Monte Carlo Simulations Explained for NZ Retirees

Most retirement calculators work like this: you enter your current KiwiSaver balance, your expected contributions, and they assume an average return of, say, 6% per year. The calculator spits out a number, you breathe a sigh of relief (or panic), and you move on with your day.

But here's the problem: markets don't deliver average returns every year. Some years you're up 15%, other years you're down 8%. The sequence of those returns, especially in the years just before and after you retire, can dramatically change whether your money lasts 20 years or 40 years.

This is where Monte Carlo simulations come in. Instead of assuming one smooth path to retirement, they run thousands of possible scenarios, each with different sequences of market returns, inflation rates, and life events. The result? A probability that tells you: "Based on historical market behavior, you have a 78% chance of not running out of money."

That's not a guess. That's math doing the heavy lifting for your future.

The Monte Carlo method was developed by mathematicians working on nuclear weapons projects in the 1940s. They needed to model complex systems with unpredictable variables, so they ran thousands of simulations using random sampling. The name comes from the famous Monte Carlo Casino in Monaco, because randomness is central to how it works.

In retirement planning, a Monte Carlo simulation works like this:

• It creates thousands of potential futures (often 10,000 or more scenarios)
• Each scenario randomly picks different market returns for each year, based on historical patterns and volatility
• It applies your withdrawal strategy to see if your money lasts through your expected lifespan
• It counts how many scenarios succeeded (you didn't run out of money) versus how many failed

The result is a percentage: your "probability of success." If 7,800 out of 10,000 scenarios showed your money lasting through age 95, you have a 78% success rate.

Think of it like a weather forecast. When meteorologists say there's a 70% chance of rain, they're not guessing. They've run computer models that simulate atmospheric conditions thousands of times, and 70% of those models produced rain. Monte Carlo retirement planning works the same way.

Let's say you retire with $500,000 in your KiwiSaver and other investments. You plan to withdraw $30,000 per year (a 6% withdrawal rate), and your investments historically average 7% returns. Simple math says you're fine, right? You're earning more than you're spending.

Not quite. Here's what can go wrong:

Scenario A: Good early years
Year 1: +12% return
Year 2: +8% return
Year 3: -5% return
Year 4: +10% return

After four years of $30,000 withdrawals, you still have around $520,000. The early gains gave your portfolio breathing room.

Scenario B: Bad early years
Year 1: -8% return
Year 2: -5% return
Year 3: +12% return
Year 4: +10% return

After four years of the same $30,000 withdrawals, you're down to around $470,000. The early losses, combined with withdrawals, created a hole your portfolio couldn't recover from, even with identical returns in a different order.

This is called sequence-of-returns risk, and it's the silent killer of retirement plans. A Monte Carlo simulation captures this risk by testing your plan against thousands of different return sequences, including brutal scenarios like the 2008-2009 financial crisis or the 1970s stagflation period.

A proper Monte Carlo simulation for retirement planning incorporates several variables:

1. Historical market volatility
The simulation uses decades of market data to understand how much stocks, bonds, and other assets typically fluctuate. For example, global share markets have historically returned around 10% annually over very long periods, but with individual years ranging from -40% to +50%.

2. Your asset allocation
A portfolio with 80% growth assets will have very different volatility than one with 30% growth assets. The simulation factors in how your chosen investment mix (like your diversified retirement portfolio) behaves under different market conditions.

3. Inflation
Most simulations include inflation adjustments to your withdrawals. If you need $50,000 in year one, the simulation increases that amount each year to maintain your purchasing power. Based on Stats NZ data, New Zealand's inflation has averaged around 2-3% annually over recent decades, though with significant variation.

4. Withdrawal strategy
Are you withdrawing a fixed dollar amount? A fixed percentage of your remaining balance? A combination with guardrails? Your withdrawal strategy significantly impacts the results.

5. Additional income streams
The simulation can incorporate NZ Super payments starting at 65, rental income, part-time work, or other income sources that reduce the burden on your investment portfolio.

6. Longevity assumptions
How long do you need your money to last? The simulation typically runs until a specified age, often 90 or 95, though you can adjust this based on your health and family history.

