Answer to Question #300436 in Finance for jeff

Question

A stockbroker gathers the following data. Stock FB splits two-for-one during the

period.

Beginning of Period  End of period

Stock  Price ($) Shares  Price ($) Shares

TA  31  6,000  29  6,000 

FB  92  300  54  600 

ZM  42  2,200  43  2,200

a. Calculate the returns on both the price-weighted index and the market value-

weighted index of three stocks over the period.

b. Explain the difference in returns between the two indexes.

Answer 1

a)  (i) price-weighted index

Price weighted index = sum of prices of stocks 

Price weighted index at $t_{0}=31+92+42=165$

Price weighted index at $t_{1}=29+54+43=126$

Rate of return=$\frac{126}{165-1}\times100\%=76.83\%$

 (ii) market value-weighted index

We will calculate the market value index at time t =0 and time t=1 and then calculate the rate of return

Market value at time t = i = $∑ P i \ Q i$

Market value at time t = 0, =$(31\times6000)+(92\times300)+(42\times2,200)=306,000$

Market value at time t = 1, =($29\times6000)+(54\times600)+(43\times2,200)=301,000$

Rate of return =$\frac{301000}{306000-1}\times100\%=98.366\%$

b) In a price-weighted index, the basic approach is to sum the prices of the component securities used in the index and divide this sum by the number of components. In other words, we compute a simple arithmetic average.