Question

A benchmark market value index is comprised of three stocks. yesterday the three stocks were priced at $12, $20, and $60. the number of outstanding shares for each is 600,000 shares, 500,000 shares, and 200,000 shares, respectively. if the stock prices changed to $16, $18, and $62 today respectively, what is the 1-day rate of return on the index?

Answer 1

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.

$Market Capitalization _{ a stock} = Market Price * No .of outstanding shares$

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.

$Weight_{Company A} =\frac{Mkt Cap of company A}{Total Market cap}$

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.

Yesterday's Index Value

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       12000000     0.41      24.66  (0.41*60)

Total                                                 29200000     1.00      34.47

We calculate the weight for stock A as follows:

$Weight_{A} =\frac{72,00,000}{2,92,00,000} = 0.2466 = 0.25$

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.

Today's index Value

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    1,24,00,000     0.40     24.80(0.40*62)

Total                                                3,10,00,000     1.00     34.98

One-day Rate of Return

We can calculate the one day rate of return on the index as follows:

$Rate of return = [\frac{(Today's index value - Yesterday's index value}{Yesterday's index value}) * 100$

$Rate of Return = ( \frac{34.98 - 34.47}{34.47}) * 100$

$Rate of return = (\frac{0.51}{34.47}) *100$

Rate of return = 0.01494 or 1.49%