Two retirees with the same average return may experience dramatically different outcomes depending on the sequence of returns they face. A period of negative returns early in retirement can significantly increase the probability of premature portfolio depletion, even if markets recover later. This is known as sequence (or sequencing) risk, and it remains one of the most under-appreciated factors in retirement strategy design.
Traditional models typically assume:
- Independent returns – ignoring serial correlation and market regimes.
- Constant volatility – failing to capture crisis periods and volatility clustering.
- Thin tails – underestimating the probability of extreme events.
To address this, we use a Monte Carlo simulation framework combined with block bootstrapping of historical or synthetic returns. This technique allows for more realistic modelling of volatility regimes, fat tails, and serial correlations — features that materially affect retirement outcomes but are often ignored in standard models.
This article presents the simplified methodology, modelling assumptions and illustrative results derived from the application of this approach. An interactive version of the simulator is also available for advisers to explore different scenarios.
Modelling assumptions and methodology
A simplified simulation was generated using a Monte Carlo methodology combined with block bootstrapping, designed to reflect real-world market dynamics more accurately than simple deterministic projections.
The key assumptions applied are as follows:
- Synthetic data generation. The monthly return series used in the simulation was generated for illustrative purposes, based on a default assumption of an annualised return of 6 per cent and an annualised volatility of 12 per cent. The data does not correspond to any actual index, strategy, or fund performance.
- Block ‘bootstrapping.’ Historical return blocks of 12 months were resampled to create realistic market paths. This preserves patterns such as volatility clustering, serial correlation, and fat tails, which are typically observed in real financial markets but ignored by standard random-draw Monte Carlo methods.
- Retirement scenario parameters
- Initial portfolio value: $1,000,000
- Annual withdrawal rate: 4% of the initial wealth (withdrawals made monthly).
- Retirement horizon: 30 years (360 months).
- Withdrawals are adjusted monthly but do not increase with inflation in this illustration.
- No investment management fees, taxes, or transaction costs were included.
- Asset allocation is assumed to be constant through time (no rebalancing dynamics are modelled).
Please note that this model has been intentionally simplified to illustrate the underlying methodology. In a real-world retirement context, pension drawdown requirements evolve over time, varying according to the retiree’s age and adjustments for inflation. These factors can materially affect the sustainability of retirement income and portfolio longevity.
Simulation settings
- Number of simulations: 5,000
- For each simulation, a unique market path was generated, and portfolio evolution was tracked over time.
- The median and 10th–90th percentile wealth trajectories were calculated to visualise central and tail outcomes.
- ‘Ruin’ probability (the likelihood of portfolio depletion before 30 years) was computed as the proportion of simulations where wealth reached zero before the horizon. In professional practice, a range of 5 per cent–15 per cent is generally considered suitable, balancing sustainable income with inevitable market uncertainty. Lower values indicate conservative strategies, while higher values suggest more aggressive approaches that may require spending flexibility or other income sources. The appropriate level depends on each client’s objectives, risk tolerance, and ability to adjust to changing conditions.
Returns are generated using a block ‘bootstrap’ Monte Carlo process, which preserves key features of real-world market behaviour such as serial correlation, volatility clustering and fat tails. This provides a richer set of plausible return paths than a simple normal-distribution model.
Key elements of the chart
- Median Path (green line): This represents the 50th percentile of all simulated retirement wealth trajectories. It shows the most typical or “central” outcome, assuming the underlying return and withdrawal assumptions hold.
- 10th–90th Percentile Range (shaded area): This band captures the dispersion of outcomes across simulations.
- The upper bound (90th percentile) represents favourable sequences of market returns.
- The lower bound (10th percentile) shows more adverse sequences, where early poor returns significantly affect portfolio longevity.
- Ruin Probability: The simulation reports a 10.8 per cent probability of ruin, meaning that in approximately one in ten simulated scenarios, the portfolio is depleted before the end of the 30-year horizon.
This ruin probability quantifies sequence risk and demonstrates that even with identical average return assumptions, different market paths can lead to widely varying outcomes. In this example, the median path remains broadly stable over the 30-year period, but the lower percentile trajectories highlight that sustained withdrawals during unfavourable return sequences can accelerate portfolio depletion.
Limitations
These results are generated from synthetic data and modelled assumptions, not actual market history. Key simplifying assumptions include:
- Returns follow a specified mean and volatility but are randomised for illustration.
- No inflation adjustments, fees, taxes, or changes to withdrawal behaviour are included.
- Asset allocation is assumed constant over time.
- Results do not reflect actual investment strategies or products offered by Atchison Consultants.
This simulation is intended as a methodological illustration, not a financial forecast. Actual outcomes may vary depending on the asset mix, market conditions, client spending patterns, and the implementation of investments.
Key insight
The chart highlights why advisers should move beyond average-return assumptions when planning retirement strategies.
The median path can look deceptively stable, suggesting that withdrawals are sustainable. However, the range between the 10th and 90th percentiles shows the wide dispersion of potential outcomes, underscoring the need to manage sequencing risk and downside scenarios explicitly.
This probabilistic framework enables advisers to communicate risks more transparently, evaluate different spending rules, and stress test portfolios against a broad range of market conditions.
Ye Peng is a data scientist and developer at Atchison.
