Margin and Profit/Loss Calculations

1. Open Position Margin

The opening margin consists of:

• Initial Margin

• Opening Loss

Including opening loss in the margin calculation helps prevent immediate liquidation due to unfavorable price movements upon order placement.

1.1 Initial Margin

$$\text{Initial Margin} = \frac{\text{Quantity} \times \text{Contract Size}}{\text{Order Price} \times \text{Leverage}}$$

1.2 Opening Loss

$$\text{Opening Loss} = \text{Quantity} \times \text{Contract Size} \times \left| \min\left(0,\ \text{Order Direction} \times \left( \frac{1}{\text{Order Price}} - \frac{1}{\text{Mark Price}} \right) \right) \right|$$

Where:

• Order Direction = 1 for long, -1 for short

Example

• Contract Type: Coin-margined (e.g., BTC/USD)

• Order Price: 60,000 USD

• Mark Price: 55,000 USD

• Quantity: 12,000 contracts

• Contract Size: 10 USD

• Leverage: 10×

Calculation:

Initial Margin:

$$\frac{12,000 \times 10}{60,000 \times 10} = 0.2\ \text{BTC}$$

Opening Loss:

$$12,000 \times 10 \times \left| \min\left(0, 1 \times \left( \frac{1}{60,000} - \frac{1}{55,000} \right) \right) \right| = 0.181819\ \text{BTC}$$

Opening Margin:

$$0.2 + 0.181819 = 0.381819\ \text{BTC}$$

2. Average Opening Price

When multiple entries are made into the same position, the average opening price is recalculated using a BTC-denominated formula:

$$\text{Average Opening Price} = \frac{\text{Total Contracts}}{\text{Total BTC Value}}$$

Example

• Position 1: 1,000 contracts @ 5,000 USD

• Position 2: 2,000 contracts @ 6,000 USD

$$\text{Total Contracts} = 1,000 + 2,000 = 3,000$$

$$\text{Total BTC Value} = \left( \frac{1,000}{5,000} \right) + \left( \frac{2,000}{6,000} \right) = 0.2 + 0.333333 = 0.533333\ \text{BTC}$$

$$\text{Average Opening Price} = \frac{3,000}{0.533333} = 5,625.00\ \text{USD}$$

3. Profit and Loss Calculation

PnL is calculated based on the difference between inverse prices, since these are reverse (coin-margined) contracts. Profits and losses are settled in the base currency (e.g., BTC), not in USD.

3.1 For Long Positions

$$\text{Unrealized PnL} = \text{Quantity} \times \left( \frac{1}{\text{Average Open Price}} - \frac{1}{\text{Mark Price}} \right)$$

Example:

• 1,000 contracts long

• Average Price: 5,000

• Mark Price: 5,500

$$= 1,000 \times \left( \frac{1}{5,000} - \frac{1}{5,500} \right) = 0.01819\ \text{BTC}$$

3.2 For Short Positions

$$\text{Unrealized PnL} = \text{Quantity} \times \left( \frac{1}{\text{Mark Price}} - \frac{1}{\text{Average Open Price}} \right)$$

Example:

• 1,000 contracts short

• Average Price: 5,000

• Mark Price: 4,500

$$= 1,000 \times \left( \frac{1}{4,500} - \frac{1}{5,000} \right) = 0.02223\ \text{BTC}$$

Important Notes

• Reverse contracts (coin-margined) are settled in the base currency (e.g., BTC).

• USD values are used only for quotation purposes, not for settlement.

• This structure ensures that traders earn and lose in the underlying asset they’re trading.