Do you understand the profit/loss ratio well?

According to the prevailing view in the money management strategy, it is required that the average loss per trade should be less than the average profit trade. However, let’s examine the concepts of profit and loss and see how this old statement can be adjusted. 

What is the relationship between profit and loss ratios?

A profit/loss ratio applies to the average profit size compared to the average loss size per trade. For instance, if you expected a profit of $900 and a loss of $300 for a particular trade, your profit/loss ratio will be 3:1. It is $900 divided by $300. Many trading books promote a profit/loss ratio of at least 2:1 or 3:1. Even though most people agree with that recommendation, this advice can be misleading and harmful to your trading account. This recommendation doesn’t consider the market’s practical realities, the individual trading style, and the APPT factor. 


The importance of average profitability per trade

APPT, average profitability per trade, applies to the average amount you can expect to win or lose per trade. Usually, people are so fixed on their profit/loss ratios that they become oblivious to a bigger picture. Your trading performance depends mainly on your APPT.


Here is the formula for average profitability per trade:

APPT = (PW×AW) − (PL×AL)

PW = Probability of win; AW = Average win; PL = Probability of loss; AL = Average loss​


Let’s examine the APPT of the following possible scenarios:

Scenario A:

Consider that you place ten trades. You profit on three of them and lose on seven of them. Therefore, your profitability is 30% or 0.3%. Meanwhile, your loss is 70%, or 0.7. 

So, trade makes an average winning of $600 and an average loss of $300.


In this situation, the APPT is:

(0.3 \x\$600) – (0.7 \x\$300) = – \$30(0.3×$600)−(0.7×$300)=−$30

The result is a negative number which means that you will possibly lose $30 for every trade you place. 

The profit/loss ratio is 2:1. However, this trading approach provides only 30% of winning trades.


Scenario B

Now examine the APPT with another example with a profit/loss ratio of 1:3. Consider that out of ten trades you place, you profit from eight of them and lose two of the trades. 

Here is the APPT:

(0.8 \x\$100) – (0.2 \x\$300) = \$20(0.8×$100)−(0.2×$300)=$20

This example shows that despite having a profit/loss ratio of 1:3, the APPT is positive. So, with this trading approach, you can be profitable over time. 


How to calculate profitability for specified periods

It is also interesting to analyze how an investment behaves during specific periods concerning the previous ones. Depending on the data you have, the periods can be weekly, monthly, quarterly, annually, etc.

To calculate the one for these periods, you have to use the simple profitability formula again.


How is the average return on investment calculated?

How to calculate the average profitability of an investment? Many investors do not do it correctly. Let’s explain why.

For example:

Year 0: Investment is $1,000

Year 1: The investment is $2,000. Profits of $1,000 (annual return + 100%).

Year 2: The investment profit to the initial $1,000. Losses of $1,000 (annual return – 50%). 

To calculate the average profitability of this investment, we have to add each year’s returns (+100% and -50%) and divide the result between 2 years. An average profit of 25% comes out.

But if you look closely, the final amount of the investment ($1,000) coincides with the initial one ($1,000). So, the total return on the investment is 0%.

How can this be? The average profit of +25% and total return of 0%?

This is because, in the example, the arithmetic means of profitability is being used instead of the geometric profitability.

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