Question

Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two for one in the last period.

P0 Q0 P1 Q1 P2 Q2

A 90 100 95 100 95 100

B 50 200 45 200 45 200

C 100 200 110 200 55 400

a. Calculate the rate of return on a price-weighted index of the three stocks for the first period ( t 5 0 to t 5 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 ( t 5 1 to t 5 2).

Answer 1

Given the following data,

	P0	Q0	P1	Q1	P2	Q2
A	90	100	95	100	95	100
B	50	200	45	200	45	200
C	100	200	110	200	55	400

Pt represents the price at time t and

Qt represents the outstanding shares at time t.

a) In order to calculate the price weighted index of three stocks for the first time period, we need to use the formula,

Price weighted index from t0 to t1 = ((Average Value of the index at P0)/(Average Value of the index at P1))-1

Average Value of the index at P0 = (90+50+100)/3

= 240/3

= 80

  Average Value of the index at P1 = (95+45+110)/3

= 250/3

= 83.33

Substituting these we get,

Price Weighted Return from t0 to t1 = (83.33/80) - 1

= 1.04167 - 1

= 0.04167

= 4.17%

Therefore, Price weighted index from t=0 to t1 is 4.17%

b)

P1	P2
95	95
45	45
110	55
sum =250	sum =195

New divisor for the period 2 is given by the following formula,

New divisor = total value of P2/ Average value of P1

Total value of P2 = 95+45+55 = 195

Average value of P1 = (95+45+110)/ 3

= 250/3

= 83.33

Substituting these we get,

New divisor = 195/ 83.33

= 2.340

Therefore, new divisor = 2.340

c) The return is zero in this case.

Since the index remains unchanged as the return in this case seperately for each stock is zero.