# Core mathematics for Forex traders. Part 1

Mathematics has never been a strong point for many people. That is why, when they come to the Forex market, the only thought about using mathematical formulas in trading makes them terrified.

n the first part of the article we will tell you about mathematical formulas, which any Forex trader should know and understand. The good news is that it is rather easy to apply these formulas, while their benefit is evident.

• Cost of a pip (price interest point);
• Margin and leverage;
• Size of a position;
• Correlation of currencies.

Movement of currency pairs in the Forex market is measured in pips. A minimum pip of the majority of currency pairs, within the framework of the exchange rates, is the fourth digit after a decimal point. The only exception is currency pairs with JPY (Japanese Yen). Their pip is the price change of 0.01, since price quotes of these pairs have two digits after a decimal point only.

For example, if the price quote of the EUR/USD currency pair has increased from 1.3510 to 1.3530, it means that its growth is 20 pips. And, on the other hand, if the price quote of the USD/JPY decreased from 95.40 to 95.10, it means that its reduction is 30 pips.

Depending on what currency pair you trade, the cost of one pip would differ. Before we start calculations, we would like to remind you that one standard lot in the Forex market is equal to 100,000 units of the base currency, while one mini-lot is 10,000 units and micro-lot is 1,000 units.

You can use the following mathematical formula for calculating the cost of one pip of any currency pair:

Cost of one pip = 1 pip / Exchange rate х Size of a trade.

Example of a calculation for the EUR/USD currency pair:

• One pip = 0.0001;
• Base currency: EUR (Euro);
• Exchange rate: 1.2500;
• Size of a trade: 100,000 (1 lot);
• Cost of a pip = 0.0001 / 1.2500 x 100,000

= EUR 8.

Another example of a calculation for the USD/JPY currency pair:

• One pip = 0.01;
• Base currency: USD (US Dollar);
• Exchange rate: 95.50;
• Size of a trade: 100,000 (1 lot);
• Cost of a pip = 0.01 / 95.50 x 100,000

= USD 10.47.

Yet another example of a calculation for the GBP/CHF currency pair:

• One pip = 0.0001;
• Base currency: GBP (British Pound Sterling);
• Exchange rate: 1.3220;
• Size of a trade: 100,000 (1 lot);
• Cost of a pip = 0.0001 / 1.3220 x 100,000

= GBP 7.56.

## MARGIN AND LEVERAGE

Many beginners that came to the Forex market confuse leverage and margin. Although these two concepts are closely connected with each other, you need to understand their differences and be able to calculate them.

What is the leverage? Leverage allows a trader opening bigger market positions using a small part of his own capital and borrowing the rest from the broker.

What is the margin? Margin is a money collateral, which the broker requests from you when opening a market position. The broker combines your collateral with collaterals of other clients and posts your trades in the world currency market through liquidity suppliers and partner banks.

Leverage is calculated by the following mathematical formula:

Leverage = Size of a trade / Size of a trading capital.

Let’s calculate the leverage using the following example. Let’s assume that you decided to execute a trade with the nominal value of USD 100,000. However, the size of your trading capital is just USD 2,000. Thus, the leverage size in this case would be 50:1.

Leverage = USD 100,000 / USD 2,000 = 50.

Leverage = USD 100,000 / USD 5,000 = 20.

American brokers provide the maximum leverage in the size of 50:1. Brokers from other countries allow (sometimes) their clients using the leverage in the size of 500:1. The higher the leverage (500:1 > 50:1), the lower the margin (collateral) is required for execution of a trade. You should always use the leverage responsibly, since it can facilitate the growth of both profit and loss.

## SIZE OF A POSITION.

Size of a position is one of the most important and frequent calculations, which every trader does. In fact, before entering into a trade, a trader has to calculate the exact size of his market position based on a calculation model he identified beforehand.

One of the simplest and most efficient models of calculation of the size of a position is a fixed fractional model. According to this model, a trader risks X% of his trading capital in each executed trade. This model envisages that 1-2% of a trading capital is an acceptable risk for one trade.

As soon as you identified the optimum risk size for one trade, you need to decide where it would be more logical to post a stop loss. As soon as you decided where to post a stop loss, you should measure the distance from this level to the point of opening the trade in pips and keep the resulting number in mind.

