Integrated cases: three-asset risk from volatilities, correlations and scenarios

In short

• Convert first: $\text{Cov}_{ij} = \rho_{ij}\,\sigma_i\,\sigma_j$. The diagonal of the covariance matrix is the variances $\sigma_i^2$.
• Portfolio variance is the double sum $\sum_i\sum_j w_i w_j \text{Cov}_{ij}$: each pair appears twice. Take the square root last.
• Expected return needs only the weights and the expected returns. Correlations and volatilities affect risk only.
• A matrix labelled in %² or '×10⁻⁴' is on a percent scale: divide by 10,000 to get decimal variances.
• With $\rho = -1$ the risk can be driven to zero at $w_A = \sigma_B/(\sigma_A + \sigma_B)$; in a scenario table, two assets whose returns always sum to the same number have $\rho = -1$.