def solve(x0,
risk_alphas,
loadings,
srisk,
cost_per_trade=DEFAULT_COST,
max_risk=0.01):
N = len(x0)
# don't hold no risk data (likely dead)
lim = np.where(srisk.isnull(), 0.0, 1.0)
loadings = loadings.fillna(0)
srisk = srisk.fillna(0)
risk_alphas = risk_alphas.fillna(0)
with Model() as m:
w = m.variable(N, Domain.inRange(-lim, lim))
longs = m.variable(N, Domain.greaterThan(0))
shorts = m.variable(N, Domain.greaterThan(0))
gross = m.variable(N, Domain.greaterThan(0))
m.constraint(
"leverage_consistent",
Expr.sub(gross, Expr.add(longs, shorts)),
Domain.equalsTo(0),
)
m.constraint("net_consistent", Expr.sub(w, Expr.sub(longs, shorts)),
Domain.equalsTo(0.0))
m.constraint("leverage_long", Expr.sum(longs), Domain.lessThan(1.0))
m.constraint("leverage_short", Expr.sum(shorts), Domain.lessThan(1.0))
buys = m.variable(N, Domain.greaterThan(0))
sells = m.variable(N, Domain.greaterThan(0))
gross_trade = Expr.add(buys, sells)
net_trade = Expr.sub(buys, sells)
total_gross_trade = Expr.sum(gross_trade)
m.constraint(
"net_trade",
Expr.sub(w, net_trade),
Domain.equalsTo(np.asarray(x0)), # cannot handle series
)
# add risk constraint
vol = m.variable(1, Domain.lessThan(max_risk))
stacked = Expr.vstack(vol.asExpr(), Expr.mulElm(w, srisk.values))
stacked = Expr.vstack(stacked, Expr.mul(loadings.values.T, w))
m.constraint("vol-cons", stacked, Domain.inQCone())
alphas = risk_alphas.dot(np.vstack([loadings.T, np.diag(srisk)]))
gain = Expr.dot(alphas, net_trade)
loss = Expr.mul(cost_per_trade, total_gross_trade)
m.objective(ObjectiveSense.Maximize, Expr.sub(gain, loss))
m.solve()
result = pd.Series(w.level(), srisk.index)
return result
def __Update_Z_Constr(pure_model: Model, constr_z: Dict[int,
int]) -> Model:
Z = pure_model.getVariable('Z')
if len(constr_z) == 1:
for key, value in constr_z.items(): # only one iteration
pure_model.constraint('BB', Z.index(key),
Domain.equalsTo(value))
if len(constr_z) >= 2:
expression = Expr.vstack([Z.index(key) for key in constr_z.keys()])
values = [value for key, value in constr_z.items()]
pure_model.constraint('BB', expression, Domain.equalsTo(values))
return pure_model
def Update_Z_Constr(self):
self.Remove_Z_Constr()
Z = self.model.getVariable('Z')
if len(self.constr) == 1:
for key, value in self.constr.items(): # only one iteration
self.model.constraint('BB', Z.index(key),
Domain.equalsTo(value))
if len(self.constr) >= 2:
expression = Expr.vstack(
[Z.index(key) for key in self.constr.keys()])
values = [value for key, value in self.constr.items()]
self.model.constraint('BB', expression, Domain.equalsTo(values))
def __rotated_quad_cone(model, expr1, expr2, expr3):
model.constraint(Expr.vstack(expr1, expr2, expr3), Domain.inRotatedQCone())
def __quad_cone(model, expr1, expr2):
model.constraint(Expr.vstack(expr1, expr2), Domain.inQCone())
def __rotated_quad_cone(model, expr1, expr2, expr3):
model.constraint(Expr.vstack(expr1, expr2, expr3), Domain.inRotatedQCone())
def __quad_cone(model, expr1, expr2):
model.constraint(Expr.vstack(expr1, expr2), Domain.inQCone())
def Build_Co_Model(self):
r = len(self.roads)
mu, sigma = self.mu, self.sigma
m, n, r = self.m, self.n, len(self.roads)
