4) In the following table, Asness (1997) [Financial Analysts Journal 53, 29-36] reports the average future monthly returns for 25 portfolios sorted independently on momentum (PAST(2,12)) and value (Log(BV/MV)). For example, the top left entry represents the portfolio of firms that fall into the lowest value quintile and the lowest momentum quintile each month. The table also shows the average momentum and value numbers for each of the 25 portfolios. Furthermore, for each momentum (value) portfolio, it presents the difference in average returns - with the respective t-statistics in parentheses - between the high value (momentum) and low value (momentum). For example, the top right entry represents the long-short value portfolio average return implemented only with past losers. Average Value-Weighted Statistic Loser PAST(2,12) Q1 (Expensive Log[BV/MVD) Q2 Q5 (Cheap Log [BV/MVI) Q5-Q1 (f-Statistic) Monthly return 0.03% 0.49% 0.80% 0.83% 1.00% 0.97% Log(BV/MV) -1.24 -0.72 -0.36 -0.12 0.29 (4.38) D/P 2.31% 3.28% 4.07% 4.34% 6.04% PAST(2,12) -0.92 -1.63 -1.72 -1.90 -2.27 Q2 Monthly return 0.61% 0.59% 0.90% 1.25% 1.35% 0.74% Log(BV/MV) -1.23 -0.72 -0.37 -0.13 0.20 (3.57) D/P 2.62% 3.66% 4.45% 4.55% 6.70% PAST(2/12) 0.03 0.03 -0.01 -0.02 -0.04 Q3 Monthly return 0.52% 0.93% 0.80% 1.19% 1.44% 0.92% Log(BV/MV) -1.31 -0.78 -0.41 -0.18 0.19 (4.94) D/P 2.40% 3.55% 4.29% 4.24% 6.98% PAST(2/12) 1.12 1.13 1.11 1.10 1.10 Q4 Monthly return 0.99% 0.97% 1.17% 1.45% 1.68% 0.69% Log(BV/MV) -1.42 -0.85 -0.49 -0.24 0.10 (3.39) D/P 2.02% 3.13% 3.80% 3.80% 6.35% PAST(2/12) 2.32 2.28 2.26 2.27 2.28 Winner PAST(2,12) Monthly return 1.50% 1.44% 1.49% 1.60% 1.62% 0.13% Log(BV/MV) -1.64 -0.88 -0.60 -0.35 0.13 (0.65) D/P 1.32% 2.32% 2.69% 2.80% 6.34% PAST(2/12) 5.01 4.34 4.31 4.35 4.47 Return difference 1.47 0.95 0.69 0.76 0.62 (1-Statistic) (5.71) (3.47) (2.66) (3.10) (2.57) a) Comment on the PAST(2,12) and Log(BV/MV) values of the 25 portfolios. What is the observed pattern? Is this pattern in accordance with your expectations? (7 marks) b) Comment on the interrelations arising between the value and momentum anomalies. When are the respective anomalies stronger? Based on the average monthly returns of the 25 portfolios, how would you combine the two factors to form one trading strategy? (8 marks)