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Monday, November 9, 2009

Why Arithmetic Stock Charts Are Worthless

Apologies ahead of time for titling the post so stridently, but I wanted it to capture people's attention. I have seen a lot of different charts on a lot of different blogs and some use Arithmetic (or Linear) Scale Price Axis charts to a) make counts and (more dangerously) b) draw trendlines on them. I disagree with this pretty vehemently and I wanted to share why.

You may have thought about this before, or you may have not. But I will invite you to do so in this post. "But a chart is a chart, right? An axis is an axis right? As long as it has all the data, you're good.... right?". This is not the case.

I am an engineer. I primarily perform thermal and structural analysis in the Aerospace industry. And it is critical to my job when analyzing and trying to comprehend data that it be viewed in the proper context. For example when looking at vibration test data, I look at Frequency Response vs. Frequency or Power Spectral Density vs. Frequency on a Log-Log plot. Same with Fatigue data (S-N curves). An Electrical Engineer looking at the band pass characteristics of a circuit would look at the signal response on a log-log plot.

Looking at any of this information on the wrong scales will improperly exaggerate signals at the top end of the axis and *hide valuable information* at the lower end of the function axis.


** There is an exception to this general statement that arithmetic charts are worthless. It is the crux of Gann's analysis, and arithmetic charts are critical to this analysis. Because there is a *very* specific way you must set up your templates to make them work. And when you do, very specific angle relationships show up that otherwise won't.

But in general an arithmetic chart with no special format will not give you proper relationships on a trendline analysis, and per my reasoning and logic exercise below, I argue that it is invalid.


So first some terminology:

1) Log-Log Scale: Both your horizontal and vertical axis are logarithmic
2) Log-Linear (or Semilog) Scale: One axis is logarithmic and the other is linear / arithmetic. For the purpose of this discussion regarding stocks, the vertical axis (price) is logarithmic and the horizontal axis is linear
3) Linear-Linear: Both axes are linear. This is they way most people generally think about graphs (temperature vs. time, for example)

We will focus on Scales 2) and 3) for this discussion (obviously, log-log stock charts are not very meaningful, since the date is a linear set)

-- Log-Linear vs. Linear-Linear Charts to plot exponential functions

Now I use this word logarithmic a lot. You may be familiar with it or not. But in this context, substitute the word "exponential". They have the same connotation here. An exponential growth in population. Cell-division is an exponential process. Everybody is familiar with this concept. Stock price movement is also exponential, but more on that in a moment.

So lets say I had some initial value of, I don't know, rabbits. And lets say that every year, the population of rabbits would grow by 60% of the previous year's value. What does this look like on the two scales?

What is the important observation here?

On the Linear Scale chart, you have an exponential data set that looks like a parabolic run up. But on the Log Scale chart the data set is a straight line!!. This is why looking at an exponential data set on a log chart gives you so much insight into the behavior. Straight lines on a semilog plot are lines of "constant exponential growth" and the growth percentage is directly related to the slope of the line.

-- Stock Price Movement is Logarithmic

Stock price movement is logarithmic / exponential. Sorry, this needs to be emphasized. ALL GAINS AND LOSSES IN THE STOCK MARKET ARE EXPONENTIAL!! NOT ARITHMETIC!!. To see why, consider this example:

Is a 200 point move equivalent to any other 200 point move? NO. If 200 point move A occurs when an index is at 4000 (5%), it is much less meaningful than if a 200 point move B occurs when an index is at 500 (40%).

This is why linear scale stock charts are almost meaningless.

Because we don’t measure stock performance on an absolute basis, we measure it on a RELATIVE basis. A 50% gain is a 50% gain. Whether you bought a stock at 10 and it moved to 15 or you bought the stock at 1000 and it moved to 1500. This makes all gains and all moves in the stock market exponential / logarithmic.

Stock data on a linear chart improperly exaggerates the importance of moves at the top of the chart and improperly diminishes the importance of moves at the bottom of the chart!!.

For the clearest example of this, lets look at the Homebuilders Index (XHB). As we all know, Home Builders have taken a thrashing the last few years. In fact XHB went from 45 at its peak down to 8, that is a drop of 82%. So, a move of 4 points when XHB was at 8 is a 50% move, whereas a move of 4 points when XHB was at 45 is a 9% move. That is a big difference!!. So how different does XHB look on a linear scale vs. a log scale? You bet, very different!:

On the Semilog (above), everything looks fine and normal.

On the Linear (below)... not so much. Read the notes on the chart.

-- The Problem with Trendlines on Arithmetic Charts

Okay, so here is where I show some problems with trendlines. Now before we get into this, the first thing you are going to think is "I see trendlines and channels get respected on arithmetic charts all the time!". And my response will be "Yes, you do" .... with a big caveat.

On small scales (relatively little difference in the max and min values on the y-axis), maybe less than a 10% difference between min and max, it is little matter if you use linear or log. You will see effectively the same chart and it will respect the same trendlines because of the only minor difference in scale.

The problem exists in charts with a large difference between the min and max value (such as the XHB example above). This is because price moved very quickly or it is even more compounded when there is both a large price difference AND a large time difference.

What am I getting at? The "Great Bear Trendline" that you see all over the place. Here is is for the SPX on a Semilog

And here it is for the Linear Scale. And I posit that it is wrong. Read the notes on the chart.

-- Conclusion

As always, this is just my take. There is no commandment handed down from on high stating “Thou shalt use log scale stock charts”. But just an exercise in logic, as I went through above, shows that this is a pretty obvious conclusion. But as an analyst and reader, you need to make up your own mind about this.

Thank you for listening to binve's Chart Analysis Public Service Announcement :)

Note 1:

I went through a similar exercise, not as focused as this one, about 6 months ago in this post
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