Question

1. Considering three stocks in the following table. Pt represents a price at day t, and Qt represents the number of shares outstanding at day t. Stock C splits ten-for-one at the beginning of day 2.

	P0	Q0	P1	Q1	P2	Q2
A	81.52	1000	85.32	1000	90.16	1000
B	48.12	2000	45.24	2000	47.52	2000
C	611.23	2000	632.25	2000	60.45	20000

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

c. What must happen to the divisor for the price-weighted index in day 2? (3 Mark)

Answer 1

a) Sum of prices P0 = 81.52 + 48.12 + 611.23 = 740.87

Sum of prices P1 = 85.32 + 45.24 + 632.25 = 762.81

Rate of return for price-weighted index from t0 to t1 = (762.81 / 740.87) - 1 = 2.96%

b) Sum of value (Pt * Qt) P0 = (81.52 * 1000) + (48.12 * 1000) + (611.23 * 2000) = 1,400,220

Sum of value (Pt * Qt) P1 = (85.32 * 1000) + (45.24 * 1000) + (632.25 * 2000) = 1,440,300

Rate of return for value-weighted index from t0 to t1 = (1,440,300 / 1,400,220) - 1 = 2.86%

c) Price weighted index value = Sum of prices / Index divisor

In the above equation, the numerator decreases due to the stock split (price of stock C would have been 604.5 without split). Thus, the index divisor will also decrease such that the index value remains constant.