Two Assets

Variance & Risk

Portfolio variance is exact; standard deviation is a rounded square root.

highlighted = computed this step

Variance is the exact spine

Portfolio variance is exact rational arithmetic. For two assets it uses the two variance terms plus the correlation cross term.

σp2=w2σA2+(1−w)2σB2+2w(1−w)ρσAσB\sigma_p^2=w^2\sigma_A^2+(1-w)^2\sigma_B^2+2w(1-w)\rho\sigma_A\sigma_B

Sigma is a square root

At zero correlation, the exact variance is 1/80. The standard deviation is the square root of that variance, shown rounded as 11.18%.

σp=1/80≈11.18%\sigma_p=\sqrt{1/80}\approx 11.18\%

Rounded risk display

Variance is the exact value. Sigma is generally irrational, so it is rounded for display. In real data work, sigma and rho would be estimated with uncertainty; here they are stated inputs. This is descriptive, not investment advice.

exact variance, rounded σ\text{exact variance, rounded }\sigma