# Polarized Fractal Efficiency

The Polarized Fractal Efficiency is a technical analysis tool used to evaluate the effectiveness of price movements, allowing traders to identify market trends, reversals, and entry/exit points more accurately

12 minutes

#### Introduction

In 1994, Hans Hannula introduced a technical analysis tool called the Polarized Fractal Efficiency (PFE) indicator. This tool is widely used to evaluate the efficiency of price movements in the market.

Hannula, who is recognized as an expert in several fields, including writing, engineering, programming, and trading, proposed the use of fractal geometry to measure market trends. Fractal geometry is a branch of mathematics that deals with complex and chaotic systems. Hannula discussed this concept in detail in the January 1994 issue of Technical Analysis of Stocks & Commodities magazine.

In addition to PFE, Hannula has authored books and articles on several trading topics, such as market cycles, astrology, neural networks, and chaos theory. The PFE indicator uses fractals, which are recurring self-similar patterns at different scales, to calculate the deviation between actual price movements and the shortest possible movement. It assigns a value ranging from -100 to +100. A high positive value suggests a smooth and efficient uptrend, while a high negative value indicates a smooth and efficient downtrend. Conversely, a value near zero implies a choppy or random market.

#### Computing the Polarized Fractal Efficiency Indicator

Traders looking to evaluate the strength and efficiency of a price trend over a specific period can turn to the Polarized Fractal Efficiency (PFE) indicator. In addition to its primary function, the PFE can also help traders identify potential trend reversals and changes.

To calculate the PFE, traders measure the actual distance that the price travels over a set number of bars, compare it to the shortest possible distance between the starting and ending points, and assign a value ranging from -100 to +100. A shorter actual distance indicates a more linear and efficient price movement, while a longer actual distance suggests a more chaotic and inefficient price movement.

The formula for the PFE indicator is straightforward:

(D / d) * 100

where:

• D is the distance the price travels during a specific period
• d is the shortest possible distance between the starting and ending points of the same period

By applying the PFE formula, traders can gain a better understanding of the current price trend’s strength and efficiency.

To calculate the Polarized Fractal Efficiency (PFE) indicator, traders must follow a set of steps.

1. First, they need to determine the period length (N) for the indicator, which represents the number of bars used to measure price efficiency.

2. Next, traders need to determine the smoothing length (M) for the indicator, which represents the number of bars used to smooth the PFE values using an exponential moving average (EMA).

3. After these initial steps, traders must complete the following five steps for each bar (i):

i. Calculate the shortest possible distance between the current price (Price_i) and the price N bars ago (Price_i-N). This distance represents the shortest distance that the price could have traveled over N bars.

ii. Calculate the actual distance that the price traveled over N bars by adding up the distances between each consecutive pair of prices from i-N to i. This distance represents the actual path that the price took over N bars.

iii. Calculate the ratio of the straight-line distance to the actual distance and multiply it by 100. This is the raw PFE value for bar i (P_i).

iv. If the current price (Close_i) is lower than the previous price (Close_i-1), then make the raw PFE value negative. This indicates a downward trend.

v. Calculate an EMA of the raw PFE values over M bars. This is the final PFE value for bar i (PFE_i).

By using the PFE indicator, traders can assess the efficiency and strength of a price trend over a specific timeframe and identify potential trend reversals or changes. The PFE value ranges from -100 to +100, with zero as the centerline. A positive PFE value signifies an upward trend, while a negative PFE value indicates a downward trend. The higher or lower the absolute value of the PFE, the stronger and more efficient the trend is. A PFE value close to zero indicates a sideways or choppy market where supply and demand are balanced.

In summary, traders can use the PFE indicator to evaluate price trends over a specific period, and the indicator can provide valuable insights into market efficiency and strength. By following a set of steps, traders can calculate the PFE and use its range of values to make informed trading decisions.

The Polarized Fractal Efficiency (PFE) indicator is an essential tool for traders to evaluate the strength and efficiency of a price trend over a given timeframe. A positive PFE value signals an upward trend, while a negative value indicates a downward trend. A PFE value closer to zero indicates a sideways or choppy market.

To further refine the PFE indicator, traders can use an exponential moving average (EMA) to reduce noise and lag. The smoothing factor can be tailored to the trader’s preference and time frame. The absolute value of the PFE determines the trend’s strength and efficiency, with higher or lower values signifying stronger trends.

In conclusion, the PFE indicator is a critical technical analysis tool for traders. It helps to measure price efficiency, identify trend strength, and forecast potential market reversals. By utilizing this indicator, traders can make informed trading decisions and enhance their overall trading strategy.

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#### Hans Hannula’s suggestions on how to use the Polarized Fractal Efficiency Indicator

Gain insights and trading recommendations from Hans Hannula, the creator of the Polarized Fractal Efficiency (PFE) indicator, on how to use this technical tool effectively.

Identify Trends

Using fractal geometry, the PFE indicator measures the price efficiency of a security over a defined period, identifying and determining the trend’s strength and efficiency. The PFE value ranges from -100 to +100, with zero as the centerline. A positive PFE indicates an upward trend, while a negative PFE indicates a downward trend. A trend is deemed stronger and more efficient when the PFE value deviates farther from zero.

Customize Indicator Settings and Use Multiple Timeframes

Hannula recommends traders experiment with different values of the period parameter and smoothing parameter to adapt to varying time frames and market conditions.

For example, he suggests a period of 10 bars for daily charts, 5 bars for weekly charts, and 20 bars for monthly charts, with a smoothing parameter of 5 bars for daily charts, 3 bars for weekly charts, and 10 bars for monthly charts. By adjusting these settings, traders can fine-tune the PFE indicator to suit their preferences and trading style.

