basic probability facts: bayes’ theorem statistics & risk management copyright © 2012 texas...

Copyright © 2012 Texas Education Agency. All rights reserved. 1

Basic Probability Facts: Bayes’

TheoremStatistics & Risk

Management


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Bayes’ Theorem

● Thomas Bayes 18th century● How to accumulate information and revise

estimates of probability.

http://en.wikipedia.org/wiki/Bayes%27_theorem


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


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.


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



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



Known Risk

You Buy


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%


Formula

𝒑 (𝒀𝑩|𝑵𝑩 )=𝒑 (𝑵𝑩|𝒀𝑩 )×𝒑 (𝒀𝑩 )

𝒑 (𝑵𝑩 )We are calculating a Degree of Belief or

Confidence

basic probability facts: bayes’ theorem statistics & risk management copyright © 2012 texas...

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