Question

A price-weighted index is comprised of three stocks. Yesterday the three stocks were priced at $15, $20, and $32. The number of outstanding shares for each is 500 shares, 2,000 shares, and 1,000 shares, respectively. If the stock prices changed to $16, $15, and $38 today respectively, what is the 1-day rate of return on the index?
① 2.7% ② 3.0% ③ 3.3% ④ 3.6%

Answer 1

The Correct Opyion is (2) 3%

Step(1) Calculation of Value of Index at the start (i.e. Yesterday)

Value of index = sum of prices of stocks in the index/number of stocks in the index.

Value of Index at the start = (15+20+32)/3 = 22.33

Step(2) Calculation of Value of Index at the End (i.e Today)

Value of index = sum of prices of stocks in the index/number of stocks in the index

Value of Index at the End  = (16+15+38)/3 = 23

Step (3) Calculation of Rate of Return on Index

Rate of Return on Index = (Value of Index at the End - Value of Index At start)/Value of Index at the start

Rate of Return on Index = (23-22.33)/22.33 = .0300 0r 3%

Hence the one day rate of return of the Index is 3%