One of the important things in trading is understanding from a probability perspective what is likely to happen, when you actually use your trading system over time.

**Why is this important.**

If we do not understand what results the trading system is likely to produce, then we cannot answer the following questions when we review our trading.

Does my system still have an edge?

Is any under performance of the trading system down to variance or is it the trader underperforming?

**What do I mean by that?**

The best way to explain this is to use an example.

We have a trading system that has win rate of 50%. The average winners are 1.5 bigger than the average losers, and we risk 1% of our account.

First let’s look at the probability of having a losing streak. There is a 76.8% chance of having 5 losers in a row.

If you were using this trading system and did not know that there is a high probability of having 5 losers in a row, then when this happens the first reaction could be the system has no edge and start looking for a new system.

Or the reaction could be that I am trading like shit and need to sort my trading out.

The above statements could be true, but having 5 losers in a row with this system is not an indicator of either of these statements.

**Is the next trade going to be a winner?**

It took me a while to understand this, but we do not know probability of the outcome of the next trade.

If we have a trading system that has a win rate of 70%, the next trade does not have a 70% chance of winning. The win rate does not refer to individual trades but to a sample size. Having a win rate of 70%, says that over a large enough sample of trades, 70% of the trades will be winners.

So what is the probability of the next one to be a winner. The answer is 50%. Why 50%, we cannot tell what order the winners and losers are going to come. So we do not know the outcome of the next trade, we just know that if we follow our trading system, that over time we will have 70% winners.

And the fact that we do not know what order the winners and losers will be in the sample size, we only know the overall percentages.

This means that over a large sample size, the actual return on the account balance can be different.

**Using Monte Carlo to understand the variance in our trading system.**

What is Monte Carlo? Here is the an article that explains it better than I could.

I am using Monte Carlo to simulate a trading system over a 500 trade period and what effect that will have on the account balance. But as we do not the outcome of each individual trade, the order if winners / losers are randomised.

I then rerun the simulation for another 50 times, and this gives me a range of returns.

The best way to look at this, is that we are comparing the returns of a trading system over 500 trade period against the same trading system x 50.

This is a trading system with a win rate of 50%, winners 1.5 r , losers 1 r and risk per trade 1% of account balance. Starting account balance is 10000 USD.

1. Across the 50 simulations, the worse draw down was 66%.

2. The highest finish account balance was 51,219 USD

3. The lowest finish account balance was 19,854 USD

Whilst the trading system is profitable, that actual returns are different, and different by 31,365 USD.

**How do I use this information?**

Every quarter I enter the previous quarters system stats into the spreadsheet, including the average number of trades per day. This will then give me likely figures for the variance in expected returns, I then break this down into months and weeks.

Once I have these figures, I use these in my end of week reviews to see how I am performing against the theoretical system. Thus giving me a benchmark range to compare my actual performance against.

I have included the excel spreadsheet at the bottom of the article so that you can run your own stats.

Here is a quick video on how to use the spreadsheet.

Here is a copy of the spreadsheet.

Critical stuff that nobody talks about! Thanks for sharing!!

Thanks for your comment. I try and share what helps me, and hopeful that helps others. #tht

Hi Adrian

First time for me in your blog. Thanks for this fantastic explanation and tool!

Hi, Thanks for the comments. Traders helping traders #tht

Great post. Most traders never talk about this. Probably because most traders never trade big enough to be called real traders.

I think the general term is statistical dispersion rather than variance although it pretty much means the same thing in common usage.

Also if you trade a 70% profitable system the probability on each trade is 70% not 50%.

Think about it with a 99% winning system, the odds of the next trade being a winner are clearly not anywhere close to 50%, its clearly 99% on each trade.

However as there are only 2 outcomes, so it can somtimes seem like the odds are 50/50 for that reason.

Thanks for the comments. I agree and disagree with you on the 50/50 thing. As most inexperienced traders are viewing the next trade a single event, a sample size of one. Then the only outcome is 50/50, if we view the trade as part of a larger sample size then I would agree with.

I was trying to demonstrate (not particular well) that as we tend to view trades as singular events and only look back over the sample to get the win rate etc, and we do not know the order of the outcomes. Then it is best to view each individual trade as 50/50, to avoid anticipating the outcome before placing the order.

Regards

Adey