Tuesday, January 09, 2007

Bull and Bear Days: A Simple Coding System and What It Tells Us

Let's create a very simple definition of bullish and bearish days in the market and see where that takes us. A bull day, at the very least, must meet three criteria:

* Its high must be greater than the high of the previous day;
* Its low must be above the low of the previous day;
* It must show a positive change from open to close.

A bear day, conversely, must display the reverse qualities:

* Its high must be below the high of the previous day;
* Its low must be below the low of the prior day;
* It must show a negative change from open to close.

Let's give one point for each of the bullish criteria. A bull day, therefore, earns a score of +3. A bear day is given a score of 0. If a day meets two of the three bull criteria, we'll call it a "near bull day" and give it a score of +2. A "near bear day", on the other hand will have met two of the three bearish criteria and will receive a score of +1.

So there we have it: A very simple coding system based on price action alone. Note that it can be used for any trading instrument for which we have open, high, low, and close prices. It can also be applied to any time frame, including intraday.

When we examine the daily data in the S&P 500 Index (SPY) going back to 2004 (N = 754 trading days), we see that we have had 409 bull and near-bull days and 345 bear and near-bear days. The day after a bull or near-bull day, SPY averages a loss of -.04% (207 up, 202 down). The day after a bear or near-bear day, however, SPY averages a gain of .13% (206 up, 139 down). Interestingly, on a next-day basis, we don't see a significant difference between bull and near-bull days or between bear and near-bear days. We can see, however, that bull and near-bull days are followed by subnormal next day returns and bear and near-bear days are followed by superior next day returns. Indeed, if we only bought the market following a bull or near-bull day and sold at the next market close, we would have lost money during the last three years of bull market!

Let's now look on a five-day basis. We'll consider a five-day period to be bullish if the sum of its daily scores is 10 or greater (meaning that the daily average is a near-bull day or stronger). Conversely, we'll consider a five-day period to be bearish if the sum of its daily scores is 5 or less (meaning that the daily average is a near-bear day or weaker). Five days following a bullish five-day period in SPY (N = 250), the market was up by an average of only .01% (135 up, 115 down). Five days following a bearish five-day period in SPY (N = 139), SPY averaged a gain of .29% (81 up, 58 down). Once again we find superior short-term returns following periods of weakness.

Finally, when we have a bull day during a bullish five-day period (N = 125), the next two days in SPY average a loss of -.03% (60 up, 65 down). However, when we have a bear day during a bearish five-day period (N = 62)--as was the case going into Monday's trade--the next two days in SPY have averaged a gain of .41% (42 up, 20 down). Clearly, we've had the best short-term returns during the bull market following bear days during short-term bearish periods.

In future posts, I'll be looking at other time frames, including weekly data, and other indices, including some of the ETFs. The simple coding system does not tell us how strong or weak a market is; only its directionality. Adding codings for strength or weakness may improve its ability to detect historical trading patterns--yet another topic for future investigation.