def portfolio_box(er, s, eta, y, side=1.0, extended_return=True):
n = er.shape[1]
N = n+1
mu = ps.first_moment(er)
P = ps.second_moment(er)
Ws = list()
for i in range(n):
W = np.zeros((N,N))
W[n, i] = 1.0
W[i, n] = 1.0
W[n, n] = -side / 2.0
Ws.append(W)
W = np.zeros((N,N))
W[n, i] = -1.0
W[i, n] = -1.0
W[n, n] = -side / 2.0
Ws.append(W)
Ws = np.array(Ws)
logging.debug('Ws = {0}'.format(Ws))
sol = eval_portfolio_box(y, mu, P, s, eta, Ws)
logging.info('Solution = {0}'.format(sol))
if extended_return:
return sol
else:
return sol[0]
def base_portfolio_extended(er, y, s, eta):
n = er.shape[1]
N = n+1
mu = ps.first_moment(er)
P = ps.second_moment(er)
init_sol = find_initial_solution(s, mu, P)
prob = dccbase.DccBaseDetFormProblem(mu, P, s, y, eta)
sol = logbar.solve_log_barrier(init_sol, prob, 0.05, 9*6, using_finite_differences=True)
logging.info('Solution = {0}'.format(sol))
return sol[-n:], prob.eval_f(sol), sol, prob.eval_g(sol)
def base_portfolio(er, s, eta, y):
n = er.shape[1]
N = n+1
mu = ps.first_moment(er)
P = ps.second_moment(er)
init_sol = find_initial_solution(s, mu, P)
prob = dccbase.DccBaseProblem(mu, P, s, y, eta)
sol = logbar.solve_log_barrier(init_sol, prob, 0.001, 2*N)
logging.info('Solution = {0}'.format(sol))
return sol[-n:]
def portfolio_unconstrained(er, y, s, eta):
n = er.shape[1]
N = n+1
mu = ps.first_moment(er)
P = ps.second_moment(er)
init_sol = gen_init_sol_sphere(y, eta, s, P)
Ws = np.zeros((N,N)).reshape((1,N,N)) # No support constraint.
prob = dccsupport.DccSupportProblem(mu, P, s, y, eta, Ws)
sol = logbar.solve_log_barrier(init_sol, prob, 0.001, 9*6)
logging.info('Solution = {0}'.format(sol))
return sol[-n:], prob.eval_f(sol), sol, prob.eval_g(sol)
def portfolio_sphere_extended_fd(er, y, s, eta):
n = er.shape[1]
N = n+1
mu = ps.first_moment(er)
P = ps.second_moment(er)
init_sol = gen_init_sol_sphere(y, eta, s, P)
Ws = np.eye(N).reshape((1,N,N))
Ws[-1] *= -1 # Radius of 1.
prob = dccsupport.DccSupportProblem(mu, P, s, y, eta, Ws)
sol = logbar.solve_log_barrier(init_sol, prob, 0.05, 9*6, using_finite_differences=True)
logging.info('Solution = {0}'.format(sol))
return sol[-n:], prob.eval_f(sol), sol, prob.eval_g(sol)
def portfolio_logbar(er, variance_bound, extended_return=True):
logging.info("Initialize parameters and calculate variance bound portfolio.")
n = er.shape[1]
mu = ps.first_moment(er)
sigma = ps.covariance(er)
sol = eval_portfolio_logbar(mu, sigma, variance_bound)
logging.info("Solution = {0}".format(sol))
if extended_return:
return sol
else:
return sol[0]
def portfolio_bounds(er, variance_bound, u_bounds, extended_return=True):
logging.info("Initialize and calculate variance bound portfolio with bounded portfolio weights.")
