time series - Choosing the right statistical test for Mutual Fund Performance Evaluation

I would like to perform a statistical test to check if:

• the aggregate alpha of all funds equals 0.


• the aggregate beta of all funds equals 1.

• Sample of 1000 mutual funds over the period 1990 to 2017. I regress funds monthly excess return over the risk free rate against the Carhart (1997) four factor model.

Since I individually regress funds over the risk parameters. Now I have 1000 alpha, 1000 beta,...

• I individually regress each funds excess return against the risk factors; and store the regression coefficients (alpha, beta, smb, hml, and mom) and their standard errors to calculate the t-statistic of coefficients.