├── IndustryMktCaps.xlsx ├── README.md ├── .gitignore ├── PortfolioConstructionFunction.py ├── Factor Data.CSV └── Return Data.csv /IndustryMktCaps.xlsx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzj1992/Portfolio_Construction/HEAD/IndustryMktCaps.xlsx -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Portfolio_Construction 2 | These are some functions for portfolio construction under different models, including Basic Mean_Variance Models, Factor Models and Black-Litterman Models. 3 | 4 | The idea behind this project is derived from the assignments of FINC6009 at the University of Sydney. If you are currently enrolling in this unit, these defined functions may help you process financial data and complete assignments more efficiently. However, you are firstly encouraged to figure out those questions to avoid plagiarism. Meanwhile, looking forward to some improvements from you guys. 感谢大神们不吝赐教! 5 | 6 | There are three files uploaded, including Return Data.csv, Factor Data.csv and IndustryMktCaps.xlsx, which may assist in familiarizing yourself with those functions. For further deployment, you can also download such data on Kenneth R. French Data Library via http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. 7 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | env/ 12 | build/ 13 | develop-eggs/ 14 | dist/ 15 | downloads/ 16 | eggs/ 17 | .eggs/ 18 | lib/ 19 | lib64/ 20 | parts/ 21 | sdist/ 22 | var/ 23 | wheels/ 24 | *.egg-info/ 25 | .installed.cfg 26 | *.egg 27 | 28 | # PyInstaller 29 | # Usually these files are written by a python script from a template 30 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 31 | *.manifest 32 | *.spec 33 | 34 | # Installer logs 35 | pip-log.txt 36 | pip-delete-this-directory.txt 37 | 38 | # Unit test / coverage reports 39 | htmlcov/ 40 | .tox/ 41 | .coverage 42 | .coverage.* 43 | .cache 44 | nosetests.xml 45 | coverage.xml 46 | *.cover 47 | .hypothesis/ 48 | 49 | # Translations 50 | *.mo 51 | *.pot 52 | 53 | # Django stuff: 54 | *.log 55 | local_settings.py 56 | 57 | # Flask stuff: 58 | instance/ 59 | .webassets-cache 60 | 61 | # Scrapy stuff: 62 | .scrapy 63 | 64 | # Sphinx documentation 65 | docs/_build/ 66 | 67 | # PyBuilder 68 | target/ 69 | 70 | # Jupyter Notebook 71 | .ipynb_checkpoints 72 | 73 | # pyenv 74 | .python-version 75 | 76 | # celery beat schedule file 77 | celerybeat-schedule 78 | 79 | # SageMath parsed files 80 | *.sage.py 81 | 82 | # dotenv 83 | .env 84 | 85 | # virtualenv 86 | .venv 87 | venv/ 88 | ENV/ 89 | 90 | # Spyder project settings 91 | .spyderproject 92 | .spyproject 93 | 94 | # Rope project settings 95 | .ropeproject 96 | 97 | # mkdocs documentation 98 | /site 99 | 100 | # mypy 101 | .mypy_cache/ 102 | -------------------------------------------------------------------------------- /PortfolioConstructionFunction.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf-8 -*- 3 | """ 4 | Created on Fri Dec 15 11:12:22 2017 5 | 6 | @author: jagger.guo 7 | """ 8 | 9 | import pandas as pd 10 | import numpy as np 11 | import random 12 | import string 13 | from sklearn.linear_model import LinearRegression 14 | 15 | # 1. Define the basic mean-variance model to construct portfolios 16 | 17 | class Mean_Variance_Model(object): 18 | 19 | def __init__(self, data, n, rf): 20 | 21 | self.data = data # Initialize the input data 22 | self.n = n # Initialize the number of assets (features) 23 | self.rf = rf # Initialize the risk-free rate 24 | 25 | def r_mean_vec(self): # Create the expected return vector 26 | 27 | expected_return_vec = np.transpose(np.mat(self.data.mean())) 28 | 29 | return expected_return_vec 30 | 31 | def ex_r_mat(self): # Create the excess