What is Monte Carlo simulation?

Why Monte Carlo instead of point-estimate calculations?

A traditional yield calculator gives you a single number: "This strategy returns 12% annualized." Reality is much messier. That 12% is an expected value that ignores everything about variability — some years the strategy returns +30%, others it returns −8%. If the strategy has a 4% probability of losing 50% of your capital, that "12% annualized" hides potentially catastrophic risk.

Monte Carlo simulation replaces the point estimate with a distribution. Instead of one number, you get:

• Median outcome (50th percentile) — the middle-of-pack result
• Bad-case (5th percentile) — 5% of sims do worse than this
• Good-case (95th percentile) — 5% of sims do better
• Max drawdown percentiles — how deep the peak-to-trough loss gets
• Probability of ruin — % of sims ending with catastrophic loss
• Probability of hitting your target — % of sims meeting or exceeding your income goal

This is honest capital-planning math. Point estimates are marketing math.

How the technique works

Step 1: Build a return distribution

You need a probability distribution to sample from. Two common approaches:

OptionIncomeTools uses bootstrap sampling from 500 days of historical daily log returns. This captures the actual distributional properties (fat tails, vol clustering) of the specific ticker being simulated.

Step 2: Simulate one path

For each iteration:

1. Start at current spot price.
2. For each day in the horizon, sample a return from your distribution and multiply.
3. Track cumulative wealth, positions, cycle events (assignments, callaways).
4. At each option cycle boundary, resolve the option based on the path's price at expiration.

The result is one simulated path from today to horizon end, with all strategy mechanics faithfully applied.

Step 3: Repeat 2,000 times

Each iteration uses a different random seed, producing a different price path and hence a different strategy outcome. After 2,000 iterations, you have 2,000 terminal wealth values.

Step 4: Aggregate

Sort the 2,000 outcomes. Compute:

• Percentiles: p5, p25, p50, p75, p95
• Distribution histogram (buckets from min to max)
• Probability metrics: % profitable, % ruined, % assigned
• Sample paths (10-20) for visualization

Worked example: SPY wheel strategy

Consider running a wheel strategy on SPY with these parameters:

• Starting capital: $50,000
• CSP target delta: 0.30
• CC target delta: 0.30
• Cycle DTE: 30 days
• Horizon: 1 year (365 days)
• Simulations: 2,000

Naive yield calculation says

Sounds reasonable. But this ignores assignments, drawdowns, held-shares appreciation, and tail scenarios.

Monte Carlo result (illustrative)

After running 2,000 simulations bootstrapped from SPY's recent 500-day return history:

• Median CAGR: +11.4% (much higher because held shares appreciate too!)
• 5th percentile CAGR: −4.2% (bad case: assigned high, held through drawdown)
• 95th percentile CAGR: +27.8% (good case: never assigned, plus appreciation)
• Max drawdown p95: 18.4% (1-in-20 sims see this or worse)
• Probability profitable: 78% (still 22% chance of ending below starting capital!)
• Probability of ruin (>50% loss): 0.4% (rare but nonzero)
• Probability of at least one assignment: 84% (assignment is not uncommon on 30-delta CSPs)

This is a very different picture than "4-5% annualized." The strategy actually has a solid median return (thanks to appreciation from held shares), but also meaningful tail risk (5% chance of −4% or worse) and 22% chance of ending in the red. The Monte Carlo tells you the truth about the distribution.

Interpreting the results

Percentiles

• Median (p50): the middle outcome. Better summary than mean because tail sims distort mean.
• 5th percentile (p5): bad-case boundary. 5% of sims produce worse outcomes. If p5 CAGR is negative, the strategy is fragile.
• 95th percentile (p95): good-case. Only 5% of sims do better.
• Inter-quartile range (p25 to p75): "typical" outcomes. Wider = more variable strategy.

Risk of ruin

Formally: probability of losing X% or more of starting capital. Standard threshold is 50%. Wheel strategies on liquid tickers with prudent parameters typically show risk of ruin under 3%. High-beta names (MSTR, TSLA) at aggressive deltas (0.40+) can reach 10-15%.

Max drawdown distribution

How deep does peak-to-trough loss get? Even winning simulations have interim drawdowns. p95 drawdown of 25% means 5% of sims experience a 25%+ drawdown at some point — even if they eventually recover.

Common misconceptions

"Monte Carlo tells me what will happen"

No. It tells you the range of what could happen if the future behaves like the historical sample. Real futures often deviate from historical samples — new regimes emerge, correlations shift, macro shocks occur. Monte Carlo is a calibration tool, not a crystal ball.

"More iterations = more accurate"

Up to a point. Standard error of a percentile estimate scales with 1/√N, so 2,000 sims is a good balance of accuracy vs compute time. 10,000 sims produce roughly √5 = 2.2× tighter estimates but 5× slower. For most decisions, 2,000 is sufficient.

"Bootstrap perfectly captures future distributions"

No. Bootstrap samples from a fixed historical window. If regime changes (e.g., inflation regime, war-time regime), bootstrap will underweight the new dynamic. The technique is best for near-term projections in a stable regime.

"Monte Carlo eliminates parameter risk"

It quantifies path risk but not strategy risk. If your parameters (delta target, cycle DTE) are wrong for the ticker, Monte Carlo will faithfully reproduce those bad choices. It's still up to you to pick reasonable parameters.

Related terms and tools

• Live Wheel Monte Carlo Simulator — run the simulation with your parameters.
• Wheel Tracker — log actual trades and compare realized results to simulated distribution.
• Income Goal Planner — capital allocation planner for income targets.
• IV Rank — vol regime metric that affects simulation inputs.
• Beta-weighted delta — portfolio-level directional exposure metric.
• Realistic Wheel Returns article — deeper analysis of typical vs advertised wheel returns.