Trendlines on Logarithmic Scale Charts

There is a big difference between charts with an arithmetic scale and those with a logarithmic, or log scale on the chart. Also referred to as a "percentage chart", the logarithmic scale spaces the different between two price points according to the percent change, rather than the absolute change. In other words, the vertical distance between $5 and $10 (100% increase) would be plotted the same as a move from $50 to $100 (100% increase). In an arithmetic scale chart, the move from $5 to $10 would be barely noticed when compared to the $50 move from 50 to 100, which is a 50 point difference rather than just a $5 move.

Here is the same price action over the same 5-year time period in $DDD plotted two difference ways:

I find log charts very valuable when looking at either longer-term charts or a specific security that has just made a massive move. The dilemma that I come across is when drawing trendlines on the log scale chart. In reality, you may be connecting several key lows or key highs, but the line is not a straight line, but rather a curved line right?

So I asked some of my favorite technicians how they felt about this dilemma and wanted to share with you some of their thoughts on log charts in general:

Richard Ross, CMT - Global Technical Strategist Auerbach Grayson @RichartRoss

In regards to trendlines in general, log or otherwise, I believe that of course they are an important tool; almost elegant in their simplicity. However, I don’t like to lean too heavily on trendlines as there is a great deal of subjectivity in terms of how they are drawn (Connecting lows, highs, closes or a combination). In addition, as charts evolve and we get more data, the trendline can change, whereas moving averages and even Fibonacci are based purely on math which is not open too subjectivity. Now we can quibble about where we draw a retracement or whether we use a simple or exponential moving average, or even which moving average to use, but the numbers are the numbers. In sum, respect the trendline, but you better build a cluster of evidence to support any strategy/trade based off of that trend. Finally, you want to size yourself correctly if your whole trade is based upon a trendline.

Peter L Brandt - CEO Factor LLC @PeterLBrandt

As a trader I do not use log charts. However, I can see some advantages to log charts for analysts who exam very very long-term trends.

The reason I do not use log charts is that they are irrelevant to me as a futures trader. The value of a $15 move in the S&P was the same to me when S&Ps traded $150 as it is today when the S&Ps are at 1700 or so, even though on a percentage basis the $15 change was 10% of the price in 1983 and less than 1% of the index today.

Ari Wald, CFA, CMT Analyst Wolfe Research @AriWald

For me, I’m a Log-always analyst.  While the differences are many times negligible, there are times that Log scaling provides a considerably stronger view of the stock’s trend vs. Arithmetic scaling, but I’ve never found the opposite to be true.  The advantage of Log is clearly seen at long-term horizons or during big price moves at lower prices.

As an extreme example, drawing a trendline on an arithmetic chart of the S&P 500 from 1930-current is not an accurate depiction of the index’s trend during that period in my view.  We realize that a 10 point move from 20 to 30 (50%) is not the same as a 10 point move from 30 to 40 (33%).  A line on a log chart would look like a curve plotted on an arithmetic scale in this example – but consider that the price on this arithmetic scale gives an inaccurate view of price, in my opinion, and therefore the curved trendline is justified.

So overall, if I’m going to use a Log chart in this situation I should maintain my defaults on Log because I won’t encounter a time when I’m at a disadvantage, only times when Log is preferred.

Anonymous, CMT - "just another struggling options broker...."

I follow the Murphy guidelines which I am sure you have studied:http://stockcharts.com/school/doku.php?id=chart_school:chart_analysis:trend_lines I am on log for everything other than intraday. Obviously your question matters when you start looking at an AAPL weekly chart going back 5 years.Your question got me thinking and I found this blog post which I think is great:http://caps.fool.com/Blogs/why-arithmetic-stock-charts/290893

This line is great and really sums it up:"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!!."Not sure if you use p&f at all but your question also has major implications there. I used to use a $5x3 chart in the gold pit when it was trading around $300. Fast forward to $1000 and $15 (5*3) is basically meaningless. 

