Question

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.

	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

b. An equally weighted index

Answer 1

a) Market Value weighted index = [ P1 * Q1 / P0 * Q0 ] * 100

                                               

Stock	P0	Q0	P0*Q0	P1	Q1	P1*Q1
A	100	100	10000	105	100	10500
B	60	200	12000	55	200	11000
C	120	200	24000	130	200	26000
			46000			47500

= [ 47500 / 46000 ] * 100

= 103.26

b) Equally weighted index

Stock	P0	P1
A	100	105
B	60	55
C	120	130
	280	290

Average price 1 = 290 / 3

   = 96.67

Average Price 0 = 280/3

   = 93.33

                         

Price weighted index = [ Average Price 1 / Average price 0 ] * 100

   = [ 96.67 / 93.33 ] * 100

   = 103.58

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