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 84 100 89 100 89 100 B 44 200 39 200 39 200 C 88 200 98 200 49 400 a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1). (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What will be the divisor for the price-weighted index in year 2? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. Calculate the rate of return of the price-weighted index for the second period (t = 1 to t = 2).

Answer 1

	P0	Q0	P1	Q1	P2	Q2
A	84	100	89	100	89	100
B	44	200	39	200	39	200
C	88	200	98	200	49	400

a) Rate of return of the index for the first period: Its just the index return, so here we can calculate avg prices for both the periods and calculate the price change in % (P1/P0-1)

P0 = (84+44+88)/3 = 72

P1 = (89+39+98)/3 = 75

So, return, R1 = 75/72-1 = 4.2%

b) What will be the divisor for the price-weighted index in year 2

Here stock split was done so taking a simple average for the index would not give a correct result. Hence, a new denominator needs to be calculated. This can be done using the values of previous period i.e just before the stock split (1). So logically, the index value will remain same.

Average of prices at T1 = Average of prices at T2

(89+39+98)/3 = (89+39+49)/x

x = 177/75.33 = 2.35

c) Return would be 0% in T2 as overall prices haven't changed, only the stock is splitted into two. This can also be inferred from the fact that average divisor has been adjusted for the stock split.