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Chapter 14 Profit and Loss Calculation
In Chapter 14, we will learn how to calculate profits and losses from executed trades on the Forex market. As an internet trader, you enter the international currency market through a dealing company, which opens an account for you in US dollars. Regardless of the currency of the trade, all profits and losses are calculated and converted into US dollars. In this chapter, we will examine the principles of profit and loss calculations in detail.
In general, the formula for calculating the financial result of a trade can be expressed as follows:
Financial result = (selling price - buying price) * lot size * number of lots - commissions * number of lots ± bank interest.
As we can see, the financial result consists of three components: the trading result, paid commissions, and bank interest.
As we know, there are two types of quotes in Forex (excluding cross rates): direct and indirect. In the case of direct quotes, the base currency is the foreign currency in relation to the US dollar and is expressed (quoted) in dollars. In the case of indirect quotes, the US dollar itself is the base currency, and it is expressed in units of the foreign currency. In the formula mentioned above, the trading result is calculated in the quoted currency. However, commissions and bank interest are typically expressed in dollars. Therefore, the formula is valid only for direct quotes.
It should be noted that in this formulation, the selling price and buying price are not components of the quote but the actual prices at which we sold and bought the currency, regardless of the order of the operations (buying or selling). If the financial result is positive, we make a profit. If it is negative, we incur losses.
For indirect quotes, the difference between the buying and selling prices is expressed in the foreign currency, while the overall financial result is expressed in dollars. Therefore, the following formula is used to calculate the financial result for indirect quotes:
Financial result = (1/buying price - 1/selling price) * lot size * number of lots - commissions * number of lots ± bank interest.
The lot size depends on the specific quote (currency pair) and the preferences of the individual internet broker. The formulas mentioned above are used when the lot size is expressed in the foreign currency (not in US dollars). For example, the lot size for the direct quote GBP/USD could be 70,000 British pounds. Or the lot size for the indirect quote USD/JPY could be 12,500,000 Japanese yen. If your internet broker specifies the lot size in dollars, then to use the formulas mentioned above, you would need to convert the dollars into the corresponding currency. In this case, the lot size in the foreign currency would not be fixed but would depend on the current exchange rate at the time of opening the position. In US dollars, the size of a standard lot is almost always equal to 100,000.
As we know, currency rates on Forex fluctuate in pips. The pip size varies in different quotes. When opening a position, it is important to know the trading result that an exchange rate change of one pip brings in US dollar equivalent. This allows us to assess our current profits or losses and close the position in a timely manner. Using the formulas mentioned above, this value can be easily calculated and depends on the type of quote (direct or indirect), the size of one lot, the currency in which the lot is denominated, and the size of one pip.
Let's consider the direct quote GBP/USD with a lot size of 70,000 British pounds and a pip size of 0.0001. Since it is a direct quote, we use the first formula to calculate the trading result. The minimum difference between the buying and selling price is always one pip, and in this case, it is equal to 0.0001. Therefore, the trading result from a one-pip change in the GBP/USD exchange rate for one lot is equal to 0.0001 * 70,000 = 7 US dollars.
Let's consider the indirect quote USD/JPY with a lot size of 12,500,000 Japanese yen and a pip size of 0.01. Since it is an indirect quote, we use the second formula to calculate the trading result. Knowing the value of one pip in the case of an indirect quote is not enough, as the trading result also depends on the actual buying and selling prices. Let's assume that the current exchange rate is 104.75 Japanese yen per US dollar. Then, the trading result from a one-pip change in the USD/JPY exchange rate for one lot is calculated as (1/104.75 - 1/104.76) * 12,500,000 = 11.39 US dollars. It is worth noting that different buying and selling prices result in different trading results. If the lot size were denominated in dollars, it would need to be converted to yen at the corresponding exchange rate at the time of opening the position. Additionally, if it were a long position (buying dollars for yen), the selling rate would be used for calculations, while for a short position (selling dollars for yen), the buying rate would be used.
As we can observe, a one-pip change in the exchange rate yields a different trading result in different quotes. In the GBP/USD quote, it is smaller compared to the USD/JPY quote. The smaller the trading result from a one-pip change, the smaller the losses you will incur in the event of an unfavorable exchange rate movement. However, on the other hand, your profits will also be smaller if the exchange rate moves in your favor. For novice Internet traders, it is recommended to work with less "aggressive" quotes, such as GBP/USD and USD/CHF.
