The Tangency Portfolio - The Efficient Frontier Step by Step

The tangency portfolio is the highest-slope risky mix under the inputs.

highlighted = computed this step

Tangency weight

The highest-slope risky mix has weight 3/7 in asset A and 4/7 in asset B.

w_A^{\text{tan}}=3/7,\quad w_B^{\text{tan}}=4/7

Tangency values

The tangency return is exactly 27/350, shown rounded as 7.71%. Its exact variance is 13/1225 and sigma rounds to 10.30%.

r_{\text{tan}}=27/350,\quad \sigma_{\text{tan}}^2=13/1225

Tangency is input dependent

The tangency portfolio is the highest-Sharpe risky mix only under the stated return, sigma, rho, and risk-free inputs. The Sharpe slope uses rounded sigma display, while weights and variance are exact. This is descriptive, not investment advice.

\text{tangency depends on stated inputs}