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Chapter 25

3. You have been assigned the task of comparing the investment performance of five different

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 = + (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(RFUND RFR)

Portfolio R2Mean

ABC0.192 1.048 94.1% 1.022%1.193%

(0.11) (0.10)

DEF0.0530.66291.60.473 0.764

(0.19)(0.09)

GHI 0.4630.59468.60.935 0.793

(0.19)(0.07)

JKL 0.3550.757 64.10.955 1.044

(0.22)(0.08)

(MNO)0.296 0.785 94.80.890 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.)