Sarah is 58 and planning to retire at 65. Here's her situation:

• Current KiwiSaver balance: $280,000
• Additional savings: $120,000 in term deposits
• Contributing $200/week to KiwiSaver until retirement
• Current asset allocation: 60% growth, 40% conservative
• Plans to withdraw $45,000 per year (indexed to inflation)
• Will receive NZ Super from age 65 ($27,664 annually for a single person living alone as of 2024)
• Needs money to last until age 93

A traditional calculator might show her ending balance at age 93 and call it a day. But a Monte Carlo simulation runs 10,000 different scenarios with varying market returns and shows:

• 65% probability of success with her current plan
• In failed scenarios, money typically ran out around age 82-86
• In successful scenarios, median ending balance was $380,000

That 65% probability tells Sarah she needs to make adjustments. Here are her options and how they change her probability:

• Work until 67 instead of 65: Increases probability to 79%
• Reduce withdrawal to $42,000/year: Increases probability to 74%
• Maintain 70% growth allocation longer: Increases probability to 71% but with higher volatility
• Combine working to 66 + $43,000 withdrawal: Increases probability to 83%

Now Sarah can make an informed choice based on trade-offs she can see clearly. Maybe working one extra year is easier than cutting $3,000 from her annual budget. Or maybe she'd rather retire at 65 and accept a 74% probability, knowing she can always cut expenses later if needed.

This is where Monte Carlo simulations move from math to philosophy. What probability is "good enough"?

90-95% success rate: This is very conservative. You're highly likely to have money left over, which might mean you worked longer than necessary or lived more frugally than you needed to. However, this might be appropriate if you have health concerns, limited ability to adjust spending, or strong legacy goals.

70-80% success rate: Many financial researchers consider this range reasonable for retirement planning. It balances security with not being overly conservative. You're unlikely to run out of money, but you're also not sacrificing unnecessarily. This range assumes you have some flexibility to adjust spending if markets perform poorly in early retirement.

Below 70% success rate: This suggests your plan needs adjustment. You're essentially betting on above-average returns or a shorter-than-expected lifespan, which isn't prudent retirement planning.

Remember that Monte Carlo simulations are not crystal balls. They're based on historical market behavior, and future markets might behave differently. They also can't predict personal circumstances like unexpected health costs, family emergencies, or opportunities to reduce expenses.

Monte Carlo simulations are powerful, but they're not perfect. Here's what they typically don't account for:

Black swan events: Simulations are based on historical data, but they may not fully capture unprecedented events like multi-year pandemics, major wars affecting global markets, or dramatic shifts in the economic system.

Personal flexibility: In real life, you can adjust your spending when markets are down. You might delay a big purchase, skip an overseas trip, or find ways to reduce costs. Most simulations assume fixed withdrawals (though more sophisticated ones can model dynamic spending).

One-time windfalls or expenses: Inheritance, selling a business, major medical expenses, or helping adult children financially aren't usually modeled in standard simulations.

Tax changes: Future changes to tax policy, superannuation, or retirement benefits could significantly impact your plan. New Zealand's relatively simple tax structure for retirees could change over a 30-year retirement.

Behavioral factors: The simulation assumes you'll stick to your withdrawal plan during market crashes. Emotionally, that's incredibly difficult. Many retirees panic during downturns and make poor decisions that aren't reflected in the math.

Despite these limitations, Monte Carlo simulations remain one of the most valuable tools for retirement planning because they incorporate volatility and sequence risk in ways simple calculators can't.

Think of your Monte Carlo probability as a starting point for decisions, not a final answer. Here's how to use it effectively:

Test different scenarios: Run simulations with different retirement ages, withdrawal amounts, and asset allocations. See how each variable affects your probability. This helps you understand which changes have the biggest impact.

Build in flexibility: If your simulation shows 75% success with $48,000 annual withdrawals, consider planning for $45,000 but knowing you could spend $48,000 in good years. Flexibility is your secret weapon.

Rerun periodically: Your Monte Carlo probability will change as you age, as your portfolio grows or shrinks, and as you get closer to retirement. Rerun the simulation every 2-3 years or after major market movements.

Consider guardrails: Some withdrawal strategies include guardrails: if your portfolio drops below a certain threshold, you reduce spending by 10%; if it grows beyond another threshold, you can increase spending. This dynamic approach can improve your probability while maintaining lifestyle quality.

Factor in NZ Super: Remember that NZ Super provides a base income from age 65. Your simulation should account for this, as it significantly reduces the burden on your personal savings.

When thinking about how much you need to retire, Monte Carlo simulations help you move from guesswork to informed probability, giving you confidence in your decisions.

This article is general information only and does not constitute personalised financial advice. For advice tailored to your situation, speak with a licensed Financial Advice Provider. You can find a registered adviser at fma.govt.nz.