Monte Carlo Simulation - Overview and FAQs

Overview

Voyant's Monte Carlo simulation is used to test a plan for success using variable, randomly generated market returns.

For each iteration, the Monte Carlo finds a randomly selected percentile return – a randomly selected position away from the standard deviation – and using this percentile, the software calculates a return for each stochastically modelled account based on the asset mix selected for that account. The simulation does this for every year of the plan. An iteration with no years of shortfall is considered a success. It does this for the number of iterations you chosen to run.

The results in the bottom chart will show the number of times a given year is shown to have successful randomly generated returns, yielding no shortfalls. The overall percentage will show the plan's overall chances of success – i.e. the number of iterations in which no shortfalls occurred.

This is a very intensive calculation and can take a few minutes to run, depending on the number of iterations you've chosen to run.

 

Market Assumptions and the Monte Carlo Simulation

The Monte Carlo simulation utilises stochastic outputs from the software's market assumptions.

The UK release of Voyant Adviser and AdviserGo arrive packaged with a set of default market assumptions provided by Rayner Spencer Mills Research (RSMR). Additional information on this market data set can be found here.

Other releases of Voyant for the US, Canada and Ireland are packaged with different sets of default market assumptions.

Market assumptions may also vary depending on whether your firm has opted to use its own market data. Bespoke market assumptions are usually added to the software and managed as part of Voyant's optional rebranding service.  

The market assumptions used within a given client case can be viewed by opening the case in Voyant Adviser. Click the cog button (Preferences) top-left, which will display the Preferences screen. On the right side of the screen in the Plan Preferences, expand the Market Assumptions panel. This panel shows the assumptions used when you choose to grow accounts -- investments, defined benefit and drawdown pensions, and in some cases cash savings -- using asset allocations.

 

Asset Allocations Must be Used to Run the Simulation

The Monte Carlo simulation is intended for use where most of the plan’s accounts are specified using asset allocations.

Accounts in Voyant can be grown using either fixed growth rates or asset allocations (model portfolios). Only accounts grown using asset allocations will come into play when running the Monte Carlo simulation. Read more >>

To run the simulation, at least one or more of the client's accounts must be set to use asset allocations, rather than fixed growth rates, to determine future growth. This is because asset allocations and the market assumptions they are based upon provide not only an average rate of return (the 50th percentile mean); they also provide a potential upside and downside, which is calculated to three standard deviations from this mean. This provides a range of potential returns within which the Monte Carlo simulation can randomly select annual returns.

The forecast of any accounts using a specified fixed growth rate is not stochastic. Therefore, if a large proportion of a plan’s accounts are defined using a fixed growth rate, the output from the Monte Carlo simulation will tend to be either close to 0% or close to 100% depending on whether your client’s goals were met at the specified growth rate.

Voyant then uses these projected investment returns, in conjunction with the information you have entered about your client, to determine for each simulation whether the plan would meet its goals. This  is repeated through a user specified number of iterations to determine the probability of success.

The upper chart of the Monte Carlo simulation illustrates the basic deterministic cash flow using the default average 50th percentile return estimates. This forecast will run until mortality as input by the user.

The lower chart represents the probability of success in each year.

Probability of success is derived from the percentage of the iterations that result in no expense shortfalls in the year. The overall probability of success, shown in the bottom right section of the screen, displays the proportion of the iterations that recorded no expense shortfalls in any year of the plan.

 

How Are Annual Returns Randomised?

As it runs through a single iteration, the Monte Carlo simulation will choose at random a percentile return for each asset class defined in the plan's market assumptions. This will randomised percentile selection be then repeated for each year or the plan.

For example, if a plan's timeline runs for 50 years and there are 10 asset classes in the plan's market assumptions, then for one 50-year iteration, the simulation will generate 500 random percentiles. One percentile is randomly selected for each asset class in each year. 

Market assumption define asset classes, their 50th percentile averages, and the standard deviation from this 50th percentile mean (normally three standard deviations from the mean). These asset classes are then correlated into a correlation matrix.

The Monte Carlo simulation will attempt to use this matrix to correlate the random percentiles for each asset class for each year. This operation is called a Cholesky decomposition. Some correlation matrices do not make it mathematically possible to perform this operation, in which case the simulation will remain completely random.

Provided that it is possible to correlate asset classes, the Monte Carlo simulation will adjust its randomly generated percentiles to account for the relationship between asset classes.

For example, two asset classes in plan are highly correlated, say a value of .8, in a plan's market assumptions. 

The Monte Carlo simulation generates a random 90th percentile return for asset class 1 and a 15th percentile return for asset class 2.

The Cholesky decomposition will then cause these two randomly assigned percentiles to be adjusted to be something more in line with their correlation value.

The percentile for asset class 1 might be adjusted downward to the 85th percentile and the percentile for asset class 2 could be adjusted upward to the 60th percentile, narrowing the difference between the two to account for their correlation.

 

Frequently Asked Questions About the Monte Carlo Simulation

Q - Does the Bottom 5% shows the results from a worst case bottom 5% performance during the simulation? I think there is some confusion over how a plan can have a 100% projected success rate even when the 5% performance marker falls below the need line.

 
A - The bottom  5% line represents the bottom 5 percentile performance for each year in the plan.  It’s the very worst performance in every year of the plan.  A Monte Carlo is randomized performance over every year of the plan.  Some individual years may actually be worse than the bottom 5 percentile, but overall, the entire trial in all probability will not perform that badly each year.  Hence, one should never expect that because the bottom 5 percentile line is below the need line the plan cannot have a 100% success rate for a given number of trials. 

 

Q  - Update Frequency – what is this?

A - The number of iterations run by the simulation before the screen refreshes.


Q - Iterations – do the number of iterations correlate to the accuracy of the simulation?

A - The number of iterations directly affects the range of probabilities that will result.  Accuracy is not a word we should use when it comes to Monte Carlo.  The number of iterations will constrain the range of probabilities that are likely to be seen as a result from the Monte Carlo.

Monte Carlo is tool to test the tolerance of a plan to market forces.  The larger the number of iterations run, the more likely it will be to get a more representative probability of just how tolerant the plan is to these market forces.

The larger the number of iterations, the longer the simulation takes to run and we don’t have a way to preserve the results, which makes long runs problematic.


Q - What is a good definition of a successful year and in turn a successful plan? One in which, over the course of in this case 100 randomized iterations no shortfalls occur?

A - A successful year within a single iteration of the Monte Carlo simulation is one in which there no shortfall occurs.  A successful iteration through a plan is an one in which all of the years are successful, meaning no shortfalls occur in any year for that iteration.


It should be stressed that the output of the Monte Carlo simulation is a probability.  A plan that receives a 90% probability of success after a 100 iterations will probably be more likely to be successful than one that returns a 10% probability of success.  Note that a plan which returns a 100% probability of success after 100 iterations could either be a very safe plan or this probability could be due to the small number of iterations used when running the simulation.