Polarized Fractal Efficiency (PFE) – Strategy, Rules, Returns

In the trading world, there are many technical indicators to help you understand market trends and many more are being created — one such indicator is Polarized Fractal Efficiency (PFE). What do you know about this indicator?

Polarized Fractal Efficiency (PFE) is a technical analysis indicator that uses fractal geometry to check whether the price is moving efficiently. The indicator uses a mathematical calculation to show whether the price action is consolidating or trending and the trend direction. Its values range from -100 to +100, with values around zero indicating a consolidation and values further away from zero indicating a trend in the corresponding direction.

In this post, we will take a look at everything you need to know about this indicator: what it is, how it works, and how you can improve your trading strategies with it. Let’s dive in!

Key takeaways

• Polarized Fractal Efficiency (PFE) is a technical analysis indicator that uses fractal geometry to check whether the price is moving efficiently.
• Its values range from -100 to +100, with zero being the midline. When the PFE value is greater than zero, there is likely an uptrend, and when the value is less than zero, there’s likely a downtrend.
• We show you a Polarized Fractal Efficiency strategy (backtested with complete trading rules).

What is Polarized Fractal Efficiency (PFE)?

Polarized Fractal Efficiency (PFE) is a technical analysis indicator that uses fractal geometry to check whether the price is moving efficiently. The indicator uses a mathematical calculation to show whether the price action is consolidating or trending and the trend direction.

Its values range from -100 to +100, with zero being the midline. When the PFE value is greater than zero, there is likely an uptrend, and when the value is less than zero, there’s likely a downtrend — the further away the PFE value is from zero, the stronger and more efficient the trend in that direction. In contrast, PFE values that cluster around zero indicate a price consolidation, meaning that buyers and sellers are in equilibrium.

The chart below shows an example of Polarized Fractal Efficiency (PFE) – in the lower pane:

You can clearly see how the indicator oscillates from oversold to overbought levels.

Polarized Fractal Efficiency (PFE) trading strategy – trading rules, returns, performance, returns

By now, you know the basics of the indicator, so let’s show you a strategy that is complete with trading rules.

We use the following trading rules:

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The rules are simple, although the indicator is a bit difficult to calculate. The trading rules don’t work particularly well on stocks such as the S&P 500 and Nasdaq 100, but they have worked well on gold and Bitcoin.

If we apply the trading rules on the ETF that tracks the gold price, which has the ticker code GLD, we get the following equity from inception until today:

Some trading statistics, facts, and performance metrics:

Table of Key Statistics (Polarized Fractal Efficiency)

Statistics and key data	Value
Number of trades	110
Average gain per trade	1.28%
Compound Annual Growth Rate (CAGR)	7.1%
Win rate	57%
Average winning trade	3.5%
Average losing trade	-1.7%
Maximum drawdown	-15%
Time invested in the market	37%
Risk-adjusted return	19%

The data from the PFE strategy reveals a modest win rate of 57%, indicating that the majority of trades are profitable. Despite this, the maximum drawdown is low at -15%, which suggests that while the strategy has periods of success, it gets this return with modest losses along the way.

The average gain per trade is 1.28%, contributing to an overall CAGR of 7.1%. Notably, the risk-adjusted return, which considers the time invested in the market, stands at an impressive 19%. This indicates a strong return relative to the amount of time the strategy is active, emphasizing its efficiency.

The numbers are encouraging, although the strategy performed best before 2012 until it picked up significantly in the last two years.

Some might argue that the strategy is overfitted. We disagree. Assets move and behave differently! You can’t expect one strategy to fit all assets—it will never happen.

Polarized Fractal Efficiency (PFE) trading strategy – complete code

The complete Amibroker for the strategy looks like this:

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How does PFE help in trading and finance?

The PFE helps in trading and finance by showing whether the market is trending or consolidating. And when the market is in a trend, it could also indicate the direction of the trend and its strength and efficiency. PFE values far above or below the zero line indicate that there is a trend, with values above zero indicating an uptrend and values below zero indicating a downtrend.

Also, in an already-established major trend, traders can use the PFE to know when a pullback has ended and the price is about to reverse to continue another impulse swing in the trend direction. So, in an uptrend, when there is a pullback and the PFE reverses from a below-zero level, it could be a signal to buy the next upswing. Similarly, in a downtrend, a downward reversal of the PFE from an above-zero level after a rally (pullback) could be a signal to short the next downswing.

What are the key components of PFE?

The key components of the PFE are the price and the period. These include the current price and the price at N-period earlier. The N refers to the number of periods under consideration.

The indicator uses the current price and price at an N-period and finds the square root function. By dividing the length of the line that is 100% efficient, it gives a measure of fractal efficiency. Then, a plus sign is attached when the move is down, and a minus sign when the move is up to get a polarized fractal efficiency.

How does PFE measure market efficiency?

The PFE indicator measures market efficiency by showing which direction the price is trending and the strength of the price action. Its values being above or below the zero line indicates the direction of the trend — above the zero line indicates an uptrend and below the zero line indicates a downtrend.

