Abstract: The effects of investment horizon on the estimate of the systematic risk are first investigated by Brennan et al,(2012). In general, the true investment horizon is unknown. The empirical work will overestimate the coefficient of the systematic risk based on the observed horizon. The copula Bayesian estimation approach is proposed to get the posterior distribution of the coefficients of the system risk beta and the investment horizon ratio gama in the Fama-French three factor model. The potent problem of the traditional Bayesian estimation is that the assumption of normal likelihood function ignores some fluctuations such as high peak and fat tail relative to kurtosis and skewness, which have been frequently, reported in financial data analyses. The copula Bayesian approach instead of the traditional Bayesian estimation is built to consider the pattern of the data with the strong correlation and the non-normal distributions. The reason why the copula function is chosen is to fit the pattern of the data. In the empirical work,the interaction of the system risk and the investment horizon is analyzed in 25 portfolios from 150 different data. Compared with the U.S. data, the correlation of the systemic risk and investment horizon is negative, and the frequency of the true horizon is higher than observed one in China. With the increase of the size of the company, the effect of the investment horizon is obviously magnified. And the appearance leads to the estimation bias of the systemic risk.

Key words: investment horizon, system risk Beta, Copula Bayesian, FF-three factor model