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010_pip_value_calculation

Pip Value Calculation: Currency Mathematics

Pip Value Calculation: Currency Mathematics

I. Introduction

Understanding pip value is fundamental to forex trading. A pip (percentage in point) represents the smallest standard price movement, and its monetary value varies based on position size, currency pair, and account currency.

II. Basic Definitions

Definition 2.1 (Pip)

For most currency pairs: 1 pip=0.00011 \text{ pip} = 0.0001

For JPY pairs: 1 pip=0.011 \text{ pip} = 0.01

Definition 2.2 (Pipette/Point)

A pipette is 1/10 of a pip: 1 pipette=0.00001 (or 0.001 for JPY)1 \text{ pipette} = 0.00001 \text{ (or 0.001 for JPY)}

Definition 2.3 (Lot Sizes)

| Lot Type | Units | Symbol | |----------|-------|--------| | Standard | 100,000 | 1.0 | | Mini | 10,000 | 0.1 | | Micro | 1,000 | 0.01 | | Nano | 100 | 0.001 |

III. Pip Value Formulas

Case 1: Account Currency = Quote Currency

PipValue=OnePip×LotSize1PipValue = \frac{OnePip \times LotSize}{1}

Example (EUR/USD, USD account): PipValue=0.0001×100,000=$10 per standard lotPipValue = 0.0001 \times 100,000 = \$10 \text{ per standard lot}

Case 2: Account Currency = Base Currency

PipValue=OnePip×LotSizeExchangeRatePipValue = \frac{OnePip \times LotSize}{ExchangeRate}

Example (USD/CHF @ 0.9200, USD account): PipValue=0.0001×100,0000.9200=$10.87PipValue = \frac{0.0001 \times 100,000}{0.9200} = \$10.87

Case 3: Account Currency ≠ Base or Quote

PipValue=OnePip×LotSizeQuoteCurrency/AccountCurrencyRatePipValue = \frac{OnePip \times LotSize}{QuoteCurrency/AccountCurrency Rate}

IV. General Formula

Theorem 4.1 (Universal Pip Value Formula)

PipValueAccountCurrency=OnePip×LotSize×AccountCurrency/QuoteCurrencyRate1PipValue_{AccountCurrency} = \frac{OnePip \times LotSize \times AccountCurrency/QuoteCurrency Rate}{1}

If Quote = Account Currency, the rate = 1.

Example 4.1 (GBP/JPY, EUR account)

  • Position: 1 mini lot (10,000 units)
  • GBP/JPY = 165.00
  • EUR/JPY = 157.00

PipValue=0.01×10,000157.00=€0.637 per pipPipValue = \frac{0.01 \times 10,000}{157.00} = €0.637 \text{ per pip}

V. Quick Reference Tables

5.1 Standard Pip Values (USD Account, 1 Standard Lot)

| Pair | Pip Value | |------|-----------| | EUR/USD | 10.00∣∣GBP/USD∣10.00 | | GBP/USD | 10.00 | | USD/JPY | ~9.09(at110.00)∣∣USD/CHF∣ 9.09 (at 110.00) | | USD/CHF | ~10.87 (at 0.92) | | AUD/USD | $10.00 |

5.2 Fractional Lot Conversion

PipValuefractional=PipValuestandard×LotFractionPipValue_{fractional} = PipValue_{standard} \times LotFraction

VI. Position Size from Pip Value

Theorem 6.1 (Position Size Formula)

LotSize=RiskAmountStopLossPips×PipValueperStandardLotLotSize = \frac{RiskAmount}{StopLossPips \times PipValue_{perStandardLot}}

Example 6.1

  • Account: $10,000
  • Risk: 2% = $200
  • Stop Loss: 40 pips
  • Pip Value: $10 (EUR/USD)

LotSize=20040×10=0.5 standard lotsLotSize = \frac{200}{40 \times 10} = 0.5 \text{ standard lots}

VII. Profit/Loss Calculation

Theorem 7.1 (P/L Formula)

P/L=PipsGained×PipValue×LotSizeinlotsP/L = Pips Gained \times PipValue \times LotSize_{in lots}

Example 7.1

  • Trade: Buy 0.3 lots EUR/USD
  • Entry: 1.1000, Exit: 1.1075
  • Pips: 75
  • Pip Value: $10 per standard lot

P/L=75×10×0.3=$225P/L = 75 \times 10 \times 0.3 = \$225

VIII. Currency Conversion Effects

8.1 Floating Pip Value

For cross pairs, pip value changes as exchange rates fluctuate: dPipValuedRate≠0\frac{dPipValue}{dRate} \neq 0

8.2 Hedge Consideration

When pip value currency differs from account currency, P/L is also affected by that exchange rate movement.

IX. Exercises

Exercise 1: Calculate pip value for 0.5 lots USD/CAD at 1.2500 (USD account).

Exercise 2: What position size gives exactly $5 per pip on GBP/USD?

Exercise 3: Calculate P/L for selling 2 mini lots EUR/GBP from 0.8650 to 0.8590 (GBP account).

Exercise 4: Derive the breakeven rate movement to cover a 2 pip spread on 1 lot EUR/USD.

X. References

  • Forex Academy. Currency Value Calculations
  • BIS (2019). Triennial Central Bank Survey
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