Timeline’s Monte Carlo analysis enables users to test how a withdrawal strategy might fare under a wide range of market conditions by simulating sequences of random portfolio returns based on a model.

Timeline produces results for the selected withdrawal strategy based on 1,000 simulations. For instance, in a 30-year retirement period, Timeline generates 1,000 different 30-year scenarios with varying annual returns and inflation in each scenario based on the user’s input.

The underlying model that we use to simulate portfolio returns is the Geometric Brownian Motion model. In such a model the prices of assets are assumed to be log-normally distributed.

**Inputs & Assumptions**

For the Monte Carlo simulation, the inputs are:

Portfolio’s expected return and corresponding standard deviation

Inflation rate, and corresponding standard deviation

While Timeline provides default inputs based on long term averages, it is up to the user to ensure that the capital market assumptions are reasoned and reasonable.

Generally, the inputs should be based on long-term return and volatility expectations for the portfolio.

The inputs should be based on the total annualised nominal return of the portfolio, and/or the aggregate from the individual asset classes within the portfolio.

**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 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.