Question 1 An investor models the returns of a mutual fund via a linear regression model using FamaFrench (1993) factors as explanatory variables. The sample size is 100 observations, the residual sum of squares is 5, and the explained sum of squares is 10. The level of significance is 5%.

i. Write down the regression model which uses Fama-French (1993) factors as explanatory variables and define the variables.

ii. What is the formula, in matrix notation, which provides the ordinary least squares estimators for the model? Define the dimensions of the vectors and matrices appearing in the formula. iii. How would you test the statistical significance of each one of the regressors on a stand-alone basis? In which case would you reject the null hypothesis of no significance? iv. Calculate the F-statistic to assess the null hypothesis of no significance of the regressors. In which case would you reject the null hypothesis? v. Define Fama-French (1993) alpha and explain how you would test whether a mutual fund delivers a positive Fama-French (1993) alpha