There is a unique ratio that can be used to describe the proportions of everything from nature’s smallest building blocks, such as atoms, to the most advanced patterns in the universe, like the unimaginably large celestial bodies. Nature relies on this innate proportion to maintain balance, but the financial markets also seem to conform to this “golden ratio.” 

The golden ratio is derived from the Fibonacci numbers, a series of numbers where each entry is the sum of the two preceding entries. Although this sequence is associated with Leonardo of Pisa, the Fibonacci numbers were actually formulated for the first time by the Indian mathematician, Virahanka, 600 years prior to their introduction to the Western world.

Here, we take a look at some technical analysis tools that have been developed to take advantage of the pattern.

History of the Mathematics

Mathematicians, scientists, and naturalists have known about the golden ratio for centuries. It’s derived from the Fibonacci sequence, named after the Pisan mathematician Leonardo Fibonacci, who lived from around 1175 A.D. until around 1250 A.D.

Although Fibonacci introduced these numbers to the Western world, they were actually discovered by Indian mathematicians hundreds of years earlier. The poet Pingala used them to count the syllables of Sanskrit poetry around 200 B.C., and the method for calculating them was formulated by the Indian mathematician Virahanka around 800 years later.

In this sequence, each number is simply the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, etc.).

But this sequence is not all that important. The essential part is that as the numbers get larger, the quotient between each successive pair of Fibonacci numbers approximates 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, the golden mean, ϕ, and the divine proportion, among others.

So, why is this number so important? Well, many things in nature have dimensional properties that adhere to the ratio of 1.618, so it seems to have a fundamental function for the building blocks of nature.

Examples of the Golden Ratio

Don’t believe it? Take honeybees, for example. If you divide the female bees by the male bees in any given hive, you will get a number around 1.618. Sunflowers, which have opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation. This same ratio can be seen in relationships between different components throughout nature.

The golden ratio also appears in the arts, because it is more aesthetically pleasing than other proportions. The Parthenon in Athens, the Great Pyramid in Giza, and Da Vinci’s Mona Lisa all incorporate rectangles whose dimensions are based on the golden ratio. It seems to be unavoidable.

But does that mean it works in finance? Actually, financial markets have the very same mathematical base as these natural phenomena. Below we will examine some ways in which the golden ratio can be applied to finance, and we’ll show some charts as proof.

Trading and Investing With the Golden Ratio

The golden ratio is frequently used by traders and technical analysts, who use it to forecast market-driven price movements. This is because the Fibonacci numbers and the golden ratio have a strong psychological importance in herd behavior. Traders are more likely to take profits or cover losses at certain price points, which happen to be marked by the golden ratio.

Curiously, the widespread use of the golden ratio in trading analysis forms something of a self-fulfilling prophecy: the more traders rely on Fibonacci-based trading strategies, the more effective those strategies will tend to be.

The Golden Ratio and Technical Analysis

When used in technical analysis, the golden ratio is typically translated into three percentages: 38.2%, 50%, and 61.8%. However, more multiples can be used when needed, such as 23.6%, 161.8%, 423%, and so on. Meanwhile, there are four ways that the Fibonacci sequence can be applied to charts: retracements, arcs, fans, and time zones. However, not all might be available, depending on the charting application being used.

1. Fibonacci Retracements

Fibonacci retracements use horizontal lines to indicate areas of support or resistance. Levels are calculated using the high and low points of the chart. Then five lines are drawn: the first at 100% (the high on the chart), the second at 61.8%, the third at 50%, the fourth at 38.2%, and the last one at 0% (the low on the chart). After a significant price movement up or down, the new support and resistance levels are often at or near these lines.

2. Fibonacci Arcs

Finding the high and low of a chart is the first step to composing Fibonacci arcs. Then, with a compass-like movement, three curved lines are drawn at 38.2%, 50%, and 61.8% from the desired point. These lines anticipate the support and resistance levels, as well as trading ranges.

3. Fibonacci Fans

Fibonacci fans are composed of diagonal lines. After the high and low of the chart is located, an invisible horizontal line is drawn through the rightmost point. This invisible line is then divided into 38.2%, 50%, and 61.8%, and lines are drawn from the leftmost point through each of these points. These lines indicate areas of support and resistance.

4. Fibonacci Time Zones

Unlike the other Fibonacci methods, time zones are a series of vertical lines. They are composed by dividing a chart into segments with vertical lines spaced apart in increments that conform to the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc.). Each line indicates a time in which major price movement can be expected.

The Bottom Line

Fibonacci studies are not intended to provide the primary indications for timing the entry and exit of a position; however, the numbers are useful for estimating areas of support and resistance. Many people use combinations of Fibonacci studies to obtain a more accurate forecast. For example, a trader may observe the intersecting points in a combination of the Fibonacci arcs and resistances.

Fibonacci studies are often used in conjunction with other forms of technical analysis. For example, Fibonacci studies, in combination with Elliott Waves, can be used to forecast the extent of the retracements after different waves. Hopefully, you can find your own niche use for the Fibonacci studies and add it to your set of investment tools.

Candlestick charts are a type of financial chart for tracking the movement of securities. They have their origins in the centuries-old Japanese rice trade and have made their way into modern-day price charting. Some investors find them more visually appealing than the standard bar charts and the price actions easier to interpret.

Candlesticks are so named because the rectangular shape and lines on either end resemble a candle with wicks. Each candlestick usually represents one day’s worth of price data about a stock. Over time, the candlesticks group into recognizable patterns that investors can use to make buying and selling decisions.

