Question

Consider the three stocks in the following table. Pt represents price at time t, and Qt...

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 100 100 105 100 105 100 B 60 200 55 200 55 200 C 120 200 130 200 65 400 Calculate the first-period rates of return on the following indexes of the three stocks: (Do not round intermediate calculations. Round your answers to 2 decimal places.) a. A market value–weighted index Rate of return % b. An equally weighted index Rate of return %

(a) A market-value-weighted index

Market value = stock price * number of Shares outstanding

Market value of Stocks at t=0

A market value = 100 * 100 = 10000

B market value = 60 * 200 = 12000

C market value = 120 * 200 = 24000

Market value of Stocks at t= 1

A market value = 105 * 100 = 10500

B market value = 55 * 200 = 11000

C market value = 130 * 200 = 26000

Market value of Stocks at t= 2

A market value = 105 * 100 = 10500

B market value = 55 * 200 = 11000

C market value = 65 * 400 = 26000

Total market value at t = 0 is: (10000 +12000 +24000 ) = 46000

Total market value at t = 1 is: (10500 + 11000 + 26000) = 47500

Rate of return = (47500/46000) - 1 = 3.26%

(b) The return on each stock is as follows:

Ra = (105/100) - 1 = 0.05

Rb = (55/60) - 1 = -0.0833

Rc = (130/120) - 1 = 0.0833

The equally-weighted average is: [0.05 + (-0.0833) + 0.0833]/3 = 0.0167

= 1.67%