Question

eBook Problem 4-02 You are given the following information regarding prices for a sample of stocks. PRICE Stock Number of Shares T T + 1 A   3,600,000 $60 $80 B 13,000,000   30   45 C 28,000,000   19   34 Construct an equal-weighted index by assuming $1,000 is invested in each stock. What is the percentage change in wealth for this portfolio? Do not round intermediate calculations. Round your answer to two decimal places.   % Compute the percentage of price change for each of the stocks. Do not round intermediate calculations. Round your answers to two decimal places. Stock A:   % Stock B:   % Stock C:   % Compute the arithmetic mean of these percentage changes. Do not round intermediate calculations. Round your answer to two decimal places.   % Compute the geometric mean of the percentage changes in Part b. Do not round intermediate calculations. Round your answer to two decimal places.   %

Answer 1

Please find the below calculations:

The answers are the same (slight difference due to rounding). This is what you would expect since Part A represents the percentage change of an equal-weightedseries and Part B applies an equal weight to the separate stocks in calculating the arithmetic average

(c) Geometric average is the nth root of the product of n items.a time series.

GM = [(1.33)(1.5)(1.7895)]^1/3 - 1 = 0.5295 or 52.95%

AM = 54.09% (Part B)

The geometric average is less than the arithmetic average. This is because variability of return has a greater affect on the arithmetic average than the geometric average. GM is generally used for compounding returns over