## Current Standard Deviation Levels for the Daily SP500 SPX

Jun 19, 2010: 2:48 PM CSTFor those of us who enjoy Bollinger Bands on our market charts, you’ll also enjoy Standard Deviation Bands… which are just extra Bollinger Band lines.

For reference, the Bollinger Band indicator takes the 20 day simple moving average of price and then calculates – draws lines – two standard deviations (a volatility indicator) up and down that mean (average) price.

Therefore, Standard Deviation bands do the same thing as the typical Bollinger Band indicator, but allow you to plot each standard deviation price (and line) for the current price.

Here – let’s look at the current Standard Deviation Levels for the S&P 500:

Other than being a very colorful, ‘busy’ chart, each line reflects a standard deviation from the blue line, the 20 day average (mean) price.

Instead of being static (one price – as you see at the right side of the chart), the bands move as volatility increases or decreases in the market.

So if we took a static picture of the moment – which is what the numbers represent – we find the following values:

Average 20 day price: 1,086

1 Standard Deviation above: 1,107

2 Standard Deviations above: 1,127

3 Standard Deviations above: 1,148

4 Standard Deviations above: 1,168

Thus, currently one standard deviation is 20.5 index points.

One could say “we are resting just under our upper Bollinger Band, or have moved 2 Standard Deviations away from the mean (average price)”.

As you can see from the past, the price tends to stay within two standard deviations of the mean – hence the value of Bollinger Bands.

However, during ‘crashes,’ price can eject up to 3, 4, or even 5 standard deviations from the mean, which happened in May.

These charts are helpful references when looking at how far price has traveled away from its average price, and what the odds are of price returning back towards that mean – a typical mean reversion play.

If anything, this is just another way to look at a standard Bollinger Band chart… kicked up a few notches.

Corey Rosenbloom, CMT

Afraid to Trade.com

Follow Corey on Twitter: http://twitter.com/afraidtotrade

June 20th, 2010 at 12:08 am

I very much enjoyed the Standard Deviation Bands Chart. It is nice to equate that a Bollinger Band is + or – two standard deviations. Thank you. May I ask, what are the odds of the price reverting back to the mean when it is 2 standard deviations away vs. 3 standard deviations, 4, etc?

June 20th, 2010 at 12:14 am

Thank you G Nail!

The assumption would be that if something is 2 standard deviations away from the mean, then only 5% of the time would that happen – thus something – statistically – spends 95% of its time between 2 standard deviations from the mean.

However, price does not conform to a normal distribution like other things in nature do – like height. So the exact calculation is more muddied than the classic 95% figure.

Take the figures for a normal distribution and add in an extra layer of flexibility when discussing price behavior. Taleb's “The Black Swan” is a good book for how prices are not normally distributed.

June 20th, 2010 at 1:14 am

Again, great stuff, Corey.

The market is treading cautiously higher at the moment…it will be interesting to see if price will revert back to the mean…

P.S. Working on a Saturday? Don't you sleep?

Cheers!

Frank

June 20th, 2010 at 11:45 am

[…] Jun 20, 2010: 11:45 AM CST I received a lot of positive responses and questions to my recent “Standard Deviation Bands for the S&P 500″ post, and I wanted to follow-up by posting the current standard deviation levels and bands for the […]

June 20th, 2010 at 12:30 pm

on the comment price behaviour is not-normal. well in reality most models use returns as following normal distribution.

what does extra layer of flexibility mean statistically and in layman terms?.

i think its very useful to separate the market as one in crash mode and one in non-crash mode before conducting a statistical experiment. would this be an extra layer of flexibility?

would you say we are back in normal(non-crash) mode now in the markets?

also what your comments on extra layer of flexibility? would be interesting to know.

tia

June 20th, 2010 at 1:15 pm

Hi Corey,

I am aware of your caution that you have given us in the last few posts – where there are declining internals, lower volume and higher highs.

On that note, I am surprised you only gave the SD's above, and not the one's below. You even wrote the phrase “However, during ‘crashes,’ price can eject up to 3, 4, or even 5 standard deviations from the mean”.

Are we not still in crash mode, or have you become bullish suddenly???

As well, if not but for me, would you please give those SD's to the down side. It'll give us a frame of reference as to how far down we could go (presuming SD bars are helpful).

Thanks.

June 20th, 2010 at 2:08 pm

Corey,

Do you recommend the book by John Bollinger? I have your lesson on Bollinger Bands, just wondering if I should have a deeper understanding of it.

Robin.

June 21st, 2010 at 12:29 pm

Corey,

Thank you very much for your response & help. As well, I greatly appreciate your work on the DOW & NASDAQ's standard deviations. Regarding a previous post about showing only the positive standard deviations…once again you are correct…the futures are UP, UP, UP this morning. Thanks for ALL your help!

Have a GREAT Day!

Greg

June 21st, 2010 at 7:30 pm

And down, down , down. <smile>