You have been assigned the task of comparing the investment performance of five differ- ent pension fund managers. After gathering 60 months of excess returns (i.e., returns in excess of the monthly risk-free rate) on each fund as well as the monthly excess returns on the entire stock market, you perform the regressions of the form:
(Rfund - RFR)t = α + β(Rmkt - RFR)t + et
You have prepared the following summary of the data, with the standard errors for each of the coefficients listed in parentheses.
REGRESSION DATA ( R FUND - RFR )
|
Portfolio
|
α
|
β R 2 Mean σ
|
|
ABC
|
0.192
|
1.048
|
94.1%
|
1.022%
|
1.193%
|
|
|
(0.11)
|
(0.10)
|
|
|
|
|
DEF
|
-0.053
|
0.662
|
91.6
|
0.473
|
0.764
|
|
|
(0.19)
|
(0.09)
|
|
|
|
|
GHI
|
0.463
|
0.594
|
68.6
|
0.935
|
0.793
|
|
|
(0.19)
|
(0.07)
|
|
|
|
|
JKL
|
0.355
|
0.757
|
64.1
|
0.955
|
1.044
|
|
|
(0.22)
|
(0.08)
|
|
|
|
|
(MNO)
|
0.296
|
0.785
|
94.8
|
0.890
|
0.890
|
|
|
(0.14)
|
(0.12)
|
|
|
|
a. Which fund had the highest degree of diversification over the sample period? How is diversification measured in this statistical framework?
b. Rank these funds' performance according to the Sharpe, Treynor, and Jensen measures.
c. Since you know that according to the CAPM the intercept of these regressions (i.e., alpha) should be zero, this coefficient can be used as a measure of the value added provided by the investment manager. Which funds have statistically outperformed and underperformed the market using a two-sided 95 percent confidence interval? (Note: The relevant t-statistic using 60 observations is 2.00.)