At first glance, the calculation methods discussed in this chapter may seem overly complex. However, there is no need for you to worry about this because all calculations related to profits and losses are performed automatically by the trading platform. Different brokerage companies may use different trading platforms, but the principles of calculation remain the same.
You don't have to be concerned about manually carrying out these calculations since the trading platform takes care of it automatically. It accurately calculates and displays your profits and losses for each trade, allowing you to have real-time information about your account status. This automated process ensures that you can make informed decisions and avoid mistakenly closing positions with losses.
Chapter 15. Comparing Forex and Casino
On the internet, you can find many articles that equate forex trading to casino gambling, particularly roulette. The authors of these articles present various arguments and often attempt to use mathematical calculations from probability theory, even without a proper understanding of the subject. In this chapter, we will attempt to debunk the myth that forex trading is akin to gambling.
Roulette is an ancient game that can be rightfully considered one of humanity's ingenious inventions. The mechanics of the game and its rules are very simple. However, beneath the apparent simplicity of winning lies a set of mathematical laws that generate billions of dollars in annual profits for gambling establishments while bankrupting millions of fortune seekers. Let's delve into the mechanics of roulette and understand why it is impossible to achieve consistent profits by playing it.
In probability theory, there are two fundamental concepts: events and the probability of their occurrence. An event can refer to anything. A sunny day after a series of cloudy days, a workers' strike at a factory, a chance encounter with an old friend on the street, a car accident, a flight delay due to technical issues with the airplane—all of these are events that occur with a certain probability.
Among the countless set of events, there are those that can occur simultaneously (referred to as a compound event), and there are those that are mutually exclusive and cannot occur simultaneously. For example, you can go outside, meet your old friend near the factory where workers are on strike, on a warm sunny day. In this example, three events occurred simultaneously. On the other hand, events like a sunny day and a rainy day are mutually exclusive and cannot occur at the same time. It is easy to understand that the probability of a compound event occurring is much lower than that of an individual simple event within it because multiple factors must align for the compound event to happen.
Let's consider another classic example - a six-sided dice. The dice has six faces, each marked with a number from 1 to 6. The outcome of rolling the dice and landing on one of the numbers is an event. Only one number can appear simultaneously in a single roll. Therefore, there are a total of 6 possible events when rolling the dice, and they are all mutually exclusive.
It is clear that when rolling the dice, we will always get some number. In other words, the probability of getting any number can be confidently taken as one or 100%. But what is the probability of getting a specific number, for example, 1 or 5? Are these probabilities the same? Let's try to understand this.
In probability theory, there is a concept called probability distribution. It represents the probability function of an event occurring based on the event itself. Without going into details, we can simply say that the outcomes of rolling a dice have a uniform probability distribution, meaning the probability of getting different numbers is the same. This occurs because the dice has a regular shape and uniform density. Since there are 6 numbers on the dice, the probability of getting each number individually is 100 / 6 = 16.6666...%.
The next important concept in probability theory is the law of large numbers. In our example with the dice, it means that if we roll the dice a large number of times, each individual number will appear in proportion to its probability. And since the probabilities of all six digits are the same, each number will appear an equal number of times. Moreover, the more times we roll the dice, the smaller the margin of error becomes for this statement. The error approaches zero as the number of rolls approaches infinity. Therefore, if we roll the dice 1,000,000 times, each number will appear approximately 166,667 times with a certain margin of error.
If the probability distribution is not uniform, the outcomes will vary accordingly. Let's consider a scenario where we cover one face of the dice with lead, altering its density distribution. The probability of getting the number 1 becomes 50%, while the probabilities of the remaining 5 numbers remain the same at 12.5% each. Now, if we roll the dice 1,000,000 times, the number 1 will appear approximately 500,000 times, while the other numbers will appear around 125,000 times each.
