Problems 1 and 2 refer to the data contained in Exhibit 9.12, which lists 30 monthly excess returns to two different actively managed stock portfolios (A and B) and three different com- mon risk factors (1, 2, and 3). (Note: You may find it useful to use a computer spreadsheet program such as Microsoft Excel to calculate your answers.)
1. a. Compute the average monthly return and monthly standard return deviation for each portfolio and all three risk factors. Also state these values on an annualized basis. (Hint: Monthly returns can be annualized by multiplying them by 12, while monthly standard deviations can be annualized 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 & 2, 1 & 3, and 2 & 3).
d. In theory, what should be the value of the correlation coefficient between the common risk factors? Explain why.
e. How close do the estimates from Part b come to satisfying this theoretical condition?
f. What conceptual problem(s) is created by a deviation of the estimated factor correlation coefficients from their theoretical levels?
2. a. Using regression analysis, calculate the factor betas of each stock associated with each of the common risk factors. Which of these coefficients are statistically significant?
b. How well does the factor model explain the variation in portfolio returns? On what basis can you make an evaluation of this nature?
c. Suppose you are now told that the three factors in Exhibit 9.12 represent the risk expo- sures in the Fama-French characteristic-based model (i.e., excess market, SMB, and HML). Based on your regression results, which one of these factors is the most likely to be the market factor? Explain why.
d. Suppose it is further revealed that Factor 3 is the HML factor. Which of the two portfolios is most likely to be a growth-oriented fund and which is a value-oriented fund? Explain why.
Text Book: Investment Analysis and Portfolio Management By Frank Reilly, Keith Brown.