def information_ratio(returns, factor_returns):
"""
Determines the Information ratio of a strategy.
Parameters
----------
returns : pd.Series or np.ndarray
Daily returns of the strategy, noncumulative.
- See full explanation in :func:`~empyrical.stats.cum_returns`.
factor_returns: float / series
Benchmark return to compare returns against.
Returns
-------
float
The information ratio.
Note
-----
See https://en.wikipedia.org/wiki/information_ratio for more details.
"""
if len(returns) < 2:
return np.nan
active_return = _adjust_returns(returns, factor_returns)
tracking_error = nanstd(active_return, ddof=1)
if np.isnan(tracking_error):
return 0.0
if tracking_error == 0:
return np.nan
return nanmean(active_return) / tracking_error
def tracking_error(returns, factor_returns):
"""
Calculate standard deviation of portfolio return - index return and annualize it
"""
active_return = returns - factor_returns
tracking_err = np.nan_to_num(nanstd(active_return, ddof=1, axis=0))
return tracking_err
def annual_volatility(returns, period=DAILY, alpha=2.0,
annualization=None):
"""
Determines the annual volatility of a strategy.
Parameters
----------
returns : pd.Series or np.ndarray
Periodic returns of the strategy, noncumulative.
- See full explanation in :func:`~empyrical.stats.cum_returns`.
period : str, optional
Defines the periodicity of the 'returns' data for purposes of
annualizing. Value ignored if `annualization` parameter is specified.
Defaults are:
'monthly':12
'weekly': 52
'daily': 252
alpha : float, optional
Scaling relation (Levy stability exponent).
annualization : int, optional
Used to suppress default values available in `period` to convert
returns into annual returns. Value should be the annual frequency of
`returns`.
Returns
-------
float
Annual volatility.
"""
if len(returns) < 2:
return np.nan
ann_factor = annualization_factor(period, annualization)
volatility = nanstd(returns, ddof=1) * (ann_factor ** (1.0 / alpha))
return volatility