A stock had returns of 8%, 14%, and 2% for the past three years. Assuming these...
A stock had returns of 8%, 14%, and 2% for the past three years. Assuming these annual returns are normally distributed, what is the probability that this stock will earn at least 20% in any one given year?
a. 0.5%
b. 1%
c.1.5%
d.2.5%
e.5%
Homework Answers
Average return = (8% + 14% + 2%) / 3 = 8%
Total squared deviation = (0.08 - 0.08)^2 + (0.14 - 0.08)^2 +
(0.02 - 0.08)^2
= 0 + 0.0036 + 0.0036
= 0.0072
Standard deviation = (0.0072 / (3 - 1))^(1/2) = 0.06 or 6%
Upper point of 95% probability range = 8% + [2 × 6%] = 8% + 12% = 20%
Probability associated with upper tail of 95% range = ½ × (100%
- 95%)
= ½ × 5%
= 2.50%
Probability that this stock will earn at least 20% in any one given year = 2.5%
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