# Research

Introduction

The Median Line method, a.k.a. Andrews’ pitchfork, is a trendline technical analysis tool used by chartists to gage market movement.  The Median Line method was developed by Dr. Alan H. Andrews to determine potential market direction by drawing a single line on the chart of any market security.  Dr. Andrews determined price returned to a Median Line drawn from the most recent pivots 80% of the time.

Below is a summary of a paper I wrote entitled, “Using Median Lines As A Trading Tool: An Empirical Study – Grain Markets 1990 – 2005”, to determine the effectiveness of the Median Line method by determining the probabilities of price acting according to Median Line theory, as well as observations the author has made since the study was completed.

The Median Line Method

The creation of the Andrews’ Median Line set is quite simple.  A definition of terms as quoted from Dr. Andrews’ course material is necessary to explain the concept.

Pivot (P) – “…a turning point.  It is the extreme on a bar chart where a change in trend takes place.”

Median Line (ML) – “Each ML starts from a pivot or turning point in trend and is drawn so that it bisects the distance between the next two Pivots (Ps).”

Median Line Parallel (MLH) – “…MLH means median line parallel.  Used to signal change in trend when price touches or pass past these lines, under specified conditions.”

~ Dr. Alan Andrews, Action-Reaction Course Figure 1. Andrews’ Median Line set (a.k.a. Andrews’ pitchfork).

Median Line Theory

Median Line theory focuses on the probability of price acting according to the following three rules in regard to price action near the Median Line:

“prices will reach the latest Median Line

prices will either reverse on meeting the Median Line or gap through it

when prices pass through the Median Line, they will pull back to it”

~ Dr. Alan Andrews, Action-Reaction Course

Andrews made the following statements concerning the expectation of price action by using the Median Line method.

“…enable the user to be one of the few who can tell where the prices are headed, and the place they will reach about 80% of the time.”

“The probability of the next P being at the latest ML seems to be about 80%.”

~ Dr. Alan Andrews, Action-Reaction Course

An important point about the term “pivot” needs to be clarified.  Andrews considered price reversals and price gaps to be pivots.  Andrews also noted price accelerations (large price bars) as having similar properties as price gaps.

“…a gap, (which is 2 P’s)” or 2 pivots, and “…a gap being a negative reversal.”

And,

“Technically and empirically the price at one extreme of a day’s range may be opposite the extreme of the next day’s range, and still have the properties of a true gap.”

~ Dr. Alan Andrews, Action-Reaction Course

As Andrews stated, price is expected to reach the Median Line about 80% of the time.  When price does not reach the Median Line, a fourth rule, the Price Failure Rule is applicable.

“when prices reverse before reaching the Median Line, leaving a “space”, they will move more in the opposite direction than when prices were rising toward the Median Line”

~ Dr. Alan Andrews, Action-Reaction Course

Median Line theory suggests the Median Line acts as a magnet to price and the outer parallels act as support and resistance.  For occasions when price moves outside of the Median Line set, a warning line (WL) is drawn.

“Warning line parallel to MLH and same distance from MLH as MLH is from ML.  Probability of a pivot at or near WLs.”

~ Dr. Alan Andrews, Action-Reaction Course Figure 2. Median Line Set With Warning Line.

The Study

An empirical study of daily charts of the grain markets (CBOT wheat, KCBOT wheat, CBOT corn, and CBOT soybeans) from 1990-2005 was conducted.  The “new crop” contract for each grain for each year was studied (July – CBOT wheat, KCBOT wheat, December – CBOT corn, November – CBOT soybeans).  The number of times market price movement acted according to the Median Line rules was determined and recorded.  The probability of price acting according to the Median Line method rules was determined and recorded.

The identification of pivots was somewhat subjective, so for the purposes of the study, a more exact definition was created.  A pivot for the study was defined as:

A reverse in price direction that reverses the previous

trend by violating the previous trendline.

The latest Median Line was drawn from either the most recent low, high, low reversal pivots or high, low, high reversal pivots.

