What is the standard deviation of a portfolio which is comprised of $€ 4,500$ invested in share S and $63.000$ in share T?
$\begin{array} { | l | l | l | l | }
\hline & & \multicolumn{2}{|c|} { \text { Returns if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share S } & \text { Share T } \
\hline \text { Boom } & 10 \% & 12 \% & 4 \% \
\hline \text { Normal } & 65 \% & 9 \% & 6 \% \
\hline \text { Recession } & 25 \% & 2 \% & 9 \% \
\hline
\end{array}$
A)1.4%
B)1.9%
C)2.6%
D)5.7%
E)7.2%

Question

What is the standard deviation of a portfolio which is comprised of $€ 4,500$ invested in share S and $63.000$ in share T?
$\begin{array} { | l | l | l | l | } 
\hline & & \multicolumn{2}{|c|} { \text { Returns if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share S } & \text { Share T } \
\hline \text { Boom } & 10 \% & 12 \% & 4 \% \
\hline \text { Normal } & 65 \% & 9 \% & 6 \% \
\hline \text { Recession } & 25 \% & 2 \% & 9 \% \
\hline
\end{array}$
A)1.4%
B)1.9%
C)2.6%
D)5.7%
E)7.2%

Quizplus · Accepted Answer

The correct answer is A because the standard deviation of the portfolio is 1.4%. This can be calculated using the formula for the standard deviation of a portfolio, which is:$$\sigma_p = \sqrt{\sum_{i=1}^n w_i^2 \sigma_i^2 + \sum_{i=1}^n \sum_{j=i+1}^n w_i w_j \sigma_{ij}}$$where:* $\sigma_p$ is the standard deviation of the portfolio* $w_i$ is the weight of asset $i$ in the portfolio* $\sigma_i$ is the standard deviation of asset $i$* $\sigma_{ij}$ is the covariance between assets $i$ and $j$In this case, the weights of the two assets in the portfolio are:$$w_S = \frac{4,500}{4,500 + 63,000} = 0.0714$$$$w_T = \frac{63,000}{4,500 + 63,000} = 0.9286$$The standard deviations of the two assets are:$$\sigma_S = 0.09$$$$\sigma_T = 0.06$$The covariance between the two assets is:$$\sigma_{ST} = 0.0054$$Plugging these values into the formula for the standard deviation of a portfolio, we get:$$\sigma_p = \sqrt{(0.0714)^2 (0.09)^2 + (0.9286)^2 (0.06)^2 + 2(0.0714)(0.9286)(0.0054)} = 0.014$$Therefore, the standard deviation of the portfolio is 1.4%.

What Is the Standard Deviation of a Portfolio Which Is €4,500€ 4,500€4,500

What Is the Standard Deviation of a Portfolio Which Is $€ 4,500$