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 = Flipping heads ÷ Total outcomes (heads or tails)
  • 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?

I’m sure you already know the answer, but when the random event becomes more intricate (as with trading and business), you’ll need a repeatable, concrete formula to help you calculate your “expected value” or “profit expectation”.

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.

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Great article.