September 2003
Numbers and Percents
| "Not everything that can be counted counts, and not everything that counts can be counted." |
| -- Albert Einstein |
OPS, WE MESSED UP. Even quants occasionally misread the numbers. More precisely, we misread the percents.
This all has to do with the technical indicators that appear each week on the Home Page. It seems that for the past two years, two of the indicators haven't been indicating much; not because they were faulty, but simply because we haven't been reading them correctly.
[In May 2002], we made some minor changes to the index, but missed the factors in question. Now that we've discovered the problem, a little late is better than never.
As always when we make a change, we backtested the results and found that there really wasn't an impact until just several months ago in early 2003. Now everything should be straight.
The Indicator
Our technical index is comprised of nine different indicators. The index reading is derived by simply subtracting the negative readings from the positive readings. Neutral results are excluded.When the index is +8 or +9, that's a buy signal. When it's -6 to -9, that's a sell signal. (For an explanation of the asymmetry between buy and sell signals, see Technical Tweak and for a complete description of the technical index, see Fundamental Technical Analysis.)
The indicator in question is the Advance/Decline Line. Actually our index uses two of them, one for the New York Stock Exchange and one for the Nasdaq.
Their calculations are relatively straightforward. Over each period -- we use the weekly average -- you simply subtract the declining issues from the advancing issues and add the result to the prior periods' total. By plotting the resulting value vs. the time period, you get a trendline known as the Advance/Decline Line. The NYSE and Nasdaq lines are shown on the charts below.
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Chart 1 NYSE Advance/Decline Line July 1992 - July 2003 |
 Data Source: A-T Financial |
The interpretation of the A/D Line is equally simple: A line moving up is bullish for the market since advancing issues are leading decliners while a line moving down is negative for the opposite reason.
The A/D Line can be even more informative if you compare it to market volume. Sharp moves in either direction are more significant if accompanied by greater volume. On the other hand, similar moves on low volume are less reliable since they may simply be the result of thin trading rather than true trends. We use volume in interpreting the A/D Line, that's why you'll notice it's included in both Charts 1 and 2.
The Problem
In essence, the A/D Line is a way to measure trends in the market. The actual point for the chart is irrelevant. Most technicians use zero as the starting point, but the actual beginning value really doesn't matter. As you'll notice from Charts 1 and 2, we used zero as our starting point back on June 30, 1992.Since then, the A/D totals have moved considerably. As of August 1, 2003, the NYSE A/D line has risen to 43,416 while the Nasdaq's has fallen to -52,404.
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Chart 2 Nasdaq Advance/Decline Line July 1992 - July 2003 |
 Data Source: A-T Financial |
Without additional information, you can't infer much from these raw numbers. For example, contrary to the divergence of the A/D values, Basline shows the Nasdaq Composite rising 208% while the NYSE Composite climbed a more modest 134% over the same period. Putting these together, you could correctly conclude that the Nasdaq charge was led by only a few of its major issues while the NYSE's gains were more broadly based. The A/D data alone would not lead to this conclusion.
So reading the A/D Line is a little more art than science. To utilize it in our technical index, we needed an easy way to get a positive or negative reading from it each week. We decided to just look at its change from the prior weeks' level and verify the finding with volume.
In other words, if it made a strong move in either direction on strong or rising volume, we'd take that as a positive or negative reading depending on the direction of the move. If the weekly move was not pronounced, it would be considered neutral. Similarly, if volume was low or declining, the reading would also be neutral regardless of the magnitude of the change
What remained was to specify what a "strong move" would be. We defined it in percentage terms: A 5% change in either direction would be considered significant enough to result in a positive or negative reading as long as it was supported by sufficient volume.
...this is one of those times when percentages don't truly align with the facts. |
That makes sense, right? Smaller percentage moves could just be noise in the market. No one ever expected the A/D Line to be flat from week to week so small moves are to be expected. Five percent is a reasonable minimum.
As reasonable as this may sound, this is one of those times when percentages don't truly align with the facts. As they say in the NFL, upon further review, this play is overturned.
