Answer:
Step-by-step explanation:
To construct the price-weighted index, we need to calculate the market value of each stock at time T and T+1.
a. Price-weighted index calculation:
First, we calculate the market value of each stock at time T by multiplying the price by the number of shares:
Stock A: 60 * 1,000,000 = 60,000,000
Stock B: 20 * 10,000,000 = 200,000,000
Stock C: 18 * 30,000,000 = 540,000,000
Next, we calculate the market value of each stock at time T+1:
Stock A: 80 * 1,000,000 = 80,000,000
Stock B: 35 * 10,000,000 = 350,000,000
Stock C: 25 * 30,000,000 = 750,000,000
To compute the price-weighted index, we sum up the market values at time T and time T+1 and divide by 2:
T: 60,000,000 + 200,000,000 + 540,000,000 = 800,000,000
T+1: 80,000,000 + 350,000,000 + 750,000,000 = 1,180,000,000
Percentage change in the price-weighted index from T to T+1:
[(1,180,000,000 - 800,000,000)/800,000,000] * 100 = 47.50% increase
b. Value-weighted index calculation:
To construct the value-weighted index, we need to calculate the market value of each stock at time T and T+1, and also the total market value of all the stocks at both times.
Total market value at time T:
60,000,000 + 200,000,000 + 540,000,000 = 800,000,000
Total market value at time T+1:
80,000,000 + 350,000,000 + 750,000,000 = 1,180,000,000
Next, we calculate the weight of each stock at time T and time T+1 by dividing the market value of each stock by the total market value:
Stock A at T: 60,000,000 / 800,000,000 = 0.075 = 7.5%
Stock B at T: 200,000,000 / 800,000,000 = 0.25 = 25%
Stock C at T: 540,000,000 / 800,000,000 = 0.675 = 67.5%
Stock A at T+1: 80,000,000 / 1,180,000,000 = 0.067 = 6.7%
Stock B at T+1: 350,000,000 / 1,180,000,000 = 0.297 = 29.7%
Stock C at T+1: 750,000,000 / 1,180,000,000 = 0.635 = 63.5%
To compute the value-weighted index, we sum up the weighted values at time T and time T+1:
T: (0.075 * 100) + (0.25 * 100) + (0.675 * 100) = 7.5 + 25 + 67.5 = 100
T+1: (0.067 * 100) + (0.297 * 100) + (0.635 * 100) = 6.7 + 29.7 + 63.5 = 100
Percentage change in the value-weighted index from T to T+1:
[(100 - 100)/100] * 100 = 0% change
c. The price-weighted index gives equal importance to all stocks based on their prices, regardless of the number of shares outstanding. In this case, the price-weighted index increased by 47.50%.
On the other hand, the value-weighted index gives more weight to stocks with higher market values. In this case, the value-weighted index did not change, indicating that the increase in the market value of the higher-weighted stocks (Stock B and Stock C) offset the decrease in the market value of the lower-weighted stock (Stock A).
The main difference in the results for the two indexes is that the price-weighted index is influenced more by the price movements of the individual stocks, while the value-weighted index is influenced more by the market value of the individual stocks. Therefore, the value-weighted index reflects changes in the market value of the overall portfolio more accurately.