Annualized Returns

perfana.core.returns.annualized_returns(r, freq=None, geometric=True)

Calculates the annualized returns from the data

The formula for annualized geometric returns is formulated by raising the compound return to the number of periods in a year, and taking the root to the number of total observations:

\[\prod_i^N(1 + r_i)^{\frac{s}{N}} - 1\]

where \(s\) is the number of observations in a year, and \(N\) is the total number of observations.

For simple returns (geometric=FALSE), the formula is:

\[\frac{s}{N} \sum^N_i r_i\]

Parameters

• r (Union[DataFrame, Iterable[Union[int, float]], ndarray, Series]) – Numeric returns series or data frame

• freq (Optional[str]) – Frequency of the data. Use one of daily, weekly, monthly, quarterly, semi-annually, yearly

• geometric – If True, calculates the geometric returns. Otherwise, calculates the arithmetic returns

Returns

Annualized returns

Return type

float or Series

Examples

>>> from perfana.datasets import load_etf
>>> from perfana.core import annualized_returns
# Get returns starting from the date where all etf has data
>>> etf = load_etf().dropna().pa.to_returns().dropna()
VBK    0.091609
BND    0.036224
VTI    0.081203
VWO    0.027670
dtype: float64
>>> annualized_returns(etf.VWO)
0.02767037698144148