For many of us, math has never been our greatest strength. In fact, the mere idea of using math formulas for trading is something that garners fear in many traders.

In this lesson, we will be discussing some of the more important math formulas that every trader should learn and have a good understanding of if they want to succeed in the market. But the good news is that most of these trade related math concepts are actually fairly simple and easy to understand even for those that are mathematically challenged.

### Pip Values

Movement in currency pairs are measured in pips. Within the currency exchange rate, the minimum pip can be seen in the fourth digit after the decimal place for most currency pairs. The exception to this rule are Yen pairs wherein their minimum pip can be seen in the second digit after the decimal place.

For example, if the EUR/USD currency pair rises from 1.3510 to 1.3530, that would be considered an increase of 20 pips for the EUR/USD pair. And on the other hand, if the USD/JPY currency pair rises from 95.10 to 95.40, that would be considered an increase of 30 pips for the USD/JPY pair.

Depending on which currency pair you are trading, the value of a pip will be differ. It is also important to note that a standard lot is 100,000 units of a currency. A mini lot is 10,000 units of a currency, and a micro lot is 1,000 units of a currency.

You can use the forex math formula below to calculate the pip value of a currency pair:

Value of a pip = 1 pip / exchange rate x trade size

Here is an example using EUR/USD

- One Pip = 0.0001
- Base Currency: EUR
- Exchange Rate: 1.2500
- Trade Size: 100,000 ( 1 lot)

Pip Value = 0.0001 / 1.2500 x 100,000

= 8 EUR

Here is a second example using USD/JPY

- One Pip = 0.01
- Base Currency: USD
- Exchange Rate: 95.50
- Trade Size: 100,000 ( 1 lot)

Pip Value = 0.01 / 95.50 x 100,000

= 10.47 USD

And a third example using GBP/CHF

- One Pip = 0.0001
- Base Currency: GBP
- Exchange Rate: 1.3220
- Trade Size: 100,000 ( 1 lot)

Pip Value = 0.0001 / 1.3220 x 100,000

= 7.56 GBP

### Margin and Leverage

Many novice forex traders tend to confuse margin and leverage. Though they are closely tied, you should understand the difference between the two, and know how to calculate each.

So, what is leverage in trading? Leverage gives a trader the ability to control a larger position by using a small portion of their own funds and borrowing the rest from their broker.

What is Margin? Margin is the good faith deposit required by your broker to allow you to open a position. Using these funds coupled with other client funds, the broker can then place trades with their liquidity providers and interbank partners.

Leverage can be calculated using the forex trading math formula below:

Leverage = Trade Size / Account Size

Let’s take a practical example to demonstrate this.

Say you decide to enter into a position in a financial instrument with a notional value of $100,000. You only have $ 2,000 in your trading account. So, you would be controlling $ 100,000 with the $ 2,000 that you have.

Leverage = $100,000 / $2,000 = 50

So, the effective leverage in this example would be expressed as 50:1

Now let’s say you decide instead to enter into a position with the same notional value of $100,000, but you have $ 5,000 in your trading account. So, you would be controlling $ 100,000 with the $ 5,000 that you have.

Leverage = $100,000 / $5,000 = 20

So, the effective leverage in this example would be expressed as 20:1

Brokers in the United States offer upto 50:1 leverage for forex trading, while Forex brokers in other jurisdictions can offer leverage upto 500:1 in some cases. But is very important to keep in mind that leverage should be used responsibly as it acts to not only amplify returns, but also magnifies losses.

### Position Sizing

Position Sizing is one of the most important and frequent calculations that you will need to make as a forex trader. In fact, before any trade that you consider entering into, you should calculate the proper position size based on your pre-defined position sizing model.

One of the simplest and most effective position sizing models is a fixed fractional model. With this position sizing strategy, you would risk a maximum of X% of your trading account on any single trade. I would suggest 1 – 2% risk per trade as a good value for the fixed fractional risk.

Once you have determined how much you plan to risk on a per trade basis, then you would start by determining where the most logical stop should be placed on a particular trade. You should look at where the most recent swings are, where Support and Resistance areas are and/or use some other technical considerations. One you have located a level where you plan on placing your stop loss, measure the distance in pips between this level and your intended entry. Then jot that number down and keep it handy.

Now the next step is to determine the value of each pip. We have discussed how to calculate the value of a pip in the previous section. Once you have this value, you are ready to calculate your position size.

Here is the trading math behind Position Sizing:

Current Account Size x Risk Per Trade / Distance between Entry and Stop x Value of Pip

Let’s take a look at concrete example:

- Current Account Size: $ 10,000
- Fixed Fractional Risk Per Trade = 2%
- Distance between Entry and Stop: 80 Pips
- Value of each Pip: $ 10

$ 10,000 x .02 / 80 x 10 = .25 Lots

So, in this example, based on our $ 10,000 account with a 2% risk per trade model, and placing a stop at our desired location, we would be allowed to take a maximum position size of .25 lots on this trade.

