Financial Risk Manager Part 1
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An investment firm classifies capital projects into three different categories, depending on risk level: Standard, Preferred, and Ultra-preferred. Of the firm's projects, 60% are standard, 30% are preferred, and 10% are ultra-preferred. The probabilities of a project making a loss are 0.01, 0.005, and 0.001 for categories standard, preferred, and ultra-preferred respectively. If a capital project makes a loss in the next year, then what is the probability that the project was standard (correct to 2 decimal places)?
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A
0.79
B
0.73
C
0.22
D
0.15
Explanation:
This is a classic Bayes' theorem application. Let:
- L = Event a project makes a loss
- S = Event of a standard project
- P₁ = Event of a preferred project
- U = Event of an ultra-preferred project
We need to find P(S|L):
Rounded to 2 decimal places, this gives 0.79, which matches option A.
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