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Why Arithmetic Stock Charts Are Worthless

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November 10, 2009 – Comments (15)

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 agree 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.

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)

 

.... continued in comments section ...

15 Comments – Post Your Own

#1) On November 10, 2009 at 1:15 AM, binve (< 20) wrote:

-- Log-Linear vs. Log-Log 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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#2) On November 10, 2009 at 1:55 AM, AdirondackFund (< 20) wrote:

I've always had the best success using Linear Charts written on 10 X 10 to the inch Graph Paper.  If you could make a chart using those inputs, you would see some truly amazing relationships.  Why, for example, has Bristol Myers always rallied in 10 X 10 format at 8 1/2 degrees?  What happens when the price action of BMY falls below this line?  Conversely what does it mean when BMY bounces off of the 8 1/2 degree downward sloping trendline?  Why does it always fall in price until it breaks through this line? 

This is the proper spacing for all charts and you should try implementing it in your next blog.  By simply running a compass backwards from recent lows to previous lows and taking the complement of 90 degrees, you can then plot the exact angle for the next rally phase and which always holds. 

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#3) On November 10, 2009 at 2:40 AM, awallejr (83.78) wrote:

"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."

I wouldn't mix science with crystal ball predicting.  There really is a big difference.  I still look at your charts and only see it trending UP, what can I say. We see what we see.  But once the future becomes the past, we will know.  And in the end that is what charts tell us, what has happened.  As always I do appreciate your commentary, however.

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#4) On November 10, 2009 at 5:20 AM, memoandstitch (< 20) wrote:

Great idea!  I'll show my wife the semilog plot when she asks about our portfolio (and don't tell her that it's down 50% from the peak).

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#5) On November 10, 2009 at 6:25 AM, dudemonkey (40.28) wrote:

If you take the word "Arithmetic" out of the title, I agree with you 100%

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#6) On November 10, 2009 at 3:57 PM, hhasia (66.02) wrote:

HI

It's been a while. Thanks for the input. How bout an update for Asia.

Lots happening here.  I've learned alot from your blogs and have applied these things to Asia.  As well, I must say there is a tug of war here because of the strength of the Chinese banks. ( Who did not get sucked under in the demise but were forced to adopt policies aimed at mittigating the impact of the export drought) Throw fuel on all those folks who save at a rate of more than 30%, to spend and go in debt? What were they thinking? Never the less, local consumer stocks are posting record earnings and the list of new high's grow daily.  So I'm keen to get it right for the pull back. I find that your charts help.

HHASIA

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#7) On November 10, 2009 at 4:11 PM, AdirondackFund (< 20) wrote:

Binve, I have your answer.  Humour me and try transposing the data you have on the correct template.  You're an Engineer, right?  You should be familiar with the 'paper' I am describing.  It is 'engineer's paper'.  It answers the question, "how does the floor 'engineer' a rally, or a decline". 

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#8) On November 10, 2009 at 4:42 PM, binve (< 20) wrote:

AdirondackFund,

I have to concede this for what you are talking about. You are describing a very specific and contolled setup to look at Gann lines and angles. I am referring to Linear stock charts in general.

awallejr,

Thanks. But the point of this post was not to make any predictions. In fact, it was very specifically prediction-free. I was discussing the technicalitys of stock movement and the proper way in which to view them. That has nothing to do with bullish or bearish moves

memoandstitch,

LOL! touche :)

dudemonkey,

yeah. Thanks for taking the time to comment.

hhasia,

Hey hhasia! I appreciate that! Yeah, I will do an Asia update soon!.

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#9) On November 11, 2009 at 12:10 PM, AdirondackFund (< 20) wrote:

Binve

Let's not jump to conclusions.  The 10 X 10 to the inch system was invented by Richard Ney in his book "Making It In The Market", which is conveniently out of print and has been since it was first published 30 years ago.  The last copy I knew existed was stolen out of the NYC Public Library.   The Gann Lines and angles do not work in this analysis as Ney has constructed a technique which he never explains in the book, but simply alludes to.  The angle lines under Ney's work are derived differently and vary from cycle to cycle.  It is not that complicated to follow, but it is very complicated to reverse engineer.  None of it works without the right paper and Ney doesn't tell you what paper he is using in his book and never alludes to which type of paper (template) works.

