Math People: Assemble

It seems every time there’s a market movement of 1% to 2% there are headlines about stocks soaring or plunging, and it got me thinking about the standard deviation of daily S&P 500 returns.

The data I’ve seen show an annualized standard deviation of S&P 500 returns of about 19% depending on the time period. My understanding is the annualized standard deviation can be divided by the square root of 250 to get the daily standard deviation, but does this provide a meaningful context for evaluating stock market fluctuations, or is this a flawed way of thinking about it? I believe the returns of the S&P 500 are negatively skewed and wondered if this might cause some issues in interpreting the standard deviation.

If not by using the method above, what would be the best way to put daily market returns into context?

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Daily returns are mostly noise.

Unfortunately, the pundits don’t get paid for saying that they’re mostly noise, so they always have a reason for whatever happens: profit-taking, interest rates, whatever.


I can prolly pull up the percentiles for it and give you a range I have this excel that tell me range of percentile for any ticker I plug.

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Don’t feel obligated. I’m satisfied with Magician’s response.

This is a valid concern. Standard deviation (and of course, variance) assumes symmetry of the distribution. It’s generally inappropriate as a measure of dispersion for variables where the outcomes are not symmetrically distributed. IQR ia a measure of dispersion that could be useful in this case.

Edited as indicated below for accuracy.

MAD assumes symmetry every bit as much as standard deviation does.

You’re right I don’t know why I included that in there-- should only be IQR for concerns of asymmetry.

This is why drawdown measures are useful. Take a look at the typical drawdown for the S&P in any 12 month period and you will be able to sleep more easily during the next market decline…and perhaps provide some comfort to your clients.

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