Blog - Investing Notes

August 26, 2009 - Extreme Days Relative to Bear Market Ends

A reader hypothesized:

"Days of extreme volatility seem to cluster and generally in bear markets, and usually closer to the end of them. Might be a good analysis task."

For a simple test, we define "days of extreme volatility" as those for which the S&P 500 Index increases or decreases by more than 3%. We define "bear markets" as peak-to-trough declines of about 20% or more. Using daily closes of the S&P 500 index for 1/2/50 through 8/21/09 (15,006 trading days over about 60 years), we find that:

The following chart, via two panels, maps extreme up days (dark green horizontal lines in left panel) and extreme down days (bright red horizontal lines in right panel) onto bull and bear market intervals (shaded light green and pink, respectively) over the entire sample period.

Some points of interest over the entire sample period are:

• Bear markets comprise about 23% of all trading days.
• There are 94 (86) extreme up (down) days, comprising about 0.6% (0.6%) of all trading days.
• About 56% (71%) of all extreme up (down) days occur in bear markets.
• About 59% of all extreme days occur during the 2000s, making the current decade very unusual.

Differences between the 1950-1999 and 2000-2009 subperiods are pronounced:

• Bear markets comprise about 19% (41%) of all trading days during 1950-1999 (2000-2009).
• Extreme days, comprising about 0.6% (4.3%) of all trading days during 1950-1999 (2000-2009).
• About 32% (47%) of all extreme up (down) days occur in bear markets during 1950-1999.
• About 74% (86%) of all extreme up (down) days occur in bear markets during 2000-2009.

Compared to the preceding five decades, the current one is very bearish and very volatile. It is arguable that the definition of "days of extreme volatility" is not stable over time.

Do extreme days (as defined) systematically cluster near the ends of bear markets?

The following table summarizes the number and positioning of extreme up and down days during each of the 12 bear markets during for the entire sample period. Relevant points are:

• Five of the 12 bear markets (mostly early ones) have no extreme days.
• Positionings of extreme days within bear markets support the hypothesis of clustering near the end in four or five of the 12 bear markets.
• The last two bear markets have about 75% of all the extreme days in the table (and about 47% of all extreme days in entire sample).

Based on the definitions used, clustering of extreme days has occurred near the ends of about a third of the bear markets since 1950.

What if we relax the definition of "days of extreme volatility" to daily movements greater than 2.5% rather than greater than 3%?

The next table summarizes the number and positioning of extreme up and down days with the alternate 2.5% up or down threshold during each of the 12 bear markets defined for the entire sample period. Results support the hypothesis somewhat more strongly, but still not reliably.

The definition of extreme days used in this analysis incorporates sample-wide look-ahead bias, since we estimate where to set the constant threshold for "extreme" based on the data in the sample. This look-ahead bias, in combination with the apparent instability of the definition of "extreme," is problematic for applying the results to real-time decisions.

Also, there may be disagreement regarding what constitutes a bear market.

In summary, evidence from a simple test applied to the last 60 years does not support a belief that extreme days reliably cluster near the ends of bear markets. It does support a belief that extreme days are more likely during bear than bull markets. Results also indicate that the threshold for "extreme" varies over time, complicating the use of extreme days as a signal.

For related research, see Blog Synthesis: Volatility Effects.