What is the variance of a portfolio consisting of $€ 3,500$ in share G and $\in 6,500$ in share H?
$\begin{array} { | l | l | l | l | }
\hline & & \multicolumn{2}{|l|} { \text { Returns if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share G } & \text { Share H } \
\hline \text { Boom } & 15 \% & 15 \% & 9 \% \
\hline \text { Normal } & 85 \% & 8 \% & 6 \% \
\hline
\end{array}$
A).000209
B).000247
C).002098
D).037026
E).073600

Question

What is the variance of a portfolio consisting of $€ 3,500$ in share G and $\in 6,500$ in share H?
$\begin{array} { | l | l | l | l | } 
\hline & & \multicolumn{2}{|l|} { \text { Returns if State Occurs } } \
\hline \text { State of Economy } & \text { Probability of State of Economy } & \text { Share G } & \text { Share H } \
\hline \text { Boom } & 15 \% & 15 \% & 9 \% \
\hline \text { Normal } & 85 \% & 8 \% & 6 \% \
\hline
\end{array}$
A).000209
B).000247
C).002098
D).037026
E).073600

Quizplus · Accepted Answer

To calculate the variance of the portfolio, we first need to determine the expected returns of shares G and H, and then calculate the portfolio's expected return and variance.1. Calculate the expected returns for shares G and H:- Expected return of G = $0.15 \times 0.15 + 0.85 \times 0.08 = 0.0225 + 0.068 = 0.0905$ or 9.05%- Expected return of H = $0.15 \times 0.09 + 0.85 \times 0.06 = 0.0135 + 0.051 = 0.0645$ or 6.45%2. Calculate the weights of shares G and H in the portfolio:- Total investment = €3,500 + €6,500 = €10,000- Weight of G = €3,500 / €10,000 = 0.35- Weight of H = €6,500 / €10,000 = 0.653. Calculate the portfolio's expected return:- Portfolio's expected return = $0.35 \times 0.0905 + 0.65 \times 0.0645 = 0.031675 + 0.041925 = 0.0736$ or 7.36%4. Calculate the variance of the portfolio:- Variance of G's returns = $0.15 \times (0.15 - 0.0905)^2 + 0.85 \times (0.08 - 0.0905)^2 = 0.15 \times 0.003525 + 0.85 \times 0.00011025 = 0.000529125 + 0.0000937125 = 0.0006228375$- Variance of H's returns = $0.15 \times (0.09 - 0.0645)^2 + 0.85 \times (0.06 - 0.0645)^2 = 0.15 \times 0.00065025 + 0.85 \times 0.00002025 = 0.0000975375 + 0.0000172125 = 0.00011475$5. Calculate the portfolio's variance:- Since the covariance between G and H is not given, and assuming they are not perfectly correlated, we simplify by considering only the variances and weights:- Portfolio variance = $(0.35^2 \times 0.0006228375) + (0.65^2 \times 0.00011475) = 0.000076198 + 0.000048487 = 0.000124685$However, without the covariance between G and H, we cannot accurately calculate the portfolio's variance using the provided data. The correct approach involves calculating the weighted sum of the variances and the covariance between G and H, but since we lack the covariance information, we cannot proceed accurately. The choice provided does not match the expected calculation process, indicating a need for clarification or additional information. Given the choices, none directly corresponds to the expected detailed calculation, suggesting a possible misunderstanding in the calculation process or an error in the provided options.

What Is the Variance of a Portfolio Consisting Of €3,500€ 3,500€3,500

What Is the Variance of a Portfolio Consisting Of $€ 3,500$