[Reading FX with Three Currencies Parity — TriParity Analysis Turning Everyday “Distortions” into Profit] Episode 4: Turning Distortion into Numbers — Measuring “Overextension” with Parity Gap and Z-Score

In this article,Parity Gap andZ-Score are used to整理 the process of turning a vague sense of “too high / too low” into numerical justification such as “Z = 2.3.”

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1. Graduating from “distorted in a vague way”

Many traders have felt the following while looking at charts:

• “Surely this has gone too far.”
• “It looks like it might bounce back.”
• “There’s a distinctive bias….”

In other words,“distortion as a feeling”is grasped intuitively. However, when trying to translate it into entry conditions,

• How much movement qualifies as “overextension”?
• How far back must it revert for the “distortion to be resolved”?

these pointsare difficult to explain in words and hard to formalize into rules. With intuition alone, you cannot determine where to enter and where to exit.

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2. Recalling the “true alignment” of the 3-currency parity

First, let’s reconfirm the “baseline” of the Triad parity.

With three currencies—euro, pound, and dollar—you can form three pairs:

• EURUSD (A/B)
• GBPUSD (B/C)
• EURGBP (A/C)

Among these three pairs, there should originally be the following relationship:

EURUSD ÷ GBPUSD ≒ EURGBP

In other words,defining the “true alignment of the three currencies” with a relationwill allow us to measure how far off it is from there.

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3. What is Parity Gap? — The gap between theoretical coherence and reality

Here is the main topic.

In the TriParity approach, the following steps extract the misalignment in triangular relationships:

1. Take the three pairs A/B, B/C, A/C,
2. From “A/B × B/C” calculatethe theoretical A/C,
3. And compare it withthe actual A/C rate.

This gap between the theoretically aligned value and the actual rate is
theParity Gap.

In mathematical form, it can be written using logarithms as follows.

Gapₜ = ln(A/C) − { ln(A/B) + ln(B/C) }

• If all three are perfectly aligned →Gapₜ ≒ 0
• If any pair is overextended →Gapₜ fluctuates positively or negatively

In short,the Parity Gap is a single number summarizing the distortion of the entire triangular relationship among the three currencies.

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4. What do the sign and magnitude of Gap mean?

Parity Gap has meaning in its sign (plus/minus) as well.

• When Gapₜ > 0
  • It is distorted toward the “overbought” direction relative to the theoretical value.
  • In the Triad EURUSD / GBPUSD / EURGBP,
    the distortion is toward Euro buying / Pound selling.This is the image.
• When Gapₜ < 0
  • It is distorted toward the “oversold” direction relative to the theoretical value.
  • For the same Triad,
    the distortion is toward Euro selling / Pound buying.This is the interpretation.

Which direction it leans and how strongly is indicated by the sign and magnitude of Gap.

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5. The problem with the raw差分 (raw difference)

However, comparing Parity Gap in its raw magnitude leads to issues.

• For a highly volatile Triad like gold (XAU),
  the raw Gap numbers tend to be large.
• Conversely, for a calm pair in a Triad like EURGBP,
  even small numbers may be “abnormal.”

Thus, simply looking at Gap size alone cannot determine which Triad is truly abnormal.

This is whereZ-scorecomes into play.

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6. Why use Z-score? — Is the distortion truly abnormal?

Z-score is, in short, a measure of“how many times the current distortion deviates from the historical standard deviation.”.

Conceptually the steps are as follows:

Step 1: Measure the past Gap’s “average” and “volatility”

• For a given Triad, collect Gapₜ over a period (t=1,2,3,…) and
  • compute the average μ
  .

Step 2: See how far the current Gap deviates from the mean

• Let current Gap be Gap_now,

Z = (Gap_now − μ) ÷ σ

• Z ≒ 0 → “roughly average, distortion is normal”
• Z ≒ +2 to +3 → “significantly overbought compared to past statistics”
• Z ≒ −2 to −3 → “significantly oversold”

Thus,Z-score standardizes the quirks of each Triad.

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7. A common yardstick for Z-scores

Once you convert to Z-scores,

• For gold
• For EURGBP

“Z = ±2” means the same meaning.

• Around −2.0: quite oversold
• Around +2.0: quite overbought
• Around 0: normal operation

With thiscommon yardstickyou can objectively judge whether a distortion is truly abnormal.

8. Distortion Line — turning distortion Z-scores into a single line

In tools that systematize TriParity analysis (FX Distortion Catcher, etc.), this Z-score is drawn on the chart as aDistortion Line.

• X-axis: Time (bars)
• Y-axis: Z-score (magnitude and direction of distortion)

• When it spikes upward (positive) →“overbought / overextension upward”
• When it spikes downward (negative) →“oversold / overextension downward”
• When it returns toward the zero line →“distortion is being resolved (reversion)”

Thus the flow “distortion → reversion” is visible in a single line. This is what makes Distortion Line fundamentally different from single-pair overextension indicators like Bollinger Bands or RSI, which are “one-pair complete” signals.

9. Where is the entry zone from? The importance of timing

Z-score quantification brings you closer to trade rules.

Rule 1: When |Z| exceeds a threshold, consider it an overextended zone

• Example: |Z| ≥ 2.0 first becomes a potential entry candidate.

Rule 2: Enter when Z begins to head back toward zero (the regression starts)

• Example: after +2.0, it moves back to +1.5 → +1.0, consider entering.

This“overextension zone” × “start of regression”is the so-called“The Tasty Zone”.

Timing is crucial. The goal is to catch the moment when Z has stretched to its limit and begins moving toward zero.Don’t rush in just before the peak; objectivize the moment with the Z line using a “Wait… now” feel.The exact Z threshold (1.5, 2.0, 2.5, etc.) can be tuned depending on the Triad and the time frame. Validate with statistical dashboards and balance win rate and profit factor to tune.

10. Where to exit? The idea of Z Exit

In distortion trading, entry is not the only important thing.

• When distortion resolves (Z ≒ 0), the edge largely disappears.
• If you hold the position greedily, you risk being caught in new distortions in the opposite direction.

Therefore, an implementation of TriParity uses

• A point where Z returns near zeroto
• Label it as “Z Exit” and treat it as a single exit candidate

.

• Entry: when Z crosses a threshold (e.g., ±2.0) and begins regression
• Exit candidate: when Z returns near zero (or within a defined zone)
• If it does not revert, use a backup: SL (stop loss) or Timeout (time limit)

The idea is to handle both the beginning of distortion and its dissolution within the Z-score framework— this is the concept of Z Exit.

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11. Summary — From words to numbers

Finally, here is a quick recap of the flow this time.

1. TriParity
   • Define the three-currency “true alignment” by a relationship equation.
2. Gap (Parity Gap)
   • The deviation from that relationship equals the distortion of the triangular relationship itself.
3. Z-Score
   • How far that distortion deviates from past standard deviation.
4. Distortion Line
   • Visualize the Z-score trend as a single line.
5. Trade
   • Use Z Entry / Z Exit to target only the “overextension → regression” interval.

In other words,
the process of turning a vague sense of “high (or low)” into a numerical basis like “Z-score 2.3”—
this was the theme of this article.

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12. Next time — to the Leading Leg

Next time, on top of this “Z and Distortion Line,” we will add

• Which pair contributes most to the distortion?
• Who is really pushing the market?

this will be the“Leading Leg (Driver Leg)”concept.
Even within the same Triad, which pair to build for the most coherent risk-taking—let’s see the clues concretely.

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