Ralph Acampora, CMT - The Godfather of Technical Analysis @Ralph_Acampora

JC, I have never been a big fan of semi-log charts simply because their trends are distorted and you can't really see any patterns. Plotting absolute prices is what gives us many technical signals and I wouldn't want to loose these valuable inputs.Having said that, I still like to see the long-term progression of price as demonstrated on these graphs.

Greg Harmon, CFA, CMT - Dragonfly Capital @harmongreg

You are right. A trendline on a log chart is a curved line if converted to a straight line scale.  Except for horizontal  Support and Resistance lines which are not impacted, and I find more important than angled trend lines.  Mathematically as the size of the scope of action shrinks the difference between log and normal scale goes to zero.  But most importantly to your question, remember a trendline, on any chart, has value and information because it is a trend line.  Meaning that it has already shown that it is important. I look at both at different times, when they seem important.  No hard and fast rule. 

Greg Guenthner, CMT - Agora Financial @GregGuenthner

I always use semi-logarithmic scaling for longer time periods. Line/curve-- either way it's a trend...an idea of direction. The main thing I care about with my long-term charts is distortion. You can turn any long-term uptrending data set into a parabola using arithmetic scaling. Not much I can do with that from an analysis standpoint. After all, how can I make sense of a bunch of hockey sticks?

Chris Kimble - Kimble Charting Solutions @KimbleCharting

I am a log guy for a couple of reasons.  Back when I started charting in the 1980's, I noticed anyone who seemed to be anyone was using log charts.  I wasn't attempting to conform, yet I did think, if the people that were in control of the most amount of money were using log versus linear, I wanted to see what key tops and bottoms they were looking at and trading around.

I don't think linear is broken by any aspect yet it reminds me of Jesse James...which was ask, "why do you rob banks and he replied, ....why not, that's where the money is!"  Is the money in log charts?  I have found that to be true over the years!

I also like what you know, in that log creates equal spacing, in that a rally from $10 to $20, gets no more value than a rally from $1,000 to $2,000.

My 2 cents from a single brain celled guy from Kansas!

Joe Bell, CMT - Schaeffer's Investment Research @joebell_trader

I normally just use a linear chart, but if I am doing some longer-term analysis and/or a more volatile name with big percentage moves over time I would check out the logarithmic to give me a better feel for the trend.  Sometimes worth checking out both just to see if the log is telling you anything different about the momentum of the trend that you are not getting from the linear chart. I would still draw lines on log chart and would still look at it as a trend line.  It’s still measuring the long-term trend of the growth of the stock, but just basing it on the percentage gains rather than price gains.  If you see a stock that is making parabolic moves on a monthly chart, it may be almost impossible to draw a meaningful trend line to identify support areas along the way.  The trend line would look more like a curve that is accelerating at an increasing rate.  By using the logarithmic chart, it may “slow” down this trend and allow you to draw a trend line that gives a better picture of where buyers have come in historically during that trend.

Andrew Thrasher, CMT - Investment Analyst @AndrewThrasher

I typically set up my charts to use log-scale. I feel log scale more accurately reflects the price action and the magnitude of a move. If you were looking for long-term trend lines in the Dow, for example, going back to the 1950, obviously there's been a large change in price since then. To not use log scale, in a way, doesn't respect the percentage of the advance that's taken place and you are unlikely to be able to draw accurate trend lines.

JC Ohara, CMT - FBN Securities

First and foremost trendlines should never be considered exact and when using trendlines it's always more of an art vs a science but having said that… ( also I can joke and say just use a moving average for log charts)…. Here are some thoughts-

Truly depends what time frame you are looking at. I think over the short term it does not matter too much what scale you use. For longer term charts ( over 2 years) and for commodity charts, I prefer LOG scale. Why?  As a technician, we examine the psychology of the market, thus respecting how traders/investors think over a certain time period does affect the scale on your charts. Longer term investors tend to think in terms of percentage gains, while over the short term investors think in terms of points. Thus shorter duration charts I stick with arithmetic, and use log for longer term charts.  An example of a great chart where you can really see the difference between log and arithmetic is HD… take the chart going back to the mid 90’s big big difference in how you view the chart.