The next step is to identify the cost of one pip. We already explained how to do it at the beginning of the article. In this example, just for convenience, we take the cost of one pip equal to USD 10. Now we can start calculating the size of our market position. Below is the formula of its calculation:

Size of the trading capital x Risk of the trade / Distance from the entry point to the stop loss x Cost of a pip.

Let’s consider a specific example:

• Size of the trading capital: USD 10,000;
• Risk of the trade: 2%;
• Distance from the entry point to the stop loss: 80 pips;
• Cost of a pip: USD 10;
• Size of a position = USD 10,000 x 0.02 / 80 x USD 10

= 0.25 lots.

Thus, based on the calculation data, the maximum size of the executed trade is 0.25 lots.

The trade expectancy is quite important in trading, that is why each trader should know about it. However, what does it mean? Briefly speaking, the trade expectancy is an average size of profit or loss, which might be expected from a trade on the basis of statistical indicators of your trading system. Below is a mathematical formula of calculation of this indicator:

(Percentage of profit-making trades x Average increase from a profit-making trade) – (Percentage of loss-making trades x Average decrease from a loss-making trade).

Now, we will consider the trade expectancy close using an example of statistical data of a standard trend following trading system. As a rule, the trend following trading system is characterized with a low percentage of profit-making trades, but also with a relatively higher average increase from a profit-making trade compared to an average decrease from a loss-making trade.

• Percentage of profit-making trades: 35%;
• Average increase from a profit-making trade: USD 1,200;
• Average decrease from a loss-making trade: USD 350;
• Trade expectancy = (0.35 x USD 1,200) — (0.65 x USD 350)

= USD 192.5.

Thus, the considered trend following trading system is characterized with the trade expectancy of USD 192.5, which is an average value of the expected profit from each trade.

Now we consider one more example. Let’s take statistical data of the mean reversion trading strategy. As a rule, this strategy has a higher percentage of profit-making trades and an average increase from a profit-making trade and average decrease from a loss-making trade are approximately equal.

• Percentage of profit-making trades: 60%;
• Average increase from a profit-making trade: USD 575;
• Average decrease from a loss-making trade: USD 525;
• Trade expectancy = (0.60 x USD 575) — (0.40 x USD 525)

= USD 135.

Thus, the considered mean reversion trading strategy is characterized with the trade expectancy of USD 135, which is an average value of the expected profit from each executed trade.

Many traders do it wrongly when they assess efficiency of a trading system based on the percentage of profit-making trades only. As you can see now, this indicator is just one of the several indicators, which are used in the formula of calculation of the trade expectancy.

## CORRELATION OF CURRENCIES

How often did you execute trades by several currency pairs at once and notice that their price quote movements were interconnected? For example, if you open long positions by EUR/USD, GBP/USD and AUD/USD pairs, you might think that you executed trades, which are not connected between themselves. However, it is not so, since the base currencies of these pairs (EUR, GBP and AUD) are traded against USD.

Correlation of currencies is a statistical indicator, which describes movements of currency pairs with respect to each other. Currency correlations could be positive, which means movement of the price quotes of two currencies in one direction (both grow or fall). They can also be negative, which means price quote movement of two currency pairs in different directions (one grows, while the other falls, and vice versa). Besides, the correlation of currency pairs could be neutral, which means absence of any noticeable interconnection between movements of price quotes of two currency pairs.

The order of calculation of currency correlations is rather complex, that is why we will not speak about it in this article. However, fortunately for us, there is no need to do it. There are many indicators that serve this purpose. They automatically calculate correlation indicators and reflect their resulting values in a table form.

The below ranges of currency correlations would help you to identify how currency pairs move with respect to each other easily and quickly:

• 0 – 0.2 — no correlation;
• 0.2 – 0.4 — low or weak correlation;
• 0.4 – 0.7 — average correlation;
• 0.7 – 0.9 — high or strong correlation;
• 0.9 – 1.0 — very strong correlation.

Remember that positive values tell us that currency pairs move in the same direction, while negative ones tell us that the pairs move in different directions.

What if we go further and use a USD index futures chart for identifying future movements of the basic currency pairs? This chart is available for free in the ATAS platform and the price movement of this futures is often opposite to the movement of basic currency pairs, in which USD goes second (EUR/USD, GBP/USD, AUD/USD, NZD/USD, etc.). In this case, a USD index futures will play the role of a leading indicator. You can read about this method of simple and efficient market analysis in our article USD index: 8 things you should know. Part 2.