Problems 4 and 5 refer to the data contained in Exhibit 7.12, to two different actively managed stock portfolios (A and B) and three different common risk factors (1, 2 and 3). (Note: You may find it useful to use a com- puter spreadsheet program such as Microsoft Excel to calculate your answers.) which lists 30 monthly excess returns 4 (a) Calculate the average monthly return and monthly standard return deviation for each port folio and all three risk factors. Also state these values on an annualised basis. (Hint: Monthly returns can be annualised by multiplying them by 12, while monthly standard deviations can be annualised by multiplying them by the square root of 12.) (b) Based on the return and standard deviation calculations for the two portfolios from Part a, is it clear whether one portfolio outperformed the other over this time period? (c) Calculate the correlation coefficients between each pair of the common risk factors (i.e. 1 and 2, 1 and 3 and 2 and 3) (d) In theory, what should be the value of the cor relation coefficient between the common risk factors? Explain why How close do the estimates from Part b come (e) to satisfying this theoretical condition? What conceptual problem(s) is created by a deviation of the estimated factor correlation coefficients from their theoretical levels EXHIBIT 7.12 Monthly excess return data for two portfolios and three risk factors Factor 3 Factor2 Factor 1 PortfolioAPortfolio B Period -1.67% -1.01% 000% 0.01% 1.08% 0.29 7.58 1.92 6.01 3 0.22 0.36 0.66 4.29 -3.62 -2.96 -3.40 2.86 4.26 -4.51 2.47 -2.72 -0.75 5.69 -5.92 -16.11 -15.46 8 -15.49 -3.76 -2.85 4.06 -3.36 6.75 7.70 10 -3.68 1.36 5.86 7.76 -4.95 -0.31 5.94 9.62 -6.16 3.47 2.73 5.25 -4.15 -5.59 -3.19 -0.55 -3.04 -3.82 5.40 2.80 2.89 7.26 3.08 3.46 -2.39 -2.87 4.33 3.42 3.66 0.70 2.01 -3.45 -3.37 -0.60 -4.06 20 -3.18 -2.68 0.15 21 -6.53 -3.19 6.01 -8.09 2.05 2.28 -9.05 6.98 7.09 24 7.20 -0.16 -2.79 -4.43 -4.8 21.49 -12.03 -2.04 26 7.81 5.13 5.25 7.53 8.59 6.24 -2.96 -4.31 5.38 -0.63 -5.86 -4.27 -3.36 29 -8.78 13.31 4.67 3.86