What is Fisher Transform

The Fisher Transform is a technical indicator created by J.F. Ehlers that converts prices into a Gaussian normal distribution. This indicator has gained popularity in recent years because it tends to generate earlier buy and sell signals than other leading indicators.

Breaking Down Fisher Transform

Market prices do not have a Gaussian probability density function or the familiar bell-shaped curve of a normal distribution. The distribution of returns tends to be rather symmetrical around their means, but the tails are fatter than expected because there are more outliers. This can make charts noisy and difficult to interpret for market technicians.

The Fisher Transform enables traders to create a nearly Gaussian probability density function by normalizing prices. In essence, the transformation makes peak swings relatively rare events and unambiguously identifies price reversals on a chart. The technical indicator is commonly used by traders looking for leading signals rather than lagging indicators. The buy and sell signals are generated by crossovers at indicator extremes, similar to the Stochastic oscillator. The Fisher Transform can also be applied to other technical indicators, such as the Relative Strength Index (RSI) or Moving Average Convergence-Divergence (MACD).

The Fisher Transform formula is calculated as:

Y = 0.5 * ln ((1+X)/(1-X)).


"ln" denotes the abbreviated form of the natural logarithm.

"X" denotes the transformation of price to a level between -1 and 1 for ease of calculation

Fisher Transform Example

This example utilizes a 9-period Fisher Transform to locate Apple buy (green) and sell (red) signals between January and May 2018. The three buy signals during the period coincided with bullish reversals that lasted for about two weeks, offering plenty of profit potential. The three sell signals during the period generated less reliable outcomes, with the first and third crossovers flagging profitable declines. However, the March 1st signal coincided with a single down day, followed by a shallow but multiday uptrend that reached a new high even though the indicator continued to fall.  

Traders using the Fisher Transform may want to experiment with different time periods and upper and lower boundaries to determine what works best for a given security or situation. Generally speaking, shorter time periods will generate a greater number of false signals, making trade decisions more difficult. Conversely, settings that are too long will miss important market turns, reducing potential profits. Fisher Transform settings often work best when tailored to specific instruments, after reviewing the long-term history of signals at different settings.