### Trade Expectancy

Trade Expectancy is one of the most important metrics that a trader should be aware of. But what does it mean? In a nutshell, trade expectancy is the average profit or loss that can be expected on each trade based on your average Win Percentage, Avg Win Size and Avg Loss Size.

Here is the mathematical formula for Trade Expectancy:

( Win % x Avg Win Size) – ( Loss % x Avg Loss Size)

Let’s take a look at this more closely using a Trend following system. Typically trend following systems tend to have low win rates, but relatively large average wins compared to average losses.

- System Type: Trend Following
- Win Percentage: 35%
- Avg Winning Trade : $ 1200
- Avg Losing Trade : $ 400

Let’s plug in the numbers:

Trade Expectancy = ( .35 x 1200) – ( .65 x 350)

= $ 192

So, this trend following system has a trade expectancy of $ 192, which is the average expected profit from each trade.

Now let’s look at yet another example. This time we will look at a Mean Reversion strategy. Mean reversion strategies tend to have higher win rates, and the average wins and losses are somewhat similar.

- System Type: Mean Reversion
- Win Percentage: 60%
- Avg Winning Trade : $ 575
- Avg Losing Trade : $ 525

Let’s plug in the numbers:

Trade Expectancy = ( .60 x 575) – ( .40 x 525)

= $ 135

So, this Mean Reversion system has a trade expectancy of $ 132, which again is the average expected profit from each trade.

Many traders make the mistake of only relying on win rates when evaluating trading systems. But as you can see, based on the trade mathematics of the Expectancy formula, win rate is only part of the equation, and you must also take into consideration a system’s Avg Win and Avg Loss numbers to truly realize the edge that a system provides.

### Currency Correlation

How many times have you entered positions in multiple currency pairs and noticed that their price movements were related? For example, if you are long in EUR/USD, GBPUSD, and AUDUSD you may think that you have three unrelated positions but in fact, it is as if you have just one big position against the US dollar.

To understand this better, you have to know what currency correlation is and how it can impact the overall risk in your portfolio.

Currency correlation is a statistical measure of how different currency pairs move in relationship to each other. Currency correlations can be positive, meaning that two currency pairs move in the same direction. Currency correlations can be negative, meaning that two currency pair move in opposite directions. And finally, currency correlation can be neutral, meaning there is no discernible price relationship between the two currency pairs.

The forex mathematics behind currency correlation can be quite complicated, so we will not get into that in this lesson. But fortunately for us, we do not need to know the trade math because there are many currency correlation tools available in the market that makes it easy for use to do our correlation analysis. Most currency correlation tools are presented in a table format.

The following summary provides a fast and easy way of interpreting a currency correlation table’s values.

- 0 to 0.2 – There is no correlation
- 2 to 0.4 – Low or weak correlation
- 4 to 0.7 – Moderate correlation
- 7 to 0.9 – High or strong correlation
- 9 to 1.0 – Extremely strong correlation

Remember that a positive value means that the pairs move in the same direction, while a negative value means they have an inverse relationship.

### Maximum Drawdown

As traders, we know that we will have losing trades and that they are a natural part of trading. But it is important to know what our strategy’s maximum drawdown has been historically so that we can have some ideas of what we might expect in terms of equity loss in the future.

Essentially, maximum drawdown is the maximum loss in equity that our portfolio incurs over a period of time. It is the largest drop from a previous equity peak to the lowest point after the peak. We can calculate the maximum drawdown after a new peak has been put in place on the equity curve.

Here is the math formula for calculating Maximum Drawdown:

Max DD = Equity Peak – Equity Low / Equity Peak

Let’s take an example:

Say that you have a starting balance of $ 10,000, and it increases to $ 15,000. Later on, your account falls to $ 8,000 and eventually increases to $ 17,000.

What is your Maximum Drawdown in this scenario?

Max DD = $ 15,000 – $ 8,000 / $ 15,000

= 46.6%

So, the Max Drawdown in this case is 46.6%.

Drawdowns can be very dangerous to the financial health of a trader because, as your drawdown increases the return needed to recover becomes larger and larger.

Let take a look at the table below:

Capital Loss (%) Gain need to Recover (%)

5 5.3

10 11.1

20 25

30 42.9

40 66.7

50 100

As you can see, the larger the max drawdown or capital loss the higher the percentage gain is needed to recover the losses. For example, to recover from a 50% loss you need to make a 100% gain. This is one reason why it is critical for traders to trade small so that they can try to keep drawdowns to a tolerable level.

### Risk of Ruin

I would venture to guess that most retail traders have either never heard of Risk of Ruin or if they have they do not really understand its power when it comes to risk analysis in the markets.

Risk of Ruin is the likelihood or probability that a trader will lose a predetermined amount of trading capital wherein they will not be able to continue trading. Many traders assume that Risk of Ruin has to mean loss of 100% of capital, but it does not have to. It could be any percentage that the trader determines will be the point at which they will stop trading a system. It could be 25%, 50%, 75%, 100% or whatever loss level the trader decides on.

