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Summary
Timeline enables users to test withdrawal strategies using two complementary approaches:
- Extensive historical (evidence-based) data.
- Monte Carlo simulations.
Historical analysis grounds financial planning in observed empirical market behaviour, while Monte Carlo expands the range of possible future outcomes through probabilistic modelling.
Description
1. Historical (Evidence-Based) Modelling
Extensive historical data takes financial planning out of a purely theoretical realm and into the empirical world. It is based on the sequences of returns of asset classes across real historical periods.
This approach frees the financial planner from having to assume how asset classes may perform in the future. Instead, it asks a clear question: How would this plan have performed across real historical periods? However, there are criticisms of the historical model:
- There are a limited number of historical scenarios.
- Past performance is not an indication of future performance.
- Global markets today are more complex than in the past.
- Future returns could be structurally worse than historical returns.
2. Monte Carlo Modelling
Monte Carlo is not a fortune teller. It models the probabilities of various possible trajectories for asset values and applies meaningful statistical metrics across the full distribution of outcomes.
At Timeline, Monte Carlo simulations are implemented using Geometric Brownian Motion (GBM). The GBM model was introduced by Paul Samuelson in the 1950s and later became a key ingredient in the 1973 Black–Scholes option pricing formula.
The model assumes that asset prices are log-normally distributed and has two inputs: the expected rate of return and the volatility. This model is well known and easy to implement.
However, Monte Carlo is only as robust as the assumptions underlying the stochastic model that drives asset prices. In addition, Monte Carlo assumes no serial correlation. Real markets exhibit both momentum (short-term) and mean reversion (long-term).
As Dr. Derek Tharp CFP notes: "Whether the prior year was flat, saw a slight increase, or a raging bull market, Monte Carlo analysis assumes that the odds of a bear market decline the following year are the same. And the odds of a subsequent decline in the following years also remains the same, regardless of whether it would be the first or eighth consecutive year of a decline! Yet, a look at real-world market data reveals that this isn’t really the case. Instead, market returns seem to exhibit at least two different trends. In the short-run, returns seem to exhibit “positive serial correlation” (i.e., momentum – whereby short-term positive returns are more likely to be followed by positive returns, and vice-versa), and, in the long-run, returns seem to exhibit “negative serial correlation” (i.e., mean reversion – whereby longer-term periods of low performance are followed by periods of higher performance, and vice-versa)."
In Practice
In practical financial planning, both approaches serve complementary purposes.
The historical (evidence-based) model evaluates a plan using actual historical sequence of returns. Each scenario reflects a real period in market history, incorporating genuine market behaviour, inflation dynamics, and asset interactions. This allows advisers to assess how a retirement plan would have performed under real-world stress conditions.
The Monte Carlo model, by contrast, generates unique sequences of returns based on the underlying capital market assumptions. Each simulation path is synthetic, meaning it creates return paths that have not necessarily occurred in history. This expands the range of possible outcomes and allows for broader stress testing.
While Monte Carlo produces new and independent sequences of returns, its outputs are only as robust as the assumptions used for expected return, volatility, and model structure. In other words, the outputs are only as good as the inputs.
In practice, a disciplined framework can combine both approaches. First, assess whether the plan has historically survived real-world extreme environments. Then, use those same historical characteristics (returns, volatility, inflation behaviour) as the backbone of a Monte Carlo analysis to generate a wider range of unique return paths and validate the evidence based approach.
Conclusion
Historical modelling anchors financial planning in empirical evidence. Monte Carlo modelling broadens the range of possible outcomes through probabilistic simulation. The historical model anchors the plan in empirical reality, while Monte Carlo extends the analysis beyond observed history. Used together, they provide a more robust validation framework for retirement planning.
For a detailed discussion of the strengths and weaknesses of historical and Monte Carlo models, please see: