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 87 100 92 100 92 100 B 47 200 42 200 42 200 C 94 200 104 200 52 400

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

b. An equally weighted index

a). Total market value (at t = 0) = (\$87 × 100) + (\$47 × 200) + (\$94 × 200)

= \$8,700 + \$9,400 + \$18,800 = \$36,900

Total market value (at t = 1) = (\$92 × 100) + (\$42 × 200) + (\$104 × 200)

= \$9,200 + \$8,400 + \$20,800 = \$38,400

Rate of return=(V1 / V0)-1= (\$38,400/\$36,900) - 1 = 1.0407 - 1 = 0.0407, or 4.07%

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

RA = (V1 / V0) - 1 = (\$92/\$87) - 1 = 1.0575 - 1 = 0.0575, or 5.75%

RB = (V1 / V0) - 1 = (\$42/\$47) - 1 = 0.0894 - 1 =-0.1064, or -10.64%

RC = (V1 / V0) - 1 = (\$104/94) - 1 = 1.1064 - 1 = 0.1064, or 10.64%

The equally-weighted average is: [5.75% + (-10.64%) + 10.64%] / 3 = 5.75% / 3 = 1.92%

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