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An investment consultant tells her client that the probability of making a positive return with her suggested portfolio is 0.90. What is the risk, measured by standard deviation that this investment manager has assumed in her calculation if it is known that returns from her suggested portfolio are normally distributed with a mean of 6%?
Compute P(X ≤ 0) = 1 - P(X > 0). Use z table that provides cumulative probabilities P(Z ≤ z) for positive and negative values of z. The inverse transformation implies that any value z of Z has a corresponding value x of X given by x = μ + zσ. Therefore, σ=x-μ/z