Three Correlations - Two-Asset Portfolios Step by Step

The same return can carry very different variance.

highlighted = computed this step

Same return, different risk

The fifty-fifty portfolio return stays 8% under every rho. The risk changes because the cross term changes.

r_p=8\%\quad\text{for each }\rho

Risk by correlation

For rho +1, the variance is 9/400 and sigma is 15.00%. For rho 0, variance is 1/80 and sigma rounds to 11.18%. For rho -1, variance is 1/400 and sigma is 5.00%.

(\rho,\sigma_p^2)=((+1,9/400),(0,1/80),(-1,1/400))

Stated inputs

The table is not estimated from market data. Sigma and rho are stated exact model inputs; in real portfolios they are estimated with uncertainty. This is descriptive, not investment advice.

\text{same inputs, different stated rho}