Many people put a lot of faith into the estimates and simplified probabilities given by experts in their field; this also gives us the great ability to confidently produce new estimates for new and more complicated questions introduced by those inevitable roadblocks in financial forecasting.

Instead of guessing or using simple probability trees to overcome these road blocks, we can now use Bayes' Theorem if we possess the right information with which to start.

For our example we will use the data below to find out how a stock market index will react to a rise in interest rates.

Here: P(SI) = the probability of the stock index increasing P(SD) = the probability of the stock index decreasing P(ID) = the probability of interest rates decreasing P(II) = the probability of interest rates increasing So the equation will be: Thus with our example plugging in our number we get: In the table you can see that out of 2000 observations, 1150 instances showed the stock index decreased.

This is how Bayes' theorem uniquely allows us to update our previous beliefs with new information.

For this article, we will be using the rules and assertions of the school of thought that pertains to frequency rather than subjectivity within Bayesian probability.

This particular rule is most often used to calculate what is called the posterior probability.

The posterior probability is the conditional probability of a future uncertain event that is based upon relevant evidence relating to it historically.

Changing interest rates can heavily affect the value of particular assets.

The changing value of assets can therefore greatly affect the value of particular profitability and efficiency ratios used to proxy a company's performance.

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