Question

Consider the three stocks in the following table. P t represents price at time t, and Q t 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 5₀ to t 5₁).

b. What must happen to the divisor for the price-weighted index in year 2?

c. Calculate the rate of return of the price-weighted index for the second period (t 5₁to t 5₂).

Short answer

a. 4.167%

b. 2.340

c. Zero

Step-by-step solution

Definition

A stock is considered as a share of ownership or equity in a company.

Solution for ‘a’

a. In order to find the rate of return, we must find the value of index at t=0 and t=1.

At t=0, the value of index is: (90+50+100)/3 = 80

At t=1, the value of index is: (95+45+110)/3= 83.3333

Therefore the rate of return is: 83.3333/80 - 1= 4.167%

Solution for ‘b’

b. Without a split, stock C would sell for 110 and the value of the index would be: (95 + 45 + 110)/3 = 83.3333

With split, stock C sells at 55.

Therefore, we need to set the divisor (d) such that:

83.3333 = (95 + 45 + 55)/d…..d = 2.340

Solution for ‘c’

c. The rate of return is zero. The price – weighted index for the period (t 5₁ to t 5₂) remains unchanged, as it should, since the return on each stock separately equals zero.