Risk-Reward Ratio (R:R) and Expected Value Thinking
Win rate alone cannot determine the quality of a trade; long-term performance requires considering both the risk-reward ratio and expected value.
What is the Risk-Reward Ratio?
The Risk-Reward Ratio (R:R) is the ratio of expected profit to the potential loss risked in a single trade. If you plan to buy at an entry price of $100, with a target price of $130 and a stop-loss price of $90, the expected profit is $30 and the risk taken is $10, making the R:R 3:1. It is commonly expressed as how many units of reward there are per unit of risk.
The key here is that the R:R is a 'planned value defined in advance at the entry point.' If you don't set a target price and a stop-loss price beforehand, you cannot calculate the R:R itself. Consequently, you might fall into a pattern of holding onto losses for too long and taking profits too early. The R:R is a mechanism that forces you to structure your risk before starting a trade.
Connecting to Expected Value
Expected Value is a concept that combines win rate and R:R. Expected value is calculated as (win rate × average profit) − (loss rate × average loss), and it indicates how much a single trade is expected to gain or lose on average over the long term. You can understand it as the average profit or loss per trade when the same rules are repeated sufficiently.
For example, a strategy with a 40% win rate, an average gain of +$30 when winning, and an average loss of −$10 when losing, has an expected value of (0.4 × 30) − (0.6 × 10) = 12 − 6 = +6. Even though it's right less than half the time, the expected value per trade is positive. Conversely, even with a 70% win rate, if the gain is +$5 and the loss is −$20, the expected value is (0.7 × 5) − (0.3 × 20) = 3.5 − 6 = −2.5, which is negative. Looking only at the win rate leads to the opposite conclusion.
The Trade-off Between Win Rate and Risk-Reward Ratio
Win rate and R:R are generally in a trade-off relationship. If you set a distant target price to increase the R:R, the probability of reaching it decreases, lowering your win rate. Conversely, if you set a close target and take profits frequently, your win rate increases, but your R:R decreases. Attempts to maximize one side usually come at the expense of the other.
It becomes easier to make decisions if you use the R:R that makes the expected value zero as a break-even threshold. For an R:R of R:1, the win rate generally needs to exceed 1/(1+R) for the expected value to be positive. For an R:R of 2:1, a win rate of about 33% is enough; for 3:1, about 25% is sufficient for a positive expected value. This means that increasing the R:R allows for survival even with a lower win rate.
How to Manage Risk-Reward in Practice
In practice, it is more stable to first set the stop-loss price based on technical analysis, and then determine the target price. For instance, placing a stop-loss below the previous support level and setting the first target two or three times that distance above it naturally establishes an R:R of 2:1 or 3:1. A rule might be to avoid entering a trade altogether if the R:R is less than 1:1.
The R:R is also directly linked to position sizing. If you fix the amount you are willing to lose in a single trade to a certain percentage of your account (e.g., 1-2%), you will reduce the quantity for stocks with a wide stop-loss range and increase the quantity for those with a narrow stop-loss range. This way, your R:R plan remains consistent, and a single failure does not significantly damage your account. This article is educational material explaining a framework for managing risk, not a recommendation for specific trades.
Common Pitfalls and Limitations
The most common pitfall is confusing the planned R:R with the realized R:R. The target price is not always reached precisely, and due to slippage, gaps, and premature exits, actual average profits tend to be smaller than planned, and average losses tend to be larger. To ensure that expected value estimates align with reality, it's crucial to track 'realized R:R' separately through backtesting or live trading records.
Another issue is the sample size. A strategy with a positive expected value can still experience long losing streaks with only a few trades, and conversely, a negative strategy might appear good in the short term due to luck. Win rate and R:R estimates are only reliable after reflecting transaction costs and taxes and accumulating a sufficient number of trades. It's also important to consider that structural costs, like transaction taxes in the Korean market or currency exchange fees in the US market, can erode expected value.
Checkpoints
In summary, the quality of a trade should be judged by its expected value, not solely by its win rate, and the R:R is a critical variable for making that expected value positive. It helps to develop the habit of explicitly defining the R:R by setting both a stop-loss price and a target price before entry, and then calculating the break-even win rate from that R:R to compare it with your actual win rate.
There are three questions to ask: What is the R:R for this trade? What win rate is needed to make the expected value positive? And is the amount lost if the trade goes wrong manageable for your account? If you can answer these three questions, you can consistently follow your rules without being swayed by the success or failure of individual trades.
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