AMZN: Arithmetic and Logarithmic Charts Explained

In this post, I'll be shedding light on the difference between arithmetic and logarithmic scale charts, and how to best use both charts to your advantage.

Arithmetic Chart
- The chart on the left is a chart that uses the arithmetic scale
- This is the chart most common to us all, and one that's easiest for traders and investors to comprehend
- An arithmetic chart represents price on the y axis, using equidistant spacing between the prices
- This is demonstrated on the arithmetic scale above; the distance between 1 and 2, is the same as the distance between 8 and 9
- Arithmetic charts demonstrate absolute value

Logarithmic Chart
- The log chart on the right side has a different approach to interpreting price movement
- The y axis uses equidistant spacing between designated prices
- This is demonstrated on the logarithmic scale above; the distance between 1 and 2, is the same as the distance between 2 to 4, 4 to 8, and so on.
- The logarithmic chart demonstrates the percentage change in the underlying asset's price

Case Study: Amazon (AMZN)
- We can take a look at Amazon's arithmetic and logarithmic charts, dividing them by significant phases to better understand the differences
- We can first see that the area marked by 'extreme volatility' on the log chart, is much more drastically demonstrated than that of the arithmetic chart
- This is because price fluctuations in terms of percentages were drastic at the time, due to the Dot-com Bubble.
- For more information on the Dot-com bubble and today's stock bubble, you can check out my other analysis below:
- However, because in terms of the absolute value changes during the Dot-com bubble are minuscule compared to the price fluctuations today, the phase of extreme volatility is barely noticeable in the arithmetic chart
- In the period of a 'steady uptrend', we can see a clear and steady uptrend in the logarithmic chart, indicating that the stock moved up at a consistent pace, percentage-wise
- The arithmetic chart, while not drastic in the uptrend's degree, demonstrates parabolic momentum building up
- We then have the 'exponential growth' phase. Here, we see a move from $400 to $3,400 on the arithmetic scale.
- However, the logarithmic chart merely demonstrates a steady uptrend without much volatility.
- This is because while the absolute value of the stock has risen significantly over time, the percentage change in the rise was consistent.

Conclusion
While the arithmetic chart is more familiar for the average trader/investor, logarithmic charts help us clearly view long term data, especially when price points show immense volatility during the short term. As such, log charts can be effectively used in for technical analysis of cryptocurrencies, as well as volatile tech stocks with long price history. The understanding of the log chart is an effective tool, but it must be used with caution, since most people intuitively interpret a chart as an arithmetic one.

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