Here's why: Consider the derivation of the Advance/Decline Line. While the starting point is arbitrary, this week's total is the sum of all the prior week's values. Our data goes back only 11 years, but you can see how the A/D total can quickly grow (or in the case of the Nasdaq, shrink). Remember, the actual A/D value doesn't mean much, it's the trend that counts.
But now compare what it takes to get a 5% change with current A/D values vs. what it would have been just a few short years ago. In August 2003 you'd need a difference of 2,100-2,500 between advancers and decliners to get a positive or negative reading out of this indicator. Unless there's a major rally or rout, this just isn't going to happen.
The problem is that the A/D lines have grown substantially in absolute terms while the number of stocks that can advance and decline hasn't.
... it's no wonder the A/D indicators have been neutral for over two years. Without a major upheaval in the market, they couldn't change. |
Given this, it's no wonder the A/D indicators have been neutral for over two years. Without a major upheaval in the market, they couldn't change.
More importantly, without their participation, the overall index couldn't send a buy signal since the total could never be greater than +7 and +8 is the minimum for a buy. That's a problem.
The Solution
Obviously this is one of those situations where percentages just won't work. With a relatively stable number of stocks, the number of potential advancers and decliners don't grow with the A/D Line. Any indicator based on the A/D Line needs to be based on a change in the number of advancers and decliners, not percentages as we've done in the past.To get an idea of what this number ought to be, we looked back over our 579 weeks of data. During that time, the NYSE's average weekly change in advancers vs. decliners was 346 while the Nasdaq averaged 349. That's remarkably close, but there's really no obvious reason why.
Now that we know what the average weekly change is, we need to define what would be considered above average. Those would be the only changes that should really concern us since they're the only ones that should generate a positive or negative reading in the indicators.
Once again, this is relatively arbitrary, but given that the average on both exchanges is just shy of 350, we decided to focus on those that were above 500. This is 44.32% greater than average on the NYSE and 43.21% on the Nasdaq.
As it turns out, over the 579 week measurement period, the NYSE had weekly A/D changes exceeding 500 25% of the time while the NASDAQ experienced
them 21% of the time. That's the percent of the time our A/D indicator would have flashed a signal -- either positive or negative. The rest of the time it would have been neutral.
That sounds about right. Again this is fairly arbitrary, but still quite plausible. In trending markets -- up, down, or just flat -- you wouldn't expect indicators to be vacillating each week. For that matter, you wouldn't expect them to be sending reaffirming signals every week, either.
The real test came in looking back over the period to see how this change would have affected the technical index. Surprisingly, it didn't have much impact.
In fact, there was no change until 2001. There were several weeks when the market experienced sharp moves in either direction, especially around 9/11 when the A/D indicator would have not been neutral as originally reported.
This also occurred during the failed bull rallies and subsequent selloffs of 2002. Still, these changes would not have been sufficient to cause a change in the overall index reading until mid-spring 2003.
As mentioned earlier, the index would still be stuck at "sell" if a 5% change in the A/D Line was required for a buy signal. On the other had, if it was based on a weekly move exceeding 500 on the A/D Line, the index would have gone from sell to neutral on April 25th and then to buy two weeks later on May 9th.
That's not bad for technical indicators. If you recall, the market hit it's "double bottom" in early March, just as the Iraq conflict was getting underway.
You may already be wondering if this is a change made with 20/20 hindsight, making the theory fit the facts |
Of course there's always the question of data mining. You may already be wondering if this is a change made with 20/20 hindsight, making the theory fit the facts. It could certainly appear that way.
But we would suggest otherwise. It's clear we were wrong to use a percentage for the A/D indicators. Once the A/D Line's absolute value grew beyond 10,000 (assuming 500 is the correct number to use), the indicator lost its effectiveness.
The index was stuck at "sell" but it could have just as easily been stuck at "buy". It's just a function of when the A/D's absolute value went over the magic number.
Yes, this change is being established retroactively but that's really the only way to correct an error. It would even be more of an mistake to continue using the index as originally constituted knowing that two of the nine indicators don't work.
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