The Risk of Ruin is calculated as follows:

Risk of Ruin = ((1 – Edge) / (1 + Edge)) ^ Capital Units

Where Edge is the defined as the probability of a Win or the Win%.

There are several simulators available for free that you can use to calculate the risk of ruin.

The one we will use in our example can be found here

So, let’s look at a strategy that is just barely profitable to see how we can greatly reduce the risk profile of such a strategy. We will use the following assumptions and plug that into the Risk of Ruin simulator:

- Probability of Win: 45%
- Win:Loss Ratio: 1.30
- Risk Amount : 5%
- Number of trades : 300
- Iteration: 1000 (# of simulations it will run)
- Loss Level % : 40% (our predetermined ruin point)

Based on the following assumptions, this strategy would have a risk of ruin (reaching a 40% loss level) of about 58%. (If you hit calculate on the simulator, it will run the simulations again so the ROR number may vary a bit)

So, what if we wanted to get our Risk of Ruin down to below 2%, what should we do? Well the factor that we would have the most control over is the Risk amount, and so we should look to adjust that input.

Ok so we will keep all the variables the same, except we will adjust the Risk amount to 2.5%. Well by doing that, you will notice that our Risk of Ruin has in fact decreased from around 58% to about 20%. An improvement for sure, but still not below our target of 2%. So, let’s go back to the drawing board, and adjust the Risk amount to 1.25%. What does that do? Well that looks like a winner. Our Risk of Ruin is hovering around 2% and so based on this, we can only use a position size 1.25% per trade in order to achieve a ROR of less than 2% trading this system.

Although the hypothetical example above illustrates the concept of Risk to Ruin using a 2% threshold, it would serve the trader best to seek a Risk of Ruin as close to 0 as possible

### Profit Factor

Profit Factor measures the profitability of your trading system or strategy. It is one of the most simple but useful metrics related to system performance.

Profit Factor can be calculated in one of two ways:

Profit Factor = Gross Winning Trades / Gross Losing Trades

Profit Factor = (Win Rate x Avg Win) / (Loss Rate x Avg Loss)

A profit factor of less than 1 means that the trading strategy is a losing strategy.

A profit factor of 1 to 1.50 means that the trading strategy is moderately profitable

A profit factor of 1.50 to 2.0 means that the trading strategy is highly profitable

A profit factor above 2 means that the trading strategy is extremely profitable.

Let’s take an example with the following metrics:

- Probability of Win: 55%
- Avg Win: $ 500
- Avg Loss: $ 350

Can you figure out the Profit Factor of this system?

Profit Factor = (.55 x 500) / (.45 x 350)

= 1.75

This system has a Profit Factor of 1.75, a highly profitable trading strategy.

Let’s take a look at one more example:

- Probability of Win: 45%
- Avg Win: $ 650
- Avg Loss: $ 550

Can you figure out the Profit Factor of this system?

Profit Factor = (.45 x 650) / (.55 x 550)

= 0.97

This system has a Profit Factor of 0,97, meaning that this is a losing strategy.

### R Multiples

The concept of R Multiples was first introduced by renown psychologist Dr. Van Tharp. R Multiple sounds like an esoteric term but it is fairly straightforward and easy to understand.

R Multiple essentially measures Risk to Reward for a particular trade. R stands for Risk and is usually denoted as 1R ( the risk in the trade). The multiple of R is your reward as compared to your Risk. So, a 3R trade for example, would simply mean that for every unit of risk you are taking, your potential profit is 3 times that risk or 3R.

As you can see by using R multiples, it allows us to standardize our risk measures and easily gauge the Risk profile of a trade.

Let’s take a look at a few examples to demonstrate:

A trade with a 50 pip stop and 100 pip target is a 2R trade.

A trade with a 70 pip stop and a 210 pip target is a 3R trade.

A trade with a 120 pip stop and a 60 pip target is a 0.5R trade.

I think you get the basic gist of it now.

By combining the Risk to Reward and using the R Multiple we can quickly and easily assess the viability of a trade setup and the potential payoff.

You can use R Multiples beyond single trade events also. For example, R Multiples can be used to express Portfolio performance, Max Drawdown as well as other related trade metrics. Basically, you would view these metrics from the lens of 1 unit of risk.

Let’s look at some examples:

If you risk approx. $ 500 per trade and at the end of the year your trading profit is equal to $20,000, then your Yearly Performance is expressed as 40R.

If you risk approx. $ 250 per trade and experience a $ 3000 Drawdown, then the Drawdown can be expressed as 12R.

### Summary

As traders, we must always be working to strengthen our edge in the market, and this all starts with using basic math in trading to understand risk. We can then apply the necessary forex mathematical tools and calculators that we have available to us.

We have discussed many different forex math formulas that are relevant to forex traders. At this point, I would urge you to practice using everything you have learned and apply it to your own trading methodology. The more you understand these simple math formulas and calculators for traders, the better you will be at applying it to your own trading and to improving your risk management skills. And maybe above all, you will no longer be fearful of using math in trading.

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