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%
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