Question

Using the data from the chart below, calculate the first-period rates of return on the following indexes of the three stocks:

Assume the equally-weighted index at time 0=100.

Calculate the geometric equally-weighted index at t=1.

Calculate the rate of return based on these two index numbers.

	P(0)	Q(0)	P(1)	Q(1)	P(2)	Q(2)
A	90	100	95	100	95	100
B	50	200	45	200	45	200
C	100	200	110	200	55	400

Answer 1

The return on Stock A for the first period is 95/90 - 1 = 5.55%. The return on Stock B for the first period is 45/50 - 1 = -10%. The return on Stock C for the first period is 110/100 - 1 = 10%. The return on an equally weighted index of the three stocks is (5.55% - 10% +10%)/3 = 1.85%.

The price-weighted index at time 0 is (90 + 50 + 100)/3 = 80. The price-weighted index at time 1 is (95 + 45 + 110)/3 = 83.33. The return on the index is 83.33/80 - 1 = 4.16%.