When many of us think of probabilities, the first thought that comes to mind is a coin toss—having a 50% chance of being correct on a given toss. Can something as simple as a coin toss be applied to investing in financial markets?

Probabilities, as with a coin toss, can indeed provide us with tools for approaching the markets, and the ideas can be applied in more ways than one might expect. For example, a trader's view on probability might be completely incorrect, and that might be the very reason why they are not making money in the markets. This article aims to help by providing an introduction to the probabilities of trading and statistics.

### Understanding the Coin Toss

Let's assume that at a given moment in time, a stock could just as easily move up as it could move down (even in a range, stocks move up and down). Thus, our probability of making a profit on a (short or long) position is 50%, which is the same as a coin flip.

### Key Takeaways

- Learning about statistics and probabilities can help gauge whether returns are likely to continue or if the returns just happened to be due to a random event.
- A coin flip often comes to mind when thinking about probabilities, as there is a 50% chance that a coin lands on heads and 50% that it falls on tails.
- The concept of probabilities can also be used as a tool when investing in financial markets.
- Determining whether superior trading is due to luck or skill often requires many years of observation, especially for longer-term investment strategies.

Although most investors would not likely initiate random short-term trades, we will start with this scenario. If we have an equal probability of making a quick profit, does a run of profits or losses signal what future outcomes will be? No! Not on random trades. Each result still has a 50% probability, no matter what outcomes came prior. The same is true of a coin toss—if it lands heads ten consecutive times, the probability of it landing on tails on the next toss is still 50%.

A consecutive streak or a run can happen in random 50/50 events. A run refers to a number of identical outcomes that occur in a row. Here is a table displaying the probabilities of such a run; in other words, the odds of flipping a given number of heads or tails in a row.

Run Length |
Chance |

1 |
50% |

2 |
25% |

3 |
12.5% |

4 |
6.25% |

5 |
3.125% |

6 |
1.5625% |

Here is where we run into problems. Let's say we have just made five profitable trades in a row. According to our table, which is giving us the probability of being right (or wrong) five times in a row based on a 50% chance, we have already overcome some serious odds. The odds of getting the sixth profitable trade look extremely remote, but actually, that is not the case. Our odds of success are still 50%.

People lose thousands of dollars in the financial markets (and in casinos) by failing to realize the randomness of probabilities. The odds from our coin-toss table are based on uncertain future events and the likelihood they will occur. Once we have completed a run of five successful trades, those trades are no longer uncertain. Our next trade starts a new potential run, and after the results are in for each trade, we start back at the top of the table, *every single time*. This means every trade has a 50% chance of working out.

The reason this is so important is that when traders get into the market, they often mistake a string of profits or losses as either skill or lack of skill, which is simply not true. Whether a short-term trader makes multiple trades or an investor makes only a few trades per year, we need to analyze the outcomes of their trades in a different way to understand if they are merely "lucky" or if actual skill is involved. It's important to remember that statistics apply to all timelines.

### Long-term Results

The above example gave a short-term trade example based on a 50% chance of being right or wrong. But does this apply to the long term? Very much so. The reason is that even though a trader may only take long-term positions, he or she will be doing fewer trades. Thus, it will take longer to attain data from enough trades to see if simple luck is involved or if it was skill. A short-term trader may make 30 trades a week and show a profit every month for two years. Has this trader overcome the odds with real skill? It would seem so, as the odds of having a run of 24 profitable months are extremely rare unless the odds have shifted more in the trader's favor somehow.

What about a long-term investor who has made three trades over the last two years that have been profitable? Is this trader exhibiting skill? Not necessarily. Currently, this trader has a run of three going, and that is not difficult to accomplish even from totally random results. The lesson here is that skill is not just reflected in the short term (whether that is one day or one year, it will differ by trading strategy); it will also be reflected in the long term. We need enough trade data to accurately determine whether a strategy is effective enough to overcome random probabilities. And even with this, we face another challenge: While each trade is an event, so is a month and year in which trades were placed.

A trader who placed 30 trades a week has overcome the daily odds and the monthly odds for a good number of periods. Ideally, proving the investment strategy over a few more years would erase all doubt that luck was involved due to a certain market condition. For our long-term trader making trades that last more than a year, it will take several more years to prove that the strategy is profitable over this longer time frame and in all market conditions.

When we consider all time frames and all market conditions, we begin to see how to be profitable in all time frames and how to move the odds more on our side, attaining greater than a random 50% chance of being right. It is worth noting that if profits are larger than losses, a trader can be right less than 50% of the time and still make a profit.

### How Profitable Traders Make Money

Of course, people do make money in the markets, and it's not just because they have had a good run. How do we get the odds in our favor? The profitable results come from two concepts. The first is based on what was discussed above—being profitable in all time frames, or at least winning more in certain periods than is lost in others.

### 1 in 13,983,816

The probability of matching and winning a six-number lottery drawing.

The second concept is the fact that trends exist in the markets, and this no longer makes the markets a 50/50 gamble as in our coin toss example. Stock prices tend to run in a certain direction over periods of time, and they have done this repeatedly over market history. For those of you who understand statistics, this proves that runs (trends) in stocks occur. Thus we end up with a probability curve that is not normal (remember that bell curve your teachers always talked about) but is skewed and commonly referred to as a curve with a fat tail (see the chart below). This means that traders can be profitable on a consistent basis if they use trends, even if it is in an extremely short time frame.

*Source: Stockcharts.com*

### The Bottom Line

Why is the 50% probability example useful? The reason is that the lessons are still valid. A trader should not increase position size or take on more risk (relative to position size) because of a string of wins, which should not be assumed to occur as a result of skill. It also means that a trader should not decrease position size after having a long, profitable run.

New traders can take solace in the fact that their researched trading system may not be faulty, but rather the method is experiencing a random run of bad results (or it may still need some refining). It also should put pressure on those who have been profitable to monitor their strategies continually, so they remain profitable over time.

This approach can also aid investors when they are analyzing mutual funds or hedge funds. Trading results are often published that show spectacular returns; knowing a little more about statistics can help us gauge whether those returns are likely to continue or if the returns just happened to be a random event.