Monte Carlo Simulation

AllocationADVISOR's Monte Carlo simulation feature helps you answer the questions:

How might my portfolio perform?
What is the probability that my portfolio will be worth a specified value?

AllocationADVISOR's analytic portfolio projections do not allow for cash flows. When a portfolio is subject to cash flows, use Monte Carlo simulation to project its future value.

A simulation consists of a series of trials. Each trial tracks the portfolio's value over a number of years. A portfolio's value for a year is based on the portfolio's previous value, the year's return, and applicable cash flows. A typical simulation includes thousands of trials. In AllocationADVISOR the default number of trials is 10,000.

In order to simulate the future value of a portfolio, you must provide an initial portfolio value, the mean (Portfolio Return) and the standard deviation (Portfolio Risk) of the portfolio. You can also specify a wealth goal, probability targets, cash flows (to be applied at various times), and a rate of inflation. The wealth goal, the probability targets, and cash flows can be inflation adjusted.

The mean and standard deviation can be set from any of the Mixes, the Active Portfolio or the Current Portfolio. Alternatively, you can enter mean and standard deviation values. The mean and standard deviation define a distribution that represents possible future returns. You can choose the distribution type - normal or lognormal.

It is an open issue whether to use a normal or lognormal distribution. Some believe the normal distribution is an inadequate description of returns. They hold that the lognormal distribution recognizes that returns are never less than -100% and that over longer time periods (such as a year) returns are positively skewed. If you share this view, use a lognormal distribution.

Simulation

This formula simulates the value of a portfolio.

where:

W_t = wealth at time t
W_{t - 1} = wealth at time t - 1, (when t = 1, W_{t - 1} = Initial Wealth)
random return at time t
t = time t
CF_k,t = cash flow k at time t
k = number of cash flows at time t

Inflation Adjusted Wealth Goal (or Target)

AllocationADVISOR provides the ability to view the wealth goal (and portfolio targets) in real or nominal terms. To view these values in real terms, they need to be inflation adjusted.

WealthGoal_t = WealthGoal₀ * (1 + InflationRate)^t

Target_t = Target₀ * (1 + InflationRate)^t

where:

t = time t

Portfolio Probabilities

The probability of the Wealth Goal (or a Target) is the number of simulation trials that meet or exceed the Wealth Goal (Target) divided by the total number of trials.

Cash Flows - Inflation Adjusted

CF_t = CF₀ * (1 + InflationRate)^t

where:

CF_t = cash flow at time t
t = time t

Cash Flows - Percent (of portfolio value)

CF_t = Percentage * PortfolioValue_t

where:

CF_t = cash flow at time t
PortfolioValue_t = portfolio value at time t
t = time t

Trials Filter - Maximum Value

If a trial's value ever exceeds the filter value, the trial is removed from the simulation.

Trials Filter - Maximum Final Value

If a trial's final value exceeds the filter value, the trial is removed from the simulation.