Position sizing – Calculating position sizes according to risk

**“Position sizing”** (a term coined by Van K. Tharp) tells you **how much you can invest in a position** based on the risk level you’ve chosen and your strategy’s performance. This is one of the most important concepts that all traders should understand!

In Van K. Tharp’s renowned book “Trade your Way to your Financial Freedom”, the author emphasises that one of the key principles of trading success is that traders should always know their initial risk before taking a position.

He suggests that this risk should be standardised, and he calls it **R**. Your profits should also be standardised to a multiple of **R**, your initial risk.

The **risk per unit** is a direct calculation of the difference in points, ticks, pips or cents between the entry point and the stop-loss multiplied by the minimum allowed value of the lots or pips.

Take, for example, the risk of a micro-lot on the EUR/USD pair:

**Size of a micro-lot**: 1000 units**Entry price**: 1.19344**Stop loss**: 1.19621**Difference between the entry price and the stop-loss**: 0.00277

Dollar risk for a micro-lot: 0.00277 * 1000 = $2.77

In this case, if the investor sets his risk as $R (the amount he wants to risk on a trade) at $100, what should his position size be?

- Position size: $100 / $2.77 =
**-36 micro-lots**(this is a short trade)

With this concept, we can standardise the size of our position based on the chosen dollar risk. For example, if the unitary risk in the previous example was $5 instead, the position size would be:

- $100/5 =
**20 micro-lots**.

You would enter into a position with a standard and controlled risk, independent of the distance between your entry price and your stop-loss.

Your profits can be standardised as multiples of the **initial R risk**. It doesn’t matter whether you increase your risk from $100 to $150. If you keep the data using **R multiples**, you’ll observe a standardised history of your system.

With sufficient results, you’ll be able to truly understand how well your system works and also assess its statistical characteristics.

Values such as the **expectation (E)**, the average **risk/reward (RR)** ratio, the **% of winning trades**, the **number of R wins that the system delivers (R multiple)** in 1 day, 1 week, 1 month or 1 year.

Knowing these numbers is very important because it will help you achieve your goals.

You already know what the **(E) expectation** is. But the beauty of this number is that together with the average number of transactions, it tells you the **R multiple** that your system delivers within a time interval.

For example, let’s say that your system executes 6 trades per day, and its **E** figure is set at 0.45R. This means that it yields $0.45 per dollar risked.

This means that the system also delivers an average of 0.45 × 6**R = 2.7R per day** and that, on average, you can expect to have 54**R** each month.

Suppose you want to use this system and that your monthly goal is $6,000. What would your risk be on each transaction?

To answer this question, you have to set 54**R** = $6,000.

Your risk per trade must therefore be set at a given level:

**R**= 6000/60 = $111.

You now know, for example, that you could make $18,000 per month by tripling the risk to $333 per trade and $36,000 if you increase your risk to $666 per trade. **You’ve turned a system into an exponential money-making machine, but with a risk-controlling attitude.**

As a trader, you also want to know what to expect from the system in terms of drawdowns.

Is it normal to have 5, 9 or 19 consecutive losses? And what are the chances that a series of these losses will occur? Is your system behaving badly, or is it on the right track? You can also answer this question using the % Losers (**PP**).

Let’s examine the case if we had a system with 50% of trades that win and the other half loses.

We know that the probability that event A and event B occur together is the probability that A will occur multiplied by the probability that B will occur:

**ProbAB = ProbA * ProbB**

For a series of losses, we need to multiply the probability of a loss by the number of times the series lasts.

So, for a series of **n** losses:

- Prob_Streak_n =
**PP**to the power of n =**PP**^{n}

For example, the probability of 2 consecutive losses in our sample system is:

**Prob_Streak_2 = 0.5**^{2}

= 0,25 or 25 %.

And the probability of 4 consecutive losses would be:

**Prob_Streak_4 = 0,5**^{4}

= 0,0625 or 6,25%

And the probability of 6 consecutive losses would be:

**Prob_Streak_6 = 0,5**^{6}

= 0,015625, or 1.5625%.

And so on and so forth…

This result is directly related to the probability of losing everything. If your **R** is such that a series of 6 losses wipes out all of your funds, there is a 1.56% chance that this will happen using this system.

We have now learned that you need to set your **R** dollar risk at an amount such that a series of losses does not cause the account to exceed your allowable drawdown percentage.

What if the system has 40% of trades that win and 60% that lose, as is typically the case in most reward/risk scenarios? Let’s see:

**Prob_Streak_2 = 0.6**^{2}= 36%**Prob_Streak_4 = 0.6**^{4}= 12.96%**Prob_Streak_6 = 0.6**^{6}= 4,66%**Prob_Streak_8 = 0.6**^{8}= 1.68%

We observe that the probability of consecutive series of the same magnitude increases, so that the probability of 8 consecutive losses in this system is now the same as that of 6 in the previous one.

This means that with systems having a lower percentage of winning trades, we should be more careful and lower our maximum risk compared to a system that has a higher win percentage.

For example, let’s do an exercise to calculate the maximum dollar risk for this system on a $10,000 account and a maximum acceptable drawdown of 30%. Let’s also say that we want to assume 8 consecutive losses (a 1.68% chance of this happening, but with the certainty of it happening in a trader’s life).

Based on this, we’ll assume a series of 8 consecutive losses, or **8R**.

**30% of $10,000 = $3,000****8R = $3,000****The maximum allowed R is: 3000/8 = $375 or 3.75% of the trading account’s balance.**

Lastly, to get a sufficiently accurate measure of the % of losing trades, you need to have a history of your system with over 100 trades (tested in advance, if possible, as back-testing often gives unrealistic results).

You can do the same calculations for winning trades series, using the % of winning trades instead, and multiplying by the average reward (an **R** multiple).

**Position sizing**is the part of the system that tells us how much we should risk on a trade.- The
**R**risk unit is a standardised symbol for the dollar risk. - You need to measure, record and know the main statistical parameters of your system: the
**expectation**, the**% of winning and losing trades**, the**risk/reward ratio**and the**average monthly R**(the average R value that your system reaches in 1 month). - You should calculate the maximum
**R**allowed by your system and the target account size you need for the maximum drawdown that you can bear, and not bet more than this amount.

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