Technical Analysis: In-Depth Understanding of the Application Value of Fibonacci Sequence in the Forex Market

The Mathematical Secret of the Golden Ratio

One of the most powerful technical analysis tools for forex traders originates from a seemingly simple yet universe-regularity-imbued mathematical sequence. The Fibonacci sequence was discovered by 13th-century Italian mathematician Leonardo Pisano, who introduced this ratio system, originally created by Indian mathematicians, to the Western world. The uniqueness of this sequence lies in: each number equals the sum of the two preceding numbers.

Observe this magical number sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765…

When we divide any number in the sequence by the previous number, the ratio approaches 1.618 infinitely, which is the legendary Golden Ratio. For example, 1597 ÷ 987 ≈ 1.618, and 610 ÷ 377 is also approximately 1.618. This ratio is believed to be the secret code maintaining balance in all things in the universe, and it also exhibits remarkable predictive power in financial markets.

Further calculations reveal that dividing a number by the next one yields a value close to 0.618, which is exactly the reciprocal of 1.618. For example, 144 ÷ 233 ≈ 0.618, and 610 ÷ 987 is also approximately 0.618. This 0.618 forms the mathematical basis of the 61.8% Fibonacci retracement level.

When dividing a number by a number two places larger, the result approaches 0.382, such as 55 ÷ 89 ≈ 0.382, and 377 ÷ 987 ≈ 0.382, forming the source of the 38.2% Fibonacci retracement level.

Fibonacci Retracement: Finding Hidden Support and Resistance

The most direct application of the Fibonacci sequence in financial markets is through retracement levels to discover potential reversal points of asset prices. This tool, known as the Golden Ratio line, is the secret weapon traders use to find buy and sell opportunities.

Components of the retracement level line

The Fibonacci retracement indicator allows traders to draw multiple horizontal reference lines between two extreme points (usually recent high and low), generating several levels at 23.6%, 38.2%, 50%, 61.8%, and 78.6%. These represent key zones where price may pause or reverse.

For example, if EUR/USD rises from a certain low to 1.5, then retraces 0.354 points, this indicates a 23.6% correction, perfectly aligning with Fibonacci sequence principles. Because Fibonacci ratios are ubiquitous in nature, they also demonstrate astonishing effectiveness in financial markets.

Real-world example: Precise prediction of gold prices

Taking the gold market as an example, suppose the price rises from $1681 to $1807.93. Using these two prices, a complete set of retracement levels can be drawn:

• 23.6% retracement: $1777.97 (Calculation: 1807.93 - (126.93 × 0.236) = 1777.97)
• 38.2% retracement: $1759.44 (Calculation: 1807.93 - (126.93 × 0.382) = 1759.44)
• 50% retracement: $1744.47 (Calculation: 1807.93 - (126.93 × 0.5) = 1744.47)
• 61.8% retracement: $1729.49 (Calculation: 1807.93 - (126.93 × 0.618) = 1729.49)
• 78.6% retracement: $1708.16 (Calculation: 1807.93 - (126.93 × 0.786) = 1708.16)

How to Use Fibonacci Retracement to Build Trading Strategies

Traders can utilize these retracement levels to determine three key elements: entry points, stop-loss placements, and target prices. When a currency pair experiences an upward move and then retraces to the 61.8% Fibonacci level, traders often see this as a strong support, setting buy orders there.

Application in Uptrend

After a significant price increase, traders need to identify the bottom point A and the top point B, then recognize where the retracement might stop at point C. During this process, the retracement levels at 23.6%, 38.2%, 50%, 61.8%, and 78.6% can serve as potential support zones. Traders judge whether the price has a rebound basis based on these levels.

Application in Downtrend

When an asset’s price drops sharply, traders start from the top point A, bounce to point B, and look for the next potential resistance point C. Any of the Fibonacci retracement levels could serve as important resistance.

Traders often combine Fibonacci retracement indicators with other technical analysis tools or trend patterns to enhance accuracy.

Fibonacci Extension: Predicting Price Targets

Compared to retracement levels used for entry points, Fibonacci extensions serve another equally important purpose—determining when to exit.

Mathematical basis of extension levels

Since 1.618 is the core ratio of the Fibonacci sequence, 161.8% becomes the basis for extension levels. Additionally, common extension levels include 100%, 200%, 261.8%, and 423.6%. These percentages help traders forecast where prices might rise or fall after breaking through retracement levels.

Application of extension in Uptrend

Traders need to identify three key prices: point X as the recent low, point A as the recent high, and point B at a Fibonacci retracement level. Once these three points are confirmed, traders can establish a long position at point B and then look for potential target points C based on extension levels. When the price reaches these extension percentages, it becomes a signal to consider taking profit.

Application of extension in Downtrend

Conversely, in a downtrend, point X becomes the recent high, point A the recent low, and point B the retracement level. Traders establish a short position at point B and predict the downward target based on extension levels.

Overall Strategy Framework

The Fibonacci sequence provides forex traders with a comprehensive logical framework: first, use retracement levels to identify support and resistance zones, then determine entry points, and finally use extension levels to forecast exit targets. This set of tools transforms market randomness into quantifiable probabilistic advantages, making trading decisions more scientific. No matter how markets fluctuate, Fibonacci ratios always guide traders through the market fog with their elegant mathematical regularity.