Series: “Famous Theories Used in Swing Trading” Part 6: Risk-Reward and R-Multiple
By reading this article, you will understand the following:
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What risk-reward (the ratio of loss to profit) is
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The relationship between risk-reward and the “required win rate”
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What the “R-multiple” popularized by Van K. Tharp is
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What you can learn by measuring performance in R (calculated using 10 hypothetical trades)
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Points of caution common to both
What are risk-reward and R-multiple? A way to measure performance by setting a single loss as “1R”
“I went 5 wins and 5 losses this month, a 50% win rate. Yet, the money in my account is decreasing.”
This is a common concern when you first start trading. The cause lies in the fact that the profit when you win and the loss when you lose are not balanced.
The tools to consider this “balance” are risk-reward and R-multiple. Since both only require division, you can apply them to your own trading starting today.
What is risk-reward?
Risk-reward is the ratio comparing the expected loss and profit of a single trade. It compares how much you might lose (risk) with how much you expect to gain (reward). Rather than a theory devised by a specific person, it is a concept widely used in the trading world.
Let’s look at a hypothetical example.
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Buy at 1,000 yen
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Stop loss (selling to keep losses small) if it drops to 950 yen
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Take profit (selling to lock in gains) if it rises to 1,100 yen
In this case, the risk is 50 yen per share, and the reward is 100 yen. Since the reward is 2 for every 1 of risk, we say the “risk-reward is 1 to 2.”
Figure 1: Reward of 100 yen against a risk of 50 yen. This is “1 to 2.”
What is important here is that risk-reward is a “plan” decided before buying. Unless you decide on the stop-loss position and the profit target, you cannot calculate the ratio.
Risk-Reward and Required Win Rate
Once you know your risk-reward ratio, you can calculate the win rate needed to break even (neither losing nor gaining). The formula is “1 ÷ (1 + Reward ÷ Risk).”
Figure 2: Win rate required to break even at various ratios
At a 1:2 ratio, you break even if you win once every three trades. Conversely, in a trade where the loss is twice the profit, you need to win two out of three times just to break even. The “losing money despite a 50% win rate” mentioned at the beginning is a state close to the bottom of this chart.
What is an R-Multiple?
The R-multiple is a concept popularized by Van K. Tharp. Tharp was an American trading coach, and the concept is said to have spread through his 1998 book, “Trade Your Way to Financial Freedom,” among others.
The concept is as follows:
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The loss incurred when you lose at the stop-loss level decided before buying is defined as “1R”
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Divide the trade result (profit or loss) by that 1R
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The resulting answer is the “R-multiple” for that trade
In the previous example, suppose you bought 100 shares. Since losing at the stop-loss of 950 yen results in a 5,000 yen loss, 1R for this trade is 5,000 yen. If you take profit at 1,100 yen, it is +10,000 yen, which is +2R. If you sell midway at 1,025 yen, it is +2,500 yen, which is +0.5R, and if you cut your losses at 950 yen, it is -5,000 yen, which is -1R.
Figure 3: When 1R = 5,000 yen, the three results converted to R are as follows
In other words, the R-multiple is a number that represents “how many times the loss you were prepared for you have won (or lost).”
If risk-reward is the “plan” before buying, the R-multiple is the “result” after selling. Even if you enter with a 1:2 plan, if you sell midway, the result will be +0.5R, and if you go all the way to the stop-loss, it will be -1R.
What can you learn by measuring performance in R?
The advantage of R-multiples is that you can compare trades with different stock prices and share counts using the same yardstick.
For example, “+20,000 yen on a 3,000 yen stock” and “+5,000 yen on a 500 yen stock” might make the former look better if you only look at the amount. However, if the former has 1R = 20,000 yen (+1R) and the latter has 1R = 2,500 yen (+2R), the latter actually earned more relative to the loss it was prepared to take.
Figure 4: Looking at it in terms of monetary amount, the former is better, but looking at it in terms of R, the latter is more profitable.
Let’s calculate using 10 hypothetical trades.
Let’s list 10 hypothetical trades in terms of R.
Figure 5: R-multiples for 10 hypothetical trades. Blue represents wins, and red represents losses.
