def gmv_monthly(self) -> Tuple[float, float]:
"""
Returns the monthly risk and return of the Global Minimum Volatility portfolio
"""
return (
Frame.get_portfolio_risk(self.gmv_weights, self.ror),
Frame.get_portfolio_mean_return(self.gmv_weights, self.ror),
)
def get_monte_carlo(self, n: int = 100, kind: str = "mean") -> pd.DataFrame:
"""
Generate N random risk / cagr point for portfolios.
Risk and cagr are calculated for a set of random weights.
"""
weights_series = Float.get_random_weights(n, self.ror.shape[1])
# Portfolio risk and return for each set of weights
random_portfolios = pd.DataFrame(dtype=float)
for weights in weights_series:
risk_monthly = Frame.get_portfolio_risk(weights, self.ror)
mean_return_monthly = Frame.get_portfolio_mean_return(weights, self.ror)
risk = Float.annualize_risk(risk_monthly, mean_return_monthly)
mean_return = Float.annualize_return(mean_return_monthly)
if kind.lower() == "cagr":
cagr = Float.approx_return_risk_adjusted(mean_return, risk)
row = dict(Risk=risk, CAGR=cagr)
elif kind.lower() == "mean":
row = dict(Risk=risk, Return=mean_return)
else:
raise ValueError('kind should be "mean" or "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
def objective_function(w, ror):
month_return_value = Frame.get_portfolio_mean_return(w, ror)
return month_return_value