When you are making retirement plans based on your portfolio results, it always pays to be a pessimist rather than an optimist. This is very unlike most things in life.

Being a pessimist on your portfolio performances means that you assume really bad performance of your portfolio in terms of drawdowns and returns. If your portfolio is still able to meet your retirement goals under such conditions, it will then be very safe to assume that you will almost definitely meet your retirement goals.

But here comes the question. What is considered pessimistic?

Let's start with the most extreme example- a black swan event.

By conventional wisdom, __a black swan event is considered a six-sigma event__. What exactly is a six-sigma event?

In probability studies, we have all come across the term- normal distribution. A normal distribution graph is what we usually called a bell curve. Below is a very good illustration of a normal distribution graph.

*(Source: https://www.studysmarter.co.uk/explanations/math/statistics/normal-distribution-percentile/)*

In this graph, 68% of the results fall within one standard deviation of the mean. 95% of the results falls within two standard deviations of the mean. 99.7% of the results falls within three standard deviations of the mean. A six-sigma event is an event that exceeds six standard divisions of the mean- so well it's very unlikely to happen and also very impractical to use as the basis of your portfolio performance over a period of time, say 10 years. It is overly pessimistic.

A better and more practical way of planning is to be prepared for a two-sigma outcome instead. That is to assume that only simulation results from the 1st to 5th percentile.

How do you do that?

By running Monte Carlo Simulations.

Throughout the history of this blog, I have always advocated the use of Monte Carlo Simulations in simulating the performances of your portfolio in various conditions. With the help of several service providers, you no longer have to code your own Monte Carlo Simulations. One great website which you can tap on is __Portfolio Visualizer__ which I have strongly encouraged the readers of this blog to explore using.

Portfolio Visualizer allows you to run Monte Carlo Simulations with just a few simple clicks. It generates 10,000 outcomes and divides the simulation results into several percentile intervals for easy visualisation.

Let's run the simulation on my passive portfolio to see how it turns out.

These are the parameters for my simulation.

- An initial sum of $500,000

- A time period of 10 years

- No additional contribution or withdrawal during this time period

- Statistical returns of my portfolio was used for simulation

- No sequence of returns risk was taken into account.

- GARCH model was used (more details __here__)

- Historical inflation used

- Rebalancing conduct annually

Below are the results from the simulations.

Remember that we are being sufficiently pessimistic here by preparing for a two-sigma outcome. Hence we only look at the results from 1st percentile, 3rd percentile and 5th percentile of the simulation results. At 5th percentile, you can see that the annual rate of return (nominal) is 3.64% with a maximum drawdown of -58.8%. The portfolio end balance (nominal) at this percentile is $964,967. At 1st percentile, the annual rate of return is just 0.25% with a maximum drawdown of -69.94%. The portfolio end balance (nominal) at this percentile is $376,646 (which is a sum even lower than the initial amount).

How cautious I am will determine which percentile of results I should be preparing for. If I am extremely cautious and look at only the 1st percentile of results, my current portfolio choices with an investment time period of 10 years is not going to make the mark. If just looking at first percentile of the result is being too cautious, I can look at the results from the other percentiles (eg. 3rd percentile or 5th percentile) and determine if those results are satisfactory to me. In short, it's all about how cautious you want to be. Bear in mind that such simulation results (1st percentile, 3rd percentile, 5th percentile) are outside of two standard deviations from the mean. This means that you are preparing for a two-sigma outcome here (which is a very careful measure in my opinion).

There are more parameters which you can utilise for your simulations. For instance, you can be very careful and take into account the sequence of return risks. You can assume the worst 1 or 2 or 3 or 4 etc years first in your simulations. You can also adjust the time period to be shorter or longer. The longer the time period is, the higher the chances of success for your portfolio are. Just take a look at the simulation results below when I change the time period to be 15 years instead.

This is also the reason why it's important to take a long term approach to your investments.

Of course, such simulation of results aren't exactly without flaws. A common argument has always been that past results doesn't guarantee future successes. The statistical returns used for simulations are all based on previous results. Based on my portfolio, below are the statistical returns used.

I would love to see Bitcoin continuing to provide an annual return of 117.55% for the next 10 years but I do know that the chances of that happening aren't exactly very high. In any case, you can always not use statistical return and use parameterised returns in your simulations instead if you think they are more practical for use.

In short, it always pays to be extra cautious when basing your retirement plans on the performance of your portfolio. While it's impractical to prepare for a black swan outcome, it still makes quite a bit of sense to prepare yourself for a two-sigma outcome. Give it a try today!

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Nicholas Taleb, in his book the Black Swan was extremely critical of anyone using gaussian (normal) distributions as he believes that they are a terrible model for financial markets. He is instead Bayesian in outlook.