If  you are drawing horizontal lines on the chart to locate levels of potential Support and Resistance, again the scale should not make a difference. While the chart will take on a different look and feel on how price moved to the level of support or resistance, the horizontal levels remain the same. Many traders in the short term will locate horizontal levels to get in or out of stock, so those levels are the same no matter what scale you use. If a horizontal level and a trend line coverage at the same point, I believe that levels becomes even more powerful. For stocks under $5 and for high flyers, high momentum stocks I prefer to use LOG scale. There are certain techniques that can be applied to log scales charts that cannot for arithmetic scale.

Basic rules of geometry is that you need 2 points to form a line and technicals call for 1 additional point to form a trendline.  Let’s also remember that points on a chart represent a price at which a transaction took place. That in itself is not important, the importance comes from what information can we the technician extract about the future movement of the stock price and the decisions that will be made based off of that next move. I will confidently say, what is NOT right is using trendlines that are not working. If I chart seems to respect a log trend line, use a log chart, and vice versa for arithmetic. Do not use a trend line that does not work! I do not consider this technical data mining I consider this really knowing the chart. Similar to how certain asset classes respect certain moving averages better than others or how certain Asian markets respect Ichimoku clouds. To conclude, I am a LOG user for longer charts but do not use them for shorter term charts. I like LOG for all times periods for commodities.  Hope that helps!

The Real JC 

Mark Arbeter, CMT - Chief Technical Strategist S&P Capital IQ @Arbeter_SPCapIQ

Good point J.C. I do use log charts for longer-term charts, but try to find the chart (log or not) that fits the trendlines the best. I use MetaStock and the trendlines on the log chart are of course straight. Do not know if this has ever been solved or even thought about with chart makers. While I think trendlines are important, I think areas of prior buying and selling (chart support/resistance) are more important. I also think trendlines are misused by some. While I respect what (certain technicians) do, some of their trendlines are just ridiculous, having nothing to do with the trend. If you get some programmer/engineer to right the code for log lines, we could call them the Parets’ Log Lines. 

Chris Burba, CMT - Co-founder/Chief Technical Strategist at miAnalysis @ChrisBurbaCMT

In my experience, I've seen trendline S/R on arithmetic charts work time and again, whereas I can't recall more than one or two instances in which I saw trendlines on log charts be relevant (and even then I'm not sure how relevant). I sometimes look to log charts to gain a perspective in terms of what kind of progress is made higher or lower in percentage terms. But when it comes to identifying relevant trendlines and proportional balance with Fibonacci retracements, I stick with arithmetic charts, even if it's on a monthly interval. One point that I do think is at work is that there's a greater likelihood of a self-fulfilling prophecy coming into play with trendlines on arithmetic charts since a lot of people are looking at them, where as that's less likely on log charts since not so many go there.

Jonathan Krinsky, CMT - Chief Technical Market Analyst Miller Tabak @jkrinskypga

The discussion of logarithmic vs. arithmetic is like Coke vs. Pepsi. Everyone has a view, and there likely isn’t a correct answer, it’s personal preference. For me, I’m generally in the camp of using log on longer-term, small dollar priced stocks, and stocks that have had large percentage moves over the last one to two years. There is also the aspect of subjectivity. As technicians, we try to be as objective as possible, but we must also have a view and be able to support that view. Two technicians can look at the same chart of a stock at new highs. One says buy it because it broke horizontal resistance with strong momentum, the other says sell it because it is hitting uptrend resistance and is overbought. You have to have a view, and to some extent show whatever metrics you deem the most valuable to support your argument. Bottom line: there are pro’s and cons to each, but at the end of the day you have to use what works for you, and what helps you make the best projection of future prices.

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What are your thoughts?