Your friend tells you he is a great stock picker, and touts his high returns. You decide to investigate his claims by compiling his past choices into a portfolio of returns and running some diagnostics. You run two regressions: one, a CAPM regression where you regress the monthly excess return of the portfolio (Rp - Rf where Rf is the risk-free rate) on the excess returns of the market (Mkt - Rf), as well as a three factor regression where the portfolio excess returns are regressed on the excess returns of the market as well as the SMB and HML portfolios from Ken French's website. Results for the two regressions are presented below: Coefficients Standard Error CAPM Intercept Mkt - Ri -0.012 0.004 1.042 0.098 Fama-French 3F Intercept Mkt - RJ SMB HML Coefficients Standard Error 0.013 0.0037 1.042 0.098 -0.254 0.076 -0.474 0.086 a. Can you reject the null hypothesis that the market beta of your friend's portfolio equals to 1? Can you reject the null hypothesis that the size beta of your friend's portfolio equals to 0? The value beta of your friend's portfolio equals to 0? b. What type of securities does your friend appear to invest in? c. Does your friend appear to be good stock picker relative to the CAPM? What about relative to the Fama-French model? If the answers are to both questions are the same, does this surprise you? If the answers are different, what might account for the difference? d. Suppose you want to have the same exposure to the Fama-French 3 factors as your friend's portfolio (the market, SMB, and HML). Assuming you have $100,000 to invest, how would you invest your money? How is your replica fund likely to be compared to your friend's in terms of Fama-French alpha? Please explain. Your friend tells you he is a great stock picker, and touts his high returns. You decide to investigate his claims by compiling his past choices into a portfolio of returns and running some diagnostics. You run two regressions: one, a CAPM regression where you regress the monthly excess return of the portfolio (Rp - Rf where Rf is the risk-free rate) on the excess returns of the market (Mkt - Rf), as well as a three factor regression where the portfolio excess returns are regressed on the excess returns of the market as well as the SMB and HML portfolios from Ken French's website. Results for the two regressions are presented below: Coefficients Standard Error CAPM Intercept Mkt - Ri -0.012 0.004 1.042 0.098 Fama-French 3F Intercept Mkt - RJ SMB HML Coefficients Standard Error 0.013 0.0037 1.042 0.098 -0.254 0.076 -0.474 0.086 a. Can you reject the null hypothesis that the market beta of your friend's portfolio equals to 1? Can you reject the null hypothesis that the size beta of your friend's portfolio equals to 0? The value beta of your friend's portfolio equals to 0? b. What type of securities does your friend appear to invest in? c. Does your friend appear to be good stock picker relative to the CAPM? What about relative to the Fama-French model? If the answers are to both questions are the same, does this surprise you? If the answers are different, what might account for the difference? d. Suppose you want to have the same exposure to the Fama-French 3 factors as your friend's portfolio (the market, SMB, and HML). Assuming you have $100,000 to invest, how would you invest your money? How is your replica fund likely to be compared to your friend's in terms of Fama-French alpha? Please explain
