Financial Risk Manager Part 1
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An investor owns shares of both Apple and Microsoft. The two companies operate independently. The investor assumes that the probability of Apple's share price declining by more than 5% this year is 0.4 while the probability of Microsoft's share price declining by more than 5% is 0.3. What is the probability that either Apple or Microsoft share prices will decline in price by more than 5% this year?
Explanation:
Explanation
This question involves calculating the probability of the union of two independent events using the addition rule of probability.
Given:
- P(Apple declines >5%) = 0.4
- P(Microsoft declines >5%) = 0.3
- The companies operate independently
Formula:
For independent events A and B: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Since the events are independent: P(A ∩ B) = P(A) × P(B)
Calculation:
P(A ∪ B) = 0.4 + 0.3 - (0.4 × 0.3) = 0.7 - 0.12 = 0.58
Why this makes sense:
- If we simply added the probabilities (0.4 + 0.3 = 0.7), we would be double-counting the overlap where both stocks decline
- The subtraction of P(A ∩ B) = 0.12 corrects for this double-counting
- The result 0.58 represents the probability that at least one of the stocks declines by more than 5%
This is a fundamental application of probability theory for independent events in financial risk analysis.