monte-carlo simulation

The Wealth and Income module within the WPA estimates future levels of wealth and income.

To estimate future wealth the WPA first simulates future returns for each asset. The WPA offers two simulation methods: Monte-Carlo or Bootstrap. Since future returns cannot be precisely forecasted, both simulation methods will generate hundreds of possible future scenarios. The scenarios are summarized to provide a probabilistic analysis of future wealth and income.

Monte-Carlo Simulation

The most commonly used simulation method, Monte-Carlo simulation, is a multi-variate normal model to simulate asset returns using the chosen return and risk estimation methods; for example, the equilibrium return estimate, and blended quiet/turbulent risk estimate.

While the number of possible future scenarios can be controlled by the user, typically the default value of 1000 is sufficient to generate reasonably stable results without exhausting computer memory (RAM).

The returns of each asset are simulated for each month (or quarter if necessary) in the horizon. Using the simulated asset returns and the portfolio weights we derive the portfolio return and level of portfolio wealth. From this distribution of wealth we can determine the portfolio wealth at any point in time and at any confidence level. The portfolios are assumed to be rebalanced every 12 months on the anniversary of inception.

Bootstrapping Simulation

Bootstrapping is procedure by which new samples are generated from an original dataset by randomly selecting observations from the original dataset. Bootstrap simulation offers the advantage of using actual empirical experience to simulate future scenarios capturing non-normal characteristics such as fat-tails. Whereas Monte-Carlo allows use of the turbulence risk estimate, the Bootstrap method can only assume the historical risk estimate.

Block Bootstrapping

Block Bootstrapping is a version of bootstrapping that differs from regular bootstrapping in that it preserves the serial dependence of the data. Block bootstrapping randomly selecting approximal observations with replacement (as opposed to individual observations) in order to create individual samples.