The Hydro Index is a price weighted stock index based on the 4
largest boat manufacturers in the nation. Consider the four stocks
in the following table. P_{t} represents price at time t,
and Qt represents shares outstanding at time t. (Please pay close
attention to stock split)
P_{0} 
Q_{0} 
P_{1} 
Q_{1} 
P_{2} 
Q_{2} 

A 
80 
200 
90 
200 
98 
200 
B 
50 
300 
40 
300 
50 
300 
C 
90 
200 
110 
200 
115 
200 
D 
100 
100 
90 
100 
40 
300 
a. What must be the divisor
for the price weighted index in year 2? (Keep your
answer to four decimals, such as 2.3456)
b. What is the price weighted index at t=1
? (Keep your answer to only two decimals, such as
81.23)
c. What is the price weighted
index at t=2? (Keep your answer to only two decimals,
such as 81.23)
For price weighte index, divisor changes with stock splits. But, initially the divisor is just the no. of stocks in the index.
So, initial divisor = 3
In year 2, clearly there was a 3 for 1 stock split in Stock D
Now if the stock split has not happened, stock price of D would have been = 40*3 = 120
so, if the stock split has not happened, price weighted average woud have been = (98+50+115+120)/4 = 95.75
so, divisor for the price weighted indec in year 2 = sum of stock prices in year 2 / price weighted average if the stock split had not happened = (98+50+115+40)/95.75 = 3.1645
b. price weighted index at t=1, = (90+40+110+90)/4 = 82.5
c. price weighted index at t=1, = (98+50+115+40)/3.1645 = 95.75
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