def TableInfluenceIntegerVariables():
"""
Illustrates the influence of the additional Integer constraints (Nmax and Wmin) on computation time. Computes,
draws and plots MAD Model computation time on N scenarios with N increasing, with the different parameters.
"""
rows = []
N = [10, 50, 100, 200, 300, 400, 500, 1000]
params = [{
'Wmin': Wmin,
'Nmax': Nmax
} for Nmax in (None, 5) for Wmin in (None, 0.005)]
print(params)
for n in N:
print("Computing with {:d} scenarios".format(n))
s, p = generateGaussianScenarios(n)
row = [n]
for param in params:
t = time()
MAD(s, p, **param).optimize()
row.append(time() - t)
rows.append(row)
rows = np.array(rows)
print("\nComputation times:\n")
headers = ['N', 'LP', 'Wmin', 'Nmax', 'Wmin and Nmax']
print(tabulate(rows, headers=headers))
for i in range(1, 5):
plt.plot(N, rows[:, i], label=headers[i])
plt.legend(loc='upper left')
plt.xlabel('Number of scenarios')
plt.ylabel('Computation time (s)')
plt.title('Influence of additional integer variables on computation time')
plt.show()
def test_same_output(self):
"""Checks that the MAD and the SemiMAD give the same output portfolio and half of the objective value."""
s, p = generateGaussianScenarios()
m = MAD(s, p).optimize()
m2 = SemiMAD(s, p).optimize()
self.assertAlmostEqual((m.getPortfolio() - m2.getPortfolio()).max(),
0,
places=4)
self.assertAlmostEqual(m.objval, 2 * m2.objval)
def test_reconfigure(self):
"""
Checks that reconfiguring the model with new scenarios/probas gives the same output as creating a new Model.
"""
s, p = self.scenarios, self.probas
s2, p2 = generateGaussianScenarios(
len(p), seed=self.seed + 1 if self.seed is not None else None)
self.assertEqual(
self.Model(s, p).update().reconfigure(s2,
p2).optimize().objval,
self.Model(s2, p2).optimize().objval)
def test_generation_student(stock1, stock2, nu=4):
r1 = Returns.iloc[:, stock1]
r2 = Returns.iloc[:, stock2]
bins1 = np.linspace(- r1.quantile(0.05), r1.quantile(0.95), 100)
bins2 = np.linspace(- r2.quantile(0.05), r2.quantile(0.95), 100)
plt.figure(1, figsize=(14, 8))
plt.subplot(321)
plt.hist(r1, normed=True, bins=bins1)
plt.subplot(322)
plt.hist(r2, normed=True, bins=bins2)
students = generateStudentTScenarios(nu, 100000)[0]
plt.subplot(323)
plt.hist(students[:, stock1], normed=True, bins=bins1)
plt.subplot(324)
plt.hist(students[:, stock2], normed=True, bins=bins2)
plt.subplot(325)
gaussians = generateGaussianScenarios(100000)[0]
plt.hist(gaussians[:, stock1], normed=True, bins=bins1)
plt.subplot(326)
plt.hist(gaussians[:, stock2], normed=True, bins=bins2)
plt.show()
def setUp(self):
self.seed = 5
self.scenarios, self.probas = generateGaussianScenarios(
100, seed=self.seed)
# Plots the beta % worst returns
plt.plot(worstIndex,
returns[worstIndex],
'o',
color='red',
label='{:.0%} Worst Cases'.format(self._beta))
plt.plot(oldWorstIndex,
equally[oldWorstIndex],
'o',
color='orange',
label='E.W. {:.0%} Worst Cases'.format(self._beta))
# Plots the mean of the beta % worst returns in equally weighted portfolio
plt.plot([S[0], S[-1]], [oldMean, oldMean], '-', color='orange')
# Plots the mean of the beta % worst returns
plt.plot([S[0], S[-1]], [mean, mean], '-', color='red')
plt.xlabel('Scenarios')
plt.ylabel('Returns')
plt.title('Conditional Value-at-Risk Optimization with {:d} scenarios'.
format(len(S)))
plt.gca().yaxis.set_major_formatter(
FuncFormatter(lambda y, _: '{:.0%}'.format(y)))
plt.legend()
plt.show()
if __name__ == '__main__':
s, p = generateGaussianScenarios(300)
CVaR(s, p, output=True).optimize().plot()
xy=(middle, values[Min]),
xytext=(middle, values[Max]),
fontsize=7,
color='red',
arrowprops=dict(arrowstyle='<->',
shrinkA=0,
shrinkB=0,
lw=2,
color='red'))
plt.plot([Min, middle], [values[Min], values[Min]],
'--',
color='red',
lw=2)
plt.plot([middle, Max], [values[Max], values[Max]],
'--',
color='red',
lw=2)
plt.xlabel('Scenarios')
plt.ylabel('Returns')
plt.gca().yaxis.set_major_formatter(
FuncFormatter(lambda y, _: '{:.0%}'.format(y)))
plt.title('GMD Optimization with {:d} scenarios'.format(len(S)))
plt.legend()
plt.show()
if __name__ == '__main__':
GMD(*generateGaussianScenarios(100)).optimize().plot()
def TestMADSemiMAD():
"""Checks that MAD and Semi MAD model lead to the same portfolio, and that MAD = 2 * SemiMAD."""
s, p = generateGaussianScenarios()
MADPort = MAD(s, p).optimize().getPortfolio()
SemiMADPort = SemiMAD(s, p).optimize().getPortfolio()
PortfolioGroup([MADPort, SemiMADPort]).plot()