def __init__(self, factors: typing.List, securities_universe,
start_date: datetime, end_date: datetime,
rebalancing_frequency: config.RebalancingFrequency):
# super().__init__()
self.factors = factors
self.asset_returns = Portfolio(assets=securities_universe).df_returns
self.securities_universe = list(self.asset_returns.columns)
self.start_date = start_date
self.end_date = end_date
self.rebalancing_frequency = rebalancing_frequency
def security_market_line(self, portfolio: Portfolio, date: datetime = None, regression_window: int = 36,
benchmark: pd.Series = None):
"""
:param portfolio:
:param date:
:param regression_window:
:param benchmark:
:return:
"""
# '''
# The Security Market Line (SML) graphically represents the relationship between the asset's return (on y-axis) and systematic risk (or beta, on x-axis).
# With E(R_i) = R_f + B_i * (E(R_m) - R_f), the y-intercept of the SML is equal to the risk-free interest rate, while the slope is equal to the market risk premium
# Plotting the SML for a market index (i.e. DJIA), individual assets that are correctly priced are plotted on the SML (in the ideal 'Efficient Market Hypothesis' world).
# In real market scenarios, we are able to use the SML graph to determine if an asset being considered for a portfolio offers a reasonable expected return for the risk.
# - If an asset is priced at a point above the SML, it is undervalued, since for a given amount of risk, it yields a higher return.
# - Conversely, an asset priced below the SML is overvalued, since for a given amount of risk, it yields a lower return.
# '''
frequency = self.factors_timedf.df_frequency
portfolio_copy = portfolio.set_frequency(frequency, inplace=False) \
.slice_dataframe(to_date=date, from_date=regression_window, inplace=False)
betas = [
self.regress_factor_loadings(portfolio=portfolio.df_returns[ticker], benchmark_returns=benchmark, date=date,
regression_window=regression_window).params[1]
for ticker in portfolio_copy.df_returns]
mean_asset_returns = portfolio_copy.get_mean_returns()
date = portfolio_copy.df_returns.index[-1] if date is None else date
risk_free_rate = macro.risk_free_rates(lookback=regression_window, to_date=date, frequency=frequency).mean() \
* portfolio.freq_to_yearly[frequency[0]]
risk_premium = macro.market_premiums(lookback=regression_window, to_date=date, frequency=frequency).mean() \
* portfolio.freq_to_yearly[frequency[0]]
x = np.linspace(0, max(betas) + 0.1, 100)
y = float(risk_free_rate) + x * float(risk_premium)
fig, ax = plt.subplots(figsize=(10, 10))
plt.plot(x, y)
ax.set_xlabel('Betas', fontsize=14)
ax.set_ylabel('Expected Returns', fontsize=14)
ax.set_title('Security Market Line', fontsize=18)
for i, txt in enumerate(portfolio.df_returns):
ax.annotate(txt, (betas[i], mean_asset_returns[i]), xytext=(10, 10), textcoords='offset points')
plt.scatter(betas[i], mean_asset_returns[i], marker='x', color='red')
plt.show()
def broker_deployment(self, broker):
"""
Of course, need to schedule that function depending on the `is_time_to_reschedule`. Potentially use AWS Lambda
:param broker:
:return:
"""
if not issubclass(broker.__class__, Broker):
raise Exception('Ensure that the broker object inherits from the `Broker` class.')
assets_to_long, assets_to_short = self.generate_assets_to_trade(datetime.now())
# TODO long for now, improve optimization to include diff constraints
weights = self.portfolio_allocation(portfolio=Portfolio(assets_to_long)).solve_weights()
broker.place_order(symbol='AAPL', side='buy')
current_positions = broker.list_positions()
for position in current_positions:
print(position)
broker.place_order()
def markowitz_efficient_frontier(self, market_portfolio: Portfolio = None, plot_assets=True, plot_cal=False):
"""
One can plot every possible combination of risky assets on the *risk-return space*, a graph with the horizontal axis
representing the *variance* (a.k.a risk), and the vertical axis representing the *expected returns*.
The left boundary of this region is parabolic, and the upper part of the parabolic boundary is the **efficient frontier**
in the absence of a risk-free asset (sometimes called *the Markowitz bullet*). Combinations along this upper edge
represent portfolios (including no holdings of the risk-free asset) for which there is lowest risk for a given
level of expected return. Equivalently, a portfolio lying on the efficient frontier represents the combination
offering the best possible expected return for given risk level.
:param market_portfolio:
:param plot_assets: Plot risk/return profile of each asset in the portfolio
:param plot_cal: Plot the Capital Allocation Line
:return: Pandas DataFrame representing optimal weights and minimun volatilities for each level of required return.
