## Money & Probability

Probability is simply the likeliness of a random event occurring. In order to fully understand probability models in trading, it is important that you know how to calculate the basic probability of a random event.

For this example, we will calculate the probability of flipping a head in a single coin toss.

• Probability of event = Number of ways event can occur ÷ Total possible outcomes
• Probability of flipping heads = 1 ÷ 2 = 0.5

The probability of any event occurring has a value between 0 and 1.

Zero represents an impossible outcome and 1 represents a certain outcome. To quickly turn the decimals into a percentage probability, simply multiply it by 100. In the example above we calculated the probability of a flipping a head in a single coin toss is 0.5 (or 50%).

Simple, right? Let’s move on.

Let’s take the previous example of a single coin toss and throw some money into the mix!

Say you have a friend called Tom who is willing to pay you \$1 every time you manage to flip heads. In return, you must pay him \$1 every time you flip tails.

How much can you expect to make?

Let’s summarize what we know about the coin toss:

• There are two possible outcomes (heads or tails)
• We have previously calculated the probability of either outcome to be 0.5 (50%)
• If you flip heads, you make \$1
• If you flip tails, you lose \$1

With this information, we can now use a “profit expectation” formula to calculate exactly how much profit we should expect to make from Tom.

• Profit expectation = (Profit scenario) + (Loss scenario)
• Profit expectation = (Profit x Probability of Profit) + (Loss x Probability of Loss)
• Profit expectation = (\$1 x 0.5) + (-\$1 x 0.5) = \$0

So from a mathematical standpoint, your expected profit in this situation is \$0. But I’m sure you already knew that would be the case. Let’s skew the numbers now and see if you can make money from a coin toss.

#### Tilting the expected value

This time, you negotiate with Tom and come to an agreement that if you flip heads he still pays you \$1, however, if you flip tails you shall only pay him 90 cents. That 10 cent difference can be a game changer.

• Profit expectation = (Profit scenario) + (Loss scenario)
• Profit expectation = (Profit x Probability of Profit) + (Loss x Probability of Loss)
• Profit expectation = (\$1 x 0.5) + (-\$0.9 x 0.5) = \$0.05

After negotiating with Tom, you now have a profit expectancy of 5 cents per coin flip!

If you toss the coin 100 times, statistically speaking you will make \$5. By “cutting your losses short” you managed to gain a profitable edge in the game.

In trading, one of the ways we achieve an edge in the market is by “cutting our losses short” with the use of trailing stops.

#### So what is an edge?

Having an edge in the market is simply having a positive profit expectancy. A trader with an edge will make money over time, as long as he gives the edge long enough to play out. There are 3 core methods we can use as traders to increase our edge:

1. Increase win rate
2. Increase profit on winning trades
3. Decrease losses on losing trades

There’s a saying in financial markets, “cut your losses short and let your profits run”. It refers specifically to methods 3 and 4 to help traders increase their edge. A powerful trading strategy with stringent risk management procedures should harness all 3 of these methods in order to increase your edge in the market.