How to Use Log Scale

2022년 8월 1일

In this post, I will explain how traders can maximize their use of log scale on Trading View. I will give examples of when you should use log scale on your charts and when you should not, as well as provide an in-depth analysis of its use cases, including how you can actually visualize the entire lifecycle of an asset using the log scale.

In the chart above, I highlight the difference that using the wrong scale can have on your trading. The chart shows the monthly candlesticks for the U.S. Dollar Index (DXY). If one applied Fibonacci levels on a log adjusted version of the chart, one would have been under the impression that the dollar index made a huge breakout above its Fibonacci level. However, if one had not applied log adjustment, one would have correctly noticed that price was actually being resisted by the Fibonacci level. From a mathematical perspective, the U.S. dollar index ordinarily should not be log adjusted. I'll explain why below.

Log adjustment simply refers to adjusting data on a logarithmic scale. Log adjustment is most suitable for visualizing data of a financial instrument or asset that is moving exponentially or in logistic growth. I will explain and illustrate both of these patterns below, but before I do so, I will discuss assets that do not move in either of these two ways and therefore should not be log adjusted.

Financial instruments that are range-bound or that oscillate up and down (e.g. the VIX), ordinarily, should not be log adjusted. Similarly, financial instruments that oscillate relative to another financial instrument, such as the U.S. dollar index (the dollar index oscillates relative to the strength of other currencies), should ordinarily not be log adjusted. Additionally, financial instruments that oscillate up or down solely due to monetary policy action, such as bonds and interest rates, ordinarily, should not be log-adjusted. In all of these oscillator examples, price action does not undergo exponential decay or logistic growth relative to time and therefore log adjustment is mostly inappropriate. Applying log scale to these assets can lead to the trader reaching the wrong conclusion, such as shown with the dollar index example above, and below with an example from the VIX.



Regardless of which one of these charts ultimately proves to be right (support holding or breaking for the VIX) it illustrates the problem with using the wrong scale on your charts. Using the wrong scale can lead to the wrong conclusion and put you on the wrong side of a trade.

On the other hand, most other financial instruments and assets move in patterns of either exponential decay or logistic growth and should be log adjusted. Most stocks, indices, derivatives, and cryptocurrencies move in patterns that should be log adjusted.

Here's an example of exponential decay:


Here's an example of logistic growth:


Many people look at this chart and incorrectly think that Monster Beverage (MNST) is growing exponentially, but in fact it is not. Applying log adjustment can help show this.



As you can see, log adjustment shows that MNST's past price action fits the S-curve of a logistic function almost perfectly. If MNST were growing exponentially, log adjustment would just show a straight line with an upward slope.

In the above example, log adjustment can actually show you hints that MNST is in the late phase of its growth cycle as price reaches capacity.



As far as I am aware, no financial asset grows exponentially, as there is a finite amount of capital and a finite amount of resources in the world. When a financial instrument appears to be growing exponentially, it is merely in the upward concavity phase/maximum growth period of a logistic function. Eventually, the financial instrument will reach its capacity and its growth will begin to flatten over time.

In virtually all cases, assets decline at some point in the future after reaching their capacity. Using log adjustments can help you avoid entering into positions of assets that are near capacity. Log adjustment reveals where an asset is currently positioned in its lifecycle. Take a look at the below example of Citigroup.



When the Great Recession hit, Citigroup began to undergo exponential decay (relative to the broader market). See the chart of Citigroup's price action relative to the broader market (S&P 500).



In some rare cases, an asset can do the opposite of this: transition from exponential decay to logistic growth. Finding and entering a position just before the inflection point can be among the most lucrative investments one can possibly make in the financial markets. Log adjustment can help you find the inflection point. In the future, I will write a post on how to find inflection points using log adjustment, and I will provide an example of an asset that is about to break out from its inflection point.

Aside from visualizing the lifecycle of a financial asset, log adjustment can help eliminate skewness to better visualize patterns. Here's an example below.





Log adjustment also allows us to run linear-log regressions. In short, a linear log regression can identify areas where price action is unusually above or below the mean for financial instruments that move up or down exponentially.



In the chart above, we see a log-adjusted chart of Money Supply (M2SL). Applying log adjustment to the money supply and then adding a linear-log regression channel shows us that the Federal Reserve was clearly adding too much money into circulation as evident by the M2SL reaching an abnormally high standard deviation from the mean and jumping above the upper line of the regression channel.

Log scales help us understand and visualize data about the world around us and the natural cycles which characterize it. Log scales and logistic growth are used in many other scientific contexts from epidemiology (e.g. tracking the spread of a virus) to demography (e.g. analyzing population growth and decline). Take a look at a log scale of Japan's Nikkei Stock Average alongside the country's population from the post-World War II era to the present day.



In summary, applying log adjustment is ordinarily suitable for assets that move exponentially or in logistic growth. Applying log adjustment on the price action of an asset that moves in this manner can better help us eliminate skewness, identify abnormal deviations using linear-log regression, and allow us to visualize the lifecycle of a financial asset.

Note: Sometimes the wrong scale can be useful in trading because so many other traders are also making the same error and basing their trades on the wrong scale. I've seen this happen quite frequently for Fibonacci retracements. So sometimes it can be helpful to toggle between log scale on and off to see which is causing a price reaction. In general, though, log adjustment is mostly suitable for assets moving in exponential decay or logistic growth, from a mathematical perspective.

2022년 8월 7일

노트

One may ask if there is any scientific proof that indeed stocks and other financial assets tend to grow according to a logistic growth curve? Indeed, there is scientific support for this conclusion and it relates to studies in the field of mathematics and human psychology. Researchers in several European universities collaborated in a study that observed a crowd applauding. They found that the growth in the number of people who began to clap during an applause, and the growth in the number of people who stopped clapping as the applause faded, both conformed to a logistic growth curve over time. When a few people started to clap it caused a huge rush of others to join in until it reached a crescendo and growth slowed and eventually stopped. This pattern of crowd psychology is similar to the interest that a financial asset garners over time, when enough early investors pile into an asset such that it causes a breakout, many more investors subsequently pile in causing rapid growth in price. After a point of maximal (seemingly exponential) growth, all financial assets eventually reach "capacity" or the phase when the rate of growth slows over time. This slowing in growth may occur for a myriad of reasons, one example is when the company has reached full penetration of the market and the prospects of further growth wanes.



Link to the study: royalsocietypublishing.org/doi/epdf/10.1098/rsif.2013.0466