One Simulation
With the assumptions on returns, standard deviations, and correlations estimated, we run a series of Monte-Carlo simulations, where portfolio returns are simulated based on the assumptions we made. Over the whole planning horizon, we simulate one return for each year and calculate the level of wealth for each year. When the plan starts to fund a goal, the projected wealth will be used to offset the required cash flows for that goal. At the end of the planning period, if there is a positive balance for projected wealth after funding all goals, then the goal is achieved for this simulation. If the projected wealth reaches zero before all required cash flows have been withdrawn, then the goal is not achieved.
Whole Simulation
Repeat the above simulation 1000 times, and record the ending wealth balance for each simulation. Rank the ending balance from the lowest to the highest, and the median balance is the amount of wealth that will be achieved with 50% probability, the balance at the low 25 percentile is the amount of wealth that will be achieved with 75% probability, and the balance at the low 10 percentile is the amount of wealth to be achieved with 90% probability.
Probability of Meeting Goal
For each simulation, there are two possible outcomes: the goal is either met or not. Give a simulation score of 1 if the goal is met, 0 otherwise. Aggregate the score and divide it by the number of simulations (1000), the resulting percentage is the “probability of meeting goal”.