# Planning your retirement with the use of statistical simulations

Updated: Dec 11, 2021

Almost 10 months ago, __I wrote an article on the possibility of retiring at 40__. In the article, some interesting conclusions are derived from the analysis. If you are interested to find out more, please check out the article in the link above.

10 months have now passed and I think it's time to relook at these simulations to see what are some of the areas which could be improved upon. For the regular readers, you all might have already known that I'm quite a fan of __Portfolio Visualizer__. I have used the tools available on the site to conduct several backtesting analysis, assets correlation studies and some other portfolio quantitative stuff which I often blogged about in the various articles.

Beside tools for backtesting and correlation analysis, Portfolio Visualizer also has other tools such as Monte Carlo simulations to allow users to use them to plan for specific financial goals such as retirement. For the uninitiated, Monte Carlo is a class of computation algorithms which rely on random sampling (key element here is randomness) to obtain a numerical result to a pre-defined problem.

Portfolio Visualizer allows you to run through **5000 simulations**- which is a pretty big number for you to derive some meaningful statistics out of.

In this article, I'm going to explore using the Monte Carlo simulations on the site to run through some retirement planning. After reading this article, you should also be able to use these simulations to run through your retirement plan.

*(source: Portfolio Visualizer)*

When you click __on this link__, you will be brought to a page with quite a lot of details to fill in. Most of the details required for the stimulation are quite intuitive in nature. **You could easily fill them up based on your goals (eg. how much is your retirement sum and how long is the simulation period which you want to run). **I'm quite pleasantly surprised by the amount of details the site actually puts you to allow you through to run simulations as realistic as possible. For example, you could choose to have historical returns, forecasted returns, statistical returns or parametrized returns for your simulation returns. If you don't think that past performances are of any good gauge for future performances, you are welcomed to use forecasted returns or parameterized returns to input your own perceptions of future returns. In fact, you could even choose fat tailed distribution instead of normal distribution for the values used in your simulations if you want to. The same goes for the inflation model. You could either choose to use historical values or you could input your own version using parametrised returns. There's quite a lot of flexibility there.

Another feature which amazes me is the ability for users to choose **GARCH (Generalized Autoregressive Conditionally Heteroscedastic) Model** for the time series information. The GARCH model is commonly used in the financial world to mimic real world conditions to estimate volatility. It is certainly not easy for individuals to try to create this model on their own so it's certainly a plus here that Portfolio Visualizer allows users to use this model as one of the options for the time series information without the need to create/code anything.

*(source: Portfolio Visualizer)*

You could input your own portfolio allocation mix into the simulations to see how well your portfolio will perform in the simulations to achieve your particular financial/retirement goal. At the end of the simulations, you will get to know what your percentage of success is like by determining how many of the 5000 simulations results in a successful outcome. Unfortunately, the site covers mainly US stocks/ETFs so you couldn't really include specific SG stocks in your simulation here.

*(source: Portfolio Visualizer)*

On the financial goal tab, you could input the specifics of your financial goal. If you are looking at a retirement goal, you could input information like how much withdrawal do you need on a frequency you determined and timeline determined by you. You could even choose to have the withdrawal amount to be adjusted for inflation.

Now, let's try to input the parameters below to get a feel of how the simulations work.

*(source: Portfolio Visualizer)*

**Retirement sum**: $ 300,000

**Simulation Period**: 50 years

**Withdrawal**: $60,000 annually for 50 years (inflation-adjusted) to begin in 10 years

**Portfolio**: For simplicity sake, I am going to use SPY (SPDR 500 S&P 500 ETF Trust)

Here are the results.

*(source: Portfolio Visualizer)*

**Based on 5000 simulations, 1275 simulations survived the withdrawals hence giving a success rate of 25.65%.**

At a glance, you could get essential information like the rate of return, max drawdown etc at different percentiles (10th, 25th, 50th, 75th). Since the success rate is 25.75%, it's no wonder that the max drawdown for 10th, 25th and 50th percentiles are all 100% (representing failure of the portfolios as these percentiles successfully survived the withdrawals). This also means that you would need the real rate of return of the portfolio to be around **8.79%** (see 75th percentile) to be successful. This do seems to be a bit high as compared to S&P 500 past performances.

You might also like to focus on the safe withdrawal rate and perpetual withdrawal rate here. Out of these two, perpetual withdrawal rate is the more commonly used one for retirement planning as it is the rate which preserves your inflation-adjusted principal sum in all scenarios. The safe withdrawal rate only ensures that you will not run into a negative sum but does not ensure you preserve your inflation-adjusted principal sum. **At 75th percentile, the perpetual withdrawal rate is 8.08% which means that you are free to withdraw this percentage of your portfolio annually as long as your real rate of return is 8.79%**.

*(source: Portfolio Visualizer)*

The results from the simulations are quite extensive as you could even get to understand the expected annual return of your portfolio at different time periods (1 Year, 3 Years, 5 Years etc) and different percentiles. This gives you some expectations on how your portfolio should be performing based on these factors from a statistical point of view. You could even see what are the probabilities for the various rate of returns in these different time periods. Definitely some good data to have here.

All in all, I do strongly feel that this tool provided by Portfolio Visualizer is great for anyone who wants to set up some financial/retirement goals and understands what his/her chances of success are like. This could help you in managing your expectations (eg. delaying your withdrawal at a later age or reducing your withdrawal amount). Going through these simulations allow you to understand the importance of allowing sufficient years for your portfolio to grow before you start making withdrawals and hence further reiterate the importance to start investing early.

Information/data provided in this tool is also very comprehensive and definitely cover more grounds than what I did in my earlier analysis 10 months ago. Moving forward, I will be constantly using this tool to chart my success in achieving an early retirement. I hope it could be a great tool for you guys too.

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