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Backtests on Stock Prices
Backtests show price trends persist and low-priced stocks underperform.
Price trends
Statisticians say large changes in stock prices occur more often than random behavior would suggest, giving a distribution chart "long tails." If this is true, stock prices would move in exaggerated trends, not in random walks.
Ten million random numbers generated in Excel were filtered with the RANDWALK.BAS Qbasic application. Because of the vast number of calculations required the application was run in qb64, which is much faster than Qbasic. The figures for Avg are unmodified, not expressed as boxes:
Generally, trend lengths are twice Min. For Min less than 20, Avg numbers are slightly higher than twice Min because of the finite pace size擁n a true random walk each pace would be infinitesimal. For Min greater than 20, Avg grows increasingly more erratic because of the diminishing number of trends.
To determine average trend lengths in stocks, daily closing prices of components of the S&P 500 Index with the longest price histories in the MSN database were analyzed with the TRENDS.BAS Qbasic application. Price histories, adjusted for splits but not dividends, started at 1/2/1962 for the first nine stocks and 1/2/1970 for the rest, and extended to 2/2/2012:
Generally, trend lengths are significantly more than twice Min. This is especially evident for Up with any Min and for Down with Min 5. Because of the upward bias of the market, this is less evident for Down with Min 10, 20, and 40.
Low-priced stocks
Backtests were performed to see if there is any correlation between price and performance. All stocks returned with the Yahoo Java screener and the Zacks screener, with the sole criterion that price >= 0, were included. The average price gain in each quarter for five price ranges and the overall average price gains were calculated:
YAHOO AVERAGE GAINS Price, $ <5 >=5 & <10 >=10 & <20 >=20 & <50 >=50 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 2010 qtr 4 18 16 10 14 11 2011 qtr 1 5 0 1 2 3 2011 qtr 2 -16 -7 -3 -2 0 2011 qtr 3 -30 -25 -19 -20 -16 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 Overall -6 -4 -3 -1 -1 ZACKS AVERAGE GAINS Price, $ <5 >=5 & <10 >=10 & <20 >=20 & <50 >=50 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 2009 qtr 4 -15 -6 0 3 -2 2010 qtr 1 10 9 7 5 3 2010 qtr 2 -12 -11 -8 -7 -8 2010 qtr 3 -10 -3 -1 2 3 2010 qtr 4 5 14 16 13 10 2011 qtr 1 6 -1 1 2 2 2011 qtr 2 -15 -8 -5 -3 0 2011 qtr 3 -27 -25 -25 -20 -16 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 覧覧覧覧覧 Overall -7 -4 -2 -1 -1
The Yahoo and Zacks results were similar, except for stocks under $5 in 2010 qtr 4. This is probably due to survivor bias. Yahoo keeps low-priced stocks if they gain, but drops them if they decline enough to be delisted. Zacks keeps stocks even if they are delisted. The Yahoo test was limited to one year because earlier results for low-priced stocks would have lacked credibility.
Average gains improved steadily with increasing price range. I choose not to buy stocks under $5 or to buy call options on stocks under $5. Choosing $10 would probably work as well, but choosing $20 would eliminate the majority of stocks.