def test_semicovariance():
df = get_data()
S = risk_models.semicovariance(df)
assert S.shape == (20, 20)
assert S.index.equals(df.columns)
assert S.index.equals(S.columns)
assert S.notnull().all().all()
S2 = risk_models.semicovariance(df, frequency=2)
pd.testing.assert_frame_equal(S / 126, S2)
def test_semicovariance():
df = get_data()
S = risk_models.semicovariance(df)
assert S.shape == (20, 20)
assert S.index.equals(df.columns)
assert S.index.equals(S.columns)
assert S.notnull().all().all()
S2 = risk_models.semicovariance(df, frequency=2)
pd.testing.assert_frame_equal(S / 126, S2)
def test_semicovariance_benchmark():
df = get_data()
# When the benchmark is very negative, the cov matrix should be zeroes
S_negative_benchmark = risk_models.semicovariance(df, benchmark=-0.5)
np.testing.assert_allclose(S_negative_benchmark, 0, atol=1e-4)
# Increasing the benchmark should increase covariances on average
S = risk_models.semicovariance(df, benchmark=0)
S2 = risk_models.semicovariance(df, benchmark=1)
assert S2.sum().sum() > S.sum().sum()
def test_semicovariance_benchmark():
df = get_data()
# When the benchmark is very negative, the cov matrix should be zeroes
S_negative_benchmark = risk_models.semicovariance(df, benchmark=-0.5)
np.testing.assert_allclose(S_negative_benchmark, 0, atol=1e-4)
# Increasing the benchmark should increase covariances on average
S = risk_models.semicovariance(df, benchmark=0)
S2 = risk_models.semicovariance(df, benchmark=1)
assert S2.sum().sum() > S.sum().sum()
def test_semicovariance():
df = get_data()
S = risk_models.semicovariance(df)
assert S.shape == (20, 20)
assert S.index.equals(df.columns)
assert S.index.equals(S.columns)
assert S.notnull().all().all()
assert risk_models._is_positive_semidefinite(S)
S2 = risk_models.semicovariance(df, frequency=2)
pd.testing.assert_frame_equal(S / 126, S2)
# Cover that it works on np.ndarray, with a warning
with pytest.warns(RuntimeWarning):
S2_np = risk_models.semicovariance(df.to_numpy(), frequency=2)
np.testing.assert_equal(S2_np, S2.to_numpy())
def test_efficient_semivariance_vs_heuristic():
benchmark = 0
es = setup_efficient_semivariance()
es.efficient_return(0.20)
mu_es, semi_deviation, _ = es.portfolio_performance()
np.testing.assert_almost_equal(mu_es, 0.2)
mean_return, historic_returns = setup_efficient_semivariance(
data_only=True)
pairwise_semivariance = risk_models.semicovariance(historic_returns,
returns_data=True,
benchmark=0,
frequency=1)
ef = EfficientFrontier(mean_return, pairwise_semivariance)
ef.efficient_return(0.20)
mu_ef, _, _ = ef.portfolio_performance()
# mu_ef *= 252
portfolio_returns = historic_returns @ ef.weights
drops = np.fmin(portfolio_returns - benchmark, 0)
T = historic_returns.shape[0]
semivariance = np.sum(np.square(drops)) / T * 252
semi_deviation_ef = np.sqrt(semivariance)
assert semi_deviation < semi_deviation_ef
assert mu_es / semi_deviation > mu_ef / semi_deviation_ef
def test_efficient_semivariance_vs_heuristic_weekly():
benchmark = 0
_, historic_returns = setup_efficient_semivariance(data_only=True)
weekly_returns = historic_returns.resample("W").sum()
mean_weekly_returns = weekly_returns.mean(axis=0)
es = EfficientSemivariance(mean_weekly_returns,
weekly_returns,
frequency=52)
es.efficient_return(0.20 / 52)
mu_es, semi_deviation, _ = es.portfolio_performance()
pairwise_semivariance = risk_models.semicovariance(weekly_returns,
returns_data=True,
benchmark=0,
frequency=1)
ef = EfficientFrontier(mean_weekly_returns, pairwise_semivariance)
ef.efficient_return(0.20 / 52)
mu_ef, _, _ = ef.portfolio_performance()
portfolio_returns = historic_returns @ ef.weights
drops = np.fmin(portfolio_returns - benchmark, 0)
T = weekly_returns.shape[0]
semivariance = np.sum(np.square(drops)) / T * 52
semi_deviation_ef = np.sqrt(semivariance)
assert semi_deviation < semi_deviation_ef
assert mu_es / semi_deviation > mu_ef / semi_deviation_ef
def test_efficient_return_semicovariance():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.efficient_return(0.12)
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.11999999997948813, 0.06948386215256849, 1.4391830977949114))
def test_min_volatilty_semicovariance_L2_reg():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.min_volatility()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.20661406151867523, 0.05551598140785206, 3.3614475829527706))
def test_max_sharpe_semicovariance():
df = get_data()
cla = setup_cla()
cla.covar = risk_models.semicovariance(df, benchmark=0)