f, h = self.f, self.h
M, N = m + n + r, 2 * m + 2 * n + r
A = self.__Construct_A_Matrix()
A_Mat = Matrix.dense(A)
b = self.__Construct_b_vector()
# ---- build Mosek Model
COModel = Model()
# -- Decision Variable
Z = COModel.variable('Z', m, Domain.inRange(0.0, 1.0))
I = COModel.variable('I', m, Domain.greaterThan(0.0))
Alpha = COModel.variable('Alpha', M,
Domain.unbounded()) # M by 1 vector
Beta = COModel.variable('Beta', M, Domain.unbounded()) # M by 1 vector
Theta = COModel.variable('Theta', N,
Domain.unbounded()) # N by 1 vector
# M1_matrix related decision variables
'''
[tau, xi^T, phi^T
M1 = xi, eta, psi^t
phi, psi, w ]
'''
# no-need speedup variables
Psi = COModel.variable('Psi', [N, n], Domain.unbounded())
Xi = COModel.variable('Xi', n, Domain.unbounded()) # n by 1 vector
Phi = COModel.variable('Phi', N, Domain.unbounded()) # N by 1 vector
# has the potential to speedup
Tau, Eta, W = self.__Declare_SpeedUp_Vars(COModel)
# M2 matrix decision variables
'''
[a, b^T, c^T
M2 = b, e, d^t
c, d, f ]
'''
a_M2 = COModel.variable('a_M2', 1, Domain.greaterThan(0.0))
b_M2 = COModel.variable('b_M2', n, Domain.greaterThan(0.0))
c_M2 = COModel.variable('c_M2', N, Domain.greaterThan(0.0))
e_M2 = COModel.variable('e_M2', [n, n], Domain.greaterThan(0.0))
d_M2 = COModel.variable('d_M2', [N, n], Domain.greaterThan(0.0))
f_M2 = COModel.variable('f_M2', [N, N], Domain.greaterThan(0.0))
# -- Objective Function
obj_1 = Expr.dot(f, Z)
obj_2 = Expr.dot(h, I)
obj_3 = Expr.dot(b, Alpha)
obj_4 = Expr.dot(b, Beta)
obj_5 = Expr.dot([1], Expr.add(Tau, a_M2))
obj_6 = Expr.dot([2 * mean for mean in mu], Expr.add(Xi, b_M2))
obj_7 = Expr.dot(sigma, Expr.add(Eta, e_M2))
COModel.objective(
ObjectiveSense.Minimize,
Expr.add([obj_1, obj_2, obj_3, obj_4, obj_5, obj_6, obj_7]))
# Constraint 1
_expr = Expr.sub(Expr.mul(A_Mat.transpose(), Alpha), Theta)
_expr = Expr.sub(_expr, Expr.mul(2, Expr.add(Phi, c_M2)))
_expr_rhs = Expr.vstack(Expr.constTerm([0.0] * n), Expr.mul(-1, I),
Expr.constTerm([0.0] * M))
COModel.constraint('constr1', Expr.sub(_expr, _expr_rhs),
Domain.equalsTo(0.0))
del _expr, _expr_rhs
# Constraint 2
_first_term = Expr.add([
Expr.mul(Beta.index(row),
np.outer(A[row], A[row]).tolist()) for row in range(M)
])
_second_term = Expr.add([
Expr.mul(Theta.index(k), Matrix.sparse(N, N, [k], [k], [1]))
for k in range(N)
])
_third_term = Expr.add(W, f_M2)
_expr = Expr.sub(Expr.add(_first_term, _second_term), _third_term)
COModel.constraint('constr2', _expr, Domain.equalsTo(0.0))
del _expr, _first_term, _second_term, _third_term
# Constraint 3
_expr = Expr.mul(-2, Expr.add(Psi, d_M2))
_expr_rhs = Matrix.sparse([[Matrix.eye(n)], [Matrix.sparse(N - n, n)]])
COModel.constraint('constr3', Expr.sub(_expr, _expr_rhs),
Domain.equalsTo(0))
del _expr, _expr_rhs
# Constraint 4: I <= M*Z
COModel.constraint('constr4', Expr.sub(Expr.mul(20000.0, Z), I),
Domain.greaterThan(0.0))
# Constraint 5: M1 is SDP
COModel.constraint(
'constr5',
Expr.vstack(Expr.hstack(Tau, Xi.transpose(), Phi.transpose()),
Expr.hstack(Xi, Eta, Psi.transpose()),
Expr.hstack(Phi, Psi, W)), Domain.inPSDCone(1 + n + N))
return COModel
