Last February, the stock market rolled over in a massive plunge that will go down in the history books as the fastest 30% sell-off on record.

Just how rare was the drop?

According to Zacks at the time, the 14% one-week drop back at the tail-end of February “shouldn't happen once but every 14,000 years.”

As we head toward the anniversary of that drop, it makes sense to take a closer look at what happened back then — and myth-bust some of the math behind those headlines.

Just how rare was last year’s COVID crash? Much less rare than market commentators claim.

The drop mentioned in the Zacks piece was what’s known as a five-sigma event. That means it was a sell-off bad enough to come in five standard deviations worse than the average weekly return of the S&P 500.

(If your statistics are rusty, standard deviation is just a measure of how spread out data are.)

Make no mistake, five-sigma events are exceedingly rare. But once every 14,000 years? That implies that investors today will never see a move that big again in their lifetimes!

And it’s totally wrong.

Whenever you see some analyst or market-watcher claim that we’ve just experienced an event that should only happen every however many years or a certain percent of the time, it’s a major red flag.

The only way to make that sort of pronouncement is by making a big assumption about the probability distribution of market returns. Usually, those assumptions are wrong.

This happens a lot.

A story a while back from Bloomberg made the following claim:

“For calendar year 2016, it would’ve taken a 1.6% decline to qualify as a two-sigma move. In 2015, a sell-off of 2% was needed for such a change in the standard deviation of the benchmark index. In English, this is a move you’d expect less than 5% of the time.”

But that’s not true either.

With both cases, Zacks’ and Bloomberg’s, the assumption is that stock returns follow a normal distribution. But it’s common knowledge that’s not true.

Assuming normality works all right when markets are behaving themselves — it falls apart in a brutal way when volatility creeps up.

It’s true that we expect normally distributed data to exceed two standard deviations above or below the average just 5% of the time… But during the financial crisis of 2008, daily returns for the S&P 500 exceeded this threshold by almost a factor of three.

The non-normality of returns is one reason why price shocks occur far more frequently than they “should.”

Ironically, it’s precisely when we’re experiencing crazy market moves that these stats tell us the least about what’s happening in the market!

I’ll spare you the math, but if we loosen our assumptions about the probability distribution that returns follow, we find that a five-sigma drop like the one last February could theoretically happen as frequently as twice a year.

That’s dramatically different from the once-every-14,000-years claim that many market watchers continue to parade.

As the old quote attributed to Mark Twain goes, “It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”

What’s the key takeaway for investors as we head into 2021? Don’t let your guard down thinking that a repeat of 2020’s volatility is “impossible” — it’s really far from it.

The good news is that for now, there’s little reason to expect a repeat in Q1.

While another COVID crash-sized sell-off is certainly more possible than media outlets reported last year, I don’t think it’s very probable in the near term.

As long as the Fed remains willing to inflate asset prices at all costs, it’s likely we see this stock market rally persist, with tech stocks leading the way.

Sincerely,

Jonas Elmerraji, CMT