Monte Carlo Simulation


Monte Carlo algorithms combine a large number of historical returns from the stock market in a random order. This one combines over the last 45 years, you can select from 45 years of backtest data, or live data, or the market data over 45 years.
When done enough times, it can give a picture of the possible future. This is used for deciding if you want to mix assets.
Here we are taking just a few of the top earning stocks and expecting gains like those stocks in the next few years.
Data Set (7 year live data vs 45 year backtest S&P data):
Number of Runs:

Number of Periods each run: Reset:

Periods are 3 months, 12 periods would be 3 years.
Live – data from the last 7 years of live testing.
45 years – the top S&P stocks since 1985 by the custom value function.
Or you can combine them.
You can run it up to a million times, and view the spread of results in the histogram below.

What is a Financial Analysis?

A financial analysis is one tool financial analysts use to determine what kind of gains can be made from an investment. In this case, we are looking at the value system that has live results over the last 7 years. Applying this to the S&P stocks since 1985, we get a spread of likely gains for a conservative use of the algorithm.

Imagine you started investing today, how would you know how much money you would have in 3 or 5 years? The assumption here is that most of the periods of stock market returns in the next 3-5 years will be somewhat like the periods in the past 45 years. Maybe next year will be like 2009, or like 2006. The system picks a year at random, then another, and slices them together to get a gain. Since we can’t count on any one run being accurate, we run a million times and average them together, and look at how each performed.

Using live data and 3 years of returns (12 periods), a million runs shows a 7.5% chance of a loss, and a 60% chance of gaining more than 100%. That may be because the last 7 years have been good, so good that you may not believe the next 5 years can match it. So you can use the 45 years of historical data instead.

In conclusion, the monte carlo approach gives us many things, it gives us an array of possible futures, and a way to calculate possible future returns. It does not guarantee that your particular future will be within the boundaries. Over time the gains from monte carlo simulations usually will mirror the gains from the future stock market over the long term. (Regression to mean). The best lesson is to look at long periods and their positive results vs. short periods and their very random results. As with most stock investment strategies, you will find the lesson here is to “stick with it.” and to try to keep yourself invested in the stock market especially during a downturn.

Below, please see the monte carlo comparison between the percentiles of gains from “average market” which is like an index fund, and the value investing. Note how the gains are almost double in value investing. In fact, the gains from the topmost investment in an index fund is about equal to the average gains with the value investing!