Financial Risk Manager Part 1
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Use the following incomplete probability matrix to compute the joint probability of a poor economy and an increase in interest rate:
Interest rates
| Economy | Increase | No increase |
|---|---|---|
| Good | 20% | 10% |
| Normal | 30% | 20% |
| Poor | X | 10% |
Other
Community
NNikitesh
A
0.2
B
0.3
C
0.1
D
0.05
Explanation:
Explanation
The joint probability matrix must sum to 1 (or 100%) since it represents all possible outcomes. The given probabilities are:
- Good economy with interest rate increase: 20%
- Good economy with no interest rate increase: 10%
- Normal economy with interest rate increase: 30%
- Normal economy with no interest rate increase: 20%
- Poor economy with no interest rate increase: 10%
- Poor economy with interest rate increase: X (unknown)
Sum of all known probabilities = 20% + 10% + 30% + 20% + 10% = 90%
Therefore, X = 100% - 90% = 10%
So the joint probability of a poor economy and an increase in interest rate is 10% or 0.1.
This is a basic probability concept where the sum of all joint probabilities in a complete probability space must equal 1.
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