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.
P_{0} | Q_{0} | P_{1} | Q_{1} | P_{2} | Q_{2} | |
A | 90 | 100 | 95 | 100 | 95 | 100 |
B | 50 | 200 | 45 | 200 | 45 | 200 |
C | 100 | 200 | 110 | 200 | 55 | 400 |
Calculate the first-period rates of return on the following indexes of the three stocks: (Do not round intermediate calculations. Round answers to 2 decimal places.)
a. A market value–weighted index
Rate of return %
b. An equally weighted index
Rate of return %
(a) Value of stock V_{t} = Price * Number of shares = P_{t}*Q_{t}
At time t = 0,
V_{A0} = 90*100 = 9000
V_{B0} = 50*200 = 10000
V_{C0} = 100*200 = 20000
At time t = 1,
V_{A1} = 95*100 = 9500
V_{B1} = 45*200 = 9000
V_{C1} = 110*200 = 22000
Returns for Period 1 :
Return_{A} = (9500 - 9000) / 9000 *100% = 5.56%
Return_{B} = (9000 - 10000) / 10000 *100% = -10%
Return_{C} = (22000 - 20000) / 20000 *100% = 10%
Market Valued weight of A = V_{A0} / (V_{A0} +
V_{B0} + V_{C0}) = 9000 / (9000 + 10000 + 20000) =
0.2308
Market Valued weight of B = V_{B0} / (V_{A0} +
V_{B0} + V_{C0}) = 10000 / (9000 + 10000 + 20000) =
0.2564
Market Valued weight of C = V_{C0} / (V_{A0} +
V_{B0} + V_{C0}) = 20000 / (9000 + 10000 + 20000) =
0.5128
Market weighted Returns = 0.2308*5.56 + 0.2564*(-10) + 0.5128*10 = 3.85%
(b) Equally weighted index return = (1/3)*5.56 + (1/3)*(-10) + (1/3)*10 = 1.85%
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