The study involved the observance of price movement related to the four rules set out by Median Line theory and quantifies the questions:

1. Does price reach the latest Median Line?
2. Upon meeting the Median Line, does price reverse or gap/accelerate through the line? An additional instance, price consolidation, was added.
3. Upon gapping or accelerating through the Median Line, does price return to the Median Line before continuing?
4. If price fails to meet the Median Line, does price move further in the other direction than it did on the approach to the Median Line?

In addition to the probabilities of the four Median Line theory rules, the additional questions were quantified:

• After a Median Line reversal/gap/acceleration, does price reach the Median Line Parallel?
• Upon meeting the Median Line Parallel, does price reverse, gap/accelerate through or consolidate?
• If price reverses, does price return to the Median Line?
• If price gaps/accelerates through the Median Line Parallel, does price return to the Median Line Parallel? Does price reach the Warning Line?
• If price consolidates, does price continue to move in the same direction it was prior to the consolidation?
• If price fails to reach the Median Line, does price reach the Warning Line?

Results

Rule #1 – Prices will reach the latest Median Line

Figure 4 illustrates the probability of price reaching the latest Median Line.  Price reached the Median Line approximately 80% of the time.  The average of Median Line successes for all four grains over the time period studied was 82%.  Soybeans were the only part of the group that recorded a price return to the Median Line less than 80% at 78%.  The assumption of price reaching the Median Line 80% of the time held true for the other three grains. Figure 4. Probability of Median Line Success.

Rule #2 – Prices will either reverse on meeting the Median Line or gap through it

Figure 5 illustrates that price most often gapped/accelerated through when reaching the Median Line.  For all grains, price gapped or accelerated through the Median line approximately 42% of the time followed by a price reversal 38% of the time and price consolidation at the Median Line 20% of the time.  The largest percentage of price reversals occurred in CBOT Wheat with 46% of the occurrences resulting in a price reversal.  The largest percentage of gaps/accelerations through the Median Line occurred in soybeans with 47% of the occurrences resulting in a gap/acceleration.  The largest percentage of price consolidation occurred in KCBOT Wheat at 26% of the time.  Price tended to consolidate the least in CBOT wheat at 11% of the time.

Andrews stated that the probability of the next pivot at the latest Median Line was about 80%.  Andrews also stated price gaps were considered pivots as well.  Andrews also stated price accelerations as having similar properties of true gaps.  Based on these statements, if price reversals, price gaps, and price accelerations are included under the term “pivot”, the probability of a “pivot” occurring at the latest Median Line for all grains was 80%. Figure 5. Probability of Price Action at the Median Line.

Rule #3 – When prices pass through the Median Line, they will pull back to it

For all grains, figure 6 illustrates that if price gapped/accelerated through the Median Line, price returned to the Median Line 64% of the time before continuing in the previous direction. Figure 6. Probability of Price Returning to the Median Line.

Rule #4 – When prices reverse before reaching the Median Line, leaving a “space”, they will move more in the opposite direction than when prices were rising toward the Median Line

In the instance of price failing to reach the Median Line, Figure 7 illustrates that price moved further in the opposite direction 55% of the time for all grains.  Soybeans moved further in the opposite direction the least at about 39%, and KCBT wheat moved further in the opposite direction the most at 70%. Figure 7. Probability of Price Moving Further in the Opposite Direction After Price Failure.

Additional probabilities – After a Median Line reversal/gap/acceleration, does price reach the Median Line Parallel?

The results show that the Median Line Parallels do act as important areas of concern.  For all grains, after a Median Line reversal, price reached the Median Line Parallel 82% of the time. Figure 8. Median Line Reversal at ML – Reach MLH Probabilities of all Grains.

For all grains, after a Median Line gap/acceleration, price reached the Median Line Parallel 71% of the time. Figure 9. Median Line Gap/Acceleration at ML – Reach MLH Probabilities of all Grains.

Additional probabilities – Upon meeting the Median Line Parallel, does price reverse, gap/accelerate through or consolidate?

