What is the standard deviation of a portfolio which is invested 20% in share A, 30% in share B and 50% in share C?
$\begin{array} { | l | l | l | l | l | }
\hline & & \multicolumn{3}{|l|} { \text { Returns if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share A } & \text { Share B } & \text { Share C } \
\hline \text { Boom } & 10 \% & 15 \% & 10 \% & 5 \% \
\hline \text { Normal } & 70 \% & 9 \% & 6 \% & 7 \% \
\hline \text { Recession } & 20 \% & 14 \% & 2 \% & 8 \% \
\hline
\end{array}$
A)0.6%
B)0.9%
C)1.8%
D)2.2%
E)4.9%

Question

What is the standard deviation of a portfolio which is invested 20% in share A, 30% in share B and 50% in share C?
$\begin{array} { | l | l | l | l | l | } 
\hline & & \multicolumn{3}{|l|} { \text { Returns if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share A } & \text { Share B } & \text { Share C } \
\hline \text { Boom } & 10 \% & 15 \% & 10 \% & 5 \% \
\hline \text { Normal } & 70 \% & 9 \% & 6 \% & 7 \% \
\hline \text { Recession } & 20 \% & 14 \% & 2 \% & 8 \% \
\hline
\end{array}$
A)0.6%
B)0.9%
C)1.8%
D)2.2%
E)4.9%

Quizplus · Accepted Answer

The standard deviation of a portfolio is calculated as the square root of the variance of the portfolio. The variance of a portfolio is calculated as the sum of the variances of the individual assets in the portfolio, weighted by their respective weights in the portfolio.In this case, the variance of the portfolio is calculated as:(0.2 * 0.15^2) + (0.3 * 0.10^2) + (0.5 * 0.07^2) = 0.0045The standard deviation of the portfolio is therefore:sqrt(0.0045) = 0.067Therefore, the correct answer is D) 0.9%.

What Is the Standard Deviation of a Portfolio Which Is