def _estimate_capm(
returns: pd.Series,
benchmark: pd.Series,
rf: float,
) -> RegressionResults:
returns, benchmark = align(adjust(returns, rf), adjust(benchmark, rf))
y = returns.to_numpy()
x = sm.add_constant(benchmark.to_numpy())
return sm.OLS(y, x).fit()
def _estimate_trailing_capm(
returns: pd.Series,
benchmark: pd.Series,
rf: float,
window: int,
) -> RollingRegressionResults:
returns, benchmark = align(adjust(returns, rf), adjust(benchmark, rf))
y = returns.to_numpy()
x = sm.add_constant(benchmark.to_numpy())
return RollingOLS(y, x, window=window).fit()
def omega_ratio(
returns: pd.Series,
*,
rf: float = 0.0,
) -> float:
adjusted_returns = adjust(returns, rf)
above = adjusted_returns[adjusted_returns > 0].sum()
under = adjusted_returns[adjusted_returns < 0].sum()
return -(above / under)
def sortino_ratio(
returns: pd.Series,
*,
rf: float = 0.0,
annualizer: Optional[float] = None,
) -> float:
adjusted_returns = adjust(returns, rf)
mr = mean_return(adjusted_returns, statistics=False, annualizer=1)
dr = downside_risk(adjusted_returns, rf=0, annualizer=1)
return (mr / dr) * np.sqrt(annualizer)
def sharpe_ratio(
returns: pd.Series,
*,
rf: float = 0.0,
annualizer: Optional[float] = None,
) -> float:
adjusted_returns = adjust(returns, rf)
mr = mean_return(adjusted_returns, statistics=False, annualizer=1)
std = volatility(adjusted_returns, annualizer=1)
return (mr / std) * np.sqrt(annualizer)
def trailing_sortino_ratio(
returns: pd.Series,
*,
rf: float = 0.0,
annualizer: Optional[float] = None,
window: Optional[int] = None,
) -> pd.Series:
adjusted_returns = adjust(returns, rf)
mr = trailing_mean_return(adjusted_returns, statistics=False, annualizer=1, window=window)
dr = trailing_downside_risk(adjusted_returns, rf=0, annualizer=1, window=window)
return (mr / dr) * np.sqrt(annualizer)
def downside_risk(
returns: pd.Series,
*,
mar: float = 0.0,
annualizer: Optional[float] = None,
) -> float:
adjusted_returns = adjust(returns, mar)
returns_under_mar = np.clip(
adjusted_returns,
a_min=-np.inf, a_max=0
)
return np.sqrt((returns_under_mar ** 2).mean()) * np.sqrt(annualizer)
def excess_returns(
returns: pd.Series,
benchmark: pd.Series,
) -> pd.Series:
return adjust(returns, benchmark)