Taxable Investing > Complexities > Monte Carlo Simulation

While investors are primarily focused on expected outcomes they are also interested in confidence intervals.  For example, the expected final value of a portfolio in year 10 is $16.0 million with a 95% confidence interval that it will be between $11.6 million and $20.7 million.  Such statements typically require that underlying statistical distributions are known.


However, given the complexity of multi-period, after-tax analysis, the exact statistical distributions of a portfolio and its components are unknown over time.  This is primarily due to the non-linear and non-smooth effects of the different tax rules on asset returns.


Monte Carlo simulations can be used as proxies for unknown statistical distributions in creating confidence intervals.  PORTAX uses expected returns for the multi-period optimizer and cash projections.  Once an investor selects a portfolio with its corresponding weights, the Monte Carlo simulation replaces all expected asset returns for each period with pseudo-random returns and recalculates the cash projections multiple times.  This process enables PORTAX to report confidence intervals for a number of different calculations including final value.


The graph to right shows expected final value with associated confidence intervals.





PORTAX Monte Carlo Simulator

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