# Margin and Profit/Loss Calculations

### **1. Opening Margin**

The **opening margin** consists of two components:

* **Initial Margin**
* **Opening Loss**

Including the **opening loss** (if any) at the time of order placement helps **prevent immediate liquidation** due to unfavorable price movement at the time of opening.

#### **1.1 Initial Margin**

$$
\text{Initial Margin} = \frac{\text{Notional Value}}{\text{Leverage}}
$$

For USDT-margined contracts:

$$
\text{Notional Value} = \text{Order Price} \times \text{Quantity} \times \text{Contract Size}
$$

#### **1.2 Opening Loss**

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

Where:

* **Order Direction** = `1` for Long, `-1` for Short

#### **Example**

* **Contract**: BTC/USDT
* **Order Price**: 60,000 USDT
* **Mark Price**: 55,000 USDT
* **Order Quantity**: 10,000 contracts
* **Contract Size**: 0.0001 BTC
* **Leverage**: 10×

$$
\text{Initial Margin} = \frac{60,000 \times 10,000 \times 0.0001}{10} = 6,000\ \text{USDT}
$$

$$
\text{Opening Loss} = 10,000 \times 0.0001 \times 5,000 = 5,000\ \text{USDT}
$$

$$
\text{Opening Margin} = 6,000 + 5,000 = 11,000\ \text{USDT}
$$

### **2. Average Opening Price**

When a trader opens **multiple positions**, the system recalculates the **average opening price** using a **weighted average**:

$$
\text{Average Opening Price} = \frac{\sum (\text{Contract Quantity} \times \text{Price})}{\sum \text{Contract Quantity}}
$$

#### **Example**

* Position 1: 0.5 BTC at 5,000 USDT
* Position 2: 0.3 BTC at 6,000 USDT

$$
\text{Total Value} = (0.5 \times 5,000) + (0.3 \times 6,000) = 2,500 + 1,800 = 4,300
$$

$$
\text{Total Quantity} = 0.5 + 0.3 = 0.8\ \text{BTC}
$$

$$
\text{Average Opening Price} = \frac{4,300}{0.8} = 5,375\ \text{USDT}
$$

### **3. Profit and Loss Calculation**

The **unrealized profit and loss (PnL)** is shown in real time and calculated differently for **long** and **short** positions.

#### **For Long Positions**

$$
\text{PnL} = \text{Quantity} \times (\text{Mark Price} - \text{Average Opening Price})
$$

**Example:**

* Quantity: 0.2 BTC
* Opening Price: 7,000
* Mark Price: 7,500

$$
\text{PnL} = 0.2 \times (7,500 - 7,000) = 100\ \text{USDT}
$$

#### **For Short Positions**

$$
\text{PnL} = \text{Quantity} \times (\text{Average Opening Price} - \text{Mark Price})
$$

**Example:**

* Quantity: 0.4 BTC
* Opening Price: 6,000
* Mark Price: 5,000

$$
\text{PnL} = 0.4 \times (6,000 - 5,000) = 400\ \text{USDT}
$$