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Answer: The one day rate of return on the stock is 1.49%
We arrive at the answer in the following manner:
First we need to calculate yesterday's and today's index values.
For that we need to find weights of each day based on market capitalization.
The weight of a company in the index is calculated by dividing the market capitalization of a company by the total market capitalization of all the companies whose shares are a part of the index.
Then, we multiply the share price of each company with their respective weights and find the total to arrive at the index value for one day.
<u>Yesterday's Index Value</u>
Stock Price No. of shares Mkt Cap Weight Weight*Price
A 12 600000 7200000 0.25 2.96 (0.25*12)
B 20 500000 10000000 0.34 6.85(0.34*20)
C 60 200000 <u>12000000</u> <u>0.41</u> <u>24.66 </u>(0.41*60)
Total 29200000 1.00 34.47
We calculate the weight for stock A as follows:
We calculate the weights of the remaining stocks in a similar manner.
Please note that the sum total of all weights must add up to 1.
The sum total of the last column (Price * Weight) is yesterday's index value.
We repeat the same steps with today's market price to arrive at today's index value.
<u>Today's index Value</u>
Stock Price No. of shares Mkt Cap Weight Weight*Price
A 16 600000 96,00,000 0.31 4.95 (0.31*16)
B 18 500000 90,00,000 0.29 5.23 (0.29*18)
C 62 200000 <u>1,24,00,000</u> <u>0.40</u> <u>24.80</u>(0.40*62)
Total 3,10,00,000 1.00 34.98
<u>One-day Rate of Return</u>
We can calculate the one day rate of return on the index as follows:
Rate of return = 0.01494 or 1.49%