Median lines can sometimes be very useful in mapping out market structure and in identifying potential profit targets. One argument against them, however, is that they are subjective and that as a result no trading strategy that incorporates them can be backtested.
Greg Fisher of www.Median-Line-Study.com addressed this problem in a paper he wrote for an MBA independent study course and subsequently published in 2009 as Using Median Lines as a Trading Tool: An Empirical Study--Grain Markets 1990-2005. He also wrote a companion piece, Finding High Probability Lines. Both are brief works (70-some pages) and in part cover material available elsewhere. But his study of the grain markets is a serious attempt at backtesting median line principles.
The thorniest problem is the choice of pivot points. They are obvious in hindsight and somewhere between tough and impossible to identify in real time. Fisher uses Andrews’ definition of a trendline: “For an uptrend within the period of consideration, draw a line from the lowest low, up and to the highest minor low point preceding the highest high. The line must not pass through prices in between the two low points. Extend the line.” A pivot is “a reverse in price direction that reverses the previous trend by violating the previous trendline.” (pp. 13-14) Once a pivot forms, a median line and its parallels are drawn.
Fisher offers a flowchart of possible price action, starting with the most basic either/or: does price reach the median line or not?
Fisher’s work is thorough and probably about as good as backtesting median lines can be. Yet, as he himself admits, it benefited from hindsight since he was working with historical data. “The study assumes all pivots were chosen correctly as it is based on known price data.” (p. 38) In real time trendlines are drawn and re-drawn. In fact, even in the figure Fisher provides to illustrate Andrews’ notion of trendlines there are obvious places to draw trendlines that misidentify the important pivot points.
This is no reason to reject median lines out of hand. Andrews’ method can be used in multiple ways, for multiple purposes. For instance, one doesn’t always have to rely on the most recent, still tentative pivot to draw median lines. Often the best sets are those that the market has already respected.
For readers who are unfamiliar with median lines Fisher’s books provide a good introduction. For those who want to subject the median line method to some Monday-morning backtesting Fisher offers a carefully thought out model.