Bayes’ Theorem

Definition

Bayes’ theorem (also known as Bayes’ Law or Bayes’ Rule) is a mathematical formula for finding a probability when other probabilities are known (Conditional Probability). This theorem is named after Thomas Bayes, an 18th- century British mathematician. It deals with exploring all necessary possibilities, predictions, or theories that concern determining a matter. In finance, however, this theorem is used to determine the risk involved in lending money to potential borrowers—risk evaluation.

Formula:

        P (A|B)  = P (A∩B)    =     P (A) P (B|A)

                   P (B)                 P (B)

Thus implies that:

P (A) = the probability of A happening

P (B) = the probability of B happening

P (A|B) = the probability of A happens given that B happens

P (B|A) = the probability of B happens given that A happens

P (A∩B) = the probability of A and B happening

NB: Bayes’ theorem gives the probability of an event occurring based on other information relative to the event. For example, if you Google “Berkshire Hathaway” other results relating to Berkshire Hathaway such as Warren Buffet would pop up.

Other Information

Bayes’ theorem allows users to update already predicted probabilities of the occurrence of an event by integrating new probabilities to it. This theorem is not only applicable in mathematics or finance but covers a wide range of applicable fields such as computing and engineering. It can also be applied to the medical field by determining the probability of a person having a disease and the accuracy of the person’s medical test.

In finance, Bayes’ theorem functions as a theory for conditional probability given that yhe probability of an event is determined by the occurrence of another event. For example, with the rate at which the Tesla stock price rocketed in a short amount of time you may then ask, “what is the probability of Tesla (NYSE: TSLA) stock price falling?” Using a conditional probability formula to determine this, you may have something like, “what is the probability of TSLA stock price falling given that the S & P 500 index fell recently?” So, the probability of the TSLA stock price falling would be relative to the fall of the S & P 500 index.