This will be well worth your while to research as it provides all of the rally lines to the exact decimal for each and every movement in stocks.  The techniques I have developed using this system are proprietary, but when folks on the floor see what I am doing (as was also the case with Burke at Investor's Intelligence), they all turn pale instantly. 

Most TA is designed wrong on purpose with trap doors everywhere.  That is the point of TA, from a market perspective, and is the Math Broker who tells you truth half the time and lies the other half of the time.

This analysis will be well worth your time and you will have the same reaction that I did (slaps forehead) when realizing exactly how the whole thing is designed.  A further realization will come to you once you understand that this system has been in force from the beginning of our country and has been handled by the same families the entire time.  Insights galore to how things actually work.

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#10) On November 11, 2009 at 5:36 PM, BlueInsight (< 20) wrote:

Go to Amazon.com.  Over 50 copies of the Ney book available.

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#11) On November 12, 2009 at 12:16 AM, Tastylunch (29.25) wrote:

"Why Arithmetic Stock Charts Are Worthless"

I gotta disgree here Binve, but only cause you painted this too broadly. For Ewave and what you do I agree Log charts are probably better.

but for many other TA tools that rely on common universal perception  all that matters is the crowd seeing it the same way.

Since most of the world still uses arithmetic charts than that is what you should use if you are trying to find cups with a handle, head an shoulders  etc in individual equities.

Think of it this way-

perhaps a weather satellite can more accurately gauge the shape of a cloud than an observer on the ground. But all that matters to cloud watching couple on the ground is whether or not that cumulus cloud looks like a Heart or not to them. What the satellite sees is not going to determine whether cloud watching guy gets lucky with cloud watching girl tonight :) 

Trust me you wouldn't want to try log charts for momentum daytrading. It would tell you nothing even in the mega movers because no one trades off them.

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#12) On November 12, 2009 at 2:31 AM, binve (< 20) wrote:

AdirondackFund, Gotcha man. Thanks for the info!

Tastylunch,

Hey man :)

I gotta disgree here Binve, but only cause you painted this too broadly

Yeah, I was trying to paint a broad swath. And I am approaching stock price from an energy perspective. If price is an indicator of "interest" (which is a measure of social mood) and further that the basis for all of the moves are relative (you gain based on a relative basis) then de facto all movement is exponential and the mood/interest can analyzed as power levels.

I know I will get a lot of eye-rolling with that one, but bear with me. .... I have been sitting here for a few minutes trying to come up with a not-so contrived example, but it is too late (or early?). When I am coming from is the idea of decibels. When stock at a high price moves down, there is an exponential power loss. Vice-versa when a price moves up. And as social creatures we tend to get greedy or get fearful and take profits after certain percentage moves. This is my fibonacci ratios are so powerful . And I am trying to articulate my idea with power levels. But maybe you see where I am going.

It is an unconcious thing. Certain energy levels show up in the charts and the moves between them are not entirely random, there are certain natural moves that show up not on a point basis, but on a *percentage* basis. On a log chart any vertical line represents a percentage move. And it is the same percentage anywhere on the chart! (Most people do not realize this). Take a ruler and look at the XHB chart above. Go to the lower end and measure 1 inch and figure out the precentage difference between the prices. Then move the ruler up to the top of the chart and do the same thing. Each one is the same percentage move!

This is exceedingly powerful (no pun indended) and on a log chart like this, coupled with my observations in the original post regarding straight lines being lines of constant exponentional growth, then the trendlines between large peaks has a meanigful basis. They can be described by power law relationships. Which I again posit is what stock price info really represents.

Trust me you wouldn't want to try log charts for momentum daytrading. It would tell you nothing even in the mega movers because no one trades off them.

Movements within the day are small (less that 10% difference between high and low. That is why I wrote this in the original post:

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.

For day trading or even short term trading, you can use arithemetic charts till the cows come home and its fine, becuase the moves in both time and price on a *relative* basis is small enough that the true log pattern is close enough to the arithmetic one.

It is for the charts with large price differences where this matters. I was trying to make that clear in the original post. Sorry if it wasn't.

perhaps a weather satellite can more accurately gauge the shape of a cloud than an observer on the ground. But all that matters to cloud watching couple on the ground is whether or not that cumulus cloud looks like a Heart or not to them. What the satellite sees is not going to determine whether cloud watching guy gets lucky with cloud watching girl tonight :)

LOL! I hear you. But I am still theorizing that the the more subconcious draw of these stock "power levels" will have power law relationships, which is why the straight lines on the log chart are meaningful and the straight lines on the arithmetic chart are more coincidental.

