Exhibit 6-13
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
A financial analyst covering Magnum Oil has determined the following four possible returns given four different states of the economy over the next period. $\begin{array}{cc}
\text { Probability } & \text { Return } \
\hline 0.10 & -.20 \
0.25 & -.05 \
0.40 & 0.15 \
0.25 & 0.30
\end{array}$
-Refer to Exhibit 6-13. Calculate the standard deviation for Magnum Oil.
A) 0%
B) 11%
C) 16%
D) 20%
E) 26%

Question

Quizplus · Accepted Answer

The standard deviation is calculated by finding the square root of the variance. First, calculate the expected return (mean): $E(R) = (0.10 \times -0.20) + (0.25 \times -0.05) + (0.40 \times 0.15) + (0.25 \times 0.30) = -0.02 + -0.0125 + 0.06 + 0.075 = 0.1025$. Then, calculate the variance: $\sigma^2 = (0.10 \times (-0.20 - 0.1025)^2) + (0.25 \times (-0.05 - 0.1025)^2) + (0.40 \times (0.15 - 0.1025)^2) + (0.25 \times (0.30 - 0.1025)^2) = 0.0256$. The standard deviation ($\sigma$) is the square root of the variance: $\sqrt{0.0256} = 0.16$ or 16%.