Blog - Investing Notes

December 26, 2006 - Out-of-Sample Test of Trading Streak Reversals

After reading the article "If a Stock Keeps Moving Higher, Should You Buy It or Sell It?", reader Dennis Page of Beverly Hills MI asks for a second opinion. In the article, TradingMarkets.com cited their past research, based on stock market index data from 1989-2003, finding that it is better to be a seller (buyer) after the market has been strong (weak) and has made multiple days of higher highs (lower lows). They also report results from their new research, based on seven million backtested trades from 1/1/95 to 6/30/06, that reaches the same conclusion with respect to individual stocks. They recommend that "...traders should look to build strategies around stocks that make at least five consecutive days of lower lows." However, they do not report the variability of their results, and they do not test the economic value of the recommended trading strategy. In this entry, using S&P 500 index data for 1/2/04-12/22/06, we perform an out-of-sample test of their original index "streak" research, including an analysis of economic value to traders. We conclude that:

The following chart shows the average returns, with subsample sizes (in parentheses) and one standard deviation variability ranges, for one trading day after various lengths of up and down streaks for the S&P 500 index. We calculate returns using the closing price on the day the streak materializes and the closing price the next trading day. Most of the subsample sizes are so small that they are meaningless for statistical inference (and useless as trading rules). The two largest subsamples, for three-day up and three-day down streaks, confirm the relative reversal effects reported above. The average daily return for the entire sample is +0.03%, while the average daily return for days after three-day up (down) streaks is -0.08% (+0.21%). However, the variability (standard deviation) of the post-streak returns is much larger than differences in average daily returns. For the day after three-day up (down) streaks, there are 26 (21) days with a return greater than 0.03% and 30 (12) days with a return less than 0.03%. If the streaks were not so rare, these small advantages might be useful. We will test their economic significance as trading indicators below.

The next chart shows the average returns, with subsample sizes (in parentheses) and one standard deviation variability ranges, for five trading days after various lengths of up and down streaks for the S&P 500 index. We calculate returns using the closing price on the day the streak materializes and the closing price five trading days later. Again, most of the subsample sizes are so small that they are meaningless for statistical inference (and useless as trading rules). The two largest subsamples, for three-day up and three-day down streaks, confirm the relative reversal effects reported above. The average five-day return for the entire sample is +0.17%, while the average daily return for days after three-day up (down) streaks is -0.01% (+0.28%). However, the variability (standard deviation) of the post-streak returns is much larger than differences in average daily returns. For the five-day period after three-day up (down) streaks, there are 29 (18) periods with a return greater than 0.03% and 27 (16) periods with a return less than 0.17%. If the streaks were not so rare, these small advantages might be useful.

The next chart shows the balance over time for $100,000 initial investments using three strategies. One strategy is buy the S&P 500 index at the close on 1/2/04 and hold, producing a gain of about 28% over roughly three years. A second strategy is to short the S&P 500 index for one trading day after each three-day up streak (56 sell-buy transaction pairs), producing a gain of about 3% over roughly three years. A third strategy is to buy the S&P 500 index for one trading day after each three-day down streak (33 buy-sell transaction pairs), producing a gain of about 6% over roughly three years. We assume each buy and sell transaction carries a $10 trading fee. We assume no additional fees for shorting. We assume no return to the two trading strategies while out of the market because of the complication of settlement periods. It would be reasonable to credit these strategies with an incremental 3% per year interest on cash. The chart shows that the trading strategies generate small positive returns with low volatility, but they substantially lag the raw return from buy-and-hold.

The final chart shows the balance over time for $100,000 initial investments using two additional strategies. The benchmark strategy is again buy the S&P 500 index at the close on 1/2/04 and hold, producing a gain of about 28% over roughly three years. One additional strategy is to short the S&P 500 index for five trading day after each three-day up streak (56 sell-buy transaction pairs), producing a loss of about 1% over roughly three years. Another additional strategy is to buy the S&P 500 index for five trading days after each three-day down streak (33 buy-sell transaction pairs), producing a gain of about 9% over roughly three years. Again, we assume each buy and sell transaction carries a $10 trading fee, no additional fees for shorting and no return to the two additional trading strategies while out of the market because of the complication of settlement periods. It would be reasonable to credit these strategies with an incremental 2% per year interest on cash. The chart shows that the volatilities of the two additional trading strategies are higher than those above, and they again substantially lag the raw return from buy-and-hold. The shorting strategy is particularly poor because the average five-day return after three-day up streaks is barely negative.

Why do these trading strategies underperform buy-and-hold, even though they generate average returns different from those of the overall sample? Because the streaks are rare, they keep a trader out of a generally rising market most of the time. The cumulative return is higher from playing 750 times compounded at 0.03% than from playing 56 times compounded at 0.8%, or 33 times compounded at 0.21% or 0.28%. In addition, the variability of returns after streaks is much larger than the average excess trading returns, making streak-reversal trading outcomes unreliable (vulnerable to bad luck). Finally, buy-and-hold minimizes trading costs.

Note that, during a generally declining market, streak-reversal traders would probably outperform buy-and-hold investors because they would be mostly out of a falling market.

Perhaps an active trader could find enough streak-reversal trades across many stocks (if such trades are not highly correlated) to keep capital continuously engaged in trading, but trading costs would go up. There might even be enough concurrent up and down streaks to maintain a zero-cost (but high turnover) portfolio that is short the former and long the latter.

In summary, while the average daily returns immediately after up (down) stock market streaks may be systematically lower (higher) than average, traders relying on index streak reversals will likely underperform a buy-and-hold investor most of the time.

For research on other trading indicators, see Blog Synthesis: Some Trading Indicators. [Update: see also the extension of index streak testing to the Nasdaq Composite index in our blog entry of 12/29/06.]