4. Pension plan sponsors place a great deal of emphasis on "universe" rankings when evaluating money managers. In fact, it appears that sponsors assume implicitly that managers who rank in the top quartile of a representative sample of peer managers are more likely to generate superior relative performance in the future than are managers who rank in the bottom quartile. We can test the validity of this assumption by simple (bivariate) linear regression. We regress percentile rankings of managers in one period on these managers' percentile rankings from the prior period.

a. Let us start by assuming that the implicit assumption of plan sponsors is true to the extent that there is perfect correlation in percentile rankings from one period to the next. Given this assumption, list the numerical values you would expect to observe for the intercept, slope, and coefficient of determination of the regression.

b. Now, let us assume that the implicit assumption of plan sponsors is false and that there is no

correlation in percentile rankings from period to period. Given this assumption, list the numerical values you would expect to observe for the intercept, slope, and coefficient of

determination of the regression.

c. Upon performing such a regression, you observe an intercept of 0.51, a slope of -0.05, and a coefficient of determination of 0.01. Based on this regression, state your best estimate of a manager's percentile ranking next period if his/her percentile this period was 0.15.