The Feasible Set

Return & Risk of a Mix

A portfolio weight maps to exact return and variance.

highlighted = computed this step

Stated inputs

Use two risky assets with stated exact inputs. Asset A has return 10% and sigma 20%. Asset B has return 6% and sigma 10%. Here rho is 0.

rA=10%,rB=6%,ρ=0r_A=10\%,\quad r_B=6\%,\quad \rho=0

Return and variance

At weight 1/2 in asset A, the portfolio return is 8% and the exact variance is 1/80.

rp=wrA+(1−w)rB=8%,σp2=1/80r_p=w r_A+(1-w)r_B=8\%,\quad \sigma_p^2=1/80

Stated model inputs

Returns, sigma, rho, and the risk-free rate are stated model inputs, not estimates from data. In reality they are estimated with uncertainty, and rho is rarely exactly zero. This is descriptive, not investment advice.

stated inputs, exact variance\text{stated inputs, exact variance}