Fundamental Mathematics for Trading

Mathematics is not everyone's favourite subject but it is essential, even in everyday life. Don't worry, it is not rocket equations but learning Mathematics for Trading is like knowing how to count apples in a grocery store. We believe that a lot in this article will be beneficial to you.

Table of contents

  • Risk Calculation
  • Trading Stats
  • Broker Fees

Risk Calculation

I believe that every trader should know how much they are willing to lose before entering a trade. By knowing how much you are willing to lose and knowing when you'd get out of the market if a trade goes against you, we can adjust our position size accordingly.

Example: EURCAD

EURCAD Long Idea by FTMO on TradingView.com

 

This is our recent trade idea on the EURCAD. Make sure to follow us on TradingView to not miss any trading content that we post regularly. In the chart, we have determined an entry point and the exit point (Stop-Loss) if the trade goes against us. In order to calculate the ideal position size for this trade, we require 2 things:

  • Distance from Entry Point to Stop-Loss
  • Currency Pair we want to trade
  • Amount of money we are willing to risk

Determining the Distance is taking the difference between the entry and exit prices, which is 1.46705 - 1.45695 (values taken from the chart). The difference is 0.0101 or 101 pips.

The currency pair is EURCAD.

Let's assume that we want to risk 1% on a 100.000 USD account on this trade (1.000 USD). One of our partnered broker - GBE Brokers offer the so-called Position Size calculator, which will give the position size, so that you risk the exact specified amount on your trade.

You can freely access the Position Size calculator here: https://gbebrokers.com/tools/position-size-calculator/ 

If the Account Currency is different from the Base Currency of your traded pair, simply copy the exchange rate from your platform to the calculator to add this information.

We have now set a position size for our trade. The trade on the EURCAD with a Stop-Loss set 101 pips away from the entry point should have the position size 1.31 lots such that we risk a maximum of 1000 USD on this trade. This, however, doesn't include commission (if any) and spread so you'd probably have to round down to 1.30 lots.

 

Trading Stats

FTMO's Application Account MetriX provides the trader with very useful stats. We recommend that traders should know how these stats are calculated and what they mean.

RRR - Reward to Risk Ratio

RRR is one of the fundamental stats of a trader. It describes the ratio between the trader's average earnings and average loss. Assume your RRR is 2:1. That means that your average earning is twice as big as your average loss. Or in other words, for every dollar you risk, you have the potential to make 2 dollars.

Formula: RRR = average Profit per Trade / Average Loss per Trade

Average Profit and average Loss can be taken from the Account MetriX. Learn more about our Account MetriX here: https://ftmo.com/en/get-account-metrix/ 

Using the stats above, our RRR = 761 EUR / 348 EUR = 2.18. Therefore, for every Euro we risk, we have a return potential of 2.18.

Win Rate 

The Win Rate is the second fundamental figure of a trader and the easiest to understand. Whenever you enter a trade, how much on average should you expect to win on a trade? If your Win Rate is 50%, then every second trade should be a winner. If it is 67%, then every 2 out of 3 trades should be winners.

Formula: Win Rate = number of Profit Trades / number of Loss Trades

Expectancy

Expectancy is the figure which tells you how much money you should expect to win on average. We will start with the Formula first.

Formula: Expectancy = (Average Win * Win Rate)  -  (Average Loss - Loss Rate)

By knowing how often you win and how much you win as well as how often you lose and how much you lose, you can project the future performance of your trading system which tells you how much you can earn on average per trade.

Your RRR and Win Rate is not correlated which means that you can have a low RRR but a high Win Rate and be profitable or you can have a high RRR and low Win Rate and be profitable.

If Expectancy is greater than 0, your systems should generate profits. 

Let us use the values from the Account MetriX above to calculate our Expectancy.

  • Average Win = 761 EUR
  • Average Loss = 348 EUR
  • Win Rate = 42%
  • Loss Rate = 1 - Win Rate = 58% 

Expectancy = (761 EUR * 42%) - (348 EUR * 58%) = 319 EUR - 202 EUR = 117 EUR

In this example, our expectancy is 117 EUR which means that on average, we can expect to earn 117 EUR per trade on average. You can also try FTMO's Equity Simulator to project these values graphically. Our Equity Simulator will input your current trading results by default.

This Equity Simulator simulates hypothetical future trades based on your current stats. If you want to find out more about Equity Simulation, visit my free Webinar recording at: https://www.youtube.com/watch?v=-rGmFuQCiNc&t=7s 

Webinar: Randomness and Probabilities in the Markets

Broker Fees

Lastly, let's talk about broker fees. We want to make traders aware of how much they pay in commission and give them a better picture of their money flow on the accounts.

% give giveaway on a trade

Each time you open a trade, you will pay the Spread and based on your Account Type, commission per lot as well. FTMO offers a great Application - Broker Review where the brokerage commissions are compared side by side in real-time.

When choosing a broker, don't just look purely at the spread, but at the commission as well. Broker Review will convert the Commission per Lot structure to overall costs.

Looking at IC Markets Raw Spread Account, you are paying 0 spreads but 7 USD per lot round turn for the transaction. This is effectively the same as trading EURUSD with 0.7 pips in Spread and 0 commission. Please bear this information in mind.

Now, how much are we giving away to the broker if you have a 10 pip target on IC Markets Raw Spread account on the EURUSD?

If you are targeting 10 pips, you are giving 0.7 pips in commission which is 7% each time you open a trade. Some traders are not aware of that which is one of the main reasons why traders lose money with short-term trading.

The story changes if you are now targetting 100 pips. You are now giving away 0.7% of your profits to your broker. Of course, we have to add swap rates etc., but the fees are significantly lower on higher timeframes.

Formula: Fee % = overall costs (in pips) / target distance (in pips)

Therefore, depending on the overall cost of a specific instrument, please think about the money you are giving to your broker before you decide to enter a trade.

Final Words

I hope that you liked this article and that it brought some added value. If you have any questions on the Maths, you can contact me on khactu@ftmo.com. I will be very happy to explain it to you in detail. Take care and happy trading!