def testNCO():
# Chapter 7 - apply the Nested Clustered Optimization (NCO) algorithm
N = 5
T = 5
S_value = np.array([[1., 2, 3, 4, 5], [1.1, 3, 2, 3, 5],
[1.2, 4, 1.3, 4, 5], [1.3, 5, 1, 3, 5],
[1.4, 6, 1, 4, 5.5], [1.5, 7, 1, 3, 5.5]])
S_value[:, 1] = 1
S_value[5, 1] = 1.1
S, instrument_returns = calculate_returns(S_value)
_, instrument_returns = calculate_returns(S_value,
percentageAsProduct=True)
mu1 = None
cov1_d = np.cov(S, rowvar=0, ddof=1)
#test baseClustering
corr1 = mp.cov2corr(cov)
a, b, c = nco.NCO()._cluster_kmeans_base(pd.DataFrame(corr1))
d, e, f = clusterKMeansBase(pd.DataFrame(corr1))
#b={0: [2, 0], 1: [1], 2: [3, 4]}
#e={0: [1, 2], 1: [3, 4], 2: [0]}
min_var_markowitz = mc.optPort(cov1_d, mu1).flatten()
min_var_NCO = pc.optPort_nco(cov1_d, mu1, max(int(cov1_d.shape[0] / 2),
2)).flatten()
mlfinlab_NCO = nco.NCO().allocate_nco(cov1_d, mu1,
max(int(cov1_d.shape[0] / 2),
2)).flatten()
cov1_d = np.cov(S, rowvar=0, ddof=1)
mlfinlab_NCO = nco.NCO().allocate_nco(cov1_d, mu1,
int(cov1_d.shape[0] / 2)).flatten()
expected_return_markowitz = [
min_var_markowitz[i] * instrument_returns[i]
for i in range(0, cov1_d.shape[0])
]
e_m = sum(expected_return_markowitz)
expected_return_NCO = [
min_var_NCO[i] * instrument_returns[i]
for i in range(0, cov1_d.shape[0])
]
e_NCO = sum(expected_return_markowitz)
vol = getVolatility(S_value)
m_minVol = [
min_var_markowitz[i] * vol[i] for i in range(0, cov1_d.shape[0])
]
NCO_minVol = [mlfinlab_NCO[i] * vol[i] for i in range(0, cov1_d.shape[0])]
def testNCO():
N = 5
T = 5
S_value = np.array([[1., 2,3, 4,5],
[1.1,3,2, 3,5],
[1.2,4,1.3,4,5],
[1.3,5,1, 3,5],
[1.4,6,1, 4,5.5],
[1.5,7,1, 3,5.5]])
S_value[:,1] =1
S_value[5,1] =1.1
S, instrument_returns = calculate_returns(S_value)
_, instrument_returns = calculate_returns(S_value, percentageAsProduct=True)
np.testing.assert_almost_equal(S, pd.DataFrame(S_value).pct_change().dropna(how="all"))
mu1 = None
cov1_d = np.cov(S ,rowvar=0, ddof=1)
#test baseClustering
corr1 = mp.cov2corr(cov1_d)
a,b,c = nco.NCO()._cluster_kmeans_base(pd.DataFrame(corr1))
d,e,f = clusterKMeansBase(pd.DataFrame(corr1))
#b={0: [2, 0], 1: [1], 2: [3, 4]}
#e={0: [1, 2], 1: [3, 4], 2: [0]}
min_var_markowitz = mc.optPort(cov1_d, mu1).flatten()
#compare min_var_markowitz with mlfinlab impl
#ml.
min_var_NCO = pc.optPort_nco(cov1_d, mu1, max(int(cov1_d.shape[0]/2), 2)).flatten()
mlfinlab_NCO= nco.NCO().allocate_nco(cov1_d, mu1, max(int(cov1_d.shape[0]/2), 2)).flatten()
cov1_d = np.cov(S,rowvar=0, ddof=1)
mlfinlab_NCO= nco.NCO().allocate_nco(cov1_d, mu1, int(cov1_d.shape[0]/2)).flatten()
expected_return_markowitz = [min_var_markowitz[i]*instrument_returns[i] for i in range(0,cov1_d.shape[0])]
e_m = sum(expected_return_markowitz)
expected_return_NCO = [min_var_NCO[i]*instrument_returns[i] for i in range(0,cov1_d.shape[0])]
e_NCO = sum(expected_return_markowitz)
vol = getVolatility(S_value)
m_minVol = [min_var_markowitz[i]*vol[i] for i in range(0, cov1_d.shape[0])]
NCO_minVol = [mlfinlab_NCO[i]*vol[i] for i in range(0, cov1_d.shape[0])]
plt.plot(range(0, len(denoised_eigenvalue)),
np.log(denoised_eigenvalue),
color='r',
label="Denoised eigen-function")
plt.plot(range(0, len(eigenvalue_prior)),
np.log(eigenvalue_prior),
color='g',
label="Original eigen-function")
plt.xlabel("Eigenvalue number")
plt.ylabel("Eigenvalue (log-scale)")
plt.legend(loc="upper right")
plt.show()
#from code snippet 2.10
detoned_cov = mc.corr2cov(detoned_corr, var0)
w = mc.optPort(detoned_cov)
print(w)
#min_var_port = 1./nTrials*(np.sum(w, axis=0))
#print(min_var_port)
#expected portfolio variance: W^T.(Cov).W
#https://blog.quantinsti.com/calculating-covariance-matrix-portfolio-variance/
minVarPortfolio_var = np.dot(np.dot(w.T, detnoed_corr), w)
#Expected return: w.T . mu
# https://www.mn.uio.no/math/english/research/projects/focustat/publications_2/shatthik_barua_master2017.pdf p8
# or I.T.cov^-1.mu / I.T.cov^-1.I
inv = np.linalg.inv(cov)
e_r = np.dot(np.dot(ones.T, inv), mu) / np.dot(ones.T, np.dot(ones.T, inv))
#Chapter 4 optimal clustering
def minVarPort(cov):
return mc.optPort(cov, mu = None)
# code snippet 7.7 - data-generating process
nBlocks, bSize, bCorr = 10, 50, .5
np.random.seed(0)
mu0, cov0 = mc.formTrueMatrix(nBlocks, bSize, bCorr)
# code snippet 7.8 - drawing an empirical vector of means and covariance matrix
nObs, nSims, shrink, minVarPortf = 1000, 1000, False, True
np.random.seed(0)
w1 = pd.DataFrame(0, index=range(0, nSims), columns=range(0, nBlocks*bSize))
w1_d = pd.DataFrame(0, index=range(0, nSims), columns=range(0, nBlocks*bSize))
for i in range(0, nSims):
mu1, cov1 = mc.simCovMu(mu0, cov0, nObs, shrink=shrink)
if minVarPortf:
mu1 = None
w1.loc[i] = mc.optPort(cov1, mu1).flatten() #markowitc
w1_d.loc[i] = optPort_nco(cov1, mu1, int(cov1.shape[0]/2)).flatten() #nco
# code snippet 7.9 - Estimation of allocation errors
w0 = mc.optPort(cov0, None if minVarPortf else mu0)
w0 = np.repeat(w0.T, w1.shape[0], axis=0) #true allocation
rmsd = np.mean((w1-w0).values.flatten()**2)**.5 #RMSE
rmsd_d = np.mean((w1_d-w0).values.flatten()**2)**.5 #RMSE
'''
>>> rmsd
0.020737753489610305 #markowitc
>>> rmsd_d
0.015918559234396952 #nco
'''