How to Read a Single Candlestick

Each candlestick represents one day’s worth of price data about a stock through four pieces of information: the opening price, the closing price, the high price, and the low price. The color of the central rectangle (called the real body) tells investors whether the opening price or the closing price was higher.

A black or filled candlestick means the closing price for the period was less than the opening price; hence, it is bearish and indicates selling pressure. Meanwhile, a white or hollow candlestick means that the closing price was greater than the opening price. This is bullish and shows buying pressure.

The lines at both ends of a candlestick are called shadows, and they show the entire range of price action for the day, from low to high. The upper shadow shows the stock’s highest price for the day, and the lower shadow shows the lowest price for the day.

Bullish Candlestick Patterns

Over time, groups of daily candlesticks fall into recognizable patterns with descriptive names like three white soldiers, dark cloud cover, hammer, morning star, and abandoned baby, to name just a few. Patterns form over a period of one to four weeks and are a source of valuable insight into a stock’s future price action. Before we delve into individual bullish candlestick patterns, note the following two principles:

1. Bullish reversal patterns should form within a downtrend. Otherwise, it’s not a bullish pattern, but a continuation pattern.
2. Most bullish reversal patterns require bullish confirmation. In other words, they must be followed by an upside price move which can come as a long hollow candlestick or a gap up and be accompanied by high trading volume. This confirmation should be observed within three days of the pattern.

The bullish reversal patterns can further be confirmed through other means of traditional technical analysis—like trend lines, momentum, oscillators, or volume indicators—to reaffirm buying pressure. There are a great many candlestick patterns that indicate an opportunity to buy. We will focus on five bullish candlestick patterns that give the strongest reversal signal.

1. The Hammer or the Inverted Hammer

• The Hammer is a bullish reversal pattern, which signals that a stock is nearing the bottom in a downtrend.
• The body of the candle is short with a longer lower shadow. This is a sign of sellers driving prices lower during the trading session, only to be followed by strong buying pressure to end the session on a higher close.
• Before we jump in on the bullish reversal action, however, we must confirm the upward trend by watching it closely for the next few days.
• The reversal must also be validated through the rise in the trading volume.

The Inverted Hammer also forms in a downtrend and represents a likely trend reversal or support.

• It’s identical to the Hammer except for the longer upper shadow, which indicates buying pressure after the opening price.
• This is followed by considerable selling pressure, which wasn’t enough to bring the price down below its opening value.

Again, bullish confirmation is required, and it can come in the form of a long hollow candlestick or a gap up, accompanied by a heavy trading volume.

2. The Bullish Engulfing

The Bullish Engulfing pattern is a two-candle reversal pattern.

• The Bullish Engulfing pattern appears in a downtrend and is a combination of one dark candle followed by a larger hollow candle.
• The second candle completely ‘engulfs’ the real body of the first one, without regard to the length of the tail shadows.
• On the second day of the pattern, the price opens lower than the previous low, yet buying pressure pushes the price up to a higher level than the previous high, culminating in an obvious win for the buyers.

It is advisable to enter a long position when the price moves higher than the high of the second engulfing candle—in other words when the downtrend reversal is confirmed.

3. The Piercing Line

Similar to the engulfing pattern, the Piercing Line is a two-candle bullish reversal pattern, also occurring in downtrends.

• The first long black candle is followed by a white candle that opens lower than the previous close.
• Soon thereafter, the buying pressure pushes the price up halfway or more (preferably two-thirds of the way) into the real body of the black candle.

4. The Morning Star

As the name indicates, the Morning Star is a sign of hope and a new beginning in a gloomy downtrend.

• The pattern consists of three candles: one short-bodied candle (called a doji or a spinning top) between a preceding long black candle and a succeeding long white one.
• The color of the real body of the short candle can be either white or black, and there is no overlap between its body and that of the black candle before. It shows that the selling pressure that was there the day before is now subsiding.
• The third white candle overlaps with the body of the black candle and shows renewed buyer pressure and a start of a bullish reversal, especially if confirmed by the higher volume.

5. The Three White Soldiers

This pattern is usually observed after a period of downtrend or in price consolidation.

• It consists of three long white candles that close progressively higher on each subsequent trading day.
• Each candle opens higher than the previous open and closes near the high of the day, showing a steady advance of buying pressure.
• Investors should exercise caution when white candles appear to be too long as that may attract short sellers and push the price of the stock further down. 

Putting It All Together

The chart below for Enbridge, Inc. (ENB) shows three of the bullish reversal patterns discussed above: the Inverted Hammer, the Piercing Line, and the Hammer.

The chart for Pacific DataVision, Inc. (PDVW) shows the Three White Soldiers pattern. Note how the reversal in downtrend is confirmed by the sharp increase in the trading volume.

The Bottom Line

Investors should use candlestick charts like any other technical analysis tool (i.e., to study the psychology of market participants in the context of stock trading). They provide an extra layer of analysis on top of the fundamental analysis that forms the basis for trading decisions.

We looked at five of the more popular candlestick chart patterns that signal buying opportunities. They can help identify a change in trader sentiment where buyer pressure overcomes seller pressure. Such a downtrend reversal can be accompanied by a potential for long gains. That said, the patterns themselves do not guarantee that the trend will reverse. Investors should always confirm reversal by the subsequent price action before initiating a trade.