Problem 1 Indexes (33 points) Consider the three stocks in the following table.
ID: 2813409 • Letter: P
Question
Problem 1 Indexes (33 points)
Consider the three stocks in the following table. Ptrepresents the price at the end of period t and Qt is the number of shares outstanding. Stock C splits 3:1 during period 2.
P0
Q0
P1
Q1
P2
Q2
A
$ 18.00
150.00
$ 15.00
150.00
$ 20.00
150.00
B
$ 30.00
400.00
$ 41.00
400.00
$ 38.00
400.00
C
$ 44.00
200.00
$ 66.00
200.00
$ 26.00
600.00
1.1 Calculate the price-weighted index of the three stocks for each period (4 points). What is the divisor for each period (4 points)? Does it change in the last period (2 points)? Why or why not (2 points)?
1.2 Calculate the price-weighted index returns for the periods ending in 1 and 2 (7 points).
1.3 Calculate the value-weighted index returns for the periods ending in 1 and 2 (7 points).
1.4 Calculate the equal-weighted index returns for the periods ending in 1 and 2 (7 points).
Please provide how to steps to solve the question
P0
Q0
P1
Q1
P2
Q2
A
$ 18.00
150.00
$ 15.00
150.00
$ 20.00
150.00
B
$ 30.00
400.00
$ 41.00
400.00
$ 38.00
400.00
C
$ 44.00
200.00
$ 66.00
200.00
$ 26.00
600.00
Explanation / Answer
1.1 The sum of all prices at P0 is 92 (18+30+44) & there are 3 Stocks. Thus,Divisor will be 3. Hence, Price Index Value on P0 will be 92/3 = 30.667.
Similarly, Divisor at P1 will also be 3, & Thus value of Index at P1 will be 122/3 = 40.667
For Calculation at P2 we have to calculate the divisor as the split after during P2. A price-weighted average is the average price of a group of stocks. It's considered "price weighted" because the same percent increase in a higher-priced stock influences the average more than that of a lower priced stock. If Stock C valued at $66 at P1 splits into three $22 stocks, the company hasn't lost value, so it would no longer be appropriate to use a simple average with $22 as the stock's price. Therefore to compensate for splits, the formula's divisor changes, even if the number of stocks in the average has not. The new divisor will be calculated as Adjusted Price after Split / Price Index Before Split. Calculation is as follows:
Price weighted Index at P2 = (20+38+26)/1.918
= 43.796
1.1 The sum of all prices at P0 is 92 (18+30+44) & there are 3 Stocks. Thus,Divisor will be 3. Hence, Price Index Value on P0 will be 92/3 = 30.667.
Similarly, Divisor at P1 will also be 3, & Thus value of Index at P1 will be 122/3 = 40.667
For Calculation at P2 we have to calculate the divisor as the split after during P2. A price-weighted average is the average price of a group of stocks. It's considered "price weighted" because the same percent increase in a higher-priced stock influences the average more than that of a lower priced stock. If Stock C valued at $66 at P1 splits into three $22 stocks, the company hasn't lost value, so it would no longer be appropriate to use a simple average with $22 as the stock's price. Therefore to compensate for splits, the formula's divisor changes, even if the number of stocks in the average has not. The new divisor will be calculated as Adjusted Price after Split / Price Index Before Split. Calculation is as follows:
P1 P1 A 15 15 B 41 41 C 66 22 (Adjusted Price after split at Prices of P1 (66/3)) 122 78 Divisor 3 Price Index at P1 40.667 New Divisor for P2 Adjusted Price after Split / Price Index Before Split 1.918Related Questions
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