Question

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	1,600,000		$72		$86
B	13,000,000		28		43
C	28,000,000		15		24

1. 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.

     %

2. 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.

     %

3. 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

Solution 4-02 Part a) Determine number of share and change in wealth Stock T Price Amount No. of T+1 Invested Shares 721 86 1000| 13.89 281 431 10001 35.71 15 2410001 66.67 Total 3000 Total Value at T+1 1194.44 1535.71 1600 4330.16 C I Change in Wealth - 44.33% 4330-3000 3000 1330 3000 Hence, change in wealth is 44.33% Part b) Calculate change and arithematic mean Stock Price T 72 28 Change % T+1 8 6 19.44% 43 53.57% 241 60.00% 151 Arithmetic Mean = Sum of % Change in all Stock Number of stock 19.44% + 53.57% + 60.00% Arithmetic Mean = Arithmetic Mean = 133.02% Arithmetic Mean = 44.34% Hence, Arithematic mean is 44.34% Part c) Calculate Geometric Mean Price Stock T+1 Change % | 72 28 15 86 19.44% 43| 53.57% 24 60.00% C -1 Geometric Mean = Geometric Mean = Geometric Mean = Geometric Mean = Geometric Mean = [(1+Ra)X(1+Rb)X(1+Rc)] (1+19.44%)/(1+53.57%)/(1+60%) 2.934784128 1.43 43.17% (1/Number of stock) (1/3) 0.333333 A Hence, Geometric mean is 43.17%