Let's go back to the roulette wheel. The wheel has 37 slots: numbers 1 to 36 and one zero (0). The probability distribution of the numbers on the roulette wheel, like the dice, is uniform. Therefore, the probability of any individual number appearing on the roulette wheel is the same and equals 1/37. The payout by the casino for correctly guessing (hitting) a specific number is 1:36. This means that for every unit (e.g., a dollar) we bet on a specific number, with a probability of 1/37, we will receive 36 units if we win. Applying the law of large numbers, if we play roulette X times, betting one unit each time on a single number, our overall winnings will be:
36/37 * X – X = X * (36/37 – 1) = –1/37 * X
You have understood it correctly—the minus sign in the obtained formula represents your loss and the casino's winnings. It doesn't matter which numbers you bet on, whether consistently on the same number or different numbers—the formula remains the same. And once again, the larger the value of X, the smaller the margin of error in the formula. With a small value of X, the margin of error can be significant. So, if you enter a casino, place a few bets, win, leave, and never return, the casino will incur losses. However, few people can resist the temptation to stop after a win, and playing roulette becomes a way of life. In the hope of winning again, people return, play continuously and frequently. The number of games played increases, reducing the margin of error in the formula, and ultimately, individuals end up losing. Even if a specific person never returns to the casino after a big win, there will always be other new fortune seekers, and the gambling industry will continue to thrive.
One important note should be made. Based on the formula, it appears that by playing a thousand games with a one-ruble bet, the player only loses 1/37 part, which is approximately 27 rubles. At this rate, one can stay afloat for a long time and derive pleasure from the game. However, in reality, few people play roulette with just one ruble. It is a person's own gambling addiction that leads to their downfall. By making risky large bets, individuals often reach a point where they no longer have enough capital to recover their losses. This lack of funds for further gameplay (recovery) is what leads to bankruptcy. If all players were billionaires, they could play for a long time, losing only 1/37 part of their bets.
1/37 represents approximately 2.73%. This is precisely the advantage that the casino has over the player. In the American version of roulette (unlike the European version), there are two zeros (0 and 00) on the wheel. In such a roulette game, the casino's advantage over the player is 2/38, which is approximately 5.26%, further worsening the conditions of the game.
Indeed, in roulette, you can place bets not only on single numbers but also simultaneously on 2, 4, or even a whole range of numbers. However, with such bets, the payout for a win proportionally decreases, meaning the formula remains the same. The casino always wins, and its expected profit can be mathematically calculated. In European roulette, this is 2.73% of all bets placed by all players, while in American roulette, it is 5.26%. Other games have their own formulas for calculating probabilities and, consequently, the expected profit for the casino. The actual profit of the casino differs from the expected profit because people simply do not have enough funds to recover their losses—they end up losing everything.
That's why it is not possible to generate a stable income in a casino. Forex, on the other hand, is a completely different story. Here we also have events (the decrease or increase in currency exchange rates relative to each other) and the probabilities of their occurrence. However, the distribution of these probabilities is non-uniform, and there is no clear mathematical formula to derive them. Moreover, these probabilities can be forecasted, and if forecasting tools (analysis) such as technical analysis and fundamental analysis are used properly, it is possible to achieve a stable income in Forex.
Why the seemingly chaotic behavior of currency exchange rates can be forecasted will be discussed in detail in subsequent sections of the website. For now, let's just say that the movement of currency exchange rates is created by people themselves (brokers, dealers, internet traders). If the majority of them are buying a currency (bullish sentiment prevails), its exchange rate rises. Conversely, if the majority of them are selling a currency (bearish sentiment prevails), its exchange rate falls. If you can timely determine the market sentiment and align with the majority, you will achieve stable profits. Since most Forex traders use similar analytical tools to determine market sentiment, all you need to do is follow the majority, do what everyone else does. However, an important clarification needs to be made. The majority in the context of Forex is determined not by the number of traders but by the volumes of their transactions. Large deals in the currency market are made only by experienced traders - dealers of major investment companies, investment funds, and banks. These are people with specialized education, years of experience, and a vast amount of knowledge. To trade successfully in Forex, you need to replicate the behavior model of such individuals in the currency market, and this is not possible without proper education.
Therefore, before starting to work in Forex, it is necessary to thoroughly study this market, as well as the tools used by professionals to forecast its behavior. This is the only possible path to success!
So, as you can see, working in Forex has little in common with playing roulette. Continue studying the material on the website, and you will learn a lot, which means that over time you will achieve a stable income in Forex. The magnitude of this income will depend solely on you. Your success is in your hands!