Consider a Fama-MacBeth regression for investigating which factors are important in generating excess returns. In the first stage, the excess returns for a portfolio are regressed against excess market returns, a factor for size of portfolio and a factor for the value of portfolio. In the second stage the effect of the estimated market beta, size factor and value factors are regressed against the mean excess return for the portfolio. The two stages are represented as below

a. Identify, using the notation above, and provide an explanation for each of the following terms in these regressions i. Excess portfolio returns ii. iii. iv. and

b. The results of the second stage regression using 4 different methods of forming the factors for size and value are presented in Table 4.1 below. Provide explanation on what is different and what is similar amongst the 4 different methods. What conclusions can you draw from these different estimations?

c. If these were the results from your project what steps might you consider taking next?

Rp.t Rp,t = ap + B(Rm,t Rp.t) + s * Sizet + h Valuet + t Rp.t p,t = 1p + 1p + 19$ + in + Ut *** Table 4.1: Results from estimating second stage regression with 4 different methods of forming factors for size and value. (p-values are in parentheses). *** significant at 1 percent, ** significant at 5%, * significant at 10%. Method 1 Method 2 Method 3 Method 4 lp 0.0067 0.0116** 0.0098*** -0.0029 (0.2199) (0.0288) (0.0485) (0.4775) -0.0034 -0.0085* -0.0067** 0.0042 (0.5043) (0.0641) (0.1215) (0.2504) 0.0014* 0.0016* 0.0015*** 0.0004 (0.0000) (0.0000) (0.0001) (0.1401) -0.0019*** -0.0019*** -0.0020*** -0.0021*** (0.0000) (0.0000) (0.0000) (0.0000) R-squared 0.45 0.46 0.48 0.39 Jacque-Bera test 2B h Rp.t Rp,t = ap + B(Rm,t Rp.t) + s * Sizet + h Valuet + t Rp.t p,t = 1p + 1p + 19$ + in + Ut *** Table 4.1: Results from estimating second stage regression with 4 different methods of forming factors for size and value. (p-values are in parentheses). *** significant at 1 percent, ** significant at 5%, * significant at 10%. Method 1 Method 2 Method 3 Method 4 lp 0.0067 0.0116** 0.0098*** -0.0029 (0.2199) (0.0288) (0.0485) (0.4775) -0.0034 -0.0085* -0.0067** 0.0042 (0.5043) (0.0641) (0.1215) (0.2504) 0.0014* 0.0016* 0.0015*** 0.0004 (0.0000) (0.0000) (0.0001) (0.1401) -0.0019*** -0.0019*** -0.0020*** -0.0021*** (0.0000) (0.0000) (0.0000) (0.0000) R-squared 0.45 0.46 0.48 0.39 Jacque-Bera test 2B h