Monte Carlo Simulation
A comprehensive guide to understanding how probability modelling helps show a range of financial outcomes and plan for uncertainty.
What is Monte Carlo Simulation?
Monte Carlo simulation is a statistical method that models many possible future scenarios to help you understand the range of potential outcomes for your financial plan. Instead of showing you one predicted result, it shows you the probability of different outcomes occurring.
Why "Monte Carlo"?
Named after the famous casino in Monaco, Monte Carlo simulation uses randomness (like rolling dice) to model uncertain outcomes. Just as you can't predict a single dice roll but can understand the probabilities of different results over many rolls, Monte Carlo helps us understand financial probabilities.
How It Works in Simple Terms
Why Monte Carlo Instead Of A Single Average Return?
A single average-return projection often uses average returns (e.g., "assume 7% growth per year"). But markets don't deliver steady returns – they fluctuate wildly. Monte Carlo simulation accounts for this real-world volatility.
❌ Traditional Average Return Approach
✓ Monte Carlo Approach
The Sequence of Returns Risk
This is a critical risk Monte Carlo helps identify. Two investors with the same average returns can have vastly different outcomes based on when the good and bad years occur. If you experience market crashes early in retirement whilst withdrawing money, you may never recover. Monte Carlo tests many different return sequences to quantify this risk, running hundreds of scenarios to give you a comprehensive view of potential outcomes.
Understanding the Results: Percentiles
Monte Carlo results are typically shown using percentiles, which tell you how your plan might perform under different levels of market luck.
| Percentile | Meaning | What It Represents |
|---|---|---|
| 10th Percentile | Worst-case scenario | Only 10% of scenarios were worse than this. You faced very poor market returns and/or bad timing of market crashes. |
| 25th Percentile | Below-average luck | 75% of scenarios did better. You experienced below-average returns, perhaps a recession early in retirement. |
| 50th Percentile (Median) | Middle outcome | Half of scenarios did better, half worse. This is the "typical" result if you experience average market conditions. |
| 75th Percentile | Above-average luck | Only 25% of scenarios did better. You benefited from strong markets and good timing. |
| 90th Percentile | Best-case scenario | Only 10% of scenarios did better. You experienced excellent market returns throughout retirement with minimal downturns. |
Example: £500,000 Retirement Portfolio
Withdrawing £25,000/year (5% initial rate), 60% stocks / 40% bonds, 30-year retirement:
Success Rates & What They Mean
The most important output from Monte Carlo simulation is the success rate: the percentage of scenarios where your money lasted through your target retirement period.
Your plan succeeds in 90% or more of scenarios. You have strong margin for error and can likely weather market downturns. This is considered a very safe retirement plan.
Your plan works in most scenarios, but there's meaningful risk of running short. Consider having flexibility in spending or making small adjustments (save a bit more, spend a bit less, or work slightly longer).
In this band the modelled plan fails about as often as it succeeds. People often then inspect savings, spending, retirement age or investment-return assumptions in the scenario to see which change moves the success rate.
In this band the modelled plan fails more often than it succeeds. That usually means the run is relying on better-than-average market paths. Changing inputs and re-running shows which assumptions drive the gap.
What a 100% success rate would mean
Not necessarily. A 100% success rate often means you're being overly conservative and may end up with far more money than needed. Many financial planners suggest 75-85% is optimal – it provides good security whilst not sacrificing too much lifestyle or leaving excessive unspent wealth.
Variables That Affect Monte Carlo Results
Several factors significantly impact your Monte Carlo success rate. Understanding these helps you make better planning decisions:
1. Withdrawal Rate
The percentage of your portfolio you withdraw annually. The biggest factor in success rate.
- • 3% withdrawal rate: ~98% success
- • 4% withdrawal rate: ~92% success
- • 5% withdrawal rate: ~75% success
- • 6% withdrawal rate: ~55% success
2. Asset Allocation (Stocks vs Bonds)
Higher stock allocation = higher potential returns but more volatility. The optimal mix depends on your withdrawal rate and time horizon.
- • 40% stocks / 60% bonds: ~85% success (more stable, lower returns)
- • 60% stocks / 40% bonds: ~92% success (balanced)
- • 80% stocks / 20% bonds: ~90% success (higher volatility)
- • 100% stocks: ~87% success (highest volatility, sequence risk)
3. Time Horizon (Retirement Length)
Longer retirements face more risk of running out. Success rates decline as retirement extends beyond 30 years.
- • 20-year retirement: ~96% success
- • 30-year retirement: ~92% success
- • 40-year retirement: ~83% success
4. Fees & Costs
Investment fees compound over time and significantly impact outcomes. Even 1% annual fees can reduce success rates by 10-15 percentage points.
- • 0.2% annual fees (index funds): ~92% success
- • 0.75% annual fees (average managed fund): ~87% success
- • 1.5% annual fees (expensive fund): ~78% success
5. Inflation Adjustments
Most people increase withdrawals each year to match inflation. This significantly impacts long-term success compared to fixed withdrawals.
- • Fixed £20,000 (no inflation): ~95% success
- • Inflation-adjusted (2.5% annually): ~92% success
- • Year 30 withdrawal: ~£42,000 with inflation
How to Use Monte Carlo Results in Planning
✓ Do Use Monte Carlo To:
- Understand uncertainty: See the range of possible outcomes, not just one prediction
- Test scenarios: Compare "retire at 60" vs "retire at 65", or different spending levels
- Identify risks: Find weak points in your plan before you retire
- Make trade-offs: Balance lifestyle today vs security tomorrow
- Set realistic expectations: Understand that no plan is 100% guaranteed
✗ Don't Use Monte Carlo To:
- Predict exact outcomes: It shows probabilities, not certainties
- Ignore worst cases: The 10th percentile outcomes can and do happen
- Set and forget: Markets and life change – review plans regularly
- Rely solely on probabilities: Personal circumstances and flexibility matter too
Practical Application Framework
Limitations of Monte Carlo Simulation
Whilst Monte Carlo is a powerful tool, it's important to understand its limitations:
Based on Historical Patterns
Monte Carlo uses historical market data to model future returns. If the future is fundamentally different from the past (e.g., sustained lower returns), the simulation may be overly optimistic.
Doesn't Account for Black Swans
Rare, extreme events (like 2008 financial crisis or COVID-19) may not be fully captured by historical data. Real-world "tail risks" can be worse than simulation suggests.
Assumes Fixed Strategy
Most simulations assume you stick to your plan regardless of market conditions. In reality, people adjust spending, re-enter workforce, or modify strategies when things go wrong.
Can't Predict Life Changes
Major life events (health issues, divorce, inheritance, career changes) aren't captured. Your actual retirement will differ from any simulation.
Sequence Risk Still Matters
Even with high success rates, you could be unlucky with timing. A market crash in your first few years of retirement can derail an otherwise "safe" plan.
Important Information
- • This is educational content only and does not constitute financial advice
- • Monte Carlo simulations are based on assumptions and historical data
- • Past performance does not guarantee future results
- • Success rates are probabilities, not guarantees
- • You may wish to speak to a regulated financial adviser for personalised guidance
- • Regular plan reviews and adjustments are essential for retirement security
Further Resources
- MoneyHelper - Pensions and Retirement
Free guidance on retirement planning and risk management
- Pension Wise - Free Guidance Service
Free, impartial retirement guidance from government
- GOV.UK - Plan Your Retirement Income
Financial Conduct Authority guidance on retirement planning