This is the second part of the **technique** to know if our **investments** are **profitable**. In the previous article detailing how to use Excel to **analyze historical results**. In this one, we will check **Montecarlo’s** **distribution** of the **results**, which will allow us to know the **probability** that the results will be **repeated** in the future.

As before, we will use historical data from an earlier version of Slowinver as the basis for the **study.**

We already verified that the system obtained an annual profitability of the order of 29% and a **maximum streak** of losses of 15%, a very good result.

The million dollar question is: Will these results be **repeated in the future?**

One way to find out is to apply a **Monte Carlo test.**

The idea of Montecarlo is very simple, let’s see it **with an example.**

Suppose we use an investment method that **obtains** these results in 21 days:

**Example montecarlo slowinver**

In the data on the left, we can see that up to day 17 (in yellow) we get a cumulative 5.19%. And after the 21 **operations,** **6.6**%.

In the data on the right, we randomly **randomized** the days. Since the results are the same, the final result is still 6.6%. However, on day 17 loses 3.4%, e.g. 8% worse than the original day 17.

The reason is that the sequence of **operations** until day 17 is worse in the 2nd case, and the two **results tables** are, in principle, just as likely.

The idea therefore of the proof of Montecarlo is to make these **disarrangements**, not once, but hundreds or thousands of times. Each one of them will give us a different result curve in the **intermediate terms;** The typical Monte Carlo chart looks like this:

- All benefit curves are
**disordered outcomes,**that is, they have all the same basic statistics in terms of mathematical hope, probability of**success, volatility,**etc., and are all**equiprobables.**Although only one of them is the**original data curve.** - The dispersion of the different lines gives us an idea of the
**possible future deviation**of our results from the past results. Therefore, the smaller the deviation of the**Montecarlo analysis,**the better.

I have applied Montecarlo to the historical results of 11 years of the system, messing it up 1000 times. Thus, I get 1000 result **curves,** and each represents the 11 years.

However, it has never seemed very practical to me to represent a graph of curves like the **previous example.** Instead of displaying graphs 1000, we will study their frequencies results in a **histogram,** just as we did in the previous article

. Thus we will see how many graphs of 10 years return a **profitability** of -5%, how many of 0%, how many of 5%, how many of 10%, etc.

Therefore, unlike the previous article, this histogram is not a daily result, but results from 1000 Monte Carlo **tests.**

**In The horizontal x** – axis shows the annual compound return (CAR) as by 1. That is each value, the **average annual** result of 11 years of operations .

**The lowest value is 0.90 e.g**. -10%. The value 1 means to stay abreast. The highest value is around 1.95, which for 1 means 95% annual **return average.**

Between the two extremes there are 998 yields **averaged annually.**

The most common profitability (fashion) is around 32% . Although the average arithmetic of all Monte Carlo simulations is a return of 28%, very similar to the result of the **original curve.**

Summary-slowinver-CARIn addition to the average, we can draw other **conclusions** from this **Monte Carlo,** analyzing the pink line of cumulative probability. We can highlight these 3:

The system is profitable in a year with a 95% : the number Montecarlos ranging between 0% and 100% return.

The system obtains yields acceptable or even better (above 14%), 77.5% of the years, more than 3 out of 4 years.

The system obtains yields **extraordinary** (over 40%) 24.7% of the year (1 in 4)

The study, therefore, of the **histogram** allows us to have realistic expectations.

But although returns are interesting, it is also important to look at the **maximum Drawdowns** ( draw down ). The chart of loss ratios of the 1000 simulations of **Montecarlo** is:

**Montecarlo-slowinver-DD**

The smallest **“worst losing streak”** (Max DD) is 0.04 (4% losing streak), and the maximum, 22%.

Recall that each value represents the worst losing streak in **almost 11 years.**

Again, we obtain **conclusions regarding** the expected DDs:

The average **maximum losses** spurts is 9.1% , a very tolerable figure.

We can infer the DD of the future. With a **reliability** of 95%, they will be **between** 3% and 17%.

Overcoming the 20% of DD occurs 1.5% of the **years,** one year out of 66.

So in any investment there is risk, but the Montecarlo test gives us a pretty rough idea of what that risk is. Ultimately any investment is a matter of numbers, which we **must analyze.**

There are other studies to check the reliability of systems, but this spreadsheet will allow us to know in depth an investment method without devoting excessive time or very **complex programs.**

Since the sheet is based on daily results, we can enter results of any asset or investment method. For example, many funds allow you to lower your **daily results** from your web pages. By copying and pasting that data into the sheet, we will have a more accurate **knowledge** of its **reliability.**

**Example Excel**

I have done it with some well-known backgrounds, with certainly **surprising results.**

If these tips help you in your investments, you are invited to comment on them in this **article,** or on **Twitter** or **Facebook.**