[Read FX with Three Currencies Parity — Turning Daily "Distortions" into Profit: TriParity Analysis] Episode 4: Turning Distortions into Numbers — Measuring "Overreach" with Parity Gap and Z-score

In this article,Parity GapandZ-Scoreare used to organize the process of turning a vague sense of “too high / too low” into numeric justification like a Z of 2.3.

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1. Moving beyond the feeling of “distorted intuitions”

Many traders have felt the following while looking at charts:

• “This is surely overextended.”
• “This looks like it’s about to rebound.”
• “There’s a peculiar bias here…”

In other words,the distortion as a feelingis subconsciously grasped. However, when trying to formalize entry criteria,

• “How much movement counts as overextension?”

and other points aredifficult to articulate and hard to standardizein reality. Relying on feeling alone does not determine where to enter or exit.

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2. Review of the “original alignment” of the 3-currency parity

First, let us reorganize the “reference line” of TriParity one more time.

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

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

These three pairs should theoretically satisfy the following relationship.

EURUSD ÷ GBPUSD ≒ EURGBP

In other words,define the “original, correct alignment of the three currencies” with a relationship,so that you can measure how much it deviates from it.

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3. What is Parity Gap? ─ The gap between theoretical consistency and reality

Now we get to the main topic.

In TriParity, the next step is to extract the misalignment in the triangle as follows:

1. Take the 3 pairs A/B, B/C, A/C,
2. From “A/B × B/C” computetheoretical A/C,
3. Subtractthe actual A/C rate from it.

This gap between the theoretically correct alignment and the actual rate is what we call
Parity Gap（パリティギャップ）.

If expressed mathematically, it can be written with 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 deviates positively or negatively

In short,Parity Gap is a single number that summarizes the distortion of the entire three-currency triangle.

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4. What do positive and negative Gaps mean?

Parity Gap also has meaning in its sign.

• If Gapₜ > 0
  • It is distorted toward the overbought side relative to the theoretical value.
  • In a Triad of EURUSD / GBPUSD / EURGBP,
    this is biased toward euro buying / pound sellingin image terms.
• If Gapₜ < 0
  • It is distorted toward the oversold side relative to the theoretical value.
  • In the same Triad,
    biased toward euro selling / pound buyingwould be the interpretation.

Which direction it is biased and by how much—the Gap’s sign and magnitude tell you that.

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5. The problem with using raw differences

However, comparing Parity Gap at its raw size can be problematic.

• In highly volatile Triads like gold (XAU),
  the raw Gap values tend to be large naturally.
• Meanwhile in calmer Triads including EURGBP,
  even small numbers may be meaningfully abnormal.

Thus, simply looking at the magnitude of Gap does not allow a fair comparison of which Triad is truly abnormal.

Enter theZ-Score.

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6. Why use the Z-Score? ─ Is that distortion truly “abnormal”?

The Z-Score, in one line, expresses“how many standard deviations the current distortion is away from the past average.”as a metric.

Conceptually, the steps are:

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

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

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

• With Gap_now as the current gap,

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,standardizing the quirks of each Triadis the purpose of the Z-Score.

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7. A common yardstick for Z-Score

Once you convert to Z-scores,

• Gold
• EURGBP (Euro-Pound)

“Z = ±2” shows the same meaning.

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

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

8. Distortion Line ─ Turning “distortion Z-score” 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.

• XAxis: Time (bars)
• YAxis: Z-score (magnitude and direction of distortion)

• If it swings strongly on the upside (+) →“overbought / extended upward”
• If it swings strongly on the downside (−) →“oversold / extended downward”
• If it returns toward the middle 0 line →“the distortion is resolving (reversion)”

Thus, the flow of “distortion → reversion” is visible in a single line. This is a key difference from typical single-pair overbought indicators like Bollinger Bands or RSI, which are limited to one pair. The Distortion Line is derived from the three-currency triangle.

9. Where is the entry zone and why timing matters

With the Z-Score, we are closer to trading rules than ever.

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

• Example: |Z| ≥ 2.0 to first consider entry candidate.

Rule 2: Consider the moment Z moves toward zero as the start of reversion

• Example: after +2.0, it retreats to +1.5 → +1.0; evaluate entering then.

This“overextended zone” × “start of reversion”is the so-called“Tasty Zone”.

Timing is crucial; the goal is to catch the moment when the Z-line stops extending and begins moving toward zero.Rather than rushing in just before the peak, objectively measure the timing with the Z line and think, “Wait… now.”

The specific Z thresholds (whether 1.5, 2.0, or 2.5) can be adjusted depending on the Triad and the time frame. We validate and tune these using statistical dashboards to balance win rate and profitability (PF).

10. Where to end? The concept of Z Exit

In distortion trading, not only the entry matters.

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

So, in a TriParity implementation, the idea is to

• Mark the point where Z returns near zeroas
• Label it as a Z Exit, making it one exit candidate

Entry: when Z exceeds a threshold (e.g., ±2.0) and starts to revert

• Exit candidate: when Z returns near zero (or within a defined zone)
• If it still does not revert, use protections: SL (stop loss) or timeout

The concept of “the start of distortion” and “the resolution of distortion” handled within the Z-score framework— this is the essence of Z Exit.

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11. Summary ─ From words to numbers

Finally, a concise wrap-up of this flow.

1. TriParity
   • Define the three-currency “original alignment” with a relationship formula.
2. Gap (Parity Gap)
   • The amount of deviation from that relationship—the distortion of the triangle itself.
3. Z-Score
   • How many standard deviations the distortion is away from past averages.
4. Distortion Line
   • Visualize the Z-Score progression as a single line.
5. Trade
   • Use Z Entry / Z Exit to target only the overextension→reversion segment.

In other words,
the process of turning the vague feeling of “high (or low)” into numeric justification like a Z-Score of 2.3—
That was the theme this time.

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12. Coming next ─ Toward the Leading Leg

Next time, on top of this Z and the Distortion Line, we will layer

• Which pair contributes most to the distortion?
• Who is truly driving the market?

the concept of“Leading Leg (Driver Leg)”.
Even within the same Triad, which pair offers the most coherent risk-taking—
we will look at concrete hints.

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