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.