Okay, but the DOW is unusual. Often, the weights are market capitalizations
for each company represented in the Index. For example,
two communication companies represented in the TSE 300 are
Aliant and
BCE. (I picked these 'cause they look like they're the first two in the TSE 300,
alphabetically speaking. They ain't, but it looks good, eh?)
assuming that the TSE 300 is a standard marketcapweighted index ... which it ain't. (See below.)
where the weights in each average are the number of outstanding shares, n. (I dunno 'bout you, but this surprised me!)
In fact, a Market Cap Weighted Index is normally nonstandard; it doesn't use the
standard formula for "weighted average of stock prices" as described above.
In fact they are calculated by an even simpler prescription than
Market Index = Σ(W P) / Σ(W)
For example, I said that the TSE 300 Index used this prescription (normal
marketcapweighted). I lied. The TSE index actually uses an even simpler
formula, namely:
TSE300_Index = 1000 Σ(n P) / Divisor
where the n is the number of outstanding shares (the "float"), P is the stock price
and Divisor changes
when a stock is dropped/added/etc. to the
set of 300 stocks. (You'd think this'd be called floatweighted, but ...)
If we set 1000/Divisor = C (for sanitary reasons), we can write:
TSE300_Index = C {
n_{1}P_{1} + n_{2}P_{2} + n_{3}P_{3} + ... +
n_{300}P_{300}
}
Now it's reasonable to ask (for example):
"What fraction of the Index does stock P_{1} represent?"

Since P_{1} provides a term C n_{1}P_{1} to the sum, we can divide
to get the fraction:
C n_{1}P_{1}/TSE300_Index
At this very moment (Sep 12/00) TSE300_Index = 10,557 and one component,
namely Nortel has a stock price of
P_{1} = $94.50 and the number
of outstanding shares is about
n_{1} = 3,000,000,000 = 3 x 10^{9} (that's 3 billion!)
so we get the fraction:
C (3 x 10^{9})(94.50)/10,557
= 27 x 10^{6} C
Now, if I only knew C = 1000/Divisor ... but since
27 x 10^{6} C = 27 x 10^{6} (1000/Divisor) = 27 x 10^{9}/Divisor
is a fraction (less then "1", right?) then Divisor must be ... uh ...HUGE!
So, I got in touch with Standard & Poor's (they're in charge of computing the TSE 300 Index)
and they kindly faxed me the current value of the Divisor (as of Sep 12/00). Are y'all ready for this?
TSE 300 Divisor = 92,251,469,343

Whooeee!
Where were we? Oh yes, the Nortel fraction (as of Sep 12/00) was:
(27 x 10^{9})/(92.251469343 x 10^{9}) = .29 or 29%
P.S. This means  and I'll leave out the math  that a 1% change in P_{1} results
in a .29% change in the Index.
A convenient formula for computational purposes can be gleaned from the above result, namely:
C (3 x 10^{9})(94.50)/10,557
= (1000/Divisor)(3 x 10^{9})(94.50/10,557 )
so, we stick in the value of the Divisor and get:
Nortel_Fraction = 32.5(94.50/10,557) = 32.5 (Nortel_Price/TSE300_Index)
so, on Sep 13/00, when Nortel closed at 99.25 and the TSE300 closed at 10,750 the fraction was
32.5 (99.25/10,750) = .30 or 30%
Of course, that 32.5 is just for Nortel. However, if that number hasn't changed since Jan, 2000
(meaning the number of outstanding shares and the magic divisor haven't changed and
no changes in the components of the TSE), then without Nortel, the TSE300 gains (to
Oct 25/00) would look like so, where we've used the gains in TSE(1Nortel_Fraction)
as the Nortel_Fraction changed, day to day, because of the change in Nortel_Price:
Although the TSEsansNortel would NOT change to TSE (1Nortel_Fraction),
because the divisor would change as well, nevertheless, the
percentage changes in
TSE (1Nortel_Fraction) should be the same as the percentage changes
in TSEsansNortel because the divisor cancels out when computing percentage changes. In case the
chart looks strange, on Oct 25, Nortel dropped about 26% on that day ... and the TSE dropped
about 8% (like, about, 30% of 26%), but almost all of the 840 point drop in the TSE was due to
Nortel. Without Nortel, the drop in the TSE299 would have been, maybe 60 points!
Okay, for any stock of the TSE 300 we got us a formula:
Stock_Fraction
= (1000/Divisor) n_{1}P_{1}/TSE300_Index
so if we substitute Divisor = 92.251 (in Billions) and we stick in
the Market_Cap = n_{1}P_{1} (also in $Billions) we get the magic formula:
TSE300 Stock_Fraction = 10.8 Market_Cap/TSE300_Index

Example: