Jumping S-curves

In this post, I will explain what jumping S-curves means and how you can identify potential S-curves before they jump.

First, let's begin with the chart above (also copied below).


This is a yearly chart of McKesson Corporation (MCK), a medical supplies company.

As you can see in the chart below, this stock has been soaring over the past year despite most other stocks being significantly lower.


Here is the performance of the S&P 500 over the same time period.


Whenever I see something highly unusual in a chart, such as extreme outperformance, I check the higher timeframes to see what's driving price on a technical level. Below is the yearly chart for MCK.


When I examine price action over a long time period, I always log adjust my chart. Below is the log-adjusted chart.


Upon seeing this chart I immediately knew what was going on: the stock price jumped S-curves. I will try to illustrate below how I reached this conclusion.

To begin, I drew Fibonacci levels from the last reaction low to the last reaction high on the yearly timeframe.

The previous reaction low was the bottom of 2008 because that bottom was a Fibonacci retracement of some earlier reaction high, the reaction high is the top in 2015 because price did not surpass that high without first undergoing a Fibonacci retracement (to the golden ratio).

As you can see above, from 2015 to 2018 the price retraced down to the golden ratio (0.618) on the yearly chart. It is often from this retracement level that the base of the second S-curve is created. (For simplicity, I only included the 0.618 Fibonacci level on the chart).

Some may say that this pattern is merely a bull flag or pennant. (See chart below)


Indeed, bull flags and pennants can be another way to visualize S-curve jumps.

Whereas, on a deeper, more mathematical level, S-curve jumps are logarithmic spirals (approximated as Fibonacci spirals or Golden spirals). If you wish to delve deeper into logarithmic spirals, including the Golden spiral, you can check out this Wikipedia page: en.wikipedia.org/wiki/Golden_spiral

These Fibonacci or Golden spirals are present on mostly every chart and they appear on mostly every timeframe (hence they are fractal).

One of the best charts you can use to visualize these spirals is the chart of Bitcoin. Below are charts of Bitcoin which attempt to show the endless fractal nature of Fibonacci spirals (or "S-curve jumps").


I've only illustrated a few of the spirals, but indeed there are numerous spirals. (I tried to do my best using the tools on Trading View to draw these spirals, but it can be quite hard to manipulate the curves perfectly to price action.)

One may ask what about when price falls? That is obviously not an S-curve jump since the price is falling.

Actually, when price is crashing it is usually just an S-curve jump, or Fibonacci spiral, on the inverted chart.


Although I have not tested it with scientific rigor, I do hypothesize that Bitcoin's price movement is a series of infinitely fractal and competing Fibonacci spirals on various timeframes, including Fibonacci spirals on inverted scales. Price movement can be thought of as an infinite series of S-curve dilemmas where infinitely fractal S-curves, including those of which are inverse S-curves, compete to govern the next price move.


Each dilemma is resolved when an S-curve reaches its inflection point, such that it governs price movement and price moves rapidly in that direction until it approaches capacity and faces its next dilemma.

Those who know Calculus may recognize this chart. Indeed this is the graph of a logistic function. The mathematical terminology for an "S-curve" is sigmoid function.


Here are some more interesting charts of S-curves (none of which is intended to be investment advice)

Meridian Bioscience (VIVO) jumps S-curves on its yearly chart

The U.S. Dollar Index jumps S-curves on its yearly chart

The entire price action of Chinese EV Company (NIO) is an S-curve that just completed a perfect golden ratio retracement


Japan's faces a population S-curve dilemma

Citigroup underwent S-curve growth up until the Great Recession.

Then it crashed or underwent S-curve growth on the inverted chart.


In summary, price movement involves an endless series of S-curves or Fibonacci spirals. Identifying an S-curve on a high time frame before it reaches its inflection point and breaks out can lead to tremendous gains (among the most lucrative gains one can realistically make in the financial markets).