Margin Account Engine Verification

Financial ServicesFormal VerificationRisk ManagementRegulatory Compliance

Overview

This case study demonstrates how CodeLogician ensures mathematical correctness in institutional trading risk management systems. We formally verify a margin account state machine that enforces regulatory requirements to prevent catastrophic losses in leveraged trading accounts.

What's at Stake

A bug in margin enforcement logic could bankrupt a broker-dealer.

The 2021 Archegos Capital collapse caused $10+ billion in losses across Credit Suisse, Nomura, and other prime brokers due to inadequate margin enforcement. This is not theoretical—it's existential risk for financial institutions.

The Business Problem

What is Margin Trading?

When clients borrow money to buy securities (margin trading), the broker must continuously monitor their equity position. If the market moves against the client and their equity falls below regulatory thresholds, the broker must force liquidation of assets.

Failure to do so exposes the broker to unlimited losses if the client becomes insolvent.

Regulatory Requirements

Regulation T (Federal Reserve)

  • Initial Margin: 50%
  • Required equity when opening positions
  • Ensures clients have "skin in the game"
  • Applies to all margin accounts

FINRA Rule 4210

  • Maintenance Margin: 25%
  • Minimum equity to avoid liquidation
  • Breach triggers margin call
  • Failure to meet = forced liquidation

The State Machine

The margin account operates as a finite state machine with three states representing account health:

Account Health States

graph LR H["HEALTHY<br/>Equity ≥ 50%"] R["RESTRICTED<br/>25% - 50%"] L["LIQUIDATION_CALL<br/>Equity < 25%"] H -->|Market Decline| R R -->|Deposit/Rise| H R -->|Market Decline| L L -->|Deposit/Rise| R L -->|Deposit/Rise| H style H fill:#059669,stroke:#047857,color:#fff style R fill:#d97706,stroke:#b45309,color:#fff style L fill:#dc2626,stroke:#b91c1c,color:#fff
StateConditionAllowed Actions

HEALTHY

Equity Ratio ≥ Initial Margin (50%)Open positions, Withdraw funds

RESTRICTED

Maintenance ≤ Equity Ratio < InitialHold positions only

LIQUIDATION_CALL

Equity Ratio < Maintenance (25%)Must liquidate assets

The Verification

Core Status Check Logic

def check_status(self) -> AccountStatus:
    """
    Determine current margin account status based on equity ratio.
 
    State Logic:
    - No position: HEALTHY (cash-only account)
    - Equity ratio >= initial_margin: HEALTHY
    - maintenance_margin <= Equity ratio < initial_margin: RESTRICTED
    - Equity ratio < maintenance_margin: LIQUIDATION_CALL
    """
    equity_ratio = self.calculate_equity_ratio()
 
    # No position means pure cash account (always healthy)
    if equity_ratio is None:
        return AccountStatus.HEALTHY
 
    # Check maintenance margin threshold (most critical)
    if equity_ratio < self.margin_requirements.maintenance_margin_pct / Decimal("100"):
        return AccountStatus.LIQUIDATION_CALL
 
    # Check initial margin threshold
    if equity_ratio < self.margin_requirements.initial_margin_pct / Decimal("100"):
        return AccountStatus.RESTRICTED
 
    return AccountStatus.HEALTHY

Equity Calculation

Equity = Cash + MarketValue - Loan
Net account value available to the client after accounting for borrowed funds.

Equity Ratio

EquityRatio = Equity / MarketValue
Percentage of position value owned outright (not borrowed). Key metric for margin compliance.

Real-World Example

Scenario: Market Decline

Initial Position

Cash Balance:
$10,000
Shares:
100 @ $400
Market Value:
$40,000
Loan Value:
$30,000
Equity:
$20,000
Equity Ratio:
50%
Status:
HEALTHY ✅

After 40% Market Decline

Cash Balance:
$10,000
Shares:
100 @ $240
Market Value:
$24,000 ↓
Loan Value:
$30,000
Equity:
$4,000 ↓
Equity Ratio:
16.7% ↓
Status:
LIQUIDATION_CALL ❌

Automatic Protection Triggered

When equity ratio drops below 25%, the system automatically enters LIQUIDATION_CALL state. This is mathematically guaranteed by formal verification—no code path can bypass this protection.

Edge Cases Handled

Division by Zero

When market value = 0 (no position), calculate_equity_ratio() returns None.Pure cash accounts are always HEALTHY.

Decimal Precision

Uses Python's Decimal type instead of float.

Prevents rounding errors that could cause margin violations to go undetected.

Boundary Conditions

Verified exact boundary behavior:
  • Equity = maintenance → RESTRICTED
  • Equity = initial → HEALTHY

Key Results

Verification Summary

Property

What We Proved

StatusImpact
Solvency SafetyLow equity MUST trigger liquidation

✅ PROVED

Broker protected from client insolvency
No Gap Risk

No withdrawal can immediately cause margin call

✅ PROVED

No "flash crash" from normal operations
Withdrawal ProtectionWithdrawals maintain initial margin

✅ PROVED

Clients can't drain equity below safety
Complete CoverageAll 4 behavioral regions identified

✅ COMPLETE

100% path coverage for testing

Business Value

Mathematical Certainty

Not "tested with 10,000 scenarios" but proven correct for ALL possible inputs. This is the difference between statistical confidence and mathematical certainty.

Regulatory Compliance

Formal proofs provide auditable evidence for Regulation T and FINRA 4210 compliance. Regulators can review the mathematical guarantees.

Risk Elimination

The Archegos-style scenario—where margin enforcement fails—is provably impossible with this verified implementation.

Production Ready

Uses Decimal arithmetic and comprehensive validation. Suitable for production deployment in institutional trading systems.

Download the Code

Python ImplementationIML Formal Model

Broader Applications

This verification approach applies to any risk management system with:

✅ Threshold-Based Rules

Margin requirements, position limits, risk scores, capital adequacy

✅ State Machines

Account status, order lifecycle, trade workflow, approval processes

✅ Financial Calculations

Interest calculations, fee computations, P&L tracking, collateral management

✅ Regulatory Requirements

Compliance rules that must be proven correct for audit

Industry Examples

  • Prime Brokerage: Margin account monitoring, securities lending, client risk management
  • Proprietary Trading: Position limits, risk controls, automated circuit breakers
  • Asset Management: Portfolio compliance, investment policy enforcement
  • Clearing Houses: Member margin requirements, default waterfall logic
  • Retail Brokers: Pattern day trader rules, options approval levels

Key Takeaways

Solvency Protected

Mathematical proof that margin enforcement cannot be bypassed. $10+ billion Archegos-style losses are provably impossible.

Regulatory Confidence

Formal verification provides auditable evidence for Regulation T and FINRA 4210 compliance.

Production Ready

Decimal arithmetic, comprehensive validation, and 4 verified behavioral regions ensure complete coverage.

Verify your risk management systems with mathematical certainty

Use CodeLogician to ensure your margin calculations, position limits, and compliance rules are provably correct.

Try CodeLogician
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