Last Updated on April 19, 2022 by Quantified Trading
The win ratio in trading is one of the most important parameters to evaluate a trading strategy.
The win ratio is the winning trades divided by the losing trades. A high win ratio is important because it reduces behavioral mistakes and ruin. It matters a lot.
Many traders underestimate the importance of the win ratio and thus commit grave behavioral mistakes when they trade their strategies live. The win ratio is important because it influences your behavior in the markets and a low win ratio increases the risk of ruin in trading.
At the end of the article, we provide a mathematical calculation to show the optimal capital allocation per trade (or strategy) to allow a margin of safety to avoid ruin.
First, how do you calculate the win ratio in trading?
To avoid any doubt about what the win ratio (win rate) in trading is, we start with a definition:
The win ratio in trading is the number of winning trades compared to the total amount of trades. Here is an example:
Let’s assume you develop a strategy that has 556 trades over the last 20 years. 349 of the trades showed a profit, 5 trades were break-even, and 202 showed a loss.
To find the win ratio you need to divide the winners by the total amount of trades: 349 divided by 556. This is 0.628. To get the percentage you need to multiply by 100 and thus 62.8% of the trades turned out to be winners.
Hence, the win ratio is 62.8%.
Profits vs. win ratio
The main idea behind trading is to maximize profits not the win ratio. A strategy can have a very low win ratio but still be very profitable if the winners are huge and offset the losers.
As an example, look at the win ratio of the 200-day moving average on the S&P 500 from 1960 until August 2021: 28%!
- The 200-day moving average: How it works, why it works, and why it doesn’t work
72% of the trades turned out to be either flat or losers. The strategy is still very profitable because the 200-day moving average lets you ride the big trends, and thus the avereage winner is substantially bigger than the average loser.
Commissions and the win ratio in trading
If you pay commissions when you buy and sell an asset you have to factor this into your win ratio. Commissions lower the win ratio.
A low win ratio increases the risk of many consecutive losers
A low win ratio means that you increase the risk of getting many consecutive losers. If you flip a coin with a 60% probability of getting head and only a 40% chance of getting coin, you’ll get longer losing streaks by betting on coin.
Let’s make an example by returning to the 200-day moving average in the S&P 500:
If you bought and sold the S&P 500 based on the 200-day moving average crossovers from 1960 until today, it shows a maximum of 9 consecutive losers. Granted, the losses are relatively modest, but it’s tough to take the tenth trade after nine losers in a row.
Our guess is that most traders have stopped trading the system before you get to the tenth trade, which eventually turned out to be a great winner.
This shows the importance of the win ratio. You want a high win ratio so you don’t stop trading the system.
Most humans are constructed to feel better after a gain than a loss, even without considering the size of the gains. If you manage to make 100 000 a year ten years in a row, you would probably feel pretty good about yourself. But if you made 1 million in the first year and nothing in the next nine years, you would have nine miserable years, even though the end result is exactly the same.
Sequence matters. Thus, the win ratio influences your emotions and your well-being.
A low win ratio increases the chances of ruin
By now most readers probably understand that a low win ratio and high bet size increase the risk of ruin. If you bet a large portion of your equity and risk many losers in a row, the risk of ruin increases substantially.
Obviously, this is very bad and something you need to avoid. A low win ratio implies a lower betting size or the need for diversification.
A low win ratio increases behavioral risk
Even if you offset the risk of ruin by diversification, you might dilute a strategy by skipping trades after a series of “bad luck”.
Behavioral risk is the mistake of, for example, selling into a panic and then reentering when it has risen 25% after the bottom.
A low win ratio increases the drawdown
A trading strategy with a low win ratio normally has a higher drawdown. We consider anything higher than 25% as high. We believe most traders can’t tolerate higher drawdowns than this. A low win ratio increases the chances of many successive losers, and thus a high drawdown.
If you have a backtest showing more than 25% drawdown, you better skip the strategy.
How to offset a low win ratio
Bob Mercer, the previous co-CEO of The Medallion Fund, once stated that their win ratio was 51% but still they managed to make money almost every day.
The reason is diversification. If you trade 50 different trading strategies even such a low win rate will make money almost every day as long as the strategies are uncorrelated, or at least lowly correlated. Correlation in trading is sometimes just as important as the trading strategy.
Unfortunately, small private traders don’t have the time nor the resources of The Medallion Fund. Most traders at best trade five trading systems and thus are not very diversified.
Because of this, you should take notice of your win ratio.
Different types of strategies have different win ratios
Mean reversion strategies typically have a high win ratio but the average losers tend to be larger than the average winner.
Opposite, trend following strategies have low win ratios but rely on the “rare” huge outliers that make a lot of money.
The win ratio is all about trade-offs: behavioral mistakes, drawdowns, and ruin
At the end of the day, trading strategies pose significant tradeoffs. Two of them are CAGR (total profits) vs max drawdowns, and the other is the win ratio and total returns.
This balance is what makes trading difficult and why many newcomers fail. If you try to maximize the total return, normally you increase the drawdowns and the risk of ruin. The win ratio is a major determinant of all those factors. It matters a lot.
Calculating the optimal capital allocation based on the win ratio
The trade-off in trading is always to find the balance between profits and losses/ruin. Let’s make some mathematical calculations to show how the win ratio influences how much you can allocate to each trade or strategy to balance profits and the risk of ruin.
What is the optimal allocation of capital per trade or per strategy?
In Technical Analysis of Stocks And Commodities in July 2001 Wolf von Rönik had an interesting article about risk and ruin. He provided a formula to find the optimal capital allocation given the win ratio and the expected gain per trade.
This is the formula:
A = Profit/loss ratio
P = The win ratio
The win ratio is described in this article, but not the profit loss ratio. The latter is simply the average gain for the winning trades divided by the average loss for the losing trades.
Let’s assume we have the following data for a strategy:
The win ratio is 60%, the average gain is 2% for the winning trades, and the average loss for the losing trades is also 2% (the profit/loss ratio is thus 1). This returns the following optimal allocation of capital:
(((1+1)*0.6)-1)/1 = 0.2
This means 20% capital allocation to each trade or each strategy.
Let’s change the parameters:
The win ratio drops to 40% but at the same time the average winner is twice the size the average loser. This returns the following optimal allocation of capital:
(((2+1)*0.4)-1)/2 = 0.1
Because the win ratio is lower, we need to allocate less money per trade to allow for a margin of safety to avoid ruin.
Let’s test a third strategy: the win ratio is 75%, the average winner is 2%, and the average loser is 2.5%. Let’s put this into the formula and we get this allocation number:
(((.8+1)*0.75)-1)/0.8 = 0.4375
Because the win ratio is higher, we can allocate more money per trade or strategy even though the losers are slightly higher than the winners.
Relevant reading for the win ratio:
- Why build a portfolio of quantified strategies
- Is this the Holy Grail of trading?
- What are negatively skewed trading strategies?
- What does correlation mean in trading?
Conclusion: why the win ratio in trading is important
The win ratio in trading is important and is an underappreciated factor in trading strategy development. A low win rate increases the chances of behavioral mistakes, high drawdowns, and ruin.
As a rule of thumb, we believe a win rate lower than 50% is not feasible for most traders. Your backtests might indicate you’ll make millions, but how you react to a losing streak and “bad luck” is what ultimately matters. Unfortunately, a long losing streak results in big drawdowns and makes most traders quit or start tweaking/curve fitting their strategies.
We believe you need both diversification and a high win ratio to minimize both the frequency and length of losing streaks. Losing streaks are inevitable, but how you react to them is often the “detail” that separates the good and bad traders. Thus, a high win ratio in trading is paramount.