Build 5 assets of portfolio matrix and the equation A portfolio consists of 4 securities, 1, 2, 3, and 4. The proportions of these securities are: w1=0.3, w2=0.2, w3=0.2, and w4=0.3. The standard deviations of returns on these securities (in percentage terms) are: σ1=5, σ2=6, σ3=12, and σ4=8. The correlation coefficients among security returns are: ρ12=0.2, ρ13=0.6, ρ14=0.3, ρ23=0.4, ρ24=0.6, and ρ34=0.5. What is the standard deviation of portfolio return?

The portfolio variance ($\sigma_p^2$) for $N$ assets is given by the formula:
$$
\sigma_p^2 = \sum_{i=1}^{N} \sum_{j=1}^{N} w_i w_j \sigma_i \sigma_j \rho_{ij}
$$
where $w_i$ and $w_j$ are the weights of assets $i$ and $j$ in the portfolio, $\sigma_i$ and $\sigma_j$ are their respective standard deviations, and $\rho_{ij}$ is the correlation coefficient between the returns of assets $i$ and $j$.  
For 5 assets ($N=5$), the equation expands to:
$$
\sigma_p^2 = \sum_{i=1}^{5} w_i^2 \sigma_i^2 + \sum_{i=1}^{5} \sum_{j=i+1}^{5} 2 w_i w_j \sigma_i \sigma_j \rho_{ij}
$$

The portfolio covariance matrix ($\Sigma$) for 5 assets is a $5 \times 5$ matrix where the diagonal elements are the variances of individual assets ($\sigma_i^2$) and the off-diagonal elements are the covariances between asset returns ($\sigma_{ij} = \sigma_i \sigma_j \rho_{ij}$).
$$\Sigma = \begin{bmatrix}
\sigma_1^2 & \sigma_1 \sigma_2 \rho_{12} & \sigma_1 \sigma_3 \rho_{13} & \sigma_1 \sigma_4 \rho_{14} & \sigma_1 \sigma_5 \rho_{15} \\
\sigma_2 \sigma_1 \rho_{21} & \sigma_2^2 & \sigma_2 \sigma_3 \rho_{23} & \sigma_2 \sigma_4 \rho_{24} & \sigma_2 \sigma_5 \rho_{25} \\
\sigma_3 \sigma_1 \rho_{31} & \sigma_3 \sigma_2 \rho_{32} & \sigma_3^2 & \sigma_3 \sigma_4 \rho_{34} & \sigma_3 \sigma_5 \rho_{35} \\
\sigma_4 \sigma_1 \rho_{41} & \sigma_4 \sigma_2 \rho_{42} & \sigma_4 \sigma_3 \rho_{43} & \sigma_4^2 & \sigma_4 \sigma_5 \rho_{45} \\
\sigma_5 \sigma_1 \rho_{51} & \sigma_5 \sigma_2 \rho_{52} & \sigma_5 \sigma_3 \rho_{53} & \sigma_5 \sigma_4 \rho_{54} & \sigma_5^2  
\end{bmatrix}$$  
Note that $\rho_{ij} = \rho_{ji}$, so $\sigma_i \sigma_j \rho_{ij} = \sigma_j \sigma_i \rho_{ji}$.

$$
\sigma_p^2 = \text{Sum of variance terms} + \text{Sum of covariance terms}
$$
$$
\sigma_p^2 = 15.21 + 18.72 = 33.93
$$

$$
\sigma_p = \sqrt{\sigma_p^2} = \sqrt{33.93} \approx 5.8249
$$
Since the individual standard deviations were in percentage terms, the portfolio standard deviation is also in percentage terms.

The standard deviation of portfolio return is $\text{5.8249%}$