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Profit & Loss Calculations

PnL Impact on Margin

Realized PnL

The margin system incorporates realized PnL when calculating margin requirements for position-closing orders. This affects both resting orders and position reversals.

Example - Position Close and then Rest

Given:

  • Current Position: Long 2 BTC at $48,000 entry
  • Current Mark Price: $50,000
  • Sell Order: 3 BTC at $50,000
  • Initial Margin Rate: 1%
Realized PnL from Close = 2 × ($50,000 - $48,000) = +$4,000
Margin Required for New Position = 1 × $50,000 × 0.01 = $500

Available Margin After Close = Initial Margin + Realized PnL

If the initial available margin was $300, the order would still be accepted because the realized PnL covers the initial margin on the resting order.

Position Reversal Scenarios

Orders that reverse positions are evaluated including the PnL from closing the existing position.

Example - Position Reversal

Given:

  • Current Position: Long 2 BTC at $45,000 entry
  • Current Mark Price: $50,000
  • Sell Order: 4 BTC at $50,000 (reverses to short 2 BTC)
  • Initial Margin Rate: 1%
  • Available Margin: $500
Step 1: Calculate Realized PnL
Realized PnL = 2 × ($50,000 - $45,000) = +$10,000

Step 2: Calculate New Position Margin
Short Position Margin = 2 × $50,000 × 0.01 = $1,000

Step 3: Evaluate Margin Requirement
New Available Margin = $500 + $10,000 = $10,500
Required Margin = $1,000

Result: Order Accepted (Available Margin > Required Margin)

Unrealized PnL Treatment

Unrealized Losses

Unrealized losses directly affect available margin by reducing the amount of balance available for margin.

Example - Unrealized Loss Impact

Given:

  • Position: Long 2 BTC at $50,000 entry
  • Current Mark Price: $48,000
  • Initial Margin Rate: 1%
  • Account Balance: $2,000
Unrealized Loss = 2 × ($48,000 - $50,000) = -$4,000
Position Margin = 2 × $48,000 × 0.01 = $960
Effective Available Margin = $2,000 - $4,000 = -$2,000

Result: Cannot place the position-opening order until more collateral is deposited or the price recovers

Unrealized Gains

Unrealized gains are excluded from margin calculations to prevent a cascade of increased leverage that could create systemic risk.

Detailed Example Scenario

Let's follow a sequence of trades to understand why this is critical:

Initial Position

Account Balance: $10,000 USD
Initial Margin Rate: 1%
Maximum Position (initially): $10,000 / 0.01 = $1,000,000 notional
Initial Position: Long 20 BTC at $50,000 ($1,000,000 notional)
Initial Margin Used: $10,000

Price Movement

Price moves from $50,000 to $60,000

Current Position Value: 20 BTC × $60,000 = $1,200,000
Unrealized Gain: $200,000

If Unrealized Gains Were Included

If the system counted unrealized gains as available margin:

New "Available" Margin: $10,000 + $200,000 = $210,000
New Maximum Position: $210,000 / 0.01 = $21,000,000 notional
Additional Position Possible: ~350 BTC at $60,000

This would create several problems:

  1. The account could open a position 17.5× larger than originally allowed by their actual collateral
  2. A price reversion to $50,000 would create a loss of: 
    Loss on Original Position: $0 (back to entry)
Loss on Additional Position: 350 × ($50,000 - $60,000) = -$3,500,000
  3. This loss far exceeds the actual account balance and unrealized gains

With Unrealized Gains Excluded

Under the actual system:

Available Margin: $10,000 (original balance only)
Maximum Position: Remains at $1,000,000 notional
Additional Position Possible: $0 (fully utilized)

Benefits of this approach:

  1. Position size remains proportional to actual deposited collateral
  2. Market reversals can only affect profits, not create system-wide losses
  3. Prevents leverage from scaling exponentially with market movements

Closing and Opening New Positions

If the trader wants to utilize their gains, they must first realize them:

1. Close 5 BTC position at $60,000
   Realized Gain: 5 × ($60,000 - $50,000) = $50,000
   New Account Balance: $60,000

2. Now can open new positions based on actual balance:
   New Maximum Position: $60,000 / 0.01 = $6,000,000 notional

Implications for Exchange Risk Management

This conservative approach provides several systemic benefits:

  1. Predictable Leverage

    • System-wide leverage remains tied to actual deposited collateral
    • Prevents exponential growth of positions during market rallies

  2. Controlled Risk

    • Losses remain proportional to actual deposits
    • Prevents cascade of forced liquidations during market reversals

  3. Market Stability

    • Reduces pro-cyclical leverage in rising markets
    • Minimizes systemic impact of price reversals

  4. Clear Capital Requirements

    • Traders must realize gains to increase position sizes
    • Creates natural circuit breaker in market dynamics

Combined Scenarios

Complex Position Management

When managing positions with both realized and unrealized PnL, the Nekuti Matching Engine:

  1. Calculates unrealized losses on remaining positions and subtracts them from available margin
  2. Calculates realized PnL from position-closing portions
  3. Calculates new position margin requirements

Example - Complex Position Management

Given:

  • Current Position: Long 3 BTC (2 BTC at $45,000, 1 BTC at $48,000)
  • Current Mark Price: $50,000
  • New Order: Sell 5 BTC at $50,000
  • Initial Margin Rate: 1%
  • Account Balance: $2,000
Step 1: Calculate Realized PnL from Position Close
PnL from 2 BTC = 2 × ($50,000 - $45,000) = +$10,000
PnL from 1 BTC = 1 × ($50,000 - $48,000) = +$2,000
Total Realized PnL = $12,000

Step 2: Calculate New Short Position Margin
New Position Size = 2 BTC
Required Margin = 2 × $50,000 × 0.01 = $1,000

Step 3: Evaluate Final Margin
Available Margin = $2,000 + $12,000 = $14,000
Required Margin = $1,000

Result: Order Accepted

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