w = cla.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(cla.tickers)
np.testing.assert_almost_equal(cla.weights.sum(), 1)
np.testing.assert_allclose(
cla.portfolio_performance(),
(0.3253436663900292, 0.21333530089904357, 1.4312852355106793),
)
def test_cla_max_sharpe_semicovariance():
df = get_data()
cla = setup_cla()
cla.cov_matrix = risk_models.semicovariance(df, benchmark=0).values
w = cla.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(cla.tickers)
np.testing.assert_almost_equal(cla.weights.sum(), 1)
np.testing.assert_allclose(
cla.portfolio_performance(),
(0.2936179968144084, 0.06362345488289835, 4.300583759841616),
)
def test_cla_max_sharpe_semicovariance():
df = get_data()
cla = setup_cla()
cla.cov_matrix = risk_models.semicovariance(df, benchmark=0).values
w = cla.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(cla.tickers)
np.testing.assert_almost_equal(cla.weights.sum(), 1)
np.testing.assert_allclose(
cla.portfolio_performance(),
(0.2686858719299194, 0.06489248187610204, 3.8322755539652578),
)
def test_max_sharpe_semicovariance():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.2972237371625498, 0.06443267303123411, 4.302533545801584))
def test_efficient_return_semicovariance():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.efficient_return(0.12)
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.12000000000871075, 0.06948386214063361, 1.4319423610177537))
def test_max_sharpe_short_semicovariance():
df = get_data()
ef = EfficientFrontier(*setup_efficient_frontier(data_only=True),
weight_bounds=(-1, 1))
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.3907992623559733, 0.0809285460933456, 4.581810501430255),
)
def test_max_sharpe_semicovariance():
# f
df = get_data()
cla = setup_cla()
cla.covar = risk_models.semicovariance(df, benchmark=0)
w = cla.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(cla.tickers)
np.testing.assert_almost_equal(cla.weights.sum(), 1)
np.testing.assert_allclose(
cla.portfolio_performance(),
(0.3253436657555845, 0.2133353004830236, 1.4281588303044812),
)
def test_max_sharpe_semicovariance():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
assert all([i >= 0 for i in w.values()])
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.2732301946250426, 0.06603231922971581, 3.834943215368455),
)
def test_max_sharpe_semicovariance():
# f
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.2972237362989219, 0.064432672830601, 4.297294313174586))
def test_max_sharpe_short_semicovariance():
df = get_data()
ef = EfficientFrontier(*setup_efficient_frontier(data_only=True),
weight_bounds=(-1, 1))
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.3564654865246848, 0.07202031837368413, 4.671813373260894))
def test_max_sharpe_semicovariance():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
assert all([i >= 0 for i in w.values()])
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.2972184894480104, 0.06443145011260347, 4.302533762060766),
)
def test_max_sharpe_short_semicovariance():
df = get_data()
ef = EfficientFrontier(*setup_efficient_frontier(data_only=True),
weight_bounds=(-1, 1))
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.3564305116656491, 0.07201282488003401, 4.671813836300796),
)
def test_max_sharpe_short_semicovariance():
df = get_data()
ef = EfficientFrontier(*setup_efficient_frontier(data_only=True),
weight_bounds=(-1, 1))
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.42444834528495234, 0.0898263632679403, 4.50255727350929),
)
def test_efficient_return_semicovariance():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.efficient_return(0.12)
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.12000000000871075, 0.06948386214063361, 1.4319423610177537)
)
def test_max_sharpe_semicovariance():
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
assert all([i >= 0 for i in w.values()])
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.2762965426962885, 0.07372667096108301, 3.476307004714425),
)
def test_cla_max_sharpe_semicovariance():
df = get_data()
cla = setup_cla()
cla.cov_matrix = risk_models.semicovariance(df, benchmark=0).values
w = cla.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(cla.tickers)
np.testing.assert_almost_equal(cla.weights.sum(), 1)
np.testing.assert_allclose(
cla.portfolio_performance(),
(0.2721798377099145, 0.07258537193305141, 3.474251505420551),
atol=1e-4,
rtol=1e-4,
)
def test_min_volatilty_semicovariance_L2_reg():
