How is Monte Carlo simulation used in retirement planning, and why is it better than a single projection?

Question

AcadiFi · Accepted Answer

Monte Carlo simulation is a powerful tool for retirement planning because it captures the full range of possible outcomes, including the risk of ruin that a single-point projection completely ignores.

## Why Single-Point Projections Fail

A deterministic projection says: "If you earn 7% per year, your $800K portfolio will be worth $1.57M in 10 years." That is the average outcome, but it tells you nothing about the distribution of outcomes. The investor might end up with $2.5M (great) or $400K (disaster) depending on the actual sequence of returns.

## How Monte Carlo Works

```mermaid
flowchart TD
    A["Define Inputs"] --> B["Return Distribution
μ = 7%, σ = 15%"]
    A --> C["Withdrawal Schedule
$48K/year, +2% inflation"]
    A --> D["Time Horizon
30 years"]
    B --> E["Run 10,000
Random Paths"]
    C --> E
    D --> E
    E --> F["Analyze Distribution
of Ending Wealth"]
    F --> G["Success Rate
87%"]
    F --> H["5th Percentile
Ending Value: $62K"]
    F --> I["Median Ending
Value: $1.2M"]
```

## Worked Example — Westbrook Retirement Plan

Eleanor Westbrook, age 60, has a $900,000 portfolio. She plans to withdraw $50,000 per year (adjusted for 2.5% inflation) for 30 years. Her portfolio is 60/40 equity/bonds.

Assumptions: E(R) = 6.5%, σ = 11%, returns are lognormally distributed.

**Single projection:** $900K growing at 6.5% with $50K withdrawals lasts comfortably for 30 years. "All clear!"

**Monte Carlo (10,000 trials):**
- Probability of ruin (portfolio hits $0 before year 30): **18%**
- Median ending wealth: $842,000
- 5th percentile ending wealth: -$124,000 (depleted in year 26)
- 95th percentile ending wealth: $3.1 million

That 18% ruin probability is critical information the single projection completely hid. Eleanor might choose to reduce her withdrawal rate, add annuity income, or adjust her asset allocation.

## Sequence-of-Returns Risk

The key insight Monte Carlo captures is **path dependency**. Two sequences with the same average return can produce wildly different outcomes when withdrawals are occurring. Bad returns early (when the balance is large) are far more damaging than bad returns late.

## Limitations

1. Results are only as good as the input assumptions (garbage in, garbage out)
2. Assumes returns are independent across periods (ignores mean reversion)
3. Cannot model behavioral responses (panic selling during crashes)

**Exam tip:** CFA Level I tests whether you understand that Monte Carlo gives a distribution of outcomes, not just a point estimate. Questions often ask about the advantages over analytical methods.

Practice more in our CFA Level I question bank.

How is Monte Carlo simulation used in retirement planning, and why is it better than a single projection?

Why Single-Point Projections Fail

How Monte Carlo Works

Worked Example — Westbrook Retirement Plan

Sequence-of-Returns Risk

Limitations

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