# Monte Carlo Portfolio Simulation

### What is it?

Monte Carlo portfolio simulation is used by financial and investment advisors to approximate the probability of portfolio returns. It allows these professionals to simulate portfolios using different market conditions and investor preferences.

### How Does It Work?

It is important to understand that while returns of stocks, bonds or other asset classes seem to be random on a monthly or yearly basis, in the long run unique patterns emerge. For example, the annualized return of large-cap stocks is 10.19% (S&P 500 index, 1926-2015). On the other hand, the annualized return of small-cap value stocks from is 13.75% (Dimensional US small value index, 1928-2015). Finally, the annualized return of gold is 7.12% (London Fixings, 1968-2015).

This suggests that if we pick enough number of random values from the returns of a particular asset class, it won’t be so random – it will be meaningful. That’s exactly what Monte Carlo simulation does. For every year of the portfolio, a historical return is randomly picked for every asset class making up that portfolio. This process is then repeated for the lifetime of that portfolio. Image below shows how a portfolio is randomly populated with historical S&P 500 returns.

Surely, only one portfolio built in a vacuum doesn’t mean anything. Monte Carlo tool builds and simulates hundreds of portfolios so that the data set is large enough to make meaningful assumptions from.

Two of the most commonly used scenarios in this simulation are growth and withdraw.

### Growth Case

Here is an example: Maria is 30 years old and she has \$50,000 dollars in her 401(k). Her portfolio consists of large-cap stocks (S&P 500) and intermediate-term bonds (10-yr treasury) – 30% and 70% allocation respectively. She is committed to adding \$10,000 to it every year. She wants to retire at age 65 which is in 35 years. When she reaches that age, how much is she going to end up with?

Using Monte Carlo Pro, we quickly can answer this question.

Monte Carlo Pro simulates 1000 portfolios just like Maria’s. When done, it shows the graphs for 75 percentile (when sorted by portfolio ending balance, 750th portfolio – an optimistic case), median (500th portfolio – most-likely case) and 25 percentile (250th portfolio – pessimistic case) portfolios. Looking at the median portfolio, we see that it finished simulation with \$1,463,429. Not too bad, huh?

### Withdrawal Case

How long can Maria survive on \$1,463,429? To be more specific, can she afford to withdraw \$60,000 for 30 years from her portfolio which consists of 35% large-cap stocks (S&P 500) and 65% intermediate-term bonds (10-yr treasury)?

This is not that different from the growth case above. This time, instead of making annual contributions, we are making annual withdrawals from the portfolio.

It is not looking so good for Maria. While the median portfolio ended up with \$61,291, only 53% of the portfolios ended the simulation with a positive balance. This means that 470 out of 1000 portfolios had no money left in them on or before the 30th year. So much for a million dollar in retirement…

### Conclusion

Hopefully this simulation technique will give you a better idea of how your portfolio will turn out in the future. While Monte Carlo simulation is very powerful, please do not make any finance decision based on Monte Carlo simulation results only. No single tool can be used to design all-weather portfolios for long-term financial success.

You can download Monte Carlo Pro here. By the way, we are its developers and we’d love to hear your feedback.

### Assumptions

As you can see in the screenshots, for Maria’s portfolio we assumed that:

• Portfolios are rebalanced at the end of every year – if necessary.
• Inflation is set to 3%.
• Expense ratio for the funds used are set 0.20% (Did you notice in the growth scenario alone Maria paid over \$41,000 in fees?).

## 11 thoughts on “Monte Carlo Portfolio Simulation”

1. Meggy Carr says:

Sounds like one million \$\$\$ in retirement isn’t much after all especially if you live in NY like I do. I need to get a second job or something.

1. Berk says:

We live in San Francisco bay area and cost of living is also costly.

2. Wayne says:

This article a bit too technical for me but I get the point. I can have more bonds in my portfolio and still retire comfortably.

1. Berk says:

Thanks for feedback Wayne. We’ll try to make it easier to understand from now on.

3. Atsuko says:

How can I get this app on my iPad?

4. Berk says:

Hi Atsuko – iOS version is not available yet but we are working on it. It should be released by the end of this year.

5. Omar M says:

Hi. Can you add commodities to your app? I’d really like to use oil and gas.

1. Berk says:

Hey Omar – We already have commodity asset class available. It’s under the “Alternative” section with REIT and gold. It uses Bloomberg Commodity Total Return Index (1992-2015). That asset class includes gas and oil along with many other commodities, such as corn, soy bean, silver and copper.

6. Sri says:

Any plans to add individual stocks to this? I would to see how my portfolio would have performed if it was 50% Walmart and 50% Ford. Also, how about adding major sectors as asset classes, such as: utilities, financials, energy, and etc, etc… Thanks.

1. Berk says:

Hey Sri – Adding sectors is on radar for the next release but we are not considering adding individual stocks in the near future. Thanks!

7. Tom Brice says:

Do you have a version available for commercial use? Would you consider licensing?