Ever Had Problems Rounding Off Figures? This Stock Exchange Has [pdf]

The articles in the pdf mention that the exchange price changed with every trade, and then mention that the S&P500 always got the rounding correct.

In 1983, when this occurred, the S&P500 index was updated once per minute. This gave them plenty of time to get the math right. They switched to updating every 15 seconds in 1986, I think.

Another thing to note is that back then, American stock prices were quoted in fractions of a dollar, using base-2 fractions (half, quarter, eighth, sixteenth, and thirty-second of a dollar). All prices were able to be represented perfectly in binary floating point, making the math a lot cleaner!

The S&P500 was weighted, but it is very plausible that the weights were massaged to also allow for more accurate math.

Lastly, it’s hard to believe that VSE chose to update their index with each trade rather than calculate it from scratch every time. But that’s what the article says they did!

This is really a story about error propagation and not a story about rounding!

Unsuspecting investors in Vancouver Stock Exchange issues have done a double-take when the speculative resource-oriented exchange opened for trading yesterday. The index measuring activity on the exchange sat at 1098.892, mysteriously up 574.081 points from Friday’s close. But VSE stock prices were unchanged in the cold light of day. Rather, the change in the index represents three weeks of work by consultants, correcting mistakes in index calculation that have been compounding themselves for the 22 months the index has been in operation.