Monthly return simulation for S&P 500 Index – (Monte Carlo Simulation)


AGNO focuses on producing investment strategies for active trading which is a high risk/reward approach. I am conscious that not everyone has the knowledge or time to implement such strategies, nor the risk profile to do so. Having this in mind, I wanted to present a simulation I run some time ago that shows how a diversified index (S&P 500) has lower chances of negative returns the more time you are willing to hold the position. In other words, in the long run a well diversified stock portfolio seems to have lower chances of loosing money which is the main point of worry regarding the stock market.

For anyone that wants to see a more detailed report. Check out the article I wrote about the topic.

After finding a probability distribution that could model monthly returns for the S&P 500. It was simulated the behavior of an investment for 1, 3, 5, 10, 20, 40 years (100,000 times per time frame). The results are as follow (2% annual inflation considered):

  • Probability of negative results (negative result cases over total cases):
    • 1 year: 37%
    • 3 years: 30%
    • 5 years: 26%
    • 10 years: 18%
    • 20 years: 9.7%
    • 40 years: 3.4%

This simulation is just an approximation and does not represent with 100% accuracy the real behavior of the stock market. However it shows that regardless of economic crisis or recessions the overall slope of the market is positive. With a fairly good chance holding a diversified stock portfolio in the long run will have positive results.

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