Consider the following portfolio of assets: $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Loan } i & \text { Weight } i & \text { Expected return i } & \sigma i & \sigma i^ { 2 } & \ \hline 1 & 0.45 & 15 \% & 6.05 \% & 36.60 \% & \mathrm { P } _ { 12 } = - 0.2 \ \hline 2 & 0.55 & 13 \% & 8.75 \% & 76.56 \% & \sigma _ { 12 } = - 4.0 \% \ \hline \end{array}$$ What is the variance of the portfolio (round to two decimals)? A)(0.45)²(36.60%) + (0.55)²(76.56%) + (0.45)(0.55)(-0.2) * (6.05%)(8.75%) = 27.95 B)(0.45)²(36.60%) + (0.55)²(76.56%) + 2(0.45)(0.55)(-0.2) * (6.05%) (8.75%) = 25.33 C)(0.45)(36.60%) + (0.55)(76.56%) + 2(0.45)²(0.55)2 (-0.2) * (6.05%)(8.75%) = 57.28 D)(0.45)(36.60%) + (0.55)(76.56%) + 2(0.45)(0.55)(-0.2) * (6.05%)(8.75%) = 53.34

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 (in percentage form) need to be converted to decimal form for calculation. The correct calculation involves squaring the weights, using the variances of each asset, and incorporating the covariance term correctly, which is done in option B.

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