I1. Consider the three stocks in the following table. P, represents price at tim
ID: 2818335 • Letter: I
Question
I1. Consider the three stocks in the following table. P, represents price at time t, and Q, represents shares outstanding at time t. Stock C splits two for one in the last period. 0o 100 200 200 P2 95 45 Pt Po 90 50 100 95 45 110 100 200 200 100 200 400 a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t 0 to t = 1). b. What must happen to the divisor for the price-weighted index in year 2? c. Calculate the rate of return for the second period (t1 to 2). 12. Using the data in the previous problem, calculate the first-period rates of return on the following indexes of the three stocks:Explanation / Answer
A. Price wiegted index is the average of the price of each stock. It considers only Price not the shares outstanding.
So, To find the rate of return first we need to calculate the Price index in T0 and T1.
Price Index i T0 = (P1+P2+P3)/3
=(90+50+100)/3= 80
Price Index i T1 = (P1+P2+P3)/3
=(95+45+110)/3= 83.33
Rate of return= (83.33-80)/80= 4.17%
B. Price weigted index adjust the divisor inorder to maintain the same index value. Thus as in given question Price index in Year 1 is 83.33 (Solved in part A). After Stock split it should remain at same level so divisor will be adjusted accordingly.
Suppose New divisor is X
(95+45+55)/X= 83.33
X= 2.34.
The Divisor will get decreased in Year 2
C. Since in Year 2 for stock split, the divisor will be adjsted to maintain the stock index at the same level as in Year 1. (as shown in Part B).
Since there is no change in the price of stocks A , B the there will be no change in the Price Index.
Rate of reurn will be 0%