Basic Probability Facts: Bayes’ Theorem Statistics & Risk Management Copyright © 2012 Texas Education Agency. All rights reserved. 1

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Bayes’ Theorem ● Thomas Bayes 18th century ● How to accumulate information and revise estimates of probability. Copyright © 2012 Texas Education Agency. All rights reserved. 3

Example ● Your Portfolio Manager suggests that you buy 2000 shares of Acme Production. ● All of the shares you have bought as per his suggestion have done well. ● 100% Probability this is good Copyright © 2012 Texas Education Agency. All rights reserved. 4

Example ● You research the industry and find out this industry on a whole is on a downward spiral ● Now you adjust the probability this will be a good investment ● 60% Probability this is good. Copyright © 2012 Texas Education Agency. All rights reserved. 5

Example ● You research this Specific Company and find out it is restructuring and struggling. ● You again adjust the probability this will be a good investment ● 40% Probability this is good. Copyright © 2012 Texas Education Agency. All rights reserved. 6

Example ● You call your Broker and she explains that one of the product lines makes it a prime candidate for a takeover. She know of several large firms which are publicly examining this company. ● You again adjust the probability this will be a good investment ● 80% Probability this is good. Copyright © 2012 Texas Education Agency. All rights reserved. 7

Known Risk You Buy Copyright © 2012 Texas Education Agency. All rights reserved. 8

Assessing Knowns p(Broker is Reliable) = p(YB) = 100% p(Industry is Sad) = p(NB) = 50% p(Company is teetering) = p(NB) = 70% p(Target for Takeover) = p(YB) = 50% Copyright © 2012 Texas Education Agency. All rights reserved. 9

Formula We are calculating a Degree of Belief or Confidence Copyright © 2012 Texas Education Agency. All rights reserved. 10