Matt Mendoza is a security analyst for the Senbet Fund. Matt believes the value

Question

Matt Mendoza is a security analyst for the Senbet Fund. Matt believes the value of the Fund through the end of 2016 will be related to the flow of credit in the U.S. economy overall. Matt estimates the probability the flow of credit improves significantly equals 0.2 and the probability the flow of credit improves marginally equals 0.5 (a third possibility is the flow of credit does not improve). Matt also estimates the following probabilities the Fund will increase in value through the end of2016: 0.9 if the flow of credit improves significantly, 0.4 if the flow of credit improves marginally, and 0.1 if the flow of credit does not improve. If the Fund increases in value through the end of 2016, use Bayes' approach to determine the probability the flow of credit improves marginally.

Explanation / Answer

Let A be the event that the fund will increase in value. Also let:

S: flow improves significantly, M: flow improves marginally and D: flow does not improve

Then,

P(S) = 0.2, P(M) = 0.5, P(D) = 1 - P(S) - P(M) = 0.3

P(A|S) = 0.9, P(A|M) = 0.4 and P(A|D) = 0.1

First we need to find out P(A)

P(A) = P(S) * P(A|S) + P(M) * P(A|M) + P(D) * P(A|D)

= 0.2 * 0.9 + 0.5 * 0.4 + 0.3 * 0.1

= 0.18 + 0.20 + 0.03 = 0.41

Prob(Flow improves marginally | Fund Increases) = P(M|A) = [P(M) * P(A|M)]/P(A)

= (0.5 * 0.4)/0.41

= 0.2/0.41

= 0.4878 (or 48.78%)

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