How far away the value is from the zero line determines the strength and efficiency of the market. If it is far, the trend is strong and there’s an imbalance in the market — the market is inefficient. On the other hand, if the value is fluctuating around the zero line, the market is in consolidation and there is a balance between the supply and demand — the market is efficient.

Why is PFE important for traders?

The PFE is important for traders because it shows if the market is trending or consolidating. And it could also indicate the direction of the trend if present, as well as the strength and efficiency. When the PFE values are far above or below the zero line, it could mean that there is a trend — with values above zero indicating an uptrend and values below zero indicating a downtrend.

The indicator also helps traders to know when a pullback has ended and is about to reverse to continue another impulse swing in the trend direction. In an uptrend, when there is a pullback and the PFE reverses from a below-zero level, it could signal a buying opportunity to ride the next upswing. Similarly, in a downtrend, a downward reversal of the PFE from an above-zero level after a rally (pullback) could be a signal to short the next downswing.

How can PFE be calculated?

The formula of PFE is complex. It’s given as follows:

Where:

N = the period of the indicator

M = the smoothing period

The calculation is too complex to be done manually. Interestingly, there are custom indicators available on many platforms that automatically calculate and plot the indicator on the chart.

What are the benefits of using PFE?

The benefits of using the PFE are many. These are some of them:

• It shows whether the market is trending or consolidating — PFE values far above or below the zero line indicate that there is a trend, while values clustering around the zero line indicate a consolidating market.
• It could also indicate the direction of the trend — values above zero indicate an uptrend and values below zero indicate a downtrend.
• It can be used to gauge the strength and efficiency of the market — the farther away from zero, the stronger the trend and the more inefficient the market, while the closer to zero, the more efficient the market and the weaker the trend (consolidation).
• In a trending market, it can be used to spot the end of a pullback so as to trade the next impulse swing in the trend direction.

What are the limitations of PFE?

The limitations of PFE include:

• It lags the price action: As with most indicators, the PFE lags the price because it is calculated from past price data over an N-period.
• It has minimal predictive power: The indicator does not tell you what would happen next. It is only a reflection of how the price has moved in the past.
• It’s prone to false signals: The PFE is prone to many false signals, especially during a choppy market. This is why you shouldn’t use it alone to identify the trend.

How does PFE compare to other trading indicators?

The PFE compares fairly well with other trading indicators, as it shows several aspects of the price action. It tells you whether the market is trending or consolidating, and when the market is in a trend, it could also show the direction of the trend and its strength and efficiency. This is unlike other indicators that only tell you about the trend direction (moving averages) or the trend strength (like the ADX) alone.

Also, in an already-established trend, the PFE can be used as a momentum indicator (like the stochastic or RSI) to know when a pullback has ended and is about to reverse to continue another impulse swing in the trend direction.

Can PFE be used for different financial assets?

Yes, the PFE can be used for different financial assets, as long as the price history and data are known. It doesn’t matter the market; the indicator can be used to identify the trend direction and gauge the strength of the trend.

If the market is predominantly range-bound, the indicator can show that too, as the values would cluster around the zero line.

How does PFE indicate market trends?

The PFE indicates market trends when its values are moving steadily away from the zero line. With its values ranging from -100 to +100 and zero being the midline, the farther away from zero the value is, the stronger the trend.

Thus, when the PFE value is greater than zero, there is likely an uptrend, and when the value is less than zero, there’s likely a downtrend — the farther away the PFE value is from zero, the stronger and more efficient the trend in that direction.

In contrast, when PFE values cluster around the zero line, it indicates a price consolidation, which means that buyers and sellers are in equilibrium — no trend.

What are the applications of PFE in technical analysis?

The applications of the PFE in technical analysis include:

• To know whether the market is trending or consolidating — PFE values far above or below the zero line indicate that there is a trend, while values clustering around the zero line indicate a consolidating market.
• To know the direction of the trend — values above zero indicate an uptrend and values below zero indicate a downtrend.
• To gauge the strength and efficiency of the market — the farther away from zero, the stronger the trend and the more inefficient the market, while the closer to zero, the more efficient the market and the weaker the trend (consolidation).
• To find an entry or exit point in a trending market — it can spot the end of a pullback so as to trade the next impulse swing in the trend direction.

How do traders interpret PFE signals?

Traders interpret PFE signals by checking the position of the indicator relative to the zero line. When the PFE is far above the zero line, it indicates an uptrend, and when it is far below the zero line, it indicates a downtrend. When the values are fluctuating around the zero line, the market is consolidating. That is, the supply and demand are in equilibrium — the market is efficient.

Traders also use the PFE as a momentum indicator to know when a pullback has ended and the price is about to reverse to continue another impulse swing in the trend direction. In an uptrend, when there is a pullback and the PFE reverses from a below-zero level, traders take it as a signal to buy the next upswing. Similarly, in a downtrend, a downward reversal of the PFE from an above-zero level after a rally (pullback) signals traders to short the next downswing.

What are the common misconceptions about PFE?

The two common misconceptions about the PFE are as follows:

• The PFE can tell you what would happen in the market: Like other indicators calculated from past price data, the PFE cannot tell you what would happen next. It only shows what has happened and you may use it to project into the future. But all predictions are based on probabilities.
• The PFE can be a trading strategy on its own: It is only an indicator and cannot be a strategy on its own. You must combine it with price action analysis or other indicators to define entry and exit criteria and risk management.

