Security X’s annual return follows Normal distribution with expected return of 5% and standard deviation of...

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Security X’s annual return follows Normal distribution with expected return of 5% and standard deviation of...

Security X’s annual return follows Normal distribution with expected return of 5% and standard deviation of 10%. What is the level of annual return that will be exceeded with 95% probability?

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Answer 1

Answer #1

Using the normal distribution 68-95-99.7 rule

68% data is within 1 standard deviation of the mean i.e. mue +/- sigma

95% data is within 2 standard deviations of the mean i.e. mue +/- 2*sigma

99.7% data is within 3 standard deviations of the mean i.e mue +/- 3*sigma

since here they are asking for 95% probability, return will be with in (mue - 2*sigma, mue + 2*sigma)

i.e. (5% - 2*10%, 5% + 2*10%)

i.e. (-15%, 25%)

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Answer 2

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