Please show work to understand how to compute and distinguish between the differ
ID: 2811783 • Letter: P
Question
Please show work to understand how to compute and distinguish between the different sections: 1.1, 1.2, 1.3, 1.4
Consider the three stocks in the following table. Pt represents the price at the end of period t and Qt is the number of shares outstanding. Stock C splits 3:1 during period 2. PO O0 P1 Q1 P2 02 69.00 150.00 S s 63.00150.00 S 72.0050.00 $ 37.00 400.00 S 42.00 400.00 S 36.00 400.00 9.00 200.00 S 12.00 200.00 7.00 600.00 1.1 Calculate the price-weighted index of the three stocks for each period (4 points).What is the divisor for each period (4 points)? Does it change in the last period (2 points)? Why or why not (2 points)? .2 Calculate the price-weighted index returns for the periods ending in 1 and 2 (7 points) .3 Calculate the value-weighted index returns for the periods ending in 1 and 2 (7 points) 1.4 Calculate the equal-weighted index returns for the periods ending in 1 and 2 (7 points)Explanation / Answer
Soln : 1.1: Price weighted index is define as the index in which each stock influences the index as per their value per share.
PWI for period 0 = 115/3 = 38.33 , PWI for period 1 = 117/3 = 39 and PWI for period 2 = 115/3 = 38.33
Divisor of each period = 3, It will not change in period 2 compare to 0 as the sum of prices of stocks is same and numerator is always same.
1.2 PWI return = (PWI in period 1- PWI period0)/PWI period0 = (39 - 38.33)/38.33 = 1.74%
For period 2 , = -1.74%
1.3 Value water index for period 0, = (69*150 + 37*400+9*200)/750 = 35.93
Divisor in each period upto 1 starting from 0, 750 and in 2 , it is 1150, It does have effect on index Henc we can say that in last period , it affect the PWI because the weightage of last stock C is increased.Similarly For period 1, VWI = 28650/750 = 38.20, For period2 , VWI = 29400/1150 = 25.57
1.3 Price weighted index return for period 1 is return on the index over this period = (VWI in period1 - VWI in period 0)/ VWI in period 0 = (38.20 - 35.93)/35.93 = 6.30%
Similarly for Period 2 = (25.57 - 38.20)/38,20 = -33.07%
1.4 Equally weighted index is when the same weightage is given to each of the stock either it is small or large stock. As in this case it is 33% weightage given to each stock
For period 1 , equity weited return = 33%* ((63-69)/69 + (42-37)/37 +(12-9)/9 ) = 12.60%(approx.)
Similarly for period 2 . Equity weighted indx return , = period 2 - period1 for each stock *33% = -13.75%
Stock P0 Q0 P1 Q1 P2 Q2 A 69 150 63 150 72 150 B 37 400 42 400 36 400 C 9 200 12 200 7 600 Sum 115 750 117 750 115 1150