Monte Carlo Risk Simulation — Modeling Portfolio Outcomes

Monte Carlo simulations let you model 100,000+ potential future paths of your portfolio, quantifying risk metrics like Value at Risk (VaR) and expected shortfall. Instead of assuming a single outcome, you see the distribution of possibilities.

Example: Run 100k simulations of your trading strategy. You'll see: 68% of outcomes profit $10-$50, 25% lose $10-$30, 5% lose $50-$200, and 2% profit $100+. Now you understand your risk profile.

Basic Geometric Brownian Motion (GBM)

Model future prices as random walks with drift and volatility:

Python — Monte Carlo price paths
import numpy as np
def simulate_price_paths(S0, mu, sigma, T, dt, n_sims=10000):
# S0: current price, mu: drift, sigma: volatility
# T: time horizon (days), dt: time step, n_sims: simulations
steps = int(T / dt)
paths = np.zeros((n_sims, steps))
paths[:, 0] = S0
for i in range(1, steps):
# dS = mu*S*dt + sigma*S*sqrt(dt)*Z
Z = np.random.normal(0, 1, n_sims)
dS = mu * paths[:, i-1] * dt + sigma * paths[:, i-1] * np.sqrt(dt) * Z
paths[:, i] = paths[:, i-1] + dS
return paths

Portfolio Risk Metrics

Value at Risk (VaR)

The loss you'd exceed in only 5% of scenarios (95% confidence):

Python — Calculate VaR
def calculate_var(simulations, confidence=0.95):
pnl = simulations[:, -1] - simulations[:, 0]
var = np.percentile(pnl, (1 - confidence) * 100)
return var # e.g., -$2,340

Expected Shortfall (CVaR)

Average loss in the worst 5% of cases:

Python — Calculate CVaR
def calculate_cvar(simulations, confidence=0.95):
pnl = simulations[:, -1] - simulations[:, 0]
var_threshold = np.percentile(pnl, (1 - confidence) * 100)
worst_5_pct = pnl[pnl <= var_threshold]
cvar = np.mean(worst_5_pct)
return cvar # e.g., -$3,800 (worse than VaR)

Strategy-Specific Simulation

Simulate your actual trading rules, not just price paths:

Python — Strategy Monte Carlo
def simulate_strategy(capital, win_rate, avg_win, avg_loss, trades_per_day=10, days=30, n_sims=10000):
results = np.zeros(n_sims)
for sim in range(n_sims):
equity = capital
n_trades = trades_per_day * days
for _ in range(n_trades):
if np.random.rand() < win_rate:
pnl = np.random.normal(avg_win, avg_win * 0.2)
else:
pnl = -np.random.normal(avg_loss, avg_loss * 0.2)
equity += pnl
if equity < capital * 0.5:
break # Stop-out at 50% loss
results[sim] = equity
return results

Stress Testing with Smart Money Signals

Model worst-case scenarios when Smart Money confidence drops:

Python — Stress test scenarios
def stress_test_scenarios(base_win_rate):
# Scenario 1: Normal conditions (HIGH confidence)
scenario_normal = simulate_strategy(10000, win_rate=base_win_rate)
# Scenario 2: Deteriorating signals (MEDIUM confidence)
scenario_medium = simulate_strategy(10000, win_rate=base_win_rate * 0.95)
# Scenario 3: Breakdown (VETO condition)
scenario_veto = simulate_strategy(10000, win_rate=0.45) # negative edge
return {
'normal': {'var': np.percentile(scenario_normal, 5), 'mean': np.mean(scenario_normal)},
'medium': {'var': np.percentile(scenario_medium, 5), 'mean': np.mean(scenario_medium)},
'veto': {'var': np.percentile(scenario_veto, 5), 'mean': np.mean(scenario_veto)}
}

Interpretation

From 10k simulations, you learn:

Stress-test strategies with Smart Money signals

Understand portfolio risk under normal, deteriorating, and VETO Smart Money conditions. Our API gives you the signals; Monte Carlo models the outcomes.

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