Monte Carlo Simulations¶

Monte Carlo simulations help you understand the range of possible retirement outcomes by running thousands of scenarios with randomized market returns.

How It Works¶

Generate random market returns based on historical distributions
Simulate portfolio growth and withdrawals over time
Track which scenarios succeed (don't run out of money)
Analyze the distribution of outcomes

Running a Basic Simulation¶

from fundedness import run_simulation

results = run_simulation(
    initial_portfolio=1_000_000,
    annual_spending=40_000,
    years=30,
    n_simulations=10_000,
)

print(f"Success Rate: {results.success_rate:.1%}")
print(f"Median Final Value: ${results.median_final_value:,.0f}")
print(f"5th Percentile: ${results.percentile_5:,.0f}")
print(f"95th Percentile: ${results.percentile_95:,.0f}")

Market Assumptions¶

Default assumptions are based on historical data:

Parameter	Default	Description
Mean Return	7%	Expected annual real return
Std Dev	15%	Annual volatility
Inflation	2.5%	Expected inflation rate

Custom Assumptions¶

from fundedness import MarketAssumptions, run_simulation

assumptions = MarketAssumptions(
    mean_return=0.06,  # More conservative
    std_dev=0.18,      # Higher volatility
    inflation=0.03,    # Higher inflation
)

results = run_simulation(
    initial_portfolio=1_000_000,
    annual_spending=40_000,
    years=30,
    assumptions=assumptions,
)

Understanding Results¶

Success Rate¶

The percentage of simulations that didn't run out of money. Common targets:

95%: Very conservative
90%: Conservative
85%: Moderate
80%: Aggressive

Percentiles¶

5th percentile: Poor outcomes (bear markets, bad timing)
50th percentile (median): Typical outcome
95th percentile: Favorable outcomes (bull markets)

Visualizing Results¶

from fundedness.viz import plot_simulation_fan_chart

fig = plot_simulation_fan_chart(results)
fig.show()

The fan chart shows:

Dark band: 25th-75th percentile (likely outcomes)
Light band: 5th-95th percentile (range of outcomes)
Line: Median trajectory

Sensitivity Analysis¶

Test how changes affect your success rate:

from fundedness import compare_scenarios

scenarios = [
    {"spending": 35_000, "label": "Conservative"},
    {"spending": 40_000, "label": "Baseline"},
    {"spending": 45_000, "label": "Aggressive"},
]

comparison = compare_scenarios(
    initial_portfolio=1_000_000,
    years=30,
    scenarios=scenarios,
)

Limitations¶

Monte Carlo simulations have limitations:

Past performance: Historical returns may not predict future results
Model assumptions: Normal distributions may underestimate tail risks
Constant spending: Real spending varies year to year
No behavioral factors: Doesn't account for panic selling

Use simulations as one input to your planning, not the sole decision tool.