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How Many Sigmas Was the Flash Correction Plunge?

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Did you know that last week's 14% plunge in the S&P 500 (SPY - Free Report) was so rare, by statistical measures, that it shouldn't happen once but every 14,000 years?

Last Friday, I assessed the damage and figured out how many "sigmas" -- or standard deviations -- the waterfall cascade from SPX 3350 to 2850 actually was.

In the video that accompanies this article, I run through the math of how to calculate this and turn the VIX into weekly sigmas.

By several measures, it was about a 5-sigma move, something that's not "supposed to" happen more than once in your lifetime -- or your prehistoric ancestors' lifetimes!

According to general statistical principles, a 4-sigma event is to be expected about every 31,560 days, or about 1 trading day in 126 years. And a 5-sigma event is to be expected every 3,483,046 days, or about 1 day every 13,932 years.

But here's how I explained it to my followers last week...

Big sigma moves happen all the time in markets, more than any other field where we collect and analyze historical data, because markets are social beasts subject to "wild randomness" that is not found in the physical sciences.

This was the primary lesson of Nassim Taleb's 2007 book The Black Swan, written before the financial crisis that found Wall Street bankers completely ignorant of randomness and the risks of ruin.

Sigmas Happen

In "TBS," as he is fond of calling it, Taleb honored one of the originators of this line of thinking, Benoit Mandelbrot, progenitor of fractal chaos mathematics and author of the 2006 book The Misbehavior of Markets: A Fractal View of Financial Turbulence, written with Richard L. Hudson.

From the Wikipedia entry on Mandelbrot...

Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

After I read Taleb and Mandelbrot, I had a new appreciation for the power of mathematics to describe a chaotic, multidimensional world that offered both order and unpredictable beauty all around us.

And I realized that market volatility was part of that unstable complexity and chaotic beauty because it was driven by millions of emotional humans, most of whom would not act rationally at either extreme of price. 

The sin of Wall Street has been in using standard deviation as a gauge of risk, wherein historical volatility measures -- and future-gazing ones like the VIX -- imply big price moves should only happen very rarely. Anybody who can read a newspaper knows better.

In my 2008 book review of TBS, I concluded "When anything can happen, there is no standard for deviation."

The Lesson: Be Ready to Buy Big Sigma Moves

While I didn't have any good short positions ready for the "waterfall cascade" last week, I did have good stock positions I liked at a good entry levels -- which means I didn't have to throw out any babies with the bath water panic.

I also had plenty of cash and a shopping list so I could buy some of my favorite stocks like Alteryx (AYX - Free Report) , Splunk (SPLK - Free Report) , and The Trade Desk (TTD - Free Report) . Maybe software won't be totally immune to the coronavirus, but most SaaS will do better during this crisis than semiconductors, hotels and banks.

I also took advantage of the extreme 5-sigma sell-off by grabbing a leveraged ETF on the Nasdaq 100, the ProShares UltraPro QQQ (TQQQ - Free Report) . In my plan, while I might debate the merits of buying AAPL or MSFT for hours, I knew I could immediately buy them both with TQQQ and be rewarded very quickly after the 14% plunge.

Here was the Buy Alert I sent to members of my TAZR Trader service on Friday morning...

Buying TQQQ Despite Panic at the Guggenheim

Posted on 2/28/20

TAZR Traders

As discussed last night, Portfolio will attempt to buy TQQQ, the QQQ 3X Bull ETF, with a 5-7% allocation between $60 and $70. Let the volatility come to you.

What I didn't talk about last night was the Goldman call for ZERO percent earnings growth this year because I thought it was getting priced-in fairly fast.

But then Barclays is out this morning with their call for a MINUS 2% EPS gut check. That will take stocks down below SPX 2900.

We already touched the 2890 level I talked about last night in futures for the fulfillment of a 15% correction.

But now I just found out one of my favorite investment chieftains was yelling fire in the theater yesterday.

Scott Minerd of Guggenheim was on Bloomberg TV yesterday afternoon and said...

Coronavirus May Be Worst Event of His Career: Stocks May Fall 35-40% If Virus Isn't Contained

Whoa! Nothing like a little panic from one of the biggest and best "bond kings" and total asset managers in the world.

Thanks a lot, Scott.

Anyway, I still believe this panic ends soon and that's why I'm buying.

When the bottom comes, you won't see it or have time to buy it before stocks are 5% higher.

(end of TAZR Buy Alert excerpt)

Then that evening, I went through the "sigma math" with these examples...

TAZR Traders

Today's Trade: Bought 7% position in TQQQ at $70.

Brings our CASH down to 10%.

I can't guarantee we've seen the bottom of this panic, especially with a weekend of probable corona hysteria to get everybody worried.

But I've seen this movie a few times and buying extreme, multiple-sigma moves almost always pays off pretty quick.

There were so many oversold, off-the-chart readings in options, breadth, and volatility that I really should have been more aggressive in adding longs.

How many sigmas (standard deviations) was this one week move?

Let's run through the math with a little thought experiment.

First, an essential fact: The VIX is simply annualized standard deviation so that a reading of 20 means the S&P 500 index will be within 20% higher or lower, one year from now, with a 68% probability.

Now, let's say that every genius who knew the VIX was going to 40 this week should have made a mint.

Then let's pretend that 40 was the "normal" volatility, i.e., what everyone should have expected if they were that smart.

Repeat After Me: Volatility is Proportional to Time

Since volatility is proportional to the square root of time, we next convert the annualized standard deviation of 40 into a weekly volatility by dividing it via the square root of time.

Our time period of interest is one week, and so the square root of 50 trading weeks in a year is about 7.

40 / 7 = 5.7% and this is our 1-standard deviation move for a week with the VIX at 40.

So since the market actually fell 14.5% (at the lows of 2855), we have ourselves a 2.5 sigma move this week (14.5/5.7 = 2.57).

But of course it's absurd to call a VIX of 40 the "normal" volatility.

A VIX of 20, implying daily moves of 1.25% on the S&P 500, would equate to a weekly volatility of 2.85% (20/7).

At an "excited" VIX of 25 (where it closed Monday), weekly volatility would be 3.57% (25/7).

So how big was this week's move? About 4 sigmas (14.5/3.6 = 4.03).

But what if we used really "normal" volatility like the 50-day or 50-week moving average for the VIX?

The 50-day MA is 15.9 and the 50-week MA is 15.2. So let's round up and just call it 16.

Following the math examples above, that would make this week's plunge look like a 6.3 sigma move.

How often are 6, or even 4, sigma moves supposed to happen?

Well, scientifically speaking (which is where standard deviation belongs, not in markets) it gets into the "1 in 10,000" to "1 in a million" probabilities of occurring.

Be sure to watch the video where I explain all this with more examples and some handy PowerPoint slides you can copy.

Kevin Cook is a Senior Stock Strategist for Zacks Investment Research where he runs the TAZR Trader and Healthcare Innovators portfolios. Click "Follow Author" above to receive his latest stock research and macro analysis.

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