A Slinky (Short-term Reversion) Effect?

Do often frenzied investors/traders tend to overdo buying and selling, coming to their senses shortly thereafter? In other words, does the broad U.S. stock market tend to revert after short-term moves up or down? To check, we relate sequential past and future return intervals of 1, 2, 3, 5, 10, 15 and 21 trading days. To avoid overlap of observations (and ensure a trader could exploit all of them), we sample at frequencies matching return measurement intervals. For example, for a 5-day return interval, we sample every fifth trading day. Using daily closes of the S&P 500 Index over the period January 1990 through most of September 2011, we find that:

The following chart shows return autocorrelations, rough indications of the degree of short-term reversion, for the specified seven S&P 500 Index measurement intervals over the entire sample period and two equal subperiods:

• The return on the last trading day to the return on the next trading day (1:1).
• The return over the last two trading days to the return over the next two trading days (2:2).
• The return over the last three trading days to the return over the next three trading days (3:3).
• The return over the last five trading days to the return over the next five trading days (5:5).
• The return over the last 10 trading days to the return over the next 10 trading days (10:10).
• The return over the last 15 trading days to the return over the next 15 trading days (15:15).
• The return over the last 21 trading days to the return over the next 21 trading days (21:21).

Overall sample sizes range from 5,477 for 1:1 to 259 for 21:21. Results show that the U.S. stock market exhibits mostly weak reversion tendencies over the short term, but the weak tendency is not highly reliable over time or across measurement intervals.

To investigate non-linearity in past-future return relationships, we look at average future returns by quintile of past returns.

The next chart shows average S&P 500 Index returns by quintile of past index returns. For example, the 5:5 series shows the average future 5-day return by quintile of past 5-day returns. The table below the chart provides the raw data. Quintile sizes range from 1,095 for 1:1 to 52 for 21:21. In general, results suggest that rebounds after the worst return intervals (not pullbacks after the best ones) drive the overall reversion effect. However, progressions are not systematic across quintiles for most return intervals.

The 5:5 reversion after the lowest past returns is perhaps the most attractive from a trading perspective, but the standard deviation of 5-day future returns associated with the 0.58% average gain is 3.37%, so trading this indication is risky.

In summary, evidence from simple tests suggest that the U.S. stock market mostly exhibits weak reversion over short intervals, but the effect is not highly reliable over time or measurement intervals and is generally small compared to associated return variability.

Cautions regarding findings include:

• The analysis is in-sample, employing the entire data set. A trader operating in real-time with purely inception-to-date data may have found different results.
• Trading the weak reversion effect would involve frictions (transaction fee and bid-ask spread) that work against profitability.
• Testing seven measurement intervals on the same data set introduces data snooping bias, so the best outcome likely overstates reasonable out-of-sample expectations.

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