"""
covariance_matrix = self.portfolio.get_covariance_matrix(to_freq='Y')
mean_returns = self.portfolio.get_mean_returns(to_freq='Y')
target_returns = np.linspace(mean_returns.min(), mean_returns.max(), 50)
minimal_volatilities, weights = [], []
for target_return in target_returns:
optimal = minimize(
# objective function for portfolio volatility. We're optimizing for the weights
fun=lambda w: np.sqrt(np.dot(w, np.dot(w, covariance_matrix))),
# initial guess for weights (all equal)
x0=np.ones((len(self.portfolio.stocks))) / (len(self.portfolio.stocks)),
method='SLSQP',
# weighted sum should equal target return, and weights should sum to one
constraints=({'type': 'eq', 'fun': lambda x: np.sum(mean_returns * x) - target_return},
{'type': 'eq', 'fun': lambda x: np.sum(x) - 1}),
# all weights should be between zero and one
bounds=Bounds(0, 1))
minimal_volatilities.append(optimal['fun'])
weights.append(optimal.x)
sharpe_arr = target_returns / minimal_volatilities
fig, ax = plt.subplots(figsize=(10, 10))
plt.scatter(minimal_volatilities, target_returns, c=sharpe_arr, cmap='viridis')
plt.colorbar(label='Sharpe Ratio')
plt.xlabel('Standard Deviation')
plt.ylabel('Expected Returns')
max_sharpe_idx = sharpe_arr.argmax()
plt.plot(minimal_volatilities[max_sharpe_idx], target_returns[max_sharpe_idx], 'r*', markersize=15.0)
ax.annotate(text='Max Sharpe', xy=(minimal_volatilities[max_sharpe_idx], target_returns[max_sharpe_idx]),
xytext=(10, 10), textcoords='offset points')
min_volatility_idx = np.asarray(minimal_volatilities).argmin()
plt.plot(minimal_volatilities[min_volatility_idx], target_returns[min_volatility_idx], 'y*', markersize=15.0)
ax.annotate(text='Min Vol', xy=(minimal_volatilities[min_volatility_idx], target_returns[min_volatility_idx]),
xytext=(10, 10), textcoords='offset points')
# Get yearly mean and std of market portfolio returns
mkt_mean, mkt_std = market_portfolio.get_mean_returns(to_freq='Y'), market_portfolio.get_volatility_returns(to_freq='Y')
if market_portfolio is not None and len(market_portfolio.df_returns.columns) == 1:
plt.plot(mkt_std, mkt_mean, 'bo', markersize=15.0)
ax.annotate(text=market_portfolio.df_returns.columns[0], xy=(mkt_std, mkt_mean),
xytext=(10, 10), textcoords='offset points')
if plot_assets:
volatilities = portfolio.get_volatility_returns()
for i, txt in enumerate(self.portfolio.stocks):
ax.annotate(txt, (volatilities[i], mean_returns[i]), xytext=(10, 10), textcoords='offset points')
plt.scatter(volatilities[i], mean_returns[i], marker='x', color='red')
if plot_cal:
# self.capital_allocation_line()
pass
plt.show()
return pd.DataFrame.from_dict({'Target Return': target_returns, 'Minimum Volatilty': minimal_volatilities,
'Sharpe Ratio': sharpe_arr, 'Optimal Weights': weights})
def solve_weights(self, risk_metric=None, objective=None, leverage=0, long_short_exposure=0):
pass
class NestedClusteredOptimization(PortfolioAllocationModel):
def __init__(self, portfolio: Portfolio):
super().__init__(portfolio)
def solve_weights(self, risk_metric=None, objective=None, leverage=0, long_short_exposure=0):
pass
if __name__ == '__main__':
assets = macro.companies_in_index(MarketIndices.DOW_JONES)
portfolio = Portfolio(assets=assets)
portfolio.set_frequency(frequency='M', inplace=True)
portfolio.slice_dataframe(from_date=datetime(2016, 1, 1), to_date=datetime(2020, 1, 1), inplace=True)
print(portfolio.df_returns.tail(10))
MPT = ModernPortfolioTheory(portfolio)
weights = MPT.solve_weights(use_sharpe=True)
print(weights)
market_portfolio = Portfolio(assets='^DJI')
market_portfolio.set_frequency(frequency='M', inplace=True)
market_portfolio.slice_dataframe(from_date=datetime(2016, 1, 1), to_date=datetime(2020, 1, 1), inplace=True)
stats = MPT.markowitz_efficient_frontier(market_portfolio=market_portfolio, plot_assets=True, plot_cal=True)
pd.set_option('display.max_columns', None)
print(stats.head())
performance, per unit of downside risk.
:param portfolio_returns: Pandas series or dataframe representing percentage changes of the security (or portfolio) returns over time. It should be same time range and frequency as risk free rates
:param target: minimum acceptable return, below which the returns are less desirable. minimum acceptable return, below which the returns are less desirable.
