Extreme Up Days Signal Market Weakness?

May 21, 2010 • Posted in Technical Trading

Given the U.S. stock market’s weakness since the extreme up day on 5/10/10, a reader wondered whether extreme up days generally portend market weakness because such days tend to occur in bear markets. Using daily returns for the S&P 500 Index over the period January 1950 through April 2010, we find that:

Assumptions for the analysis are:

  • The 100 biggest daily percentage gains in the S&P 500 Index are extreme up days.
  • Return calculations are all close to close.
  • Any market weakness after extreme up days should be evident at horizons of 5, 10, 21 and/or 63 trading days.
  • Extreme up days may cluster such that associated future return intervals overlap (and therefore confound a simple exploitation strategy). A winnowing approach to remove overlapping future return intervals takes the first extreme up day in any cluster (as a trader would probably do).

The following chart summarizes average returns 5, 10, 21 and 63 trading days after: (1) all trading days in the sample; (2) the 100 biggest daily percentage gains; and, (3) the 100 biggest daily percentage gains winnowed to eliminate future return interval overlaps. Winnowing reduces the number of instances for future intervals of 5, 10, 21 and 63 trading days to 81, 71, 55 and 38, respectively.

Results are mixed based on raw (unwinnowed) data, with average returns relatively low for future intervals of 5, 21 and 63 trading days and relatively high for a future return interval of 10 trading days. None of the four average returns are negative. As noted, because of clustering, the raw data count some days more than once.

Results for winnowed (tradable) data indicate relatively high returns after extreme up days for all four future return intervals.

The 100 extreme up days tend to occur during times of high market volatility, limiting confidence in these results. For example, removing just the consecutive days of 9/18/08 and 9/19/08 from the sample boosts the average 21-day future return for raw data from 0.32% to 0.77% and the average 63-day future return for raw data from 1.38% to 1.94%. In other words, a very few instances substantially drive average returns, and results are therefore very sensitive to sampling technique.

Note that the definition of extreme days used in this analysis incorporates sample-wide look-ahead bias, setting the threshold for “extreme” based on the data in the sample. This look-ahead bias, in combination with the sensitivity of results to sampling technique, is problematic for realistic backtesting. A trader operating in real time would not have known where to set the threshold early in the sample period and would have adjusted the threshold based on newly arriving data.

In summary, evidence from simple tests mostly does not support a belief that extreme U.S. stock market up days reliably portend (tradable) subsequent market weakness.

See also the closely related “Extreme Days Relative to Bear Market Ends”.

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