For what that's worth :) Thanks man!!..

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#13) On November 12, 2009 at 12:11 PM, Tastylunch (29.25) wrote:

And I am approaching stock price from an energy perspective

That's an interesting approach/analogy. However I find it to be too logical/rational to explain stock behavior.

At the end of the day it's not liquidity (the decibel power in your model) the powers the market but the participants' willingness to use liquidity and perhaps more importantly their perception of availability of liquidity. The former is not tied to rationality and the latter assumes that market participants are able to accurately gauge it. Last year's money market is proof that isn't always the case, liquidity availability isn't as simple as it appears. (how often do you hear lines about the "money on the sidelines" BS ?) market participants seem to dramtically swing between denial and panic if you ask me.

So at least for me I don't think your explanation best fits what actually occurs.

 And as social creatures we tend to get greedy or get fearful and take profits after certain percentage moves.

You would think that, but according to research I've read Ticker price is actually more important. I.e. people get more excitable at Dow crossing 10,000 then a 5 % daily move. That's really stupid but it what a whole mess of people do. Some whole numbers seem to be especially powerful on individual stocks, 1, 5, 2, 10, 50 and 100 in particular..

Most retail investors at mixers etc I know seem to fixate exclusively on price (" ohoho Muffy did you know Prechter&Gamble is at ONE HUNDRED Dollars? "Dear it's Procter and Gamble." - it makes me sad how many times I've had this similiar conversations with people). Talk %s and they'll stare at you like you are from the moon. It should also be noted most retail investors also badly underperform the market which is easy to forget when you spend most of your time talking to above average investors (or at least smart people). It's easy to forget that the so called "smart money" acts less like hot money than "dumb money"

It is for the charts with large price differences where this matters. I was trying to make that clear in the original post. Sorry if it wasn't.

Movements within the day are small (less that 10% difference between high and low. That is why I wrote this in the original post

No I did get that. I disagreed with you.

You might be surprised about intraday volatility. At least it's not the stuff I bother to daytrade. High volatility days can see big movers swing 20% and if you are playing with an OTC stock 100% moves up are not uncommon. Especially now that there the levered ETFs. They are absolutely fantastic day trading vehicle. Last winter FAZ/FAS were swinging 30%+ intraday. Daytraders pound the crap out of those.

And they all use arthimetic charts to trade them. Why? well primarily because that's what most brokers offer.

I myself only trade when I perceive ADR > 15% ona vehcile usually.

In short Binve, TA only makes rational sense to me if it explains people's behavior.And people collectively are kinda stupid. :)

At the the end of the day, most of short term trading is zero sum - money taking game. All that matters is knowing what the other guy on the otherside thinks about the trade and what he's gonna think.

well that's been my experience anyway.

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#14) On November 12, 2009 at 1:08 PM, binve (< 20) wrote:

Tastylunch,

Hey man, thanks for the comments! I definitely wasn't expecting a lot of agreement on this post (and as the comments testify, I didn't) :). I am just a guy with an opinion. And I share my opinion, very forecfully because I have a reason for why I think what i think. But at the end of the day, it is just an opinion :)..

Last year's money market is proof that isn't always the case, liquidity availability isn't as simple as it appears. (how often do you hear lines about the "money on the sidelines" BS ?) market participants seem to dramtically swing between denial and panic if you ask me.

So at least for me I don't think your explanation best fits what actually occurs.

That is a very good point. And I agree the "money on sidelines" argument is BS.

You would think that, but according to research I've read Ticker price is actually more important. I.e. people get more excitable at Dow crossing 10,000 then a 5 % daily move. That's really stupid but it what a whole mess of people do. Some whole numbers seem to be especially powerful on individual stocks, 1, 5, 2, 10, 50 and 100 in particular..