return matrix 32 | 33 | excess_return_matrix = np.mat(self.data - self.data.mean()) 34 | 35 | return excess_return_matrix 36 | 37 | def get_cov_mat(self): # Create the sample covariance matrix 38 | 39 | ex_r_mat = self.ex_r_mat() 40 | cov_matrix = np.mat((1 / (len(ex_r_mat) - 1)) * np.dot(ex_r_mat.T, ex_r_mat)) 41 | 42 | return cov_matrix 43 | 44 | def num_abcd(self): # Calculate the numbers of a, b, c, d 45 | 46 | ones_vec = np.ones((self.n, 1)) 47 | cov_matrix = self.get_cov_mat() 48 | expected_return_vec = self.r_mean_vec() 49 | 50 | a = ones_vec.T * (cov_matrix.I) * ones_vec 51 | b = ones_vec.T * (cov_matrix.I) * expected_return_vec 52 | c = expected_return_vec.T * (cov_matrix.I) * expected_return_vec 53 | d = (a*c - b**2) 54 | 55 | return a, b, c, d 56 | 57 | def tp_x_vec(self): # Calculate the X vector, the expected return and standard deviation of the tangency portfolio 58 | 59 | a, b, _, _ = self.num_abcd() 60 | risk_aversion = b - self.rf * a # Set the risk-free rate as 0 61 | cov_mat = self.get_cov_mat() 62 | r_mean = self.r_mean_vec() 63 | 64 | x_vec = np.multiply(1/risk_aversion, np.dot(cov_mat.I, r_mean - 65 | (np.zeros((self.n,1))))) 66 | expected_return_tp = np.dot(r_mean.T, x_vec) 67 | sd_tp = np.sqrt(np.dot(np.dot(x_vec.T, cov_mat), x_vec)) 68 | 69 | return x_vec, expected_return_tp, sd_tp 70 | 71 | def gmvp_x_vec(self): # Calculate the X vector, the expected return and standard deviation at the GMVP point 72 | 73 | a, b, _, _ = self.num_abcd() 74 | x_vec = np.dot(np.multiply(1/a, self.get_cov_mat().I), np.ones((self.n, 1))) 75 | expected_return_GMVP = np.array((b/a)) 76 | sd_GMVP = np.array(np.sqrt(1/a)) 77 | 78 | return x_vec, expected_return_GMVP, sd_GMVP 79 | 80 | 81 | # 2. Define the factor model to construct portfolios 82 | 83 | class Factor_Model(object): 84 | 85 | def __init__(self, return_data, factor_data, n, factors, rf): 86 | 87 | self.r_data = return_data # Initialize the input data 88 | self.f_data = factor_data 89 | self.n = n # Initialize the number of assets (features) 90 | self.factors = factors 91 | self.rf = rf # Initialize the risk-free rate 92 | 93 | def r_mean_vec(self): # Create the expected return vector 94 | 95 | expected_return_vec = np.transpose(np.mat(self.r_data.mean())) 96 | 97 | return expected_return_vec 98 | 99 | def ex_r_mat(self): # Create the excess return matrix 100 | 101 | excess_return_matrix = np.mat(self.r_data - self.r_data.mean()) 102 | 103 | return excess_return_matrix 104 | 105 | def get_AlphaBeta(self): # Create the Alpha vector and Beta matrix 106 | 107 | alpha_vec = [] 108 | beta_mat = [] 109 | reg = LinearRegression() 110 | 111 | if self.factors == 1: 112 | 113 | for i in range(0,self.n): 114 | 115 | reg.fit(np.array(self.f_data.iloc[:, 0: self.factors]).reshape(len(self.f_data), self.factors), 116 | np.array(self.r_data.iloc[:, i]).reshape(len(self.r_data), 1) - 117 | np.array(self.rf * np.ones((len(self.r_data),1)))) 118 | 119 | alpha_vec.append(reg.intercept_) 120 | beta_mat.append(reg.coef_[0,0]) 121 | 122 | alpha_vec = np.array(alpha_vec).reshape(self.n,1) 123 | beta_mat = np.array(beta_mat).reshape(self.n,1) 124 | 125 | else: 126 | 127 | for i in range(0,self.n): 128 | 129 | reg.fit(np.array(self.f_data.iloc[:, 0: self.factors]).reshape(len(self.f_data), self.factors), 130 | np.array(self.r_data.iloc[:, i]).reshape(len(self.r_data), 1) - 131 | np.array(self.rf * np.ones((len(self.r_data),1)))) 132 | 133 | alpha_vec.append(reg.intercept_) 134 | beta_mat.append(reg.coef_[0,0: self.factors]) 135 | 136 | alpha_vec = np.array(alpha_vec).reshape(self.n,1) 137 | beta_mat = np.mat(beta_mat) 138 | 139 | return alpha_vec, beta_mat 140 | 141 | def get_cov_mat(self): # Create