Question

(Pt represents price at time t, and Qt represents shares outstanding at time t. )

Stock C splits 3 for 1 in year 2018 and Stock D splits 2 for 1 in year 2019

Name	P17	Q17	P18	Q18	P19	Q19
W	170	100	175	100	172	100
X	95	200	98	200	97	200
Y	180	200	57	600	60	600
Z	100	200	110	200	55	400

A. What is the new divisor for the price-weighted index in 2018?

B. Calculate the rate of return on a price-weighted index of the four stocks from the year 2017 to 2018?

C.What is the new divisor for the price-weighted index in 2019?

D.Calculate the rate of return on a price-weighted index of the four stocks from the year 2018 to 2019?

E.Calculate the rates of return on a market value-weighted index of the four stocks from the year 2017 to 2018?

F.Calculate the rates of return on an equally weighted index of the four stocks from the year 2018 to 2019?

Answer 1

A) Price before split for the year 2018 ----  175 + 98 + 57 + 110 = 440

therefore the total = 440 ; divisor = 4 ; index value = 440/4= 110

Price after split for the year 2018 ---- 175 + 98 + 19 + 110 = 402 ; ( since 57/3 = 19)

therefore the total = 402 ; index value = 110 ; divisor = 402/110 = 3.654

hence new divisor for the price weighted index in 2018 is 3.654

B) for the year 2017 - 170 + 95 + 180 + 100 = 545

total= 545 ; divisor = 4 ; index value = 545/4 = 136.25

now the rate of return on price weighted index of the four stocks from 2017 to 2018 is calculated by the formula --{ (ending index value/ begining index value) - 1 } * 100

= {(110/136.25) - 1} x 100

=(-26.25/136.25) x 100

= - 0.19266 x 100

= - 19.266