 ### Introducing the R concept When trading on the Forex markets, we are living in a world of leveraged instruments. Therefore our potential to control asset sizes exceeds by far our own trading capital. But this carries its own Damocles sword. Traders have huge opportunities to profit, but at the same time, they are exposed to huge risks.  That means traders need to apply a rigorous methodology to their position sizing if they want to maximize their returns and, at the same time, control risk and reduce their probability to go broke.

In the previous article, we have already introduced the concept of Reward Factor, which we have defined as a multiplier that tells us how many risk-units is the reward of a trade. Let’s imagine this Reward Factor applied to a standard risk unit that we call R (A term introduced by Dr Van K. Tharp in his book Trade Your Way to your Financial Freedom).

Using the R concept, we are normalising the trade profits as a multiple of a basic unit of risk R. If our strategy delivers a mean profit similar to our mean loss then our R = 1. If they are two times the mean loss our R = 2, and if losses are 2 times the mean profit, our R =0.5.

### Normalising our trade risk using R and dollar-R concepts

We will always define one R as the difference between the entry-level and its invalidation point.

Consider the following example:

Let’s compute the lot risk of this EURUSD hourly chart setup long entry:

```           pip risk: \$10.00
Entry point: 1.13266
Stop loss: 1.12931```

R  = (1.13266 – 1.12931)*10,000 =  33,5 pips

If we had been trading one full lot, or dollar_R, would have been R x pip_risk:

Full_lot_Dollar_R = 33.5 x 10 = \$335

Using this R concept, we can standardise our positional dollar risk. For example, if  we wanted our current risk to be set to \$150 instead of the risk of the full lot we would need to enter a fraction of a lot:

Position size = MyDollar_R/ Full_lot_dollar_R. in this case,

Position size = \$150/\$335 =0.45 lots or 45 mini-lots.

If the next trade’s full-lot dollar_R were \$200, then our position size for that trade would have been:

Position size = \$150/\$200 =0.75 lots or 75 mini-lots.

As we see our position size changes from trade to trade, but our dollar-risk is kept constant.

### Profit targets as multiples of R As we’ve already mentioned, using this methodology we standardise our profits as well as multiples of a basic R factor or risk unit. If we keep our records using the R reward factor, we have normalised our track record as well.

With sufficient data, we will be able to measure and understand the performance of the system and measure its main parameters: Expectancy (E), reward-to-risk ratio (RR), % gainers, and the mean amount of R-units the system can deliver on a time interval, daily, monthly and yearly. Moreover, Knowing how many R-units can give our system is quite important, even crítical, because it opens the path to compute returns and plan our financial objectives reliably.

### The Mathematics of Profitability Expectancy is one of the key parameters when measuring the performance of a trading system. It tells us if the system is profitable long-term and, also how much profit should we expect, on average, on any trade.

Expectancy is the mean value of winner trades (E+) less the mean value of loser trades (E-)

(E+) = ∑(G)/(N+)  x  %Winners
(E-) = ∑(L)/(N-)  x  %Losers

∑(G): The gross dollar profit on our sample history
∑(L): The gross dollar loss on our sample history

(N+): Number Gainers
(N-): Number of Losers

The system’s expectancy E is:

E = (E+) – (E-)

The above Expectancy dissection is to get the concept more clearly,  but we can compute it more easily as the mean value of the total trade sample.

Where N= total number of trades,

So E is the normalised mean or total results divided by the number of trades n.

If E shows a positive figure, the system is good. The higher the E, the better the system is.  If it is zero or negative, the system is a loser, even though it shows over 90% gainers. Of course, if the system shows a high per cent gainers, we should analyse why E is negative and try to eliminate the cause of this abnormal behaviour because it surely is a matter of controlling the losses.

### Defining objectives using R and E The beauty of the combination of R and E is that we can compute the standard R returns that a system is able to deliver in a time lapse.

For example, let’s assume we have a system that delivers 25 trades per week or 5 trades daily; and that, after examining our trading record and computed our system’s E we find that E = 0.25, meaning it delivers \$0.25 per dollar risked.

Then we know that the system can deliver 25*0.25 R = 6.25R per week or about 25R per month. That means we are getting 25 times our risk every month. Therefore, if we were risking \$100 (our dollar_R is \$100) then, we could expect \$2,500 monthly using it.

Now, if we wanted to set our objectives to \$5,000, we know we should raise our dollar-R risk to \$200 instead. And that the Dollar-R risk needed to obtain \$10,000 monthly must be \$400. We can convert our system in exponential money-making machinery.

Of course, we should also find out how much risk our trading account can withstand. That is, so we would need enough cash to support the individual trade risk and, also the implied max drawdown.

### Results are Variable The dark side of trading is the drawdown. Drawdowns are unavoidable. They are a consequence of the random nature of things. There is no trading system 100% right. Therefore, there is a certain probability of a loss on every trade.

The probability of a loss is the 1 – prob_of_gainers

But what is the likelihood of this happening twice, or three, four, five times in a row?

Simple statistics tell that the probability of an event A  happening n times in a row is the probability of one event happening multiplied by itself n times, which is Prob_A to the power of n.

Prob_NX_A = Prob_A^n

As an example let’s find out what is the probability of having a 5-losing streak on a system that has 60% winning trades.

Loss_P = 1- Gain_P = 1-60% = 40%

Prob 5-LStreak = Loss_p^5

= 0.4^5

= 1.024%

That means one every one hundred 5-trade patterns will be one 5-losing streak. A trader has to be prepared to this happening from time to time. Also, we should be aware that as the trading system’s per cent of winners diminish its per cent of losers will grow. It’s not uncommon for a system to expect 10 to 15 losing trades in a row. Therefore, the trader should be prepared to withstand this.

### Computing the dollar_R risk on our system. We will cover position sizing and risk control strategies in further articles, but to end this article, I’d like to offer you a simple method to define the dollar_R number for your trading system ( and for yourself). This method can be universally adopted because it relies on your account balance and your particular acceptance to assume risk. The process is as follows:

The first thing you need to define is your tolerance for risk. Some traders are comfortable with 30% to 40% drawdowns; others cannot accept more than 20% while the nimbler ones are already worried about a 5% to 10% drawdown.

So, let’s assume here a moderate 20% max allowed drawdown is the trader’s choice. Also, let’s assume we wanted to be protected against a 10-losing streak. That means we expect a very low probability that our system had 10 consecutive losers. Under these conditions, the simple formula to guarantee that we won’t exceed our 20% drawdown target is:

MyDollar_R = 20%/10 = 2%

Then If our trading account balance was \$10,000 our dollar_R Should be:

MyDollar_R = 2% *Acc_Balance = 10,000*0.02 = \$200

Therefore, if we apply this figure to the system of the example above, whose E = 0.25, we’ll find out that the system will deliver \$5,000 monthly on average using the Dollar_R = \$200, and the projected drawdown will be 20%. We also know that if we wanted to get a \$10,000 monthly return, we should raise the trading balance to \$20,000 or accept 40% potential drawdowns.

### Conclusions

What we have learned here is the most critical information you’re going to find for your trading career. The majority of traders lose because they usually take too much risk. Now you have a method to consistently decide your risk and rewards based on your capacity to accept drawdown and the size of your trading account.

We have also shown the methodology to analyse the profitability of your system and apply it to compute the monthly system’s returns and balance it with the risk to make robust money-making machinery.