Sunday, February 24, 2008

Financial Price Change Distributions 2

One index I never trade in is probably the most widely known index, the Dow Jones Industrial Average (^DJI) AKA the Dow 30 or just 'Wall Street'.

The reason I avoid it is because it is an average over the share price of each composite company. Each company's share of the index is not weighted by market capitalisation as is the norm for most other indexes. This means that a relatively small company's price can go up say 10% but cause the index to go up by a disproportionate amount. E.g. say it causes the index to rise by 2% but that the company is miniscule compared to the other 29 in the index. The overall market cap of those 30 companies has not risen by anything like 2%.

This oddity has always led me to believe there will always be a greater degree of randomness in the Dow than most other indices, and possibly some weird dynamics unique to the Dow (hmm, maybe there could be something to profit from there?) and thus to just avoid it in favour of some other large cap index such as the S&P 500. If the PE is high in the S&P 500 I feel a lot safer shorting it than I would the Dow, which I feel is more likely to spring a surprise on me, e.g. a small company (with a larger share than it's market cap warrants) posting strong results.

Following on from yeserday's post then, I was wondering if this oddball index exhibits a distribution curve significantly different to market cap weighted indices. Here is a graph comparing the daily percentage price change distributions for the Russell 2000, The Dow and the S&P500. For comparison the frequencies for the Russell 2k and the S&P are scaled up to match the DOW at its peak.

And let's have a peek at one of the tails.

Note that the blip in the Dow at about -22% is from the crash of 1929.

I did wonder if the extra random element (the arbitrary weighting) in the Dow would make it's curve a bit more gaussian, apparently not. Of course there is potentially a significant effect from the buying and selling of the Dow directly, through various derivatives. If we were to take 30 random companies from the S&P 500 and construct our own unweighted index using historic data would that index still have a Levy Skew alpha-stable distribution?

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