Interpreting PnL Formulas Across Asset Units and Multipliers
Summary
The document compares a price-difference PnL calculation with an inverse-price formula, then explains that PnL depends on the units used to express the position and cash flows. Its example calculates a Bitcoin trade’s gain in dollars from the price change and quantity, and describes converting that gain into Bitcoin terms. The multiplier is presented as a conversion between units or currency buckets rather than as leverage.
The explanation is a brief conceptual answer, not a full treatment of contract specifications. It does not resolve every product convention: inverse contracts, contract multipliers, quote currency, and settlement rules can differ by instrument. Traders should identify the contract’s payoff definition and reporting currency before applying a formula; the simple quantity-times-price-change expression is not universal without those assumptions.
Key ideas
- PnL expressed in the quote currency can be calculated from the price change times quantity when the instrument is linear.
- The same economic result can be reported in another currency or asset unit through an appropriate conversion.
- A multiplier generally reflects contract sizing or unit conversion and should not automatically be interpreted as leverage.
- Inverse-price formulas apply to particular payoff or denomination conventions rather than to every asset class.
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Full text
# realized/unrealized PnL with multiplier # realized/unrealized PnL with multiplier Look at this trade: ``` Sequence Side Quantity @ Price 1. Buy 1000 @ 1000 2. Sell 1000 @ 1250 ``` The calculation of the realized PnL: version 1: ``` realizedPnL = (1000-1250)*1000 = 25000$ ``` But looking at other PnL-formulas, for example: - https://www.bitmex.com/app/pnlGuide - https://support.bitforex.com/hc/en-us/articles/360029616532-How-to-calculate-the-unrealized-and-realized-profits-and-loss-PNL- they use: version 2: ``` realizedPnL = (1/1000-1/1250)*1000 = 0,2$ ``` by the formula: ``` Realized PNL = quantity * multiplier * (1 / Entry Price - 1 / Exit Price) ``` or I do not understand the "1/x"-part and the "multiplier"-part: - When and why should I take version 2 instead of version 1? - Which version is correct? - Has the "1/x" something to do with leverage? Or has the "multiplier" something to do with leverage? For example, if I trade Forex or CFD with a "leverage=1", then "contract multiplier=1". Or do I mix something up? ## Answer by nimo23 (score 1) https://quant.stackexchange.com/a/53519 There is no need to use the following confusing formula: ``` PNL = quantity * multiplier * (1 / Entry Price - 1 / Exit Price) ``` For all asset classes the following formula is sufficient: ``` PNL = quantity * (ExitPrice - EntryPrice) ``` The "multiplier" is only used when converting from one bucket (e.g. currency) to another. Looking at the following example: ``` Sequence Side Quantity @ Price in $ 1. Buy 1 BTC @ 10000 2. Sell 1 BTC @ 11000 ``` We have ``` PnL = (11000-10000)*1 = +1000$ (profit) ``` in percentage: ``` PnL = (11000/10000) = +0,1% (profit) ``` If I want to express the PnL in BTC instead of $, then I can do the following: ``` PnL = 1/1+0,1 = +0,909BTC ``` The "`1/x`" is fixed and independent of any multiplier. 1 represents 100%. That`s all.
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