Basic rules for trading as per Hannula

Hannula, the creator of the PFE indicator, has further proposed some guidelines for trading with this tool. These guidelines include:

• Entering a long position when the PFE value crosses above zero from below, signaling a reversal from a downtrend to an uptrend.
• Entering a short position when the PFE value crosses below zero from above, indicating a reversal from an uptrend to a downtrend.
• Opening a long position when the PFE reaches a new high above zero, signaling a strong and efficient uptrend.
• Opening a short position when the PFE reaches a new low below zero, indicating a strong and efficient downtrend.
• Closing long positions when the PFE value reaches a peak above zero and begins to decline, suggesting a potential exhaustion or overextension of the trend.
• Closing short positions when the PFE value reaches a trough below zero and starts to rise, indicating a possible exhaustion or overextension of the trend.
• Closing positions or taking profit when the PFE returns to zero from above or below, suggesting a loss of momentum or efficiency in the trend.

Explore other ways the PFE indicator can be used for trading:

• Smooth out fluctuations by applying a moving average to the PFE indicator to reveal the dominant trend direction. An upward PFE moving average suggests an uptrend, while a downward PFE moving average suggests a downtrend.
• Determine whether the market is trending or ranging by setting a threshold level. If the PFE indicator is above +10 or below -10, the market is considered to be trending. If the PFE indicator is between -10 and +10, the market is considered to be ranging.
• Identify potential trend reversals by looking for divergences between the PFE indicator and the price. A bullish divergence appears when the price hits a lower low, but the PFE indicator shows a higher low. A bearish divergence appears when the price reaches a higher high, but the PFE indicator shows a lower high.
• Generate trading signals using the PFE indicator and its moving average crossovers. A buy signal arises when the PFE indicator crosses above its moving average, indicating a rise in efficiency and momentum. A sell signal arises when the PFE indicator crosses below its moving average, indicating a decline in efficiency and momentum.

Combine with other technical tools

To validate support and resistance levels, combining the PFE indicator with price action analysis is recommended. It’s also useful to use additional technical indicators, such as trend lines or moving averages, to confirm the signals provided by the PFE indicator. For example, if the PFE line is trending upward and the price rebounds from a support level, it could indicate an opportunity for a long trade entry.

Advanced techniques for using the PFE indicator in trading were introduced by Hannula. He discussed the concept of polarized fractal bands (PFB), which can serve as dynamic support and resistance levels derived from the PFE values. Hannula also described how to use the PFB to identify breakout points, trend continuation patterns, and reversal patterns. He also demonstrated how to use the PFE indicator to detect divergences between price and momentum, which can indicate potential trend changes or corrections.

Set appropriate stop-loss levels

Managing risk is essential in any trading strategy, so it’s important to set appropriate stop-loss levels. The PFE indicator can be helpful in identifying where to place stop-loss orders to mitigate potential losses.

Use with discretion

While the PFE indicator is a useful tool, it may generate false signals like any technical indicator. Therefore, it’s recommended to use it as a tool to assist in making informed trading decisions, but always take into account other factors and use your discretion.

Test and optimize

Testing the PFE indicator on historical data and optimizing its parameters can assist in finding the best settings for the market being traded. This helps refine your trading strategy and improve the accuracy of your trading signals.

Keep learning

Continuous learning is crucial in trading since markets and trading tools constantly evolve. Staying up-to-date with the latest technical analysis developments is essential for improving your trading skills and staying ahead of the curve. Therefore, it’s recommended to keep learning and refining your trading strategies to remain competitive in the markets.

To sum up, Hannula highlighted the PFE indicator as a flexible and potent tool that enables traders to analyze price movements and trends across different markets and time frames. He urged traders to explore various PFE settings and combinations with other technical indicators to find their optimal trading strategies. Nonetheless, he advised caution in choppy or sideways markets, where the PFE indicator may not work effectively due to low price efficiency and fluctuating PFE values around zero.

#### Advantages & Limitations of the Polarized Fractal Efficiency Indicator

The PFE indicator is a technical analysis tool that utilizes fractals to measure price efficiency. While it can assist in identifying market trends and breakouts, it also has its advantages and limitations that traders should be aware of. Here’s a breakdown of its advantages and limitations:

• Versatile: The PFE indicator is flexible and can be adjusted to suit different market conditions and time frames by varying its period.
• Filters out noise: The PFE indicator uses an EMA to smooth out price data, reducing the impact of market noise and choppy price movements.
• Provides clear signals: The PFE indicator oscillates around a zero line and has upper and lower bands, giving clear signals for entry and exit points.

Limitations

• Lags behind price: Due to the EMA and fractal dimension calculation, the PFE indicator may lag behind the price action.
• False signals: The PFE indicator may generate false signals during choppy or sideways markets due to high or low efficiency values that do not reflect the true trend direction.
• Affected by extreme price movements: The PFE indicator may produce inaccurate signals when the price experiences extreme movements that suggest a reversal, but instead continues moving in the same direction.

Overall, while the PFE indicator is a useful tool for technical analysis, traders should use it in conjunction with other tools and take its limitations into account to make informed trading decisions.

The PFE indicator is a powerful technical analysis tool that traders can use to evaluate the effectiveness of price movements within a specific time frame. It’s especially helpful in identifying potential trend reversals and breakouts, which can improve traders’ entry and exit timing. By utilizing the PFE indicator, traders can enhance their accuracy and make more informed trading decisions.

Trading involves significant risk and the use of the PFE indicator does not guarantee profits or prevent losses. The PFE indicator is a technical analysis tool that should be used in conjunction with other indicators and analysis techniques to make informed trading decisions. Traders should be aware of its limitations and exercise caution when trading in markets with low volatility or no clear trend.

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