How to compute the volume of an index from the volume of its constituents?

Question

I'm trying to understand how to compute the daily volumes of the Dow Jones Industrial Average but I haven't found the proper formula yet.

I thought it was the sum of the price*volume of each constituent but the result doesn't match.

For example, on 2012-08-23 the last prices and volumes were:

Company             |    Volume   | Price  | Volume x Price
------------------- | ----------- | ------ | --------------
3M Co               |   1 953 688 | 114,40 |    223 501 907
Alcoa               |  11 141 890 |   8,05 |     89 692 215
American Express    |   2 521 379 |  73,65 |    185 699 563
AT&T                |  29 728 622 |  34,29 |  1 019 394 448
Bank of America     |  67 699 182 |  14,57 |    986 377 082
Boeing              |   3 017 610 | 105,48 |    318 297 503
Caterpillar         |   4 487 260 |  83,89 |    376 436 241
Chevron             |   4 682 301 | 119,53 |    559 675 439
Cisco Systems       |  41 268 535 |  23,86 |    984 667 245
Du Pont de Nemours  |   2 674 462 |  57,90 |    154 851 350
Exxon Mobil         |   9 206 422 |  87,52 |    805 746 053
General Electric    |  20 691 132 |  23,78 |    492 035 119
Hewlett-Packard     |  22 069 135 |  22,40 |    494 348 624
Home Depot          |   7 743 049 |  73,89 |    572 133 891
Intel               |  23 088 692 |  22,44 |    518 110 248
IBM                 |   2 295 092 | 185,42 |    425 555 959
Johnson & Johnson   |   7 714 990 |  88,41 |    682 082 266
JPMorgan Chase      |  11 126 713 |  52,32 |    582 149 624
McDonald's          |  12 274 162 |  95,13 |  1 167 641 031
Merck               |   9 181 807 |  47,73 |    438 247 648
Microsoft           | 225 493 737 |  34,75 |  7 835 907 361
Pfizer              |  18 507 496 |  28,34 |    524 502 437
Procter & Gamble    |   5 228 946 |  80,01 |    418 367 969
Coca-Cola           |  11 303 083 |  38,52 |    435 394 757
Travelers Companies |   1 336 935 |  80,19 |    107 208 818
United Technologies |   2 608 836 | 102,80 |    268 188 341
UnitedHealth Group  |   3 218 469 |  72,54 |    233 467 741
Verizon             |   6 779 268 |  47,61 |    322 760 949
Wal-Mart            |   5 475 169 |  73,44 |    402 096 411
Walt Disney         |   5 510 670 |  61,73 |    340 173 659
                    |             |        | 
Total               |             |        | 21 964 711 900

But the DJIA volume for this day was actually 131 855 227:

https://www.google.com/finance/historical?cid=983582&startdate=Aug+19%2C+2013&enddate=Aug+26%2C+2013

So what is the right formula?

Answer 1

The volume reported for the DJIA is the sum of the volumes (in shares) of the individual components, including trades executed on their respective primary markets only.

For the 23rd of August, it looks like:

Ticker  Exchange    Shares Traded
MMM     New York       496,789
AA      New York     2,400,280
AXP     New York       613,379
T       New York     4,886,455
BAC     New York    12,040,541
BA      New York       750,949
CAT     New York     1,456,577
CVX     New York     1,386,990
CSCO    NASDAQ GS   10,916,222
KO      New York     2,786,460
DD      New York       780,407
XOM     New York     2,357,309
GE      New York     5,896,019
HPQ     New York     5,304,441
HD      New York     2,399,417
INTC    NASDAQ GS    7,082,188
IBM     New York       593,065
JNJ     New York     1,839,555
JPM     New York     2,302,471
MCD     New York       876,265
MRK     New York     3,387,386
MSFT    NASDAQ GS   48,203,961
PFE     New York     4,478,299
PG      New York     1,475,610
TRV     New York       269,658
UTX     New York       832,110
UNH     New York       968,481
VZ      New York     1,704,463
WMT     New York     1,443,304
DIS     New York     1,971,379

        Total      131,900,430

Also note that the volume for the DJIA as reported on Bloomberg is 131,900,430 for that day - not sure where google is getting the number from.