## Introduction to Robust Statistics in trading

*Robust statistic in trading most often is referred to as a robust statistical unit of measurement of a certain performance criteria of a trading plan.*

*Robust statistic in statistics is referred to as statistic with good performance when data can vary drastically. These statistics are very resistant to outliers (In statistics, an outlier is an observation point that is distant from other observations. (Outlier (Wikipedia))*

Just the fact that you opened this blog post tells me that as a trader, you already understand, that statistics is the key to winning in the game of trading. If, however, you do not understand that yet – then whatever miracle lead you to this post, you should thank it… because it lead you to the right place!

Either way, whether you are new to statistics altogether, or are already trying to introduce it to your trading, I’m sure you will leave with a great deal to think about.

Now before we start I want to run ahead and note one thing. Below I provide a hypothetical example of trading performance to better illustrate the power of robust statistics. Units I am using for the illustration are CAGR% (Compound Annual Growth Rate %) and RAR% (Regressed Annual Returns % – a robust equivalent of CAGR%). While CAGR% can be calculated by only having the starting and ending account size values and a look back period, RAR% is way more complicated and requires to have a full P&L curve of said period to calculate. Therefore in the example below the % given of CAGR% are actual CAGR% values of such trading performance, but RAR% values are only hypothetical values that were not calculated because I did not set up a full P&L curve of the example given. However, from my experience, these are more or less accurate numerical comparisons of the two units of measurement.

The reason I am not providing actual data, is because this is only an introductory post into Robust statistical measurements, I did not want to get too technical in this post and wanted to only help you understand the potential benefit of using robust statistics over their non-robust equivalents.

In the upcoming blog posts I will be reviewing RAR% (and other robust units) in extreme detail and will explain how you could calculate RAR% if you have a full P&L data yourself. There you will find actual samples of this unit and not just hypothetical numbers.

Let’s begin. As stated above, a robust statistic in trading most often is referred to as a statistical unit of measurement of a certain performance criteria of a trading plan. Most often it will be an improved version of an already existing measurement of trading performance (such as, let’s say, a Sharpe ratio).

**Why do we need Robust statistics if we already have standard units of measurement?**

The problem with standard measurements of trading performance is that they depend too much on the period of trading that is overviewed.

Imagine you are using a particular trading plan for two years. The trading plan performs very well the first 18 months and gains 30% profit, but then the last 6 months it experiences a drastic drawdown of 35%. Now you gave this trading plan a 2 year test run to see how it performs, and the time has come to evaluate it.

So you calculate the Compound Annual Growth Rate % (CAGR%) and find it to be roughly -2.5%.

These results do not shine – you think… and so you decide not to pursue this trading approach anymore.

Now let’s imagine you were a smart cookie and did not give up on the trading plan just after seeing the CAGR%. You instead found out about these fancy robust statistics and calculated yourself a Regressed Annual Return % (RAR%) and figured out, let’s say, that your RAR% is actually 8% (hypothetical). Now 8% per year is not a miracle but it is definitely better than -2.5% and it might actually make you consider following this same trading plan and seeing where it gets you.

**How can the results be so different, and why should I trust the RAR% over CAGR%?**

The RAR% actually draws a better picture of the trading performance, as the logic behind the value makes it a lot more immune to the period of look-back, therefore the huge drawdown of 35% has less of an impact on the ending % of RAR because, RAR also considers the way the trading was going in the first 18 months as well. And seeing as it made 30% in 18 months steadily and only experienced a drawdown in the last months RAR shows a statistically better % as of what could actually happen in the future if you keep using this trading plan.

Now as to why you should trust RAR over CAGR – imagine that your period of testing this trading plan was 18 months instead of 2 years. You do not have all that huge drawdown that happened in the end, therefore your CAGR will roughly be a whopping 16%. A huge change of 18.5% (from -2.5% if testing period was 2 years), and you only eliminated 6 months (25%) of your look-back period. Now what would happen to RAR%? RAR would most likely jump from being 8% to maybe around 10% (hypothetical).

Using Robust Statistics over their non-robust equivalents can help you see a clearer picture of the future when it comes to analyzing a performance of a particular trading plan.

This is only an introductory post into Robust Statistics, over the coming weeks I will be going into detail and explaining each robust unit of measurement you can benefit from. With actual samples and formulas. I’ll even try and include actual excel spreadsheets you could use to automate the calculation of these things.

P.S. trying to find more info online about these robust statistics (such as RAR%, R^{3} or Robust Sharpe ratio) can prove to be a challenge, as for some reason nobody is talking about them… <I wonder why?…>

So if you want to be notified, when I upload a new blog post overviewing a new robust unit, put your email in the box below, and ill make sure to send you a message once a new post is up.

Best,