The financial planning process involves forecasting future investment returns based on a set of agreed upon assumptions in order to develop robust financial planning recommendations. Forecasting the future is an impossible task and financial forecasting is a process fraught with error.
Traditionally, the process of forecasting future investment returns has involved deterministic modeling, or time value of money forecasting. However, deterministic modeling excludes randomness and variability in future projections, which significantly reduces its usefulness in developing robust financial planning recommendations.
Stochastic modeling (involving random sampling of inputs), including Monte Carlo simulations, incorporates randomness into models based on probabilistic inputs (mean, standard deviation, and correlation) to better predict an uncertain future. This allows for the development of more robust financial planning recommendations, better able to withstand variable future outcomes. In Monte Carlo simulations, the random or probabilistic variables in the model may include future investment returns, lifespan, or inflation.
Deterministic projections inherently provide planners with a 50% probability of success based on any assumed rates of return (assuming geometric returns are correctly used). This introduces significant uncertainty into long term financial plans. Monte Carlo simulations can improve upon this probability of success, though probabilities of success are still likely to be overstated in Monte Carlo projections.
In addition, as a result of better incorporating future randomness or variance, Monte Carlo simulations more accurately model variance drain or volatility drag (reflecting geometric returns as opposed to arithmetic returns). Similarly, Monte Carlo simulations also better model sequence of returns risk. In comparison, variance drain and sequence of returns risk are less accurately modeled in deterministic projections, where a fixed rate of return is assumed (here, inputting geometric returns more accurately reflects these than arithmetic returns).
Limitations of financial forecasting via Monte Carlo simulations are myriad and are typically a consequence of user errors or limitations inherent to modeling tools. Notably, inputs in Monte Carlo simulations must include arithmetic returns, not geometric returns, a common user error (this may be estimated as: geometric return ≈ arithmetic return – variance / 2 [note: variance = standard deviation ^ 2]). Whereas, deterministic or time value of money projections require geometric returns (compounded annual growth rates as opposed to arithmetic returns).
Additionally, results are highly dependent on quality inputs (“garbage in, garbage out”). Notably, inputs are typically based on historical data. This is problematic as it incorrectly assumes that future outcomes can be predicted by historical performance.
Additional limitations include the assumption of normal distributions in many tools, which may not accurately model inputs that follow non-normal distributions, and the potential exclusion of auto-correlations in many tools (where returns of a variable may be correlated over time, as may be the case with inflation or bond returns).
Compared to deterministic models, stochastic modeling methods, including Monte Carlo simulations, add greater confidence to financial projections. They better aid in understanding the uncertainty of the future and in developing more robust financial planning recommendations. However, all models must be interpreted with caution and within the context of the investor’s full financial profile. All modeling tools, including Monte Carlo simulations, represent estimates based on a set of imperfect assumptions. Any recommendations based on these estimates must be monitored and adjusted over time to incorporate new information.