When prices move randomly, a completely inexperienced trader can still make profitable trades purely by chance. Theoretically, if that person trades long enough, they would break even over time. However, reality is different. Their trading account will be impacted by transaction costs, errors, and other risks, creating significant barriers that prevent them from breaking even. Moreover, most beginners tend to act contrary to what is necessary for successful trading. They often take profits too early and let losses grow for too long. These traders become the source of profits for other participants in the market.
Our trading objective is to generate profits and achieve capital growth as illustrated in the image below:
.png)
Since price movements are random, we cannot be correct 100% of the time when trading. Therefore, the outcome of each trade we make is also random. If we aim to create an upward capital growth curve, we need to have a positive expectation. In financial trading, the formula for calculating the expected value of a trade is expressed as follows:
EV = (Pw × Rw) − (Pl × Rl)
Where:
- EV: Expected value
- Pw: Probability of winning (win rate)
- Rw: Average profit from winning trades
- Pl: Probability of losing
- Rl: Average loss from losing trades
If we want to be profitable in the long run, our EV must be greater than 0, and we aim for it to be as high as possible. When this is achieved, we are considered traders with an edge. Using past trading data, calculating this value is simply a matter of statistics, but the challenge becomes more complex when forecasting for the future. Some traders prefer trades with a high probability of winning, while others focus on finding trades with a high reward-to-risk ratio (R:R) but lower win rates. Let’s consider a few examples:
You can apply this formula to calculate the expected value of various gambling games such as lotteries, numbers games, or casino games. All of these typically have a negative expectation, meaning we will lose money if we play them over the long term. This highlights the fundamental difference between trading and gambling: in trading, we can work to change the win rate or the reward-to-risk ratio (R:R) to gain an edge. In gambling, however, these factors are fixed and cannot be altered.
.png)
The image above illustrates the relationship between the reward-to-risk ratio (R:R) and the win rate. When we try to increase the win rate, the R:R decreases, and conversely, if we aim to increase the R:R, the win rate will drop. The black curve represents systems with an expectation of zero—these are break-even systems where we neither gain nor lose money over time. Trading systems with both metrics above the black curve are profitable systems, while those below the curve are losing systems. From my observations, there is no trading strategy that achieves both a very high win rate and a high R:R simultaneously. To be profitable in the long term, we only need these two metrics to be slightly above the black curve.
This phenomenon occurs because the market comprises a wide variety of participants and trading styles. If a particular method or strategy achieves outstanding performance, many participants can easily identify and adopt it, which directly reduces its effectiveness. A good trading system that can be used in the long term is one that is not overly prominent and is challenging to execute. As a result, its edge will be modest. Because the edge is not significant, the system will naturally go through periods of drawdowns and losses interspersed with periods of wins. These drawdown phases will discourage and filter out those who lack the persistence to stick with the strategy. This very process helps the strategy maintain stable performance over time. We neither need nor should seek strategies with excessively high expected values. Instead, we only need strategies that remain slightly above the black curve to generate long-term profits.
To illustrate this point more clearly, consider the chart below, which shows the profit statistics of a trading strategy. This strategy has a win rate of 33.81% and an R:R of 2.257. Although it is just slightly above the black curve, it managed to generate a total return of 3327.75% over 17 years, equivalent to a CAGR (Compound Annual Growth Rate) of 60%.
CAGR, short for "Compound Annual Growth Rate," measures the annual growth rate of an investment over time while accounting for the effects of compounding. This example demonstrates how even a marginally profitable system, when applied consistently over the long term, can yield remarkable results.
You don’t need to aim for numbers significantly higher than the black curve, such as a 50% win rate with an R:R of 2, or a 70% win rate with an R:R of 1. In most cases, you only need a 50% win rate with an R:R of 1.2, or a 52% win rate with an R:R of 1. Even with these modest figures, you can achieve growth sufficient to outperform the market's average return. Any CAGR (Compound Annual Growth Rate) greater than 20% per year is enough to place you among the legends of the trading world. This highlights the power of consistency and disciplined execution over chasing perfection in trading metrics.
Do not set overly high or unrealistic expectations. If you hear anyone advertising astronomical numbers that are far beyond the curve, question it and stay cautious. Such claims are often scams, miscalculations, or based on an insufficient amount of statistical data. In the short term, the market may generate unusually high expected values, but over the long term, these values tend to converge closer to the curve. This underscores the importance of being realistic and relying on solid, long-term data when evaluating trading strategies.
From a purely mathematical perspective, the expected value represents the average amount we can win or lose per trade, but it only holds significance when the sample size is sufficiently large. During the trading process, we may experience streaks of consecutive wins or losses, which can result in substantial short-term profits or losses. Random data often produces longer streaks than we might anticipate, which is a primary reason why strategies like Martingale or doubling down frequently fail. With a sufficiently large sample size, however, the actual results will converge toward the expected value. This highlights the importance of patience and consistency in trading, as short-term fluctuations can be misleading and should not dictate major changes to a well-planned strategy.
The key to trading success lies in having an edge, which is reflected in a positive expected value. If you cannot statistically and quantitatively define your edge, everything else becomes meaningless. Inexperienced traders often believe that psychological factors are the primary cause of their trading outcomes. An entire industry exists to cater to this belief, offering hope to traders that resolving their psychological issues will lead to profits effortlessly. Executing trades, managing risk, maintaining discipline, and having the right mindset are all important for trading success. However, they are meaningless if your trading system lacks a positive expected value. These factors only become effective when you have a statistical edge, but they themselves are not the edge. Without a sound strategy that provides a quantifiable advantage, focusing on psychological and behavioral aspects alone will not lead to consistent profitability.
If you correctly identify the entry and exit points in the market, and with a sufficiently large sample size, the total profit from your winning trades exceeds the total loss from your losing trades, then you have an edge. Another metric to assess the strength of your edge is the Profit Factor, which is calculated using the formula: total profit from all winning trades divided by the total loss from all losing trades. A strategy with an edge will have a profit factor greater than 1, while a strategy without an edge will have a profit factor less than 1. The higher the profit factor, the stronger your edge.
When building a system, I typically look for strategies with a profit factor of 1.1 or higher after accounting for all costs. On average, the profit factor of strategies ranges from 1.1 to 2. Be cautious of any trading strategy with an excessively high profit factor (>2). Similar to expected value, this is often a sign of fraud, calculation errors, or the use of an insufficient sample size or overly short time frames.
Nhận xét
Đăng nhận xét