverse assets. The nonparametric methods used in this research are the robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MMestimator). The Jackknife, the resampling technique, is also employed to validate the results. According to finance literature and common practices, these coecients have often been estimated using Ordinary Least Square (LS) regression method and monthly return data set. The empirical results of this research pointed out that the robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MM-estimator) performed much better than Ordinary Least Square (LS) in terms of eciency for large-cap stocks trading actively in the United States markets. Interestingly, the empirical results also showed that daily return data would give more accurate estimation than monthly return data in both Ordinary Least Square (LS) and robust Least Trimmed Square (LTS) and Maximum likelihood type of Mestimator (MM-estimator) regressions.

Abstract
 1. Introduction
 2. Literature Review
 3. Data Description and Empirical Results
  3.1. Beta estimates with robust MM and LSmethods with daily data.
  3.2. Beta estimates with robust MM, LTS and LSmethods with monthly vs. daily data.
 4. Jackknife Methodology and Efficiencyof Estimators
 5. Conclusions
 References

• Le Tan Phuoc(Becamex Business School, Eastern International University) Corresponding Author
• Kee S. Kim(Finance and General Business Department Missouri State University)
• Yingcai Su(Mathematics Department, Missouri State University)