11. Consider the three stocks in the following table. P, represents price at tim

Question

11. Consider the three stocks in the following table. P, represents price at time t, and Q, represents 21 22. shares outstanding at time t. Stock C splits two for one in the last period. 02 100 200 200 100 90 50 100 100 200 200 95 45 110 95 45 400 a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1). b. What must happen to the divisor for the price-weighted index in year 2? c. Calculate the rate of return for the second period (t 1 tor 2). Using the data in the previous problem, calculate the first-period rates of return on the following indexes of the three stocks: a. A market-value-weighted index. b. An equally weighted index. 12.

Explanation / Answer

Three Stocks a.A market value–weighted index The return of such an index from period 0 to 1 {(95 × 100 + 45 × 200 + 110 × 200) ( 90 × 100 + 50 × 200 + 100 × 200)}/ (90 × 100 + 50 × 200 + 100 × 200) = (40,500 39,000)/39,000 = 3.85% b.An equally weighted index The amount of money invested in each stock is the same in an equally weighted index. Let x, y and z denote the number of shares of asset A, B and C that the portfolio would hold at the beginning of period 0. Therefore, 90x = 50y = 100z {95x + 45y+ 110z - (90x+50y+100z)}/(90x+50y+100z) {(95-90)x + (45-50)y + (110-100)z}/(90x+50y+100z) = - 90x+50y+100z = 3*90x = 3*50y=3*100z Therefore, the return on the equally weighted index is: (1/3)*[{(95-90)/90} + {(45-50)/50} + {(110-100)/100}] = 1.85%

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