:return:
"""
return hpm(portfolio_returns, target, 1) / math.sqrt(lpm(portfolio_returns, target, 2))
def roys_safety_first_criterion(portfolio_returns: pd.Series, minimum_threshold=0.02, period=252):
"""
:param portfolio_returns: Pandas series or dataframe representing percentage changes of the security (or portfolio) returns over time. It should be same time range and frequency as risk free rates
:param minimum_threshold: minimum acceptable return, below which the returns are less desirable.
:param period: period to compute statistics of returns for. For instance, to compute yearly, then input 252, and to compute monthly, then input 21.
:return:
"""
return (portfolio_returns.mean() * period - minimum_threshold) / (portfolio_returns.std() * math.sqrt(period))
if __name__ == '__main__':
from portfolio_management.Portfolio import Portfolio
from datetime import datetime
assets = ['AAPL', 'V', 'KO', 'CAT']
portfolio = Portfolio(assets=assets)
portfolio.slice_dataframe(to_date=datetime(2021, 1, 1), from_date=datetime(2016, 1, 1))
# portfolio_returns = portfolio.get_weighted_sum_returns(weights=np.ones(len(assets)) / len(assets))
# print(portfolio_returns.head())
print(roys_safety_first_criterion(portfolio_returns=portfolio.df_returns, minimum_threshold=0.02, period=252))
def select_stocks(group):
returns_df = pd.DataFrame()
from_date = group.index.values[0][0]
from_date_idx = group.index.levels[0].to_list().index(from_date)
try:
# TODO think about inclusive at rebalancing day
to_date = group.index.levels[0][from_date_idx +
1] - timedelta(days=1)
except:
to_date = self.end_date
if 'SMB' in group.columns:
# Do the Fama French / AQR Way
small_size_stocks, large_size_stocks = split_stocks_quantile(
df=group, factor='SMB')
for factor in group.columns:
if factor != 'SMB':
bottom_quantile_stocks, top_quantile_stocks = split_stocks_quantile(
df=group, factor=factor)
small_top_stocks = set.intersection(
set(small_size_stocks), set(top_quantile_stocks))
big_top_stocks = set.intersection(
set(large_size_stocks), set(top_quantile_stocks))
small_bottom_stocks = set.intersection(
set(small_size_stocks),
set(bottom_quantile_stocks))
big_bottom_stocks = set.intersection(
set(large_size_stocks),
set(bottom_quantile_stocks))
cross_section_returns = {
name: {}
for name in [
'Small Top', 'Big Top', 'Small Bottom',
'Big Bottom'
]
}
for name, stocks in zip([
'Small Top', 'Big Top', 'Small Bottom',
'Big Bottom'
], [
small_top_stocks, big_top_stocks,
small_bottom_stocks, big_bottom_stocks
]):
if len(stocks) > 0:
portfolio = self.asset_returns[stocks]
# To allocate weight, need history of returns up to now
weights = allocation_method(
Portfolio(portfolio.loc[:from_date])
).solve_weights()
cross_section_returns[name]['Weight Allocation'] \
= [(stock, weight) for stock, weight in zip(portfolio.columns, weights)]
returns = np.sum(
weights * portfolio.loc[from_date:to_date],
axis=1)
cross_section_returns[name][
'Returns'] = returns
else:
dates = pd.date_range(
start=from_date + timedelta(days=1) -
timedelta(seconds=1),
end=to_date + timedelta(days=1) -
timedelta(seconds=1)).to_list()
cross_section_returns[name][
'Returns'] = pd.Series(
np.zeros((to_date - from_date).days +
1),
index=dates)
cross_section_returns[name][
'Weight Allocation'] = [('', 0)]
