USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)

-Refer to Exhibit 4.6. If an equal-weighted index is constructed on Day T with $10,000 in each stock, what is the percentage change in wealth for this index on Day T + 1? Assume a base index value of 100 on Day T.
A) 8.65 percent
B) 10.14 percent
C) 15.69 percent
D) 30.42 percent
E) 47.08 percent

Question

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
 
-Refer to Exhibit 4.6. If an equal-weighted index is constructed on Day T with $10,000 in each stock, what is the percentage change in wealth for this index on Day T + 1? Assume a base index value of 100 on Day T.
A) 8.65 percent 
B) 10.14 percent 
C) 15.69 percent 
D) 30.42 percent 
E) 47.08 percent

Quizplus · Accepted Answer

To calculate the percentage change in wealth, we need to calculate the total value of the index on Day T and Day T + 1. On Day T, the total value of the index would be 100 (base index value) x 5 (number of stocks) x $10,000 (amount invested in each stock) = $500,000. 
On Day T + 1, the index value would be calculated as follows:
Stock A: (700/600) x $10,000 = $11,667
Stock B: (50/40) x $10,000 = $12,500
Stock C: (400/450) x $10,000 = $8,889
Stock D: (80/100) x $10,000 = $8,000
Stock E: (25/20) x $10,000 = $12,500
Total value of the index on Day T + 1: $53,556
Percentage change in wealth: ($53,556/$500,000 - 1) x 100 = 10.14 percent. Therefore, the best choice is B.