A portfolio has a standard deviation of 15.8% and an average return of 14.2%. What loss is associated with a 2.5% probability?
$\begin{array}{cr}
\text { Probability } & \text { "z" value } \
\text { of loss } & \
1.0\% & 2.326 \
2.5 & 1.960 \
5.0 & 1.645
\end{array}$

A)12.03%
B)14.87%
C)16.77%
D)17.38%
E)19.36%

Question

A portfolio has a standard deviation of 15.8% and an average return of 14.2%. What loss is associated with a 2.5% probability?
$\begin{array}{cr}
\text { Probability } & \text { "z" value } \
\text { of loss } & \
1.0\% & 2.326 \
2.5 & 1.960 \
5.0 & 1.645
\end{array}$

A)12.03%
B)14.87%
C)16.77%
D)17.38%
E)19.36%

Quizplus · Accepted Answer

Assuming a normal distribution, we can use the z-score formula:

z = (x - μ) / σ

where:
x = the loss we want to find 
μ = the average return = 14.2% 
σ = the standard deviation = 15.8%

We want to find the loss associated with a 2.5% probability, which means we're looking for the z-score at the 2.5 percentile, or -1.96 (from a standard normal distribution table).

Plugging in the values: 
-1.96 = (x - 14.2) / 15.8

Solving for x: 
x = -1.96 * 15.8 + 14.2 = -16.77%

So the answer is C) 16.77%.

A Portfolio Has a Standard Deviation of 15 Probability "z" value of loss 1.0%2.3262.51.9605.01.645\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array} Probability of loss 1.0%2.55.0​ "z" value 2.3261.9601.645​

A Portfolio Has a Standard Deviation of 15 $\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array}$