A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has assumed in his calculation if it is known that returns are normally distributed with a mean of 6.6%? Use Table 1. (Round "z" value to 2 decimal places and final answer to 3 decimal places.)
What is the Standard deviation ?
Hint: $Z = \frac{X-\mu}{\sigma}$, they told you that $P(X\geq0)=81\%$ and its mean is $6.6\%$. Re-write the Z-formula to get $\sigma Z + \mu = X$. Now, $P(Z\leq \frac{-\mu}{\sigma})=P(X\leq 0)=1-.81$. You need to find Z that satisfies this equation, then use it to solve for $\sigma$, i.e, $\sigma = \frac{-6.6\%}{z}$, where z satisfies the above equation, as previously stated.