You have a portfolio which has an average return of 10.3%. In any given year, you have a 2.5% probability of earning either a zero or a negative annual return. What is the approximate standard deviation of your portfolio?
$\begin{array}{cr}
\text { Probability } & \text { "z" value } \
\text { of loss } & \
1.0\% & 2.326 \
2.5 & 1.960 \
5.0 & 1.645
\end{array}$

A)5.26%
B)6.43%
C)6.94%
D)7.60%
E)8.14%

Question

You have a portfolio which has an average return of 10.3%. In any given year, you have a 2.5% probability of earning either a zero or a negative annual return. What is the approximate standard deviation of your portfolio?
$\begin{array}{cr}
\text { Probability } & \text { "z" value } \
\text { of loss } & \
1.0\% & 2.326 \
2.5 & 1.960 \
5.0 & 1.645
\end{array}$

A)5.26%
B)6.43%
C)6.94%
D)7.60%
E)8.14%

Quizplus · Accepted Answer

The correct answer is A because the standard deviation of a portfolio is approximately equal to the square root of the variance of the portfolio. The variance of a portfolio is equal to the sum of the variances of the individual assets in the portfolio, weighted by their respective weights in the portfolio. In this case, the portfolio has only one asset, which has an average return of 10.3% and a probability of 2.5% of earning either a zero or a negative annual return. The variance of this asset is equal to the square of the standard deviation of the asset, which is equal to 5.26%. Therefore, the variance of the portfolio is equal to 5.26%, and the standard deviation of the portfolio is equal to the square root of 5.26%, which is 2.29%.

You Have a Portfolio Which Has an Average Return of 10.3