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przemyslaw-radomski

Which scale is better: linear scale or logarithmic scale?

March 31, 2011, 12:00 PM Przemysław Radomski , CFA

You are using the Stockcharts system for your articles and analysis. The vertical axis is logarithmic. Stockcharts themselves have a link which outlines the benefits of linear/arithmetic charts against logarithmic. I would be very interested in your comments on this aspect.

Generally, the log scale (to be precise - the semi-logarithmic scale) is much more useful than the linear one, which is precisely why we use it. The logic behind that is also the root of technical analysis – emotionality. Which will cause the same emotional swing as an increase in the value of something from $1 to $1.50? Will it be an increase from $50 to $50.50, or an increase from $50 to $75? Naturally, the latter, because in both cases the move is substantial and offers a possibility of a 50% gain on invested capital.

Why do people invest/speculate? Naturally, because they want to improve their financial situation and the way to do that is by making profits. Profits are calculated by dividing a gain on a given position by the capital that was invested in the first place, so they are important in relative terms. Consequently, people care about a given asset’s performance relative to its previous price, not in absolute terms. In other words, 50-cent move is irrelevant for a $500 stock, but it is groundbreaking for a 20-cent junior.

Moving back to scales - semi-logarithmic scale lets you know about stocks’ relative performance, which is in tune with what people are interested in and what influences their trading decisions. So, if technical analysis’ job is to reflect people's emotionality and to then position ourselves accordingly, then we should use tools that enable us to reach this goal. In this case it's the semi-log scale.

There's one more point we would like to make. On the Stockcharts page there are also two points that suggest that in some cases arithmetic scale is better.

Arithmetic scales are useful when the price range is confined within a relatively tight range.
Arithmetic scales are useful for short-term charts and trading. Price movements (particularly for stocks) are shown in absolute dollar terms and reflect movements dollar for dollar.

We disagree that it's better in these cases. Arithmetic scale is almost as good as the semi-log one (in case of long-term charts the semi-log scale wins decisively), but it’s not better. The first reason is that people's emotionality doesn't change for short-term moves, so points made earlier still hold. The second reason is that the difference between semi-log scale and an arithmetic one is barely visible for the very-short-term charts, so the difference in usefulness is also barely seen. In other words, arithmetic scale works quite well in the short term, because in short term it's almost the same as the semi-log one.

Why? Actually, you've already read the explanation - because people perceive prices in relative terms, not the absolute ones. The point is that in the very-short-term chart you generally have very small moves in percentage terms - say +0.1% or so. In this case, it makes little difference if the stock moves by $0.01 or 0.1% - it's still almost nothing. Of course the situation is different in the case of a stock that's worth $0.01, but that's an extreme and rare case and we would like to explain the general concept.

Since taking relative and absolute overview on prices don't provide different emotional responses, both scales are ok - and in fact, they will look alike. Still, based on the way technical analysis works, the arithmetic scale cannot be better than the semi-log one - it can only be very close. If you studied physics, then this explanation might be useful - only at the quant level would these two be identical. In all other cases the semi-log scale wins, and the greater the distance from the quant level, the bigger the difference in usefulness of both scales.

If you're interested in comparing the usefulness of both types of lines, then you'll probably be also interested in the current outlook for the market and in seeing how these lines are applied in practice. Good news - we have a free newsletter in which we let people know about our free analyses (we cover gold, silver, crude oil, stocks, forex and bitcoin). The signup for the free newsletter is accompanied by a bonus of 7-day access to our premium Gold & Silver Trading Alerts, so we encourage you to check it out. Use the following link to continue. Sign me up!  

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