Calculating DJIA
Q: It was previously my understanding that the DJIA was equal weight among all 30 components. That is, if the largest company rose 100% in one day while all others stayed equal, the Dow as a whole would rise 100/30 = 3.33%. The same would occur if it were the smallest company that rose 100%.
A:
The implication you describe is correct. That low price stock
doubling could be like $5. The high price stock doubling could be
like $85. Either way, it is the dollar change times what is now
the MULTIPLIER. This means that the higher price stocks always have
a disproportionate influence on the Dow averages. Thus, it has
always been.
If the average consisted of three stocks - A ($10), B ($20) and C ($30), the
price-weighted average of the three stocks is 20.00. Now, if stock A were to
split 2:1 overnight, the prices would be A ($5), B ($20) and C ($30) and the
average would seem to be 18.33, which would make it look like the averaged
changed in value while the stock market was closed. In order to keep
continuity in the average despite the split, a divisor of 0.917 is
introduced after the split so that the average is $18.33/0.917=20.00, which
is where it was when the market closed. Every time there is a another split,
the divisor changes again.
If your head isn't spinning too much yet, consider the two cases of
1) a stock doubling first and then splitting 2:1
and
2) a stock splitting 2:1 first and then doubling.
If you use the same three stocks:
A ($10), B($20) and C ($30) = the price weighted average is 20.00.
Now if stock A doubles in price you would have
A ($20), B($20) and C ($30) = the price weighted average is 23.33.
Then if stock A splits 2:1 you would have
A ($10), B($20) and C ($30) = the divisor is 0.857 and the price weighted
average remains at 23.33.
HOWEVER,
Starting with the same scenario:
A ($10), B($20) and C ($30) = the price weighted average is 20.00.
If stock A were to split 2:1 first you would have
A ($5), B ($20) and C ($30) = the divisor is now 0.917 and the price weighted
average is still 20.00.
Then if stock A doubles after the split you would have
A ($10), B ($20) and C ($30) = the divisor is still 0.917 and the price
weighted average is 21.82.
See? The average comes out looking better in the first scenario, even though
the total market value of A, B & C wind up at the same place in both
alternatives.