Without Bayes, John Nash would not have been able to come up with the idea of Game Theory.
Without Bayes, insurance companies would have to guess instead of calculate the risk of underwriting their policies.
Without Bayes there would be no Billy Beane, the guy who revolutionized the way baseball managers built their rosters.
And without Bayes, forecasting the stock market would simply be a crap shoot.
What Bayes' Theorem Does
Bayes took an intuitive mental exercise (assigning a probability to some future event, like the onset of an economic recession, or the arrival of a bear market in stocks) and came up with a formula that transformed educated guesswork into a refined probability statistic. His formula has been tested for nearly 300 years under real-world conditions, and it has proven to be very effective in improving probability.
How it works
When formulating a forecast and assigning a probability to the forecast being correct, Bayes gave a name to the initial estimate of probability - he called it the "Prior" probability. This is the baseline probability, based on a combination of observation and intuition.
For example, let's say you plan to take your family on a picnic and you want to get an idea of whether or not it will rain that day. You could just use your weather app on your phone, but Thomas Bayes didn't have a weather app, so he used math to calculate the chance of rain.
You begin with the baseline, or prior probability, which in this case is a 12% chance of rain on any given day in the area where the picnic will take place. Next, you refine that probability by looking out your window and taking note of any clouds in the sky. If there are clouds, the probability of rain will go up. If there are no clouds, the probability will go down. In this case, there are some clouds in the sky, so you know that the odds of rain will be higher than 12%.
The Formula
The equation for Bayes' Theorem is P(A|B) = [P(B|A) * P(A)] / P(B). This formula calculates the updated probability of event A (it will rain today) given that event B has occurred (there are rain clouds present) (P(A|B)), by considering the probability of B given A (P(B|A)), the prior probability of A (P(A)), and the total probability of B (P(B)).
Don't let this formula put you off because there are plenty of YouTube videos that walk you through the process of calculating probabilities using Bayes Theorem. Here is one that I found very helpful.
Bayes' Theorem and the stock market
I use Bayes' Theorem every day as I maintain my two models - one for the economy and one for the stock market. For the stock market, my prior probability is that the market will go up by 10% per year, which is the long-term average.
Then I look at certain key indicators like GDP growth, corporate earnings growth, and employment growth to refine my baseline probability using Bayes' formula. I end up with a forecast that is more accurate than the baseline alone, or my intuition as an experienced portfolio manager.
Final thoughts
With the help of Bayes' Theorem, I have been able to give my clients a more accurate estimate of where the stock market will be in 6 months. The stock market has a mind of its own, so my forecasts aren't always accurate. But they are more accurate than they would be without the help of Bayes' Theorem.