Question

A benchmark index has three stocks priced at $7, $43, and $56. The number of outstanding shares for each is 500,000 shares, 405,000 shares, and 553,000 shares, respectively. If the prices changed to $14,44 and 52 and the number of outstanding shares for each changed to 250,000 shares 405,000 shares and 553,000 shares today, What is the price-weighted (PW) index value and equally weighted (EW) index value today if yesterday PW index and EW index value were 910 and 1012?

Answer 1

Solution :-

For price weighted index we shall calculate the divisor as first stock goes reverse split.

We first caclulate the average of the stocks:

(7+43+56)/3=35.33

Now this shall be used to calculate the value of the divisor:

Divisor = New Value of all stock/Initial average value

=(14+44+52)/35.33=3.1984

New average value = (14+44+52)/3.1984= 34.39

Return= (34.39/35.33)-1=-2.66%

New index value = 910*(1-2.66%)=886

For equal weighted index we calculate the total value adjusting for as if split has not occured:

Since stocks for first stock have halved, this means reverse split has occured for the same.

Stock	Initial	After	Return
1	$                      7.00	$          7.00	0
2	$                    43.00	$        44.00	0.023256
3	$                    56.00	$        52.00	-0.07143
Total	$                  106.00	$      103.00	-4.82%
		Average	-1.61%
	New value	$            996
	(1012*(1-1.61%))

Therefore Price weighted index is 886

And Equally weighted index is 996

If there is any doubt please ask in comments