Finance and Fibonacci

J

Just recently I chanced upon this article titled Fibonacci Numbers Are Forecasting Higher DGTX Prices and my interest was immediately piqued. To my complete surprise, I read that:

Stock market investors have been using Fibonacci (colloquially known as “Fib”) numbers for decades. The use of Fib numbers within the investing community dates back to the stock market boom of the 1920s. These days, Fibonacci numbers are more popular than ever among traders and investors. Why? Because Fib numbers work remarkably well in forecasting support and resistance levels.

The article however, didn't explain how these support and resistance levels are determined mathematically. These levels are 23.6%, 38.2%, 50% and 61.8%. On Investopedia, I found an article titled What is Fibonacci retracement, and where do its ratios come from? that explained the whole business very clearly. Of course, I didn't understand what a retracement was and nor did I really understand what was meant by support and resistance levels. Fortunately, Investopedia has a very helpful glossary of terms. Firstly, what is a Fibonacci retracement?

A Fibonacci retracement is created by taking two extreme points (usually a major peak and trough) on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8% and 100%. Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels. Source

The previous link also contains a short video. Retracement is clear enough and so what is meant by support and resistance levels?

Support, or support level, refers to the price level that an asset does not fall below for period of time. An asset's support level is created by buyers entering the market whenever the asset dips to a lower price. In technical analysis, the simple support level can be charted by drawing a line along the lowest lows for the time period being considered. Source

The previous link also contains a short video that explains the concepts of support level and resistance level succinctly.

Resistance, or a resistance level, is the price point at which the rise in the price of an asset is halted by the emergence of a growing number of sellers who wish to sell at that price. Resistance levels can be short-lived if new information comes to light that changes the overall market’s attitude toward the asset, or they can be long lasting. In terms of technical analysis, the simple resistance level can be charted by drawing a line along the highest highs for the time period being considered. Source

The Fibonacci sequence of numbers begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... The determination of the support and resistance levels is as follows:

• 1st level: divide a Fibonacci number by the number immediately to its right. It's best to be a little further down the sequence so let's take 21/34 = 61.8% approximately.
• 2nd level: divide a Fibonacci number by the number two from its right. Here 21 /55 = 38.2% approximately.
• 3rd level: divide a Fibonacci number by the number three from its right. Here 21 /89 = 23.6% approximately.

Again to quote:

The 50% retracement level is not really a Fibonacci ratio, but it is used because of the overwhelming tendency for an asset to continue in a certain direction once it completes a 50% retracement.

Furthermore, 100% represents the peak and 0% the trough. Using the Fibonacci calculator on this site, Figure 1 shows the retracements for a peak of 500 and a trough of 200 on a downtrend (bear market):

Figure 1: retracements for a peak of 500 and a trough of 200 (downtrend)

Figure 2 shows the retracements for a trough of 200 and a peak of 500 on an upward trend (bull market):

Figure 2: retracements for a peak of 500 and a trough of 200 (uptrend)

Note that the calculator also makes use of the 76.4% mark which is 100% - 23.6% and also 138.2% = 100% + 38.2%. Figure 3 is a chart taken from a September 1st 2018 article from coindesk titled Crypto Trading 101: The Fibonacci Retracements showing the retracements in action:

Figure 3: NEO’s (NEO/BTC) 

The general consensus seems to be that used Fibonacci retracements alone are not reliable enough and they need to be combined with other indicators. There's quite a lot of information out there once you start looking. However, in this post, I was mainly interested in the mathematics underlying the calculation of these support and resistance levels and I succeeded in doing that.