Polarized Fractal Efficiency (PFE) is a technical indicator developed by Hans Hannula that was invented to determine price efficiency over a user-defined time period. This indicator fluctuates between -100 and +100 with 0 as the center line. Securities with a PFE greater than zero are deemed to be trending up, while a reading of less than zero indicates the trend is down. Polarized Fractal Efficiency's signature characteristic is its use of fractal geometry in determining how efficiently a security's price is moving.
The strength of the trend is measured by the position of the Polarized Fractal Efficiency (PFE) relative to the zero line. As a general rule, the further the PFE value is away from zero, the stronger and more efficient the given trend is. A PFE value that fluctuates around the zero line could indicate that the supply and demand for the security are in balance and price may trade sideways.
Generally, strategies using PFE as a signal consider a buy sign as a reversal in the direction of the indicator and its movement from its minimum value to zero. A signal to close a position arises as the value of the indicator reaches its peak above zero. An indicator shift from peak to zero presents a sell signal. As a rule of thumb, all short positions should be covered after a new minimum is formed for the indicator.
Polarized Fractal Efficiency indicators are also helpful in assessing the strength of a market trend. The higher the indicator value; the stronger the trend. This means that a value of 100 indicates a very strong uptrend and a value of -100 indicates a very strong downtrend.
Hans Hannula's work follows in the footsteps of Benoit Mandelbrot, whose work as a mathematician and contemporary polymath culminate in his now infamous book, The Misbehavior of Markets: A Fractal View of Financial Turbulence. Mandelbrot's 2006 book has gone on to score legions of follows for its revolutionary reevaluation of the standard tools and models of modern financial theory. Its premise is elegantly captured through fractal geometry for financial market applications. Hannula's and Mandelbrot's research has brought the much-needed study of chaotic systems to financial systems. Increasingly, participants are recognizing Chaos Theory, and nonlinear relationships are a significant driver of investment behavior.