Unexpectedly Intriguing!
February 27, 2018

The last month has been an exciting time for the U.S. stock market, where if you wanted to describe it in one word, volatile would probably be the word that best describes it!

But to understand how exciting it has been for investors and traders, we need to put the last month of stock price volatility into some historical context. Which we've done in the following chart showing the daily volatility as the percentage change in the closing price of the S&P 500 since 3 January 1950, which updates one we first featured two-and-a-half years ago.

S&P 500 Daily Volatility (Percent Change Between Closing Value and Previous Day's Closing Value), 3 January 1950 - 26 February 2018

By and large, the pattern daily volatility in the S&P 500 and its predecessor indices over the last sixty-eight years and almost two months follows something that looks a lot like a normal distribution, although with considerably more datapoints (~79%) falling within one standard deviation of the flat, near-zero mean trend line than would be expected if that pattern of variation really applied (~68%).

Conveniently, one standard deviation is roughly equivalent to a percentage change of 1%.

Otherwise, about 95% of all the day-to-day datapoints fall within two standard deviations (or 2%) of the mean, and 99% of all the datapoints fall within three.

Datapoints that fall outside one standard deviation of the mean would therefore be evidence of a heightened level volatility for stock prices, while falling more than three standard deviations (or 3%) away from the mean would be evidence of an "extraordinary" amount of volatility.

Our second chart zooms in on the last month for the S&P 500, from Friday, 26 January 2018 through Monday, 26 February 2018.

S&P 500 Daily Volatility (Percent Change Between Closing Value and Previous Day's Closing Value), 26 January 2018 - 26 February 2018

In this chart, we can see that over the past calendar month covering some 21 trading days, 9 of the datapoints fall within the most "typical" range that we would expect based on the historical data, which is between 7 and 8 fewer than would be expected for that period of time.

The remaining 12 days are consistent with at least a heightened level of volatility in the S&P 500, where we would expect to see just 4 or 5 such days during the course of a month's time. Of those days, two fall more than three standard deviations from the mean, indicating just how extraordinary volatile the month has been for the index.

On one of those days, Monday, 5 February 2018, the S&P 500 dropped more than 4% (or four standard deviations) below the historical mean. Going over all the 17,148 trading days since 3 January 1950, we find that a 4% or larger percentage change from the previous day's close has only been recorded on 86 occasions, where the historic odds of that happening work out to be 1 in 199.

Coincidentally, the total point decline of 113.19 points from the previous day's closing value on 5 February 2018 is the largest single-day point decline on record for the S&P 500, but that's not a terribly impressive figure when you consider that the previous day's closing value for the index was 2,762.13.

The S&P 500's largest ever single day percentage decline was 20.47%, which occurred back on 19 October 1987, a day that became forever known to investors as Black Monday. In terms of actual points however, the index fell by 57.87 points, which is a little over half the value in points that the S&P 500 fell nearly 31 years later on 5 February 2018, when it fell by 4.1%.

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