markowitz.py

def markowitz(mu, cov, hedge=None):
  z = mu
  K = np.linalg.inv(cov)

  if hedge is not None:
    Q = hedge @ K @ hedge.T
    beta = np.linalg.inv(Q) @ hedge @ K @ mu
    z = mu - beta @ hedge

  z = K @ z
  z = z / sum(abs(z))
  return z