Monte Carlo Simulation

Nothing spurs action like a deadline. If you have yet to purchase a gift two hours before meeting your grandmother for lunch on her birthday, you're likely to either rush to the store or even stop by the local florist on your way to the restaurant. For investors, the mean–variance optimization approach has a deadline that's established by its use of a single-period framework. That period could be a month, a year, or even several years. But the basis of expectations across the time period used remains the same, and that can be a problem. What computer simulation approach would help address this limitation of the mean–variance optimization?

Exactly! Monte Carlo simulations can help analysts address the time-period limitations of the mean–variance optimization approach. For example, by running multiple simulations with different variables, you can forecast different results for the investor. This allows you to then present different outcomes for the investor to select from, which can help you further determine the investor's personality. How could it do so?

No. That's not a computer simulation.

Not quite. That's going to involve a lot of work for the analyst.

Yes! The Monte Carlo simulation is going to help reveal the investor's risk tolerance through the calculation of potential results. These results will include the potential outcomes, probability of meeting various goals, distribution values of the portfolio, and potential maximum losses. Even taxes, rebalancing, and trading costs can be factored into the analysis. But you'll want to be careful to ensure you're using the right type of Monte Carlo simulation model—these models can vary in the multivariate returns, serial and cross correlations, tax rates, distribution requirements, an adaptive asset allocation schedule, traditional investments, and human capital.

Not quite. The volatility of different outcomes might reveal biases, but those aren't personality issues.

Not really. That should already be known so that the Monte Carlo simulations can focus on meeting that requirement.

Once you've got the proper Monte Carlo model, the real benefits are easily identified. You can practically change any variable and see the overall impact on the investor's portfolio. But there's also another benefit that really comes in handy. For example, think about how clients save and invest over time. When life events happen, like a car accident or job loss, investors don't keep saving, and sometimes they may even need to make a withdrawal. This makes cash flows relevant to your asset allocation and investing strategy and really impacts the importance of returns that determine the ending value of wealth. If cash flows are relevant, how would you describe the path of terminal wealth?

Not really. The path of terminal wealth doesn't follow a straight line.

No. Cash flows move in and out of the account, so that's not really sequential.

That's it! The path of terminal wealth is dependent on cash flows, so that's a real benefit of the Monte Carlo simulation. Just think about trying to calculate the ending wealth value by hand if cash flows are realistically unknown. It would take forever! So Monte Carlo really comes in handy for investors who expect to take withdrawals from their portfolios. If the investor doesn't anticipate needing to take withdrawals, then the asset allocation evaluation process becomes much easier.

After you've run your Monte Carlo simulation and developed strategic portfolios for your client's review, it's important to make sure that your ending terminal wealth goal or rate of return requirement matches the inflation categorization (real or nominal) of the client. For example, most analysts present ending wealth in real terms to include the impact of inflation, so it's crucial to make sure that those inflation terms match. It's also important to evaluate the relative range of probabilities that a Monte Carlo simulation will produce for a given portfolio. For instance, if the client desires a 75% probability of a certain terminal wealth value, you'll need to ensure that for a given age, the portfolio's ending value meets that requirement.

To sum it up: [[summary]]

Monte Carlo

Regression to the mean analysis

Mean–variance multiperiod optimizations

It helps you determine risk tolerance

It helps you understand cognitive biases

It helps you validate the return requirement

Linear

Sequential

Dependent

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