Quote from bwolinsky:
Buy it or not, that's a mathematical thing.
An example is a two stock index, 1 for $10 per share, and 1 for $100 per share. Assume that sharesunderstanding is equal 1 for the $10 stock and 2 shares for the $100 stock.
The price weighted index and value weighted index will both start with a baseline value of 1
So our index (10+100)/2=55 and our value is also the same (10+200)/2=105
Now, move both prices in the indexes up 1% and see the change.
(10.10+101)/2=55.55/55-1=1% as expected
(10.1+202)=212.1/105-1=2%
If the difference isn't obvious it should be. You have the price weighted index less on the same move in the value weighted one. The value weighted version goes up by 2% because the value of the two shares of $100 per share increased by $1 increasing the value of the index by about 2%.
It is an average mathematical result to keep going down this line of thought and you'll find that price weighted indexes exhibit downward bias. If it's not obvious by this example I don't think another would help, but if you have questions....
Unless I'm missing something, the only thing you've demonstrated so far is that the value weighted one is more volatile than the price weighted one. The value weighted will also drop 2% on a 1% change in each of its 2 components in the above example, and the price weighted one will drop 1%. That doesn't demonstrate that the price weighted one has a downward bias, only that its delta is less than the delta on the value weighted one given an equivalent price change.
This is the same as that example that if something goes up by 10 from 100, it has to drop by 11 from 110 to have the same percent effect. Which means nothing if your entry is 100, since a 10 point move in either direction is 10% from 100, and as far as your p/l is concerned, the entry, not where it went at some point in between, is your fixed point of reference.
So, what am I missing?
:eek: