The Simplex Gravitational Illusion: A Repulsive Center
Look at an equilateral triangle — the probability simplex for three assets. Each interior point is a portfolio: non-negative shares summing to one. The triangle's center, the barycenter, corresponds to an equal-weight allocation (1/3, 1/3, 1/3). It seems that by moving toward this point, you lower risk and avoid dangerous edges.