# HML = 1/2 (Small Value + Big Value) - 1/2 (Small Growth + Big Growth).
long_stocks = small_top_stocks | big_top_stocks
short_stocks = small_bottom_stocks | big_bottom_stocks
for factor_ in self.factors:
if factor_.__class__.__name__ == factor:
# TODO
df = pd.DataFrame(
columns=['Long Stocks', 'Short Stocks'],
data=0)
factor_.holdings.append()
returns = 0.5 * (cross_section_returns['Small Top']['Returns'].add(
cross_section_returns['Big Top']['Returns'], fill_value=0)) \
- 0.5 * (cross_section_returns['Small Bottom']['Returns'].add(
cross_section_returns['Big Bottom']['Returns'], fill_value=0))
returns.name = factor
returns_df = returns_df.join(
[returns], how='inner'
) if not returns_df.empty else returns.to_frame()
for factor, returns in returns_df.iteritems():
factor_obj = None
for f_ in self.factors:
if f_.__class__.__name__ == factor:
factor_obj = f_
factor_obj.returns = returns
# factor_obj.holdings =
return returns_df
cross_section_returns['Big Bottom']['Returns'], fill_value=0))
returns.name = factor
returns_df = returns_df.join(
[returns], how='inner'
) if not returns_df.empty else returns.to_frame()
for factor, returns in returns_df.iteritems():
factor_obj = None
for f_ in self.factors:
if f_.__class__.__name__ == factor:
factor_obj = f_
factor_obj.returns = returns
# factor_obj.holdings =
return returns_df
factor_returns = pipeline_df.groupby(level=0,
axis=0).apply(select_stocks)
factor_returns.index = factor_returns.index.droplevel(0)
return factor_returns
if __name__ == '__main__':
# sp_500_market = Portfolio(assets=['AAPL'])
# capm = CapitalAssetPricingModel(frequency='Monthly', to_date=datetime.today(), from_date=80)
# reg = capm.regress_factor_loadings(portfolio=Portfolio(assets=['MSFT']))
# print(reg.params)
ff3 = FamaFrench_ThreeFactorModel(frequency='Monthly',
to_date=datetime.today())
reg = ff3.regress_factor_loadings(portfolio=Portfolio(assets=['MSFT']))
print(reg.params)
def historical_simulation(self):
results = []
portfolio = Portfolio(assets=[], balance=self.starting_capital, trades=[], date=self.starting_date)
# First, populate stock returns universe
securities_universe_prices_df = pd.DataFrame()
for stock in os.listdir(path=config.STOCK_PRICES_DIR_PATH):
ticker = stock.strip('.pkl')
series = pd.read_pickle(os.path.join(config.STOCK_PRICES_DIR_PATH, stock))['Adj Close']
dummy_dates = pd.date_range(start=series.index[0], end=series.index[-1])
zeros_dummy = pd.Series(data=np.zeros(shape=len(dummy_dates)).fill(np.nan),
index=dummy_dates, name='Dummy', dtype='float64')
series = pd.concat([series, zeros_dummy], axis=1).iloc[:, 0]
securities_universe_prices_df[ticker] = series.ffill()
securities_universe_returns_df = securities_universe_prices_df.pct_change()
for date in pd.date_range(start=self.starting_date, end=self.ending_date):
portfolio.date = datetime(year=date.year, month=date.month, day=date.day)
for trade in portfolio.trades: # update portfolio float
date_loc = trade.stock.index.get_loc(date - timedelta(seconds=1))
daily_pct_return = (trade.stock.iloc[date_loc] - trade.stock.iloc[date_loc - 1]) \
/ trade.stock.iloc[date_loc - 1]
daily_doll_return = daily_pct_return * trade.stock.loc[date - timedelta(seconds=1)] * trade.shares
portfolio.float = portfolio.float + daily_doll_return if trade.direction \
else portfolio.float - daily_doll_return
if not (self.is_time_to_reschedule(current_date=date,
last_rebalancing_day=portfolio.last_rebalancing_day)
or date == self.starting_date):
continue
portfolio.last_rebalancing_day = date # rebalancing day, now can go on:
stocks_to_trade = self.generate_assets_to_trade(portfolio.date)
long_stocks, short_stocks = stocks_to_trade
for trade in portfolio.trades: # close portfolio trades that no longer meet condition
if trade.stock.name not in long_stocks + short_stocks:
portfolio.make_position(trade, entry=False)
# Get portfolio returns of selected stocks up to current date, and optimize portfolio allocation
portfolio.df_returns = securities_universe_returns_df[long_stocks]
sliced_portfolio = portfolio.slice_dataframe(to_date=date, inplace=False)
weights = self.allocation_regime(portfolio=sliced_portfolio)
portfolio.rebalance_portfolio(long_stocks=securities_universe_prices_df[long_stocks],
short_stocks=securities_universe_prices_df[short_stocks],
weights=weights, commission=self.commission,
fractional_shares=self.fractional_shares)
# Aggregate trades for better formatting in the dataframe
dictionary = dict()
for trade in portfolio.trades:
dictionary[trade.stock.name] = dictionary.get(trade.stock.name, 0) + trade.shares
aggregated_trades = [(key, val) for (key, val) in dictionary.items()]
results.append([date.strftime("%Y-%m-%d"), aggregated_trades,
round(portfolio.balance, 2), round(portfolio.float, 2)])
evolution_df = pd.DataFrame(results, columns=['Date', 'Holdings', 'Balance', 'Float'])
evolution_df.set_index('Date', inplace=True)
evolution_df['Cumulative (%) Return'] = evolution_df.filter(['Float']).pct_change().apply(
lambda x: x + 1).cumprod()
evolution_df['Float'].plot(grid=True, figsize=(10, 6))
plt.show()
with pd.option_context('display.max_rows', None, 'display.max_columns', None):
print(evolution_df.to_string())
return evolution_df