The efficient frontier
Sweep the weight w on asset A to trace the frontier of risk and return. A lower correlation ρ bows it toward the return axis, the diversification benefit. The minimum-variance portfolio is its leftmost point.
Current portfolio (wA = 0.50)11.0% · σ 13.5%
MVP risk σ 11.3%MVP weight w* 0.83
Weight on A, w0.50
Correlation ρ0.20
E(R) of A8.0%
σ of A12.0%
E(R) of B14.0%
σ of B22.0%
Risk is below the weighted-average volatility whenever ρ < 1. The frontier bends most as ρ falls toward −1, where the right mix drives risk close to zero. The MVP holds w* = 0.83 in A.
Try this. Set ρ = +1 — the frontier collapses to a straight line, so there is no diversification benefit. Now set ρ = −1 — it bends sharply and the right mix can push risk almost to zero.