# Risk Reward Ratio And Expectancy

## Risk Reward Ratio And Expectancy

In this short post we will look at the subject of risk reward ratio and expectancy.  We discuss how - contrary to popular belief - the key to success is not just anticipating the next directional move from the market.

How many times have you had a series of winning trades only to see the profits wiped out with a few losers?  Did you allow your losing trades to run to the full stop loss (or worse), hoping the market would turn around, but take profit as soon as the position went in the desired direction by a handful of pips only to see your original profit target hit?

If you answered yes then you are not alone, this is a recurring theme for many market participants.

Traders often obsess over entry strategies and never allow their winners to run, this not only has an adverse affect on the account balance but also the individuals state of mind.  The reality is that humans have a natural tendency to want to be right all of the time, it feels good, and we are taught to be this way; we don’t typically handle losses gracefully.  However, trading should be looked at in terms of probabilities which can take some getting used to.

### Risk Versus Reward

The risk reward ratio is calculated by weighing the possible gain against a potential loss.  The example table below represents a series of trades where only 50% turn out to be winners, in this scenario the trader would still be profitable to the tune of £10k.

The risk reward ratio is only part of the puzzle though.  A trading system that gives a 2:1 risk reward ratio but only has 2 out of 10 trades as winners is not going to be any good.  This brings us on to an important concept….expectancy.  This losing system with a 2 in 10 win ratio has a negative expectancy of -400 but the system shown in the table above has a positive expectancy of 1000.  Let’s look at this further and discuss the profit expectancy equation.

### Expectancy

You will often hear other traders referencing axioms like “the risk reward ratio must be greater than  2:1 in order to be profitable” or similar. The reality is that the so called “expectancy” of a system provides a better way of understanding whether there is actually an edge associated with your trading strategy.  Expectancy gives an approximation of  the average amount you could expect to win (or lose) for every pound you risk.

Expectancy takes into account these four elements:

• Winners – W%.
• Losers – L%.
• Average win  - Ave W.
• Average loss  - Ave L.

The expectancy of a trading system can be calculated using the following formula:

Expectancy = (W% x Ave W) – (L% x Ave L)

So taking our example above with the series of ten trades

(0.5 x 3000) – (0.5 x 1000)

= 1500 – 500 = 1000

This shows the example system has a positive expectancy.  Hopefully it goes with out saying that a sample size of ten trades is not adequate.  In reality, traders will look at hundreds of trades in order to gain a view on how a system may perform and demo trading is one way of gathering this data.  Even with this data there is no guarantee/assurance that future trades will mimic the historical data, but that is the nature of risk taking.  Nonetheless, our trade log does give an invaluable insight and is a necessary reference regardless.

Do you need to let your winners run further in order to gain a positive expectancy?  You should constantly monitor how your trading system is performing in this respect to track the viability of a strategy.  The fact that a trader can lose on over 50% of trades and still make money with the right risk reward ratio is certainly worthy of note. Play with the figures yourself after you have a reasonable amount of historical data to reference and see how a better risk reward ratio would affect your statistics.  The alternative view is that some traders have an extraordinary win to loss ratio and these individuals can afford to take quick profits as the losers are few and far between.  Nonetheless, the majority of traders do not have an ultra-high win rate and could potentially benefit from a higher R/R ratio.

Expectancy and position sizing are two critical factors associated with trading success.  Professional traders typically have a solid understanding of expectancy and use good money management practices – while applying these with discipline and in accordance with their rules – in order to gain as much from their edge as possible; essentially they constantly strive to maintain a positive expectancy and use a position size that fits their risk profile. If you are struggling in your trading it may be time to go back to a demo account and look at the risk reward and expectancy elements of your trading strategy.

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