df = get_data()
ef = setup_efficient_frontier()
ef.gamma = 1
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.min_volatility()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
assert all([i >= 0 for i in w.values()])
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.23803779483710888, 0.0962263031034166, 2.265885603053655))
def test_max_sharpe_semicovariance():
# f
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.max_sharpe()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.2972237362989219, 0.064432672830601, 4.297294313174586)
)
def test_min_volatilty_semicovariance_L2_reg():
# f
df = get_data()
ef = setup_efficient_frontier()
ef.cov_matrix = risk_models.semicovariance(df, benchmark=0)
w = ef.min_volatility()
assert isinstance(w, dict)
assert set(w.keys()) == set(ef.tickers)
assert set(w.keys()) == set(ef.expected_returns.index)
np.testing.assert_almost_equal(ef.weights.sum(), 1)
np.testing.assert_allclose(
ef.portfolio_performance(),
(0.20661406122127524, 0.055515981410304394, 3.3567606718215663)
)
def handle_data(context, data):
date = data.today()
if date in context.balance_dates:
temp = {}
for code in context.stocks:
history_price = data.history_bars(code,
context.expected_return_days,
'1d', 'close')
if history_price is not None:
temp.update({code: history_price})
history_prices = pd.DataFrame(temp)
mu = expected_returns.mean_historical_return(history_prices)
if context.cov_method == 'sample':
S = risk_models.sample_cov(history_prices)
elif context.cov_method == 'semi':
S = risk_models.semicovariance(history_prices)
elif context.cov_method == 'exp_cov':
S = risk_models.exp_cov(history_prices)
ef = EfficientFrontier(mu, S)
if context.opt_criterion == 'max_sharpe':
weights = ef.max_sharpe()
elif context.opt_criterion == 'efficient_return':
weights = ef.efficient_return(context.target_return)
elif context.opt_criterion == 'efficient_risk':
weights = ef.efficient_risk(context.targe_risk,
context.risk_free_rate)
elif context.opt_criterion == 'min_volatility':
weights = ef.min_volatility()
if context.cleaned_weights is True:
weights = ef.clean_weights()
weight = []
prices = []
for code in context.stocks:
weight.append(weights[code])
prices.append(data.latest_price(code, "1d"))
data.order_target_percent(context.stocks, weight, prices)
def handle_bar(context, api):
date = api.now()
#if date in context.balance_dates:
history_prices = {}
for stock in context.stocks:
history_price = api.history_bars(stock, context.expected_return_days,
'1d', 'close')
history_prices.update({stock: history_price})
history_prices = pd.DataFrame(history_prices)
mu = expected_returns.mean_historical_return(history_prices)
if context.cov_method == 'sample':
S = risk_models.sample_cov(history_prices)
elif context.cov_method == 'semi':
S = risk_models.semicovariance(history_prices)
elif context.cov_method == 'exp_cov':
S = risk_models.exp_cov(history_prices)
ef = EfficientFrontier(mu, S)
if context.opt_criterion == 'max_sharpe':
weights = ef.max_sharpe()
elif context.opt_criterion == 'efficient_return':
weights = ef.efficient_return(context.target_return)
elif context.opt_criterion == 'efficient_risk':
weights = ef.efficient_risk(context.targe_risk, context.risk_free_rate)
elif context.opt_criterion == 'min_volatility':
weights = ef.min_volatility()
if context.cleaned_weights is True:
weights = ef.clean_weights()
prices = []
weight = []
for stock in context.stocks:
weight.append(weights[stock])
prices.append(api.latest_price(stock, "1d"))
api.order_target_percent(stocks, weight, prices)
tickers = ['BLK', "BAC", "AAPL", "TM", "WMT",
"JD"] # "INTU", "MA", "UL", "CVS",
# "DIS", "AMD", "NVDA", "PBI", "TGT"]
ohlc = yf.download(tickers, period="max")
prices = ohlc["Adj Close"]
prices.tail()
#various types of expected returns; these will be used for expected future returns
mu = expected_returns.james_stein_shrinkage(prices)
mum = expected_returns.mean_historical_return(prices)
mummy = expected_returns.capm_return(prices)
#different risk models; guessing that you can also use the pandas.cov function
S = risk_models.semicovariance(prices)
T = risk_models.CovarianceShrinkage(prices).ledoit_wolf()
plotting.plot_covariance(S)
plotting.plot_covariance(T)
#equal weights
initial_weights = np.array([1 / len(tickers)] * len(tickers))
print(initial_weights)
#transaction cost objective
ef = EfficientFrontier(mum, T)
# 1% broker commission
ef.add_objective(objective_functions.transaction_cost,
w_prev=initial_weights,
k=0.01)