n = er.shape[1]
mu = ps.first_moment(er)
sigma = ps.covariance(er)
sol = eval_portfolio_bounds(mu, sigma, variance_bound, u_bounds)
logging.info("Solution = {0}".format(sol))
if extended_return:
return sol
else:
return sol[0]
def portfolio(excess_returns, mean_weight, risk_aversion, eta):
first_moment = ps.first_moment(excess_returns)
u = np.zeros(excess_returns.shape[1])
active_samples = msv_active_samples(u, excess_returns, eta)
has_converged = False
while not has_converged:
grad = msv_grad(first_moment, excess_returns, active_samples,
mean_weight, risk_aversion, eta)
u_prime = msv_hess_inv_prod(grad, excess_returns, active_samples, risk_aversion)
active_samples_prime = msv_active_samples(u_prime, excess_returns, eta)
has_converged = all(active_samples == active_samples_prime)
if has_converged:
break
u = u_prime
active_samples = active_samples_prime
return u_prime
def portfolio_sphere_bounds(er, s, eta, y, radius, u_bounds,
extended_return=True):
n = er.shape[1]
N = n+1
mu = ps.first_moment(er)
P = ps.second_moment(er)
Ws = np.eye(N).reshape((1,N,N))
Ws[0,-1,-1] = -radius
logging.debug('Ws = {0}'.format(Ws))
sol = eval_portfolio_sphere_bounds(y, mu, P, s, eta, Ws, u_bounds)
logging.info('Solution = {0}'.format(sol))
if extended_return:
return sol
else:
return sol[0]
def portfolio_sphere(er, semivar_bound, eta, y=0.0, radius=1.0,
extended_return=True,
verbose=False):
n = er.shape[1]
N = n+1
mu = ps.first_moment(er)
P = ps.second_moment(er)
Ws = np.eye(N).reshape((1,N,N))
Ws[0,-1,-1] = -radius
logging.info('radius: {0}'.format(radius))
sol = eval_portfolio_sphere(y, mu, P, semivar_bound, eta, Ws, verbose)
# print 'Solution = {0}'.format(sol)
if extended_return:
return sol
else:
return sol[0]
def bench_exact_hess(x):
test_prob.eval_hess_bar_g(x)
def benchmark_fd_exact_hess_bar_g():
print(timeit.timeit('bench_fd_hess()', setup='from dccsupport import bench_fd_hess',
number=1000))
print(timeit.timeit('bench_exact_hess()', setup='from dccsupport import bench_exact_hess',
number=1000))
# test_xm = np.concatenate([np.array([[ -1.3125 , -1.125 , -1.0625 , -0.5625 ],
# [ -1.125 , -1.8125 , -1.25 , -0.90625],
# [ -1.0625 , -1.25 , -1.3125 , -0.625 ],
# [ -0.5625 , -0.90625, -0.625 , -1.025 ]]).reshape(-1),
# np.array([0.1667, 0.3333, 0.5])]) / 10.
# test_xm = init_tau(test_xm, 3, 1)/100.
# test_xm_extended = init_tau(test_xm, 3, 2)/100.
if __name__ == '__main__':
test_er = loaddata.load_fama_french_10_industry().values[-300:, :3]
mu, sigma = ps.first_moment(test_er), ps.covariance(test_er)
# mu, P = ps.shrinkage_moments(test_er.values[300:,:3], bootstrap_size=100)
variance_bound = 0.03
u_bounds = {'lower': -0.1*np.ones(3), 'upper': 0.5*np.ones(3)}
test_prob = MVProblem(mu, sigma, variance_bound, u_bounds)
# test_prob_extended = DccSupportProblem(mu, P, s, y, eta, extended_Ws)
bar_hess = np.sum(map(logbar.eval_log_bar_hess_f, g, jac_g, hess_g), axis=0)
def bench_exact_hess(x):
test_prob.eval_hess_bar_g(x)
def benchmark_fd_exact_hess_bar_g():
print(timeit.timeit('bench_fd_hess()', setup='from dccsupport import bench_fd_hess',
number=1000))
print(timeit.timeit('bench_exact_hess()', setup='from dccsupport import bench_exact_hess',
number=1000))
if __name__ == '__main__':
test_er = loaddata.load_fama_french_10_industry().values[-300:, :3]
mu, P = ps.first_moment(test_er), ps.second_moment(test_er)
# mu, P = ps.shrinkage_moments(test_er.values[300:,:3], bootstrap_size=100)
y = 0.1
eta = 0.004
s = 0.005
Ws = np.eye(4).reshape(1, 4, 4)
radius = 3.0
Ws[0, 3, 3] = -radius
extended_Ws = np.concatenate([np.eye(4).reshape(1,4,4),
np.diag(np.linspace(1,4,4)).reshape(1,4,4)])
u_bounds = {'lower': -0.1*np.ones(3), 'upper': 0.5*np.ones(3)}
test_prob = DccSupportProblem(mu, P, s, y, eta, Ws, u_bounds)
# test_prob_extended = DccSupportProblem(mu, P, s, y, eta, extended_Ws)
bar_hess = np.sum(map(logbar.eval_log_bar_hess_f, g, jac_g, hess_g), axis=0)
def bench_exact_hess(x):
test_prob.eval_hess_bar_g(x)
def benchmark_fd_exact_hess_bar_g():
print(timeit.timeit('bench_fd_hess()', setup='from dccsupport import bench_fd_hess',
number=1000))
print(timeit.timeit('bench_exact_hess()', setup='from dccsupport import bench_exact_hess',
number=1000))
if __name__ == '__main__':
test_et = loaddata.load_fama_french_10_industry()
mu = ps.first_moment(test_et.values[300:,:3])
P = ps.second_moment(test_et.values[300:,:3])
y = 0.1
eta = 0.004
s = 0.005
test_prob = DccBaseProblem(mu, P, s, y, eta)
# test_xm = np.concatenate([np.array([[ -1.3125 , -1.125 , -1.0625 , -0.5625 ],
# [ -1.125 , -1.8125 , -1.25 , -0.90625],
# [ -1.0625 , -1.25 , -1.3125 , -0.625 ],
# [ -0.5625 , -0.90625, -0.625 , -1.025 ]]).reshape(-1),
# np.array([0.1667, 0.3333, 0.5])]) / 10.
def portfolio(excess_returns, mean_weight):
mu = ps.first_moment(excess_returns)
sigma = ps.covariance(excess_returns)
return mean_weight * 0.5 * la.solve(sigma, mu)