I do agree that nice round numbers are psycologically attractive. But what I am saying is that on the whole, the crowd move stock prices between energy states. This is a product of social mood. Which is the whole basis behing Elliott Wave and Fibonacci Relationships. Fib ratios describe the "least amount of energy needed to add complexity to an up down advancement and decline sequence (a wave structure)". I happen to believe these quantiies are all related. But I respect the point of view that one might believe they are not. Like I said, this is my opinion and reason for it. But it is just an opinion

No I did get that. I disagreed with you.

Gotcha :)

You might be surprised about intraday volatility.

Not really. I have seen a lot of crazy moves.

Yes OTC stock move like crazy because they are easily manipulated (small market cap and low volume make them suspectible to moves by a few powerful hands). This is why I don't analyze them from and EW perspective. They are not valid because they are not driven by social mood (collections of many people) but by the actions of a few.

Nor are 3x ETFs valid just on a percentage basis, because they are meant to track the underlying 1x index. (e.g. a 30% move on a 3x is rought a 10% move on the main index) which is why I do analyis on the underlying index and NEVER on a leveraged ETF. I trade them, but I don't do analysis on them.

At the the end of the day, most of short term trading is zero sum - money taking game. All that matters is knowing what the other guy on the otherside thinks about the trade and what he's gonna think.

Another very fair point.

Thanks for the comments man!.

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#15) On November 12, 2009 at 3:22 PM, Tastylunch (29.25) wrote:

Np man

I didn't expect to convince you eitherand to be fair I have no empirical proof to present with my case.

I used to attempt analyze markets from the hard science approach as you are attemtping. Perhaps you will make it work for you as you are more accomplished than I am/was in the field.

But at least for me my biology training was more useful than my geology training in explaining markets in a way I can actually make money.

If nothing else running my retail business ha been very educational in learning how poorly humans perceive things and how they make decisions.

:)

But what I am saying is that on the whole, the crowd move stock prices between energy states

I know I understood that.And it is where we differ it looks like. I don't think it does behave that way. Or more accurately if it does it's only a component of the move (Which would particularly frustrating as it would appear to show up fairly often but perhaps not with reliable predictability)

The odd thing about herd pyschology is the more people who are into a stock the more others want to be to (and vice versa). This is why Momentum trading is rational and makes sense . This seems to happen until all the buyers have bought or all the sellers have sold.Which owuld fit into your energy state model to some degree.

 

But assumption I do see in the energy state model is that the participants aren't ever surprised. I.e. new information doesn't suddenly arrive, interrupting the swing. In my experience "news" is unpredictable, frequent and serves as the spur to the stampede (look at Garmin after Google basiclaly said they'd offer the same product for free) .

Also ngelected by the model  is supply/demand for the equity and the company's underlying fundamentals act as short of circuit breakers on the stampede in either direction. One reason I love low float stocks is when they get going spurred by good fundamental news they can really run due to supply/demand.

I think's why Swing trading methods like CANSLIM and the DARvas method work (buy high, sell higher) and bottom picking like Schloss can both work despite their inverse methodlogies. And why Fibs can appear to work since the market does gravitate towards them in the abscence of "meaningful" news (although if you ask me they don't work enough to be tradable, but that's just me). I find the other methods fundamnetals, momentum to be more tradable since they are easier to measure possible cause and effect (and also to be able to tell which of those factors is dominant). At least for me.

Well that's just my experience.I'd love to be proven wrong, it'd make trading easier.

I have seen AC's work on FIb Fans, it is tantalizing stuff.

Yes OTC stock move like crazy because they are easily manipulated

and yet they are actually really easy to predict. Which is why I like trading them.  The only hard part (and it happens to be meaningfully hard) about trading them is getting good fills.Bid/Ask will kill you if you aren't careful.

Well that and the strategy doesn't scale.

Nor are 3x ETFs valid just on a percentage basis, because they are meant to track the underlying 1x index. (e.g. a 30% move on a 3x is rought a 10% move on the main index) which is why I do analyis on the underlying index and NEVER on a leveraged ETF. I trade them, but I don't do analysis on them.

Agreed but simple momentum analaysis seems to work wonders on them. As long as you don't hold them overnight... I saw a great daytrader I've met trade FAZ 23 for 24 in one day once! He scalped 1-3% every time.

Unfortunately i don't have the necesary time/practice to put inot as he does, so I know bette than to try my hand to often at it as he does. But I know it's very doable.

The times I get crushed on the ETFs is from drastic new opens and the ^$^%$% 7 day window in CAPS.

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