Suppose stock returns follow a normal distribution. Over the last 60 years stock
ID: 3325451 • Letter: S
Question
Suppose stock returns follow a normal distribution. Over the last 60 years stocks returns have an average of 10%. Let's assume these returns have a standard deviation of 10% as well. I'm thinking of investing money in the stock market for one year to see how it goes. Please compute in four steps the chance my investment will experience returns between 5% to 20%.
Suppose I pick 4 stocks randomly that have a mean return and standard deviation of 10% as above and are Normally distributed. They are also uncorrelated. Please compute the chance that at least one of these stocks will have returns between %5 and 20%?
Explanation / Answer
A) P(0.05 < x < 0.2)
= P((0.05 - mean)/SD < (x - mean)/SD < (0.2 - mean)/SD)
= P((0.05 - 0.1)/0.1 < Z < (0.2 - 0.1)/0.1)
= P(-0.5 < Z < 1)
= P(Z < 1) - P(Z < -0.5)
= 0.8413 - 0.3085 = 0.5328 = 53.28%
B) P(0.05 < x < 0.2)
= P((0.05 - mean)/(SD/sqrt(n) ) < (x - mean)/(SD/sqrt(n)) < (0.2 - mean)/(SD/sqrt(n))
= P((0.05 - 0.1)/(0.1/sqrt(4)) < Z < (0.2 - 0.1)/(0.1/sqrt(4))
= P (-1 < Z < 2)
= P(Z < 2) - P(Z < -1)
= 0.9772 - 0.1587
= 0.8185 = 81.85%
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