the covariance matrix 142 | 143 | _, beta = self.get_AlphaBeta() 144 | 145 | sd_assets = np.std(self.r_data) 146 | for i in range(self.factors): 147 | locals()['sd_factor'+str(i)] = [] 148 | for i in range(self.factors): 149 | sd_factor = np.std(self.f_data.iloc[:, i]) 150 | locals()['sd_factor'+str(i)].append(sd_factor) 151 | 152 | cov_mat_factors = np.zeros((self.factors, self.factors)) 153 | for i in range(self.factors): 154 | cov_mat_factors[i, i] = [x**2 for x in locals()['sd_factor'+str(i)]][0] 155 | 156 | rows = [] 157 | columns = [] 158 | for i in range(self.n): 159 | random_string = ''.join(random.sample(string.ascii_letters + string.digits, 8)) 160 | rows.append(random_string) 161 | columns.append(random_string) 162 | results = pd.DataFrame(0.0, columns = columns, index = rows) 163 | 164 | for a in range(0, self.n): 165 | 166 | for b in range(0, self.n): 167 | 168 | if columns[a] == rows[b]: 169 | 170 | results.iloc[a, b] = sd_assets[a]**2 171 | 172 | else: 173 | 174 | results.iloc[a, b] = np.dot(np.dot(beta[a,:], cov_mat_factors), np.transpose(beta)[:,b]) 175 | 176 | results = np.mat(results) 177 | 178 | return results 179 | 180 | def num_abcd(self): # Calculate the numbers of a, b, c, d 181 | 182 | ones_vec = np.ones((self.n, 1)) 183 | cov_matrix = self.get_cov_mat() 184 | expected_return_vec = self.r_mean_vec() 185 | 186 | a = ones_vec.T * (cov_matrix.I) * ones_vec 187 | b = ones_vec.T * (cov_matrix.I) * expected_return_vec 188 | c = expected_return_vec.T * (cov_matrix.I) * expected_return_vec 189 | d = (a*c - b**2) 190 | 191 | return a, b, c, d 192 | 193 | def tp_x_vec(self): # Calculate the X vector, the expected return and standard deviation of the tangency portfolio 194 | 195 | alpha, beta = self.get_AlphaBeta() 196 | cov_mat = self.get_cov_mat() 197 | a, b, _, _ = self.num_abcd() 198 | 199 | risk_aversion = b - self.rf * a 200 | cov_mat = self.get_cov_mat() 201 | r_mean = self.r_mean_vec() 202 | 203 | mu_factors = np.mat((self.f_data.iloc[:, 0:self.factors]).mean()).T 204 | 205 | x_vec = np.multiply(1/risk_aversion, np.dot(cov_mat.I, r_mean - 206 | (np.zeros((self.n,1))))) 207 | expected_return_tp = np.dot(x_vec.T, np.add(alpha, np.dot(beta, mu_factors))) 208 | sd_tp = np.sqrt(np.dot(np.dot(x_vec.T, cov_mat), x_vec)) 209 | 210 | return x_vec, expected_return_tp, sd_tp 211 | 212 | def gmvp_x_vec(self): # Calculate the X vector, the expected return and standard deviation at the GMVP point 213 | 214 | a, b, _, _ = self.num_abcd() 215 | x_vec = np.dot(np.multiply(1/a, self.get_cov_mat().I), np.ones((self.n, 1))) 216 | expected_return_GMVP = np.array((b/a)) 217 | sd_GMVP = np.array(np.sqrt(1/a)) 218 | 219 | return x_vec, expected_return_GMVP, sd_GMVP 220 | 221 | 222 | # 3. Define the Black-Litterman model to construct portfolios 223 | 224 | class Black_Litterman_Model(object): 225 | 226 | def __init__(self, return_data, factor_data, MktCap_data, n, factors, rf): 227 | 228 | self.r_data = return_data # Initialize the input data 229 | self.f_data = factor_data # Initialize the factor data 230 | self.m_data = MktCap_data # Initialize the market capitalisation data 231 | self.n = n # Initialize the number of assets (features) 232 | self.factors = factors 233 | self.rf = rf # Initialize the risk-free rate 234 | 235 | def get_MktCap(self): # Calculate the market capitalisation vector 236 | 237 | x_mktcap = [] 238 | 239 | for i in self.m_data: 240 | total = sum(self.m_data) 241 | weight = i/total 242 | x_mktcap.append(weight) 243 | 244 | return x_mktcap 245 | 246 | def get_Amkt(self): # Calculate the coefficient of risk aversion of the market portfolio 247 | 248 | market_return = (self.f_data['Mkt-RF'] + self.f_data['RF']).values 