Risk-reward ratio is the ratio of maximum possible profit (reward) and maximum loss (risk) of an option position. Generally, the greater reward relative to risk, the better. But is there something like a "good" risk-reward ratio – a R/R level which could be used as a trading rule and filter of potential trades?
The Bad Answers
In various materials about options you may encounter two different kinds of answers to this question:
- "Never take trades with R/R worse than 2" (or some other magical R/R value).
- "There is no such thing as good R/R, it depends."
The first answer is wrong, and can be dangerous.
The second is kind of correct, but not very useful.
Let's start with short explanation why the first one is wrong and then we will try to improve the second one and see if we can still make a good, practically usable, quantifiable rule.
The Problem with Hard R/R Rules
If you follow a rule like this:
"Only take trades with risk-reward ratio better than 2" (or 1.5 or 3 or 5 or any fixed number)
... it will hurt your bottom line in two ways:
- You will take trades which you should not take.
- You will leave good opportunities on the table.
The reason is that different trades have different probabilities of wins and losses.
If a trade makes $500 10% of times and loses $100 90% of times and you take 10 such trades, you can expect to win $500 once but lose $100 nine times, and total expected result will be a $400 loss. Sometimes 5:1 reward-to-risk is not good enough.
Conversely, if a trade makes only $100 when it wins and loses $200 when it loses, but wins 80% of time, if you take it 10 times you can expect to make $400 profit (8x $100 – 2x $200).
Risk-reward ratio is a useful risk metric, but it does not tell the complete story.
Therefore, there is no such thing as "good" risk-reward ratio if you look at risk-reward ratio alone.
But there may be "good" and "bad" risk-reward ratio levels when you add other things (mainly the probabilities of winning and losing).
Break-Even R/R for Different Win%
It is possible to find the exact "break-even" risk-reward ratio that is required to profit in the long run with given win rate (probability of profitable trades):
1 trade 10 trades Win% R/R* Profit Loss Profit Loss Total 95% 0.05 5.26 -100 50 -50 0 90% 0.11 11.11 -100 100 -100 0 85% 0.18 17.65 -100 150 -150 0 80% 0.25 25.00 -100 200 -200 0 75% 0.33 33.33 -100 250 -250 0 70% 0.43 42.86 -100 300 -300 0 65% 0.54 53.85 -100 350 -350 0 60% 0.67 66.67 -100 400 -400 0 55% 0.82 81.82 -100 450 -450 0 50% 1.00 100.00 -100 500 -500 0 45% 1.22 122.22 -100 550 -550 0 40% 1.50 150.00 -100 600 -600 0 35% 1.86 185.71 -100 650 -650 0 30% 2.33 233.33 -100 700 -700 0 25% 3.00 300.00 -100 750 -750 0 20% 4.00 400.00 -100 800 -800 0 15% 5.67 566.67 -100 850 -850 0 10% 9.00 900.00 -100 900 -900 0 5% 19.00 1900.00 -100 950 -950 0 *R/R is expressed as reward/risk
If your strategy wins 50%, you break even when the wins are at least same size as the losses (R/R=1).
If you improve the win rate to 60%, you only need the wins to be 2/3 the size of the losses (reward-to-risk = 2/3).
But if your win rate is only 25% (profit once in 4 trades), the profits must be at least 3x the size of the losses.
There is a universal formula that calculates break-even risk-reward ratio for given win rate:
R/R = ( 1 – Win% ) / Win%
Ratio of Maximum vs. Average Profit and Loss
There is a problem with our nice risk-reward ratio table and formula: It applies to the ratio of average profit and average loss, not the ratio of maximum profit and loss.
While the risk-reward ratio in options trading (at least the one calculated from option payoff) is typically understood as the ratio of maximum profit and maximum loss, the ratio which (combined with Win%) affects our long-term profitability is the ratio of average profit and average loss. These can be very different.
Most option trades do not have only two possible outcomes (the maximum profit and the maximum loss). They can also end up being smaller profits or smaller losses. For example, a bull call spread position makes maximum profit above the higher strike, maximum loss below the lower strike, and something in between in the area between the two strikes. As a result, average profit and average loss can be much smaller than the maximums.
Therefore, the break-even risk-reward ratios from the above table should be considered the required ratios of average profit and average loss. The risk-reward ratio of maximum profit and maximum loss is usually a good proxy (good enough to be practically usable for pre-trade evaluation), but you should be aware of the difference.
Another problem is: How do we know the Win% in the first place?
Calculating Probability of Profit
Like many other things in trading and life, the win rate is very easy is know for past trades, but much harder to predict for the future ones.
That said, we can estimate it using relatively simple financial models.
Generally, the probability of an option position to be profitable at expiration depends on the following inputs:
- Distances of the break-even points from current underlying price.
- Time to expiration.
In general, underlying price ending up at or beyond a break-even point is more likely if:
- The break-even point is closer to current price.
- Time to expiration is longer (price has more time to move).
- Volatility is higher (price moves faster).
Time to expiration is well known.
Volatility is the hardest part. We can assume the expectations of the options market as whole about future volatility are accurate, and use implied volatility of the options for our volatility input. Or we can calculate historical volatility of the underlying asset and assume future volatility will be the same (and possibly adjust it for seasonality and known upcoming events such as earnings releases).
Once we have the volatility, we can calculate the probabilities of underlying price ending up above or below the break-even points, and the total probability of our position to be profitable. Then we can plug the probability into the formula above to get the required risk-reward ratio.