When price reached the Median Line Parallel following a reversal at the Median Line, price reversed at the Median Line Parallel 25% of the time, gapped/accelerated through the Median Line Parallel 45% of the time and consolidated around the Median Line parallel 30% of the time. Figure 10. Median Line Reversal at ML with MLH Probabilities of all Grains.

When price reached the Median Line Parallel following a gap/acceleration through the Median Line, price reversed at the Median Line parallel 46% of the time, gapped/accelerated through the Median Line Parallel 44% of the time, and consolidated around the Median Line Parallel 10% of the time. Figure 11. Median Line Gap/Acceleration at ML with MLH Probabilities of all Grains.

Additional probabilities – Upon meeting the Median Line Parallel, if price reverses, does price return to the Median Line?

For all grains, the highest probability pattern followed the configuration: Median Line reversal, and a reversal at the Median Line parallel.  Price returned to the Median Line 93% of the time after following this pattern. Figure 12. Median Line Reversal at ML, reversal at MLH – Probability of Return to ML.

Another high probability pattern existed when price gapped/accelerated through the Median Line and then reversed at the Median Line Parallel.  Price returned to the Median Line 92% of the time after following this pattern. Figure 13. Median Line Gap/Acceleration at ML, reversal at MLH – Probability of Return to ML.

Additional probabilities – If price gaps/accelerates through the Median Line Parallel, does price return to the Median Line Parallel?  Does price reach the Warning Line?

If price initially reversed at the Median Line and proceeded to the Median Line Parallel where price gapped/accelerated through the Median Line Parallel, price returned to the Median Line Parallel before proceeding 67% of the time.  Price also reached the Warning Line 67% of the time. Figure 14. Median Line Reversal at ML, Gap/Acceleration at MLH – Probability of Return to MLH and Price Reaching WL.

If price initially gapped/accelerated through the Median Line and proceeded to the Median Line Parallel where price gapped/accelerated the Median Line Parallel, price returned the Median Line Parallel before proceeding 44% of the time.  Price reached the Warning Line 72% of the time. Figure 15. Median Line Gap/Acceleration at ML, Gap/Acceleration at MLH – Probability of Return to MLH and Price Reaching WL.

Additional probabilities – If price consolidates, does price continue to move in the same direction it was prior to the consolidation?

If price consolidated around the Median Line, price continued in its original direction after the consolidation 55% of the time.  If price originally reversed at the Median Line, and then reached the Median Line Parallel and consolidated, price proceeded in its original direction 83% of the time.  If price originally gapped/accelerated through the Median Line and then consolidated at the Median Line parallel, price moved in its original direction after the consolidation 50% of the time.

Additional probabilities – If price fails to reach the Median Line, does price reach the Warning Line?

Price reached the first Warning Line after a price failure approximately 60% of the time. Figure 16. Probability of Price Reaching the Warning Line After a Price Failure.

Summary

Andrews’ statement that the probability of price returning to the most recent Median Line is 80% appears to have held true on the markets under study.  Andrews’ statement that the probability of the next pivot occurring at the Median Line is about 80% appears to have held true as well when considering a price reversal, a price gap, and a price acceleration under the term “pivot”.

Price tended to return to the Median Line after gapping or accelerating through almost 2/3rds of the time.

The Price Failure Rule tended to be less reliable as only a little more than half of the occurrences moved further in the opposite direction after price failed to reach the Median Line.

The additional probabilities revealed that after a price reversal at the Median Line, price reached the Median Line Parallel the same percentage of the time as price reached the Median Line itself at 82%.  After a gap/acceleration at the Median Line, price reached the Median Line parallel 71% of the time.

The most impressive statistic is when the Median Line and Median Line parallels acted as support and resistance.  When price reached the Median Line and reversed, then reached the Median Line parallel and reversed, price then returned to the Median Line 93% of the time.  This pattern occurred in 14 of the 233 Median Line sets drawn in the study (about 6% of all occurrences).

Similarly, when price reached the Median Line and gapped/accelerated through, then reached the Median Line parallel and reversed, price returned to the Median Line 92% of the time.  This pattern occurred in 24 of the 233 Median Line sets drawn in the study (about 10% of all occurrences).

Median Line Books by Greg Fisher