# Chapter 25 3 You have been assigned the task of comparing the investment performance of five differe

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 (ie, 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 ? ? R2 Mean ?

ABC 0192 1048 941% 1022% 1193%

(011) (010)

DEF ?0053 0662 916 0473 0764

(019) (009)

GHI 0463 0594 686 0935 0793

(019) (007)

JKL 0355 0757 641 0955 1044

(022) (008)

(MNO) 0296 0785 948 0890 0890

(014) (012)

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 (ie,

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 200)