Financial Risk Manager Part 1
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An empirical study of ABC stock listed on the New York Exchange reveals that the stock has closed higher on one-third of all days in the past few months. Given that up and down days are independent, determine the probability of ABC stock closing higher for six consecutive days.
Explanation:
Explanation
Given:
- Probability of closing higher = 1/3
- Days are independent
- We need probability of 6 consecutive higher closes
Since the days are independent, we can multiply the individual probabilities:
[P(\text{6 consecutive highs}) = \left(\frac{1}{3}\right)^6 = \frac{1}{729}]
Now calculate the decimal value:
[\frac{1}{729} \approx 0.001371742]
Comparing with the options:
- A: 0.17 (too high)
- B: 0.0137 (10 times higher than correct)
- C: 0.03704 (27 times higher than correct)
- D: 0.00137 (matches our calculation)
Therefore, the correct answer is D. 0.00137
Key Concept: When events are independent, the probability of multiple events occurring consecutively is the product of their individual probabilities.