The fear throughout the summer has been that a frothy equity market (up double digits YTD), a Federal Reserve that has been reluctant to aggressively lower rates, trade wars with China and other countries, an inverted yield curve, and the cusp of a Presidential election would all serve to dampen the economic outlook and give...Read More

Since 2015, the gold market and bond market (I use the $TLT 20-Year Bond ETF as a proxy for bond market performance) has been highly correlated. Both asset classes are viewed as a risk-off flight to safety. While past performance does not predict future performance, it is worth noting that many are viewing the bond...Read More

The long term log chart of natural gas (weekly) should give pause to any remaining bulls expecting an inflation-fueled price rise in the coming months. Since 2008, the price of natural gas has been locked in a consistent pattern of lower highs (3) and lower lows (3).Read More

Gold has been on an epic run since early May, breaking out of a six-year base and launching almost $300 per ounce in the span of three months. Momentum favors the bulls, and the technicals look very strong over the long term. The backdrop of lower global yields and potential monetary stimulus are key fundamental...Read More

One of my favorite charts is the ratio of the 20-Year Bond ETF, $TLT, to the High Yield Corporate Bond ETF, $HYG. The chart communicates investor risk appetite between low risk, lower yielding US bonds and high risk, higher yielding corporate bonds.Read More

The chart of steel (US Midwest Domestic Hot-rolled Coil Steel) is one of the cleaner technical charts in my queue . . . and it is a disaster zone. I’m looking at the front month weekly chart as a proxy for steel prices. Some key features of the chart:Read More

Fibonacci refers to the sequence of numbers made famous by thirteenth-century mathematician Leonardo Pisano, who presented and explained the solution to an algebraic math problem in his book *Liber Abaci* (1228). The Fibonacci sequence and the ratios of its sequential numbers have been discovered to be pervasive throughout nature, art, music, biology, and other disciplines, and they form the foundation for Fibonacci trading tools. Traders apply these Fibonacci levels to help interpret market behavior and to isolate higher probability setups and market pivots.

The sequence begins with 0 and 1 and is comprised of subsequent numbers in which the nth number is the sum of the two previous numbers. The equation for finding a Fibonacci number can be written like this:

Fn = F(n-1) **+** F(n-2). The starting points are F1 = 1 and F2 = 1.

Each number in the Fibonacci sequence is identified with a subscript 1, 2, 3, 4 …… to indicate which term of the sequence we are talking about. Thus F16 refers to the sixteenth Fibonacci number.

Related to the Fibonacci sequence is another famous mathematical term: the **Golden Ratio**. When a number in the Fibonacci series is divided by the number preceding it, the quotients themselves become a series that follows a fascinating pattern: 1/1 = 1, 2/1 = 2, 3/2 = **1.5**, 5/3 = **1.666**…, 8/5 = **1.6**, 13/8 = **1.625**, 21/13 = **1.61538**, 34/21 = **1.619**, 55/34 = **1.6176**…, and 89/55 = **1.618**… The first ten ratios approach the numerical value 1.618034… which is called the “Golden Ratio” or the “Golden Number,” represented by the Greek letter Phi (Φ, φ). After these first ten ratios, the quotients draw ever closer to Phi and appear to converge upon it, but never quite reach it because it is an irrational number. Phi (Φ), 1.61803 39887…, is also the number derived when you divide a line in mean and extreme ratio, then divide the whole line by the largest mean section; its inverse is phi (φ), 0.61803 39887…, obtained when dividing the extreme (smaller) portion of a line by the (larger) mean. In the image below, the ratio of the smaller part of a line (CB), to the larger part (AC) – i.e. CB/AC – is the same as the ratio of the larger part, AC, to the whole line AB. Therefore, CB/AC = AC/AB.

Phi and phi are also known as the Golden Number and the Golden Section. The formula for Golden Ratio is: F(n) = (x^n – (1-x)^n)/(x – (1-x)) where x = (1+sqrt 5)/2 ~ 1.618 The Golden Ratio represents a fundamental mathematical structure which appears prevalent – some say ubiquitous – throughout nature, and is used as the basis for Fibonacci tools in trading.

Did you know you can download a FREE copy of *Master Fibonacci* with a free membership on Fibonacci.com?

Paperback: 128 pages

Author: Shelley Allen, M.A.Ed.

Publisher: Fibonacci Inc.; 1st edition (2019)

Language: English