3. Suppose we construct a portfolio according to the Fama-French three- factor model and the five-factor model. Historical monthly returns in percentage for each portfolio are reported in the table below. Size Book-to Market 1 (Small) 1.45 1 (Growth) 0.67 1 (Loser) 0.59 1 (Illiquid) 1.41 2 1.36 2 0.72 2 0.68 2 1.35 3 4 1.28 1.15 3 4 0.80 0.84 3 4 0.74 0.83 3 4 1.241.13 5 1.03 5 0.92 5 0.96 5 1.04 6 0.95 6 1.02 6 1.10 6 0.96 7 8 9 0.87 0.74 0.65 7 8 9 1.13 1.22 1.34 7 8 9 1.17 1.28 1.33 7 8 9 0.88 0.79 0.68 10 (Large) 0.62 10 (Value) 1.44 10(Winner) 1.42 10 (Liquid) 0.62 Momentum Liquidity. Define size premium as the difference between historical average returns of the bottom 50% (small) stocks and that of the top 50% (large) stocks. Define value premium as the difference between historical average returns of stocks that fall into the top 30% book- to-market ratio and those that fall into the bottom 30% book-to- market ratio. Based on the information provided, calculate the size premium (SMB) and value premium (HML). (20 Marks) (b) Suppose the estimated three-factor model for stock is as follows: nj - r = a + 1.2 x (T-1) + 0.5 XSMB + 0.7 X HML In addition to the result from part (a), we further know that risk-free rate () is 3%, the market return (rm) is 3.8%, and the stock return (n) is 5.5%. Calculate the excess return a in that month. (15 Marks) (c) Suppose the estimated five-factor model is as follows: n r = a + 1.2 x (Mr ) + 0.5 XSMB +0.7 X HML + 0.3 X MOM +0.4 X LIQ Given that the monthly historical return on momentum factor (MOM) is 0.4%, the monthly historical return on liquidity factor (LIQ) is 0.5%, and the other values are the same as before, recalculate the abnormal monthly return a. 25 Marks) (Total 50 Marks)