There are 4 wins and 6 losses, for a win rate of 40%. However, adding them up for 10 trades gives +2.2R, and the average per trade is +0.22R.
This ‘average R per trade’ is the concept Tharp used as expected value (how much you gain on average per trade). If the average is positive, it means you can expect to increase your capital as you repeat the same method. The concept of expected value itself is explained in detail in the introductory article ‘The Story of “Expected Value” You Should Learn First in Swing Trading’ article.
Looking only at the win rate, it’s a performance that might make you feel discouraged, thinking, ‘I’ve lost 6 times.’ But when looking at it in terms of R, the losses are kept to almost -1R, while the wins extend to +2R and +3R. It becomes easier to see what needs to be fixed and what doesn’t.
Points of Caution and Limitations
While this is a convenient way of thinking, there are some points to be careful about. I will list five of them first, then look at them one by one.
Figure 6: Five things to be careful about with risk-reward and R-multiples
If the stop-loss position is not decided, R cannot be determined.
The R-multiple starts from the ‘stop-loss decided before buying.’ If you buy without deciding the stop-loss position, you won’t know how much 1R is. Even if you look back later, you won’t be able to measure your performance in R. Before buying, you need to decide on a place on the chart where you can say, ‘If it breaks below this, I was wrong.’
Do not change 1R later.
There are times when you might change the stop-loss position after buying. However, when measuring performance, the basic rule is to calculate 1R based on the stop-loss decided at the beginning. If you change it midway, the yardstick itself changes.
Losses can be greater than -1R.
If the stock price opens significantly lower than the previous day’s closing price (gapping down), it may be sold at a price lower than the stop-loss price.
For example, if you bought at 1,000 yen and set a stop-loss at 950 yen, but it opened at 935 yen the next morning. If you sell at 935 yen, the loss is 65 yen per share, which exceeds the 1R of 50 yen and becomes -1.3R. Depending on how much it drops, it can sometimes be -1.5R. Please keep in mind that losses do not always stop at 1R.
Figure 7: If it starts below the 950 yen stop-loss, it will not stop at -1R
A higher ratio is not necessarily better
If you set your profit target further away, you can make the risk-reward ratio 1:3 or even 1:5. However, the further the target, the less frequently it will be reached, and your win rate is likely to drop. You cannot simply look at the ratio and call it a ‘good trade’ because it is 1:5. It is important to look at the ratio and win rate together and consider whether the average R becomes positive.
How much to set 1R is a separate matter
The R-multiple is a yardstick for measuring performance; it does not tell you ‘how much 1R should be.’ How much of your capital you risk on a single loss is handled by the Kelly Criterion in (7) or Elder’s 2% rule in (2).
Summary
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Risk-reward is a ‘loss:profit’ plan decided before buying. At 1:2, you break even with a win rate of about 33%
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The R-multiple is a concept popularized by Van K. Tharp. The loss incurred when you lose at your initially determined stop-loss is defined as 1R, and the result is divided by 1R
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Measuring in R allows you to compare trades with different stock prices and share counts using the same yardstick. The average R per trade becomes your expected value
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If you buy without setting a stop-loss position, 1R cannot be determined. The basic rule is not to move 1R after it is set
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If the price gaps down, you may lose more than -1R. Look at it in conjunction with your win rate, not just the ratio
To start, just take your last 5 trades, write down the ‘buy price, initial stop-loss, and sell price,’ and convert them into R. More than the number of wins and losses, whether or not your losses were contained at -1R will teach you much more.
Next Steps
📖 Other articles in the series ‘Famous Theories Used in Swing Trading’ (Free)
How much of your capital to risk on a single trade is covered in (2) Elder’s “Three M’s” and the 2% / 6% rule, as well as the following (7) Kelly Criterion. The psychology behind selling winning trades too early is addressed in (8) Prospect Theory and the Disposition Effect.
Basics of Expected Value here: Introductory article: “The Story of ‘Expected Value’ You Should Learn First in Swing Trading”
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※ This article is a general explanation of theories and does not recommend buying or selling any specific stocks. Please make your own investment decisions.
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