Let it be the asset j's return, rft the risk-free rate, and rmt the market return at time t. SMB and HML measure the excess returns on small capitalization (caps) stocks over big caps and on value stocks over growth stocks respectively. Consider an OLS regression: rjt rft = ; + m(rmt t) + SMB + HML + jt a. Explain the inclusion of the SMB and HML factors in the above model. (30%) b. If the estimated alpha is statistically different from zero, is the APT true or not? (30%) C. Assume we have N stocks, if we use OLS regressions to estimate alphas and betas for each of the N stocks what can we say about the alpha, betas, and idiosyncratic risk of an equally weighted portfolio? (Hint: consider a portfolio P such that 'pt - ft = wj (rjt Yft) where w, is the weight of asset j in the portfolio P.) (40%) Let it be the asset j's return, rft the risk-free rate, and rmt the market return at time t. SMB and HML measure the excess returns on small capitalization (caps) stocks over big caps and on value stocks over growth stocks respectively. Consider an OLS regression: rjt rft = ; + m(rmt t) + SMB + HML + jt a. Explain the inclusion of the SMB and HML factors in the above model. (30%) b. If the estimated alpha is statistically different from zero, is the APT true or not? (30%) C. Assume we have N stocks, if we use OLS regressions to estimate alphas and betas for each of the N stocks what can we say about the alpha, betas, and idiosyncratic risk of an equally weighted portfolio? (Hint: consider a portfolio P such that 'pt - ft = wj (rjt Yft) where w, is the weight of asset j in the portfolio P.) (40%)