249 | mkt_var = (np.std(market_return, ddof = 1))**2 250 | 251 | A_market = np.average(self.f_data['Mkt-RF']) / mkt_var 252 | 253 | return A_market 254 | 255 | def get_cov_mat(self): # Calculate the covariance matrix 256 | 257 | ex_r_mat = np.mat(self.r_data - self.r_data.mean()) 258 | cov_matrix = np.mat((1 / (len(ex_r_mat) - 1)) * np.dot(ex_r_mat.T, ex_r_mat)) 259 | 260 | return cov_matrix 261 | 262 | def get_pi(self): # Calculate the equillibrium return 263 | 264 | am = self.get_Amkt() 265 | cov_mat = self.get_cov_mat() 266 | xm = np.array(self.get_MktCap()) 267 | 268 | pi = np.array(am * np.dot(cov_mat, xm)) 269 | 270 | return pi.reshape(self.n,1) 271 | 272 | def get_Return(self, omega_matrix, p_matrix, q_vector, tau): # Calculate the expected return vector under the Black-Litterman Model 273 | 274 | cov_mat = self.get_cov_mat() 275 | pi_vec = self.get_pi() 276 | 277 | first_part = ((tau*cov_mat).I + np.dot(np.dot(p_matrix.T, omega_matrix.I), p_matrix)).I 278 | second_part = np.dot((tau*cov_mat).I, pi_vec) + np.dot(np.dot(p_matrix.T, omega_matrix.I), q_vector) 279 | 280 | done = np.dot(first_part, second_part) 281 | 282 | return done 283 | 284 | def get_x_bl(self, Return_BL): # Calculate the weight allocation vector 285 | 286 | am = self.get_Amkt() 287 | cov_mat = self.get_cov_mat() 288 | 289 | rbl = Return_BL - (np.average(self.f_data['RF'])*np.ones((len(Return_BL), 1))) 290 | x = ((am**(-1)) * np.dot(cov_mat.I, rbl)).tolist() 291 | 292 | revised_x = [] 293 | for i in x: 294 | x_new = i / np.sum(x) 295 | revised_x.append(x_new) 296 | 297 | revised_x = np.array(revised_x) 298 | 299 | return revised_x 300 | 301 | # 4. Define the function to derive the standard error of intercept 302 | 303 | def lsqfity(X, Y): 304 | """ 305 | ***Copy from StackFlow*** 306 | 307 | Calculate a "MODEL-1" least squares fit. 308 | 309 | The line is fit by MINIMIZING the residuals in Y only. 310 | 311 | The equation of the line is: Y = my * X + by. 312 | 313 | Equations are from Bevington & Robinson (1992) 314 | Data Reduction and Error Analysis for the Physical Sciences, 2nd Ed." 315 | pp: 104, 108-109, 199. 316 | 317 | Data are input and output as follows: 318 | 319 | my, by, ry, smy, sby = lsqfity(X,Y) 320 | X = x data (vector) 321 | Y = y data (vector) 322 | my = slope 323 | by = y-intercept 324 | ry = correlation coefficient 325 | smy = standard deviation of the slope 326 | sby = standard deviation of the y-intercept 327 | 328 | """ 329 | 330 | X, Y = map(np.asanyarray, (X, Y)) 331 | 332 | # Determine the size of the vector. 333 | n = len(X) 334 | 335 | # Calculate the sums. 336 | 337 | Sx = np.sum(X) 338 | Sy = np.sum(Y) 339 | Sx2 = np.sum(X ** 2) 340 | Sxy = np.sum(X * Y) 341 | Sy2 = np.sum(Y ** 2) 342 | 343 | # Calculate re-used expressions. 344 | num = n * Sxy - Sx * Sy 345 | den = n * Sx2 - Sx ** 2 346 | 347 | # Calculate my, by, ry, s2, smy and sby. 348 | my = num / den 349 | by = (Sx2 * Sy - Sx * Sxy) / den 350 | ry = num / (np.sqrt(den) * np.sqrt(n * Sy2 - Sy ** 2)) 351 | 352 | diff = Y - by - my * X 353 | 354 | s2 = np.sum(diff * diff) / (n - 2) 355 | smy = np.sqrt(n * s2 / den) 356 | sby = np.sqrt(Sx2 * s2 / den) 357 | 358 | return my, by, ry, smy, sby -------------------------------------------------------------------------------- /Factor Data.CSV: -------------------------------------------------------------------------------- 1 | ,Mkt-RF,SMB,HML,RF 2 | 20140102,-0.88,-0.27,0.11,0 3 | 20140103,0.03,0.36,0.05,0 4 | 20140106,-0.34,-0.57,0.26,0 5 | 20140107,0.68,0.4,-0.41,0 6 | 20140108,0.04,0.01,-0.11,0 7 | 20140109,0.02,0.17,-0.38,0 8 | 20140110,0.27,0.53,-0.77,0 9 | 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