def test_mpo_tcost():
# test MPO with no t-cost and constraints
N = 10
rtns = sim.generate_forecasts(n_periods=3, N=N, seed=9984)
# simulate cash = 0 return
rtns.values[:, -1] = 0
forecasts = M.MPOReturnForecast(rtns)
init_mkt_values = pd.Series([100.0 for _ in range(N)])
# tcost, test constant tcost
# stay in cash for the first trade
tcost = np.ones_like(rtns) * 0.14
# cash has no tcost
tcost[:, -1] = 0.0
costs = [C.TCost(tcost)]
cons = [C.LongOnly()]
prob = M.MPO(forecasts, constraints=cons, costs=costs)
output = prob.solve(init_mkt_values, verbose=True)
trade_vals = output.get("trade_values")
obj_val = output.get("objective")
assert len(trade_vals) == N
assert not np.isnan(obj_val)
assert not np.isnan(trade_vals).any()
print(f"Trade values = {trade_vals}")
assert np.isclose(obj_val, 0.14478828790994064, rtol=1.0e-7)
def test_NoSell():
# test MPO with no t-cost and constraints
N = 10
rtns = sim.generate_forecasts(n_periods=3, N=N, seed=9984)
print(rtns.to_string(float_format="{:.1%}".format))
forecasts = M.MPOReturnForecast(rtns)
init_mkt_values = pd.Series([100.0 for _ in range(N)])
no_trade_idx = pd.Series([0, 6])
cons = [C.LongOnly(), C.NoSell(no_trade_idx)]
prob = M.MPO(forecasts, constraints=cons)
output = prob.solve(init_mkt_values, verbose=True)
trade_vals = output.get("trade_values")
trade_weights = output.get("trade_weights")
assert len(trade_vals) == N
assert not np.isnan(trade_vals).any()
# robust way to test <= in numpy
assert np.all(
np.greater(trade_vals[no_trade_idx.values], 0.0)
| np.isclose(trade_vals[no_trade_idx.values], 0.0, atol=1e-6)
)
# assert np.allclose(trade_weights.iloc[:, no_trade_idx.values], 0.0)
assert np.all(
np.greater(trade_weights.iloc[:, no_trade_idx.values], 0.0)
| np.isclose(trade_weights.iloc[:, no_trade_idx.values], 0.0, atol=1e-6)
)
def test_MPOReturnForecast_weighted_returns():
rtns = sim.generate_forecasts(n_periods=3, N=10)
z = cvx.Variable(10)
m = M.MPOReturnForecast(rtns)
s = m.weighted_returns(weight=z, step=1)
assert isinstance(s, Expression)
assert s.shape == (1,)
def test_MPOReturnForecast_weighted_returns_multi():
rtns = sim.generate_forecasts(n_periods=5, N=10)
# 10 assets, 3 steps
z = cvx.Variable((10, 3))
m = M.MPOReturnForecast(rtns)
s = m.weighted_returns_multi(weights=z, start=1, end=4)
assert isinstance(s, Expression)
assert s.shape == ()
def _run_mpo_simple(cons=None, costs=None, risk=None, seed=9984):
# test MPO with no t-cost and constraints
N = 10
rtns = sim.generate_forecasts(n_periods=3, N=N, seed=seed)
print(rtns.to_string(float_format="{:.1%}".format))
forecasts = M.MPOReturnForecast(rtns)
init_mkt_values = pd.Series([100.0 for _ in range(N)])
prob = M.MPO(forecasts, constraints=cons, costs=costs, risk_penalty=risk)
output = prob.solve(init_mkt_values, verbose=True)
return output
def test_factor_penalty():
# build risk model
_, factor_cov, factor_exp, _, spec_cov = sim.generate_factor_returns(
T=3, K=5, N=10
)
# TODO build 3D risk models
factor_cov_arr = np.tile(factor_cov.reshape((-1, 1)), 3).T.reshape(
(3, 5, 5)
)
factor_exp_arr = np.tile(factor_exp.reshape((-1, 1)), 3).T.reshape(
(3, 10, 5)
)
spec_cov_arr = np.tile(spec_cov.reshape((-1, 1)), 3).T.reshape((3, 10, 10))
model = risk.FactorRiskModel(
factor_exp_arr, factor_cov_arr, spec_cov_arr, has_benchmark=False
)
gamma = 1.0
penalty = risk.RiskPenalty(gamma, model)
# test MPO with no t-cost and constraints
N = 10
rtns = sim.generate_forecasts(n_periods=3, N=N, seed=9984)
# simulate cash = 0 return
rtns.values[:, -1] = 0
forecasts = M.MPOReturnForecast(rtns)
init_mkt_values = pd.Series([100.0 for _ in range(N)])
# tcost, test constant tcost
# stay in cash for the first trade
tcost = np.ones_like(rtns) * 0.14
# cash has no tcost
tcost[:, -1] = 0.0
costs = [C.TCost(tcost)]
cons = [C.LongOnly()]
# add risk model
prob = M.MPO(forecasts, constraints=cons, costs=costs, risk_penalty=penalty)
output = prob.solve(init_mkt_values, verbose=True)
trade_vals = output.get("trade_values")
obj_val = output.get("objective")
assert len(trade_vals) == N
assert not np.isnan(obj_val)
assert not np.isnan(trade_vals).any()
print(f"Trade values = {trade_vals}")
def test_mpo_simple():
# test MPO with no t-cost and constraints
N = 10
rtns = sim.generate_forecasts(n_periods=3, N=N, seed=9984)
forecasts = M.MPOReturnForecast(rtns)
exp_max = rtns.values[range(len(rtns)), rtns.idxmax(axis=1).values].sum()
init_mkt_values = pd.Series([100.0 for _ in range(N)])
cons = [C.LongOnly()]
prob = M.MPO(forecasts, constraints=cons)
output = prob.solve(init_mkt_values, verbose=True)
trade_vals = output.get("trade_values")
obj_val = output.get("objective")
assert np.isclose(obj_val, exp_max, rtol=1.0e-7)
assert len(trade_vals) == N
assert not np.isnan(trade_vals).any()
print(f"Trade values = {trade_vals}")
def test_max_turnover():
# test MPO with no t-cost and constraints
N = 10
rtns = sim.generate_forecasts(n_periods=3, N=N, seed=9984)
forecasts = M.MPOReturnForecast(rtns)
init_mkt_values = pd.Series([100.0 for _ in range(N)])
MAX_TO = 0.5
cons = [C.LongOnly(), C.MaxTurnover(MAX_TO)]
prob = M.MPO(forecasts, constraints=cons)
output = prob.solve(init_mkt_values, verbose=True)
trade_vals = output.get("trade_values")
trade_weights = output.get("trade_weights")
assert len(trade_vals) == N
assert not np.isnan(trade_vals).any()
assert (trade_weights.abs().sum(axis=1) <= MAX_TO).all()