I can hear you asking:”What in the blue hell is an EVRatio?” To put it simply, the EVRatio (as we shall choose to refer to the **E**xpected **V**alue **Ratio**) is the **true Reward/Risk ratio** of a trading method, **after the probabilities of the exits** (both target and stop) being hit have been taken into account,. this is done, as we have previously demonstrated, by calculating the expected values of the gains (by the target being hit first), and the losses (by the stop being hit first).

We have spent the earlier part of this series, Parts 1 and 2 explaining what the *Expected Value* is, and showing how to calculate it in the most elementary manner. If you have forgotten, here are the links:

- Trading with Expectation/Expected Value – Part 1a: Will our exits be hit?
- Trading with Expectation/Expected Value – Part 1b: Examining the counts.
- Trading with Expectation/Expected Value – Part 1c: Calculating probability.
- Trading with Expectation/Expected Value – Part 2a: My reward to risk is always 3:1. Why am I still losing?
- Trading with Expectation/Expected Value – Part 2b: Calculating the Expectations

In this post, we shall bring it all together, still using the unspecified trading method that we have been examining, using sample values so far. To recap, we have so far calculated, as per Part 2b:

*Expected Value*of loss,**EV**= 0.8 x 10 ticks = 8 ticks._{loss}*Expected Value*of gain,**EV**= 0.2 x 30 ticks = 6 ticks._{profit}

Clearly we have a target (30 ticks) and a stop loss (10 ticks) that satisfies the oft-cited guru ratio of 3:1. But is that the whole story?

### How the probabilities change things

By simply looking at the ordinary meaning of the words, “gain” and “loss”, we can calculate the net Expected Value of the trading method. It is simply the Expected Value of the gain, less the Expected Value of the loss. Therefore, we can say that given our statistics for this trading method, the net Expected Value of the trading method,

**EV _{net}** =

**EV**–

_{profit}**EV**= 6 – 8 = –2 ticks: a net 2 tick loss per trade.

_{loss}But, you say, how can I be losing when I am following that magic guru 3:1 R/R ratio? Well, first of all, there is nothing magical about 3:1. It is simply another rule of thumb that somehow became very popular, and is now seen by some traders (usually unprofitable ones, but that is another story) as some divine rule of trading that must never be broken. However, as that ratio does not take into account the probability of the exits being hit, it is missing a part of the story.

A **EV _{net}** = –2 only tells us that our method is statistically, most likely a losing one. It does not really tell us how bad it is. To do that, we look at the

**EV**as a value relative to the Expected Value of the risk we are taking. In other words, we normalize the values that we are examining. After all, it we were risking a large value, with an expected average net loss of only 2 ticks, we might have a system that is close enough to break even that it may be worth our time to re-examine it in order to see if we can make it profitable. On the other hand, if we have a system that is showing a large net expected value of loss relative to a small risk, it would mean that our stops may be too tight, and are simply getting hit by the ordinary noise of the market.

_{net}So, in this particular case, our ratio of net Expected Value to Expected Value of risk (loss) is **EV _{net}** ÷

**EV**= –2/8 = 0.25 = 25%. This simply means that statistically, over the long run, we can expect to lose 25% of our risk equity if we continue to trade this method.

_{loss}Whereas this tell us the statistical, expected percentage loss/gain of our method, it might be even easier to just look at what conditions we need in order for a trading method to have a positive Expected Value. All we need is that **EV _{profit}** should be larger than

**EV**Written in arithmetic fashion: for a profitable trading method,

_{loss.}**EV _{profit}** >

**EV**

_{loss}So that we can normalize things, as a ratio of our **EV _{loss}** , we simply need to divide both sides of the inequality by

**EV**. So, for a profitable method,

_{loss}**EV _{profit}** /

**EV**>

_{loss}**EV**/

_{loss}**EV**or

_{loss}**EV _{profit}** /

**EV**> 1

_{loss}But what have we just written? We say that for a profitable method the Expected Value of gain, divided by the Expected Value of loss, should be greater than 1. So **EV _{profit}** /

**EV**is just what we have been calling the EVRatio.

_{loss}EVRatio =

EV/_{profit}EV, must be greater than one, for a profitable trading method._{loss}

So now, for those that insist on some magic ratio, it is not the raw reward/risk ratio that is the criterion: it should be the probability-adjusted reward/risk ratio, which we are calling the EVRatio that should be the criterion. If you insist on using 3:1, then it is the EVRatio that must satisfy the ratio.

Note that this can often mean that the stop loss may be further away than the target, which many traders will derisively say: “Your R/R is inverted, so you must lose in the long run.” That is what happens when one does not take *probability* into account. Does this mean that no matter the size of the inversion, if the EVRatio is greater than 1, then the trades must always be taken? No. That question too just shows a rigid mentality that is not taking all factors into consideration. In other words, a profitable trading method must take at minimum 3 factors into account:

- The EVRatio. If this is less than the preset value, as has been
*a priori*determined by the trader using the method, the trade should simply not be taken. Nothing else need be examined.**An EVRatio that is less than 1 must always automatically mean that the trade should not be taken**. To take such a trade is simply an exercise in imbibing hopium. - After the EVRatio is valid for a trade, the trader must determine if the logical placement of the stop would exceed the maximum value that the trader is willing to lose on a trade. This maximum value should have been predetermined as part of the trading method, not decided on the fly, when the trader is under pressure. If the Stop Loss order, placed at the logical place for it, per the market structure, is greater than the maximum allowed loss, then the trade is disqualified and should not be taken.
- After the Stop Loss criterion is passed, the trader must determine if the target placement will be such that if hit, the gain would be larger than the minimum acceptable gain. Only then should the trade be taken.

We shall examine this question in much greater depth in a later post, where we shall apply these concepts to a complete trading method that you can test and use in suitable markets.

In the meantime, why not leave a comment? Even if you do not agree with what we have written.