Problem 18-03

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:

(R_fund RFR)_t = + (R_mkt RFR)_t + e_t

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	0.473		0.596		65.2	%		0.940	%	0.792	%
	(0.19)		(0.09)
DEF	-0.060		0.656		95.4			0.482		0.766
	(0.19)		(0.11)
GHI	0.192		1.046		92.7			1.012		1.203
	(0.11)		(0.12)
JKL	0.365		0.758		62.9			0.955		1.034
	(0.21)		(0.10)
MNO	0.294		0.775		91.2			0.890		0.885
	(0.14)		(0.13)

1. Which fund had the highest degree of diversification over the sample period? How is diversification measured in this statistical framework?

   -Select-Portfolio ABCPortfolio DEFPortfolio GHIPortfolio JKLPortfolio MNOItem 1 had the highest degree of diversification over the sample period. -Select-R2Item 2 is a a measure of diversification.

2. Rank these funds performance according to the Sharpe, Treynor, and Jensen measures.

   Portfolio	Rank (Sharpe measure)	Rank (Treynor measure)	Rank (Jensen measure)
   ABC	-Select-12345Item 3	-Select-12345Item 4	-Select-12345Item 5
   DEF	-Select-12345Item 6	-Select-12345Item 7	-Select-12345Item 8
   GHI	-Select-12345Item 9	-Select-12345Item 10	-Select-12345Item 11
   JKL	-Select-12345Item 12	-Select-12345Item 13	-Select-12345Item 14
   MNO	-Select-12345Item 15	-Select-12345Item 16	-Select-12345Item 17

3. 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% confidence interval? (Note: The relevant t-statistic using 60 observations is 2.00.)

   -Select-ABC and MNOABC and GHIABC, GHI, and MNODEF and MNODEF, GHI, and JKLAll portfoliosNo one portfolioItem 18 have/has statistically outperformed the market at a 95% level of confidence.

   -Select-ABC and MNOABC and GHIABC, GHI, and MNODEF and MNODEF, GHI, and JKLAll portfoliosNo one portfolioItem 19 have/has statistically underperformed the market at a 95% level of confidence.