def max_cagr_asset(self) -> dict:
"""
Find an asset with max CAGR.
"""
max_asset_cagr = Frame.get_cagr(self.ror).max()
ticker_with_largest_cagr = Frame.get_cagr(self.ror).nlargest(1, keep='first').index.values[0]
return {'max_asset_cagr': max_asset_cagr,
'ticker_with_largest_cagr': ticker_with_largest_cagr,
'list_position': self.symbols.index(ticker_with_largest_cagr)
}
def target_cagr_range_left(self) -> np.ndarray:
"""
Full range of cagr values (from min to max).
"""
max_cagr = self.global_max_return_portfolio['CAGR']
min_cagr = Frame.get_cagr(self.ror).min()
return np.linspace(min_cagr, max_cagr, self.n_points)
def max_cagr_asset_right_to_max_cagr(self) -> Optional[dict]:
"""
The asset with max CAGR lieing to the right of the global
max CAGR point (risk should be more than self.max_return['Risk']).
Global max return point should not be an asset.
"""
tolerance = 0.01 # assets CAGR should be less than max CAGR with certain tolerance
global_max_cagr_is_not_asset = (self.get_cagr() < self.global_max_return_portfolio['CAGR'] * (1 - tolerance)).all()
if global_max_cagr_is_not_asset:
condition = self.risk_annual.values > self.global_max_return_portfolio['Risk']
ror_selected = self.ror.loc[:, condition]
if not ror_selected.empty:
cagr_selected = Frame.get_cagr(ror_selected)
max_asset_cagr = cagr_selected.max()
ticker_with_largest_cagr = cagr_selected.nlargest(1, keep='first').index.values[0]
return {'max_asset_cagr': max_asset_cagr,
'ticker_with_largest_cagr': ticker_with_largest_cagr,
'list_position': self.symbols.index(ticker_with_largest_cagr)
}
def get_monte_carlo(self, n: int = 100) -> pd.DataFrame:
"""
Generate N random risk / cagr point for rebalanced portfolios.
Risk and cagr are calculated for a set of random weights.
"""
weights_df = Float.get_random_weights(n, self.ror.shape[1])
# Portfolio risk and cagr for each set of weights
portfolios_ror = weights_df.aggregate(Rebalance.rebalanced_portfolio_return_ts, ror=self.ror, period=self.reb_period)
random_portfolios = pd.DataFrame()
for _, data in portfolios_ror.iterrows():
risk_monthly = data.std()
mean_return = data.mean()
risk = Float.annualize_risk(risk_monthly, mean_return)
cagr = Frame.get_cagr(data)
row = {
'Risk': risk,
'CAGR': cagr
}
random_portfolios = random_portfolios.append(row, ignore_index=True)
return random_portfolios
def minimize_risk(
self,
target_return: float,
monthly_return: bool = False,
tolerance: float = 1e-08,
) -> Dict[str, float]:
"""
Finds minimal risk given the target return.
Returns a "point" with monthly values:
- weights
- mean return
- CAGR
- risk (std)
Target return is a monthly or annual value:
monthly_return = False / True
tolerance - sets the accuracy for the solver
"""
if not monthly_return:
target_return = Float.get_monthly_return_from_annual(target_return)
ror = self.ror
n = ror.shape[1] # number of assets
init_guess = np.repeat(1 / n, n) # initial weights
def objective_function(w):
return Frame.get_portfolio_risk(w, ror)
# construct the constraints
weights_sum_to_1 = {"type": "eq", "fun": lambda weights: np.sum(weights) - 1}
return_is_target = {
"type": "eq",
"fun": lambda weights: target_return
- Frame.get_portfolio_mean_return(weights, ror),
}
weights = minimize(
objective_function,
init_guess,
method="SLSQP",
constraints=(weights_sum_to_1, return_is_target),
bounds=self.bounds,
options={"disp": False, "ftol": tolerance},
)
if weights.success:
# Calculate point of EF given optimal weights
risk = weights.fun
# Annualize risk and return
a_r = Float.annualize_return(target_return)
a_risk = Float.annualize_risk(risk=risk, mean_return=target_return)
# # Risk adjusted return approximation
# r_gmean = Float.approx_return_risk_adjusted(mean_return=a_r, std=a_risk)
# CAGR calculation
portfolio_return_ts = Frame.get_portfolio_return_ts(weights.x, ror)
cagr = Frame.get_cagr(portfolio_return_ts)
if not self.labels_are_tickers:
asset_labels = list(self.names.values())
else:
asset_labels = self.symbols
point = {x: y for x, y in zip(asset_labels, weights.x)}
point["Mean return"] = a_r
point["CAGR"] = cagr
# point['CAGR (approx)'] = r_gmean
point["Risk"] = a_risk
else:
raise Exception("No solutions were found")
return point