def weights_for_target(cov, target_var, rank=2, w3=0):
'''
return the weight for risky asset in the vol target problem
'''
# check cov is valid?
if rank == 2:
a = cov[0, 0] + cov[1, 1] - 2 * cov[0, 1]
b = 2 * cov[0, 1] - 2 * cov[1, 1]
c = cov[1, 1] - target_var
try:
weights = solve_quadratic_equation(a, b, c)
except Exception, e:
weights = None, None
return weights
def weights_for_target(cov, target_var, rank=2, w3=0): ''' return the weight for risky asset in the vol target problem ''' # check cov is valid? if rank == 2: a = cov[0, 0] + cov[1, 1] - 2 * cov[0, 1] b = 2 * cov[0, 1] - 2 * cov[1, 1] c = cov[1, 1] - target_var try: weights = solve_quadratic_equation(a, b, c) except Exception, e: weights = None, None return weights
a = cov[0, 0] + cov[1, 1] - 2 * cov[0, 1]
b = 2 * cov[0, 1] - 2 * cov[1, 1]
c = cov[1, 1] - target_var
try:
weights = solve_quadratic_equation(a, b, c)
except Exception, e:
weights = None, None
return weights
elif rank == 3:
a = cov[0, 0] + cov[1, 1] - 2 * cov[0, 1]
b = cov[1, 1] * (2 * w3 - 2) - cov[1, 2] * 2 * w3 + cov[
0, 2] * 2 * w3 + cov[0, 1] * 2 * (1 - w3)
c = cov[2, 2] * w3 * w3 + cov[1, 1] * (
1 - 2 * w3 + w3 * w3) + 2 * cov[1, 2] * (1 - w3) * w3 - target_var
return solve_quadratic_equation(a, b, c)
def simple_weight(vol, target_vol):
# assuming no correlation
mat = np.array([vol * vol, 0, 0, 0]).reshape(2, 2)
return weights_for_target(mat, target_vol * target_vol)[0]
def make_simple_weight(target_vol):
def weight(vol):
return simple_weight(vol, target_vol)
return weight
# check cov is valid? if rank == 2: a = cov[0, 0] + cov[1, 1] - 2 * cov[0, 1] b = 2 * cov[0, 1] - 2 * cov[1, 1] c = cov[1, 1] - target_var try: weights = solve_quadratic_equation(a, b, c) except Exception, e: weights = None, None return weights elif rank == 3: a = cov[0, 0] + cov[1, 1] - 2 * cov[0, 1] b = cov[1, 1] * (2 * w3 - 2) - cov[1, 2] * 2 * w3 + cov[0, 2] * 2 * w3 + cov[0, 1] * 2 * (1 - w3) c = cov[2, 2] * w3 * w3 + cov[1, 1] * (1 - 2 * w3 + w3 * w3) + 2 * cov[1, 2] * (1 - w3) * w3 - target_var return solve_quadratic_equation(a, b, c) def simple_weight(vol, target_vol): # assuming no correlation mat = np.array([vol * vol, 0, 0, 0]).reshape(2, 2) return weights_for_target(mat, target_vol * target_vol)[0] def make_simple_weight(target_vol): def weight(vol): return simple_weight(vol, target_vol) return weight
