Question

# The Hydro Index is a price weighted stock index based on the 4 largest boat manufacturers...

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. Pt represents price at time t, and Qt represents shares outstanding at time t. (Please pay close attention to stock split)

 P0 Q0 P1 Q1 P2 Q2 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