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Monte Carlo Simulation on Timeline

Summary

  • Tests a withdrawal strategy across 1,000 simulated market scenarios.
  • Generates unique sequences of returns and inflation based on user-defined inputs.
  • Uses a Geometric Brownian Motion framework to model portfolio behaviour.

Description

Timeline’s Monte Carlo analysis evaluates how a retirement plan might perform under a wide range of potential market environments. For a 30-year retirement, the system generates 1,000 distinct 30-year scenarios, each with different sequences of annual returns and inflation derived from the selected assumptions.

The simulation is based on a Geometric Brownian Motion (GBM) model, where asset prices are assumed to follow a log-normal distribution. This allows the model to produce realistic return paths while incorporating both expected return and volatility.

It is important to note that inputs drive outputs. While Timeline provides long-term historical defaults, advisers are responsible for ensuring that capital market assumptions are reasonable and appropriate for the client’s portfolio. Expected returns should be input as arithmetic means. Using geometric returns would effectively double-count volatility drag, since geometric returns already incorporate that effect.

Aggregate Portfolio Returns

The annual estimates for the portfolio aggregate return and volatility are used within the simulation model to produce monthly returns for the portfolio.

Bear in mind that if one uses geometric returns as inputs in Monte Carlo, the projection will essentially count the impact of 'volatility drag' twice. This is because geometric returns already include volatility drag. Accordingly, we strongly recommend using the arithmetic mean for the expected returns input. 

Asset Level Return

Timeline uses historical data going back to 1915 for all the major asset classes' indices to calculate the estimates for the arithmetic mean return and volatility.

The portfolio mean return is calculated as a weighted average, based on asset allocation, of the historical mean returns of the underlying assets and the portfolio volatility is calculated using Markowitz's model.

For the correlation of the asset classes, we use the historical mean correlation for each combination of assets in the portfolio. To do so, we first calculate the correlation matrix for every monthly rolling scenario based on the years of simulation.

Conclusion

Monte Carlo simulation in Timeline provides a forward-looking stress-testing framework built on statistically generated return sequences. Its effectiveness depends entirely on the quality of the input assumptions. When grounded in evidence-based capital market expectations, Monte Carlo complements historical analysis by testing retirement plans across thousands of plausible, but unseen, future paths.