Assume that a brokerage firm concentrates on a few closely related industries. It has produced a set of estimates of earnings for 1985 and subsequently recorded the earn-ings that actually occurred. These data are given below:

Industry Firm Previous Earnings Estimated Earnings Actual Earnings

A 1 1.05 1.10 1.05

2 1.32 1.37 1.35

3 3.50 4.25 3.25

B 4 2.06 2.10 2.12

5 2.08 2.13 2.12

6 2.60 3.25 2.80

7 1.07 1.06 1.06

C 8 2.00 2.70 2.40

9 0.55 0.52 0.54

10 1.18 1.16 1.20

A - Plot these points on a Predictive Realization Diagram. What can we learn about the forecast pattern of this firm from the PRD?

B - Calculate the mean square foretasted error for this firm

C. Decompose the error by level of aggregation. That is, determine what percentage of the error was due to the inability to forecast earnings for this sector of the economy, what percentage was due to an inability to forecast each industry, and what percentage was due to an inability to forecast differences for each firm.

D. Examine another level of decomposition. Assume that there are three analysts, each following one industry. What is the mean squared error of each analyst? How much of the error of each analyst is due to the analyst's inability to predict the future of the industry followed, and how much is due to an inability to dif-ferentiate between the firms in the industry?

E. Decompose the error by forecast characteristics. Find what percentage of the error is due to bias, what percentage is due to variance, and what percentage is due to covariance.