How can traders optimize PFE for their strategies?

Traders can optimize the PFE for their trading strategies by combining the indicator with price action analysis or other trading indicators to create a unique trading strategy with clear entry and exit criteria, position sizing, and risk management plans.

While some may be tempted to use the PFE alone to decide when to enter or exit a trade, that is not a smart way to trade. It is better to use it with other analysis tools to have a better understanding of the market structure and price movements.

What historical data does PFE consider?

The historical data the PFE considers are the price data and the trader’s chosen period. The price data here refer to the current price and the price at N-period earlier.

The N is the number of periods the trader chooses. In most platforms with the indicator, these data are automatically pulled by the platform to calculate the indicator.

What are some practical examples of PFE analysis?

Here are a few practical examples of the PFE analysis both for identifying trends and for picking entries:

Example 1: Identifying an uptrend:

In the chart below, we used a 30-period PFE with 10-period smoothing. It clearly shows an uptrend when the indicator stays above the zero level. Notice how smooth the indicator is because of the settings we used.

Example 2: Identifying a downtrend:

In the chart below, we used the same 30-period PFE and 10-period smoothing to find a downtrend. Notice how the indicator stayed mostly below the zero level as the price swings lower.

Example 3: Using the PFE to find a buy entry in an uptrend

In the chart below, we used the default 10-period PFE and 5-period smoothing. You can see that the indicator now looks like a momentum oscillator. It spotted a good buy entry to ride the next upswing when it turned upward from below the zero level after a price pullback.

Example 4: Using the PFE to find a sell entry in a downtrend

In the chart below, we used the same default 10-period PFE and 5-period smoothing in a downtrend. The indicator, now functioning like a momentum oscillator, spotted a good sell entry to ride the next downswing when it turned downward from above the zero level after a price rally (pullback).

How does PFE relate to volatility in markets?

The PFE does not directly relate to volatility in markets, but it can give a clue about market choppiness and the efficiency of the market. When the indicator is fluctuating around the zero level, then, the price is considered choppy and consolidating — not trending.

This means that the market is relatively efficient, as the supply and demand are in a relative equilibrium at that point. On the other hand, when the PFE is smooth and far above/below zero, then, the price is trending up/down as the case may be.

Can PFE be used for short-term trading strategies?

Yes, the PFE can be used for short-term trading strategies if used correctly. In this case, you use another tool to identify the trend and use the PFE as a momentum indicator to know when a pullback is over so you can ride the next impulse swing in the trend direction.

For instance, in an uptrend, when there is a pullback and the PFE reverses from a below-zero level, it could signal a buy to ride up the next upswing. Similarly, in a downtrend, a downward reversal of the PFE from an above-zero level after a rally (pullback) could signal a short-sell to ride down the next downswing.

How does PFE assist in risk management?

The PFE does not directly assist in risk management, as it neither tells the trader how much position size to use, nor which level to keep their stop-loss order. However, the indicator can be used to formulate a reasonable trading strategy that can be backtested to find the most optimal risk management variables to use while trading.

In other words, data from backtesting can tell you the right amount to risk per trade, the appropriate position size per trade, and the right level for your stop-loss order.

What are the common challenges in applying PFE?

The common challenges in applying the PFE include:

• Knowing the right timeframe to use: The right timeframe to perform the analysis would depend on the trader’s trading style.
• Knowing the period to put in the setting: This would depend on how smooth the trader wants the indicator to be.
• Knowing the right level of the PFE to consider the market trending: The trader can use a Fibonacci number as their cutoff — say anything beyond the 38% or 50% level is considered a trending market and anything less than the 38% level is considered too close to the zero line and, hence, a consolidation.

How can beginners learn to use PFE effectively?

Beginners can learn to use the PFE effectively by seeking trading education from the right sources. They would need to learn how the price moves and how indicators like the PFE try to use price data to distill out specific information about the market. Then, they should learn how to use the indicator alongside other tools to formulate a robust trading strategy and backtest it.

What are the future prospects of PFE in trading?

The future prospect of PFE in trading is mass adoption in algorithmic trading. The PFE uses a complex calculation, but even at that, many platforms are adding it to their systems. Algo traders can use it in combination with other tools to create automated trading systems.

How do experts recommend integrating PFE into trading systems?

For integrating the PFE into trading systems, experts recommend combining it with other trading tools to create a functional trading strategy with entry and exit rules and risk management parameters.

Then, the strategy is to be backtested and forward-tested for profitability and robustness. It may be best to code the strategy into a trading algo, as it makes backtesting and forward-testing easier.

What resources are available for further learning about PFE?

Some of the resources available for further learning about the PFE are the works of Hans Hannula, who is credited for developing the indicator.

Also, Benoit Mandelbrot, in his now infamous book, “The Misbehavior of Markets: A Fractal View of Financial Turbulence”, treated extensively the idea of price fractals. Other sources are financial websites like therobusttrader.com and quantifiedstrategies.com.