Consider the following portfolio of assets: $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Loan } i & \text { Weight } i & \text { Expected return } i & \sigma 1 & \sigma 1^ { 2 } & \ \hline 1 & 0.30 & 13 \% & 9.06 \% & 82.0 \% & \mathrm { P } _ { 12 } = - 0.87 \ \hline 2 & 0.70 & 11 \% & 8.72 \% & 76.0 \% & \sigma _ { 12 } = - 75.0 \% \ \hline \end{array}$$ What is the variance of the portfolio (round to two decimals)? A)(0.3)²(82.0%) + (0.7)²(76.0%) + (0.3)(0.7)(-0.87) * (9.06%)(8.72%) = 30.19 B)(0.3)²(82.0%) + (0.7)²(76.0%) + [(0.3)(0.7)]² * (-0.87) * (9.06%)(8.72%) = 41.59 C)(0.3)²(82.0%) + (0.7)²(76.0%) + 2(0.3)(0.7)(-0.87) * (9.06%)(8.72%) = 15.75 D)(0.3)(82.0%) + (0.7)(76.0%) + 2(0.3)(0.7)(-0.87) * (9.06%)(8.72%) = 48.93

Question

Quizplus · Accepted Answer

The variance of a two-asset portfolio is calculated using the formula: $\sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_{12}$, where $w_1$ and $w_2$ are the weights of the assets, $\sigma_1^2$ and $\sigma_2^2$ are the variances of the assets, and $\sigma_{12}$ is the covariance between the assets. The given variances (82.0% and 76.0%) should be in decimal form (0.82 and 0.76), and the correlation coefficient ($P_{12}$) is -0.87. The covariance ($\sigma_{12}$) can be calculated as $\sigma_1\sigma_2P_{12}$. Substituting the given values and calculating gives the variance of the portfolio as 15.75%.

Consider the Following Portfolio of Assets What Is the Variance of the Portfolio (Round to Two