elapsed. Once the longest of the time periods passes, the quantification process becomes inactive, remaining dormant until the indicator generates a new signal. In contrast, the other two approaches are always active, calculating market performance with every data update.

The subsequent-performance approach is thus applicable to indicators that are more useful for providing indications about one side of a market, indicating market advances or market declines. And it is especially useful for indicators with signals that are most effective for a limited amount of time, after which they lose their relevance. The results for a good buy-signal indicator are shown in Figure 11.7, which lists market performance over several periods following signals produced by a 1.91 ratio of the 10-day advance total to the 10-day decline total.

Figure i i .7 signals based on 10-day total of NYSE (New York Stock Exchange) advances over 10-day total of NYSE declines, concept

courtesy of dan sullivan, modified by ned davis research. all-period results are based on data from 6/23/47 through 6/30/96.

Signals based on 10-day total of NYSE advances over 10-day total of NYSE declines. Concept courtesy of Dan Sullivan, modified by Ned

Davis Research. All-period results based on data from 6/23/47 through 6/30/96.

Source: Ned Davis Research, Used by permission.

In its most basic form, the results might list performance over the next five trading days, 10 trading days, and so on, summarizing those results with the average gain for each period. However, the results can be misleading if several other questions are not addressed. First of all, how is the average determined? If the mean and the median are close, as they are in Figure 11.7, then the mean is an acceptable measure. But if the mean is skewed in one direction by one or a few extreme observations, then the median is usually preferable. In both cases, the more observations the better.

Second, what is the benchmark? While the zone approach uses relative performance to quantify results, trade-signal analysis includes a comparison of per annum gains with the buy-hold statistic. Likewise, the subsequent-performance approach can use an all-period gain statistic as a benchmark. In Figure 11.7, for instance, the average 10-day gain in the Dow Industrials has been 2 percent following a signal, nearly seven times the 0.3 percent mean gain for all 10-day periods. This indicates that the market has tended to perform better than normal following signals. That could not be said if the 10-day gain was 0.4 percent following signals.

A third question is how much risk has there been following a buy-signal system, or reward following a sell-signal system? Using a buy-signal system as an example, one way to address the question would be to list the percentage of cases in which the market was higher over the subsequent period, and to then compare that with the percentage of cases in which the market was higher over any period of the same length. Again using the 10-day span in Figure 11.7 as an example, the market has been higher after 75 percent of the signals, yet the market has been up in only 57 percent of all 10-day periods, supporting the significance of signals. Additional risk information could be provided by determining the average drawdown per signal (i.e., the mean maximum loss from high to low following signals). The mean for the 10-day period, for example, was a maximum loss of 0.7 percent per signal, suggesting that at some point during the 10-day span, a decline of 0.7 percent could be considered normal. The opposite approaches could be used with sell-signal indicators, with the results reflecting the chances for the market to follow sell signals by rising, and to what extent.

Along with those questions, the potential for double counting must be recognized. If, for example, a signal is generated in January and a second signal is generated in February, the four-month performance following the January signal would be the same as the three-month performance following the February signal. This raises the question of whether the three-month return reflects the impact of the first signal or the second one. Moreover, such signal clusters give heavier weight to particular periods of market performance, making the summary statistics more difficult to interpret.

Problems related to double counting can be reduced or eliminated by adding a time requirement. The signals in Figure 11.7 used the condition that in a 50-day window, if the ratio reaches 1.92, drops to 1.90, and then returns to 1.92 two days later, only the first occurrence will have a signal. This time requirement eliminates the potential for double-counting in any of the periods of less than 50 days, though the longer periods still contain some overlap in this example.

Another application of subsequent-performance analysis is shown in Figure 11.8, which is not prone to any double counting. The signals require that three

Figure 11.8 Confirmation occurs, and a case identified, when the DJIA

and the index in question both reach 52-week highs, the first such joint

occurrence in at least a year. chart is sorted based on percentage of cases in which the index was higher over the subsequent 52-week periods (shaded column). "% all periods" is the DJIAs mean gain for all 26-, 39-, 52-week periods starting with the beginning of the data in question.

conditions are met, all for the first time in one year-the Dow Industrials much reach its highest level in a year, another index must reach its highest level in a year, and the joint high must be the first in a year. The significance for the various indices can then be compared in conjunction with their benchmarks (i.e., the various all-period gains). Figure 11.9 uses twelve of those indices to show how subsequent performance analysis for both buy signals and sell signals can be used together in an indicator. For each time span, the charts box lists the markets performance after buy signals, after sell signals, and for all periods.

Reversal-Probability Analysis

Finally, the subsequent performance approach is useful for assessing the chances of a market reversal. In Figure 11.10, the "signal" is the markets year-to-year change at the end of the year, with the signals (years) categorized by the amount of change-years with any amount of change, those with gains of more than 5 percent, and so on. In this case, the subsequent-performance analysis is limited to the year after the various