Annualized Return in Pandas

Question

I am seeking to confirm that my representation of the annualized return formula (using monthly returns) is optimal.

The annualized return formula I am using (where M is a monthly return and D is the total count of monthly returns) where the count of monthly returns is greater than 12 is as follows:

Alternatively, the this would change in the case of the monthly return count being less than 12:

Here is my representation of this formula in Pandas:

ann_return = observations.apply(lambda y: y.apply(lambda x: x+1))
ann_return = (ann_return.prod() ** (np.min(12/len(ann_return.index.values)) if len(ann_return.index.values) > 12 else 12/len(ann_return.index.values)))-1

Answer 1

This calculates the annualized return percentage. It works with both an individual number or a Pandas dataframe. In the latter case, the first argument percent and optionally the second argument months can be a dataframe.

This was tested with Python 3.7.0 and Pandas 0.23.4 with NumPy 1.15.2.

def annualize_return(percent: float, months: int) -> float:
    """Return the annualized return percentage given the holding return percentage and the number of months held.

    >>> annualize_return(1.5, 1)  # doctest: +ELLIPSIS
    19.56...
    >>> annualize_return(6.1, 3)  # doctest: +ELLIPSIS
    26.72...
    >>> annualize_return(30, 12)  # doctest: +ELLIPSIS
    30.00...
    >>> annualize_return(30, 15)  # doctest: +ELLIPSIS
    23.35...
    >>> annualize_return(float('nan'), 15)
    nan
    >>> annualize_return(0, 0)
    0

    References:
        https://en.wikipedia.org/wiki/Holding_period_return
        https://www.wikihow.com/Calculate-Annualized-Portfolio-Return
    """
    # Ref: https://stackoverflow.com/a/52618808/
    if months == 0:
        return percent
    rate = percent / 100
    years = months / 12
    rate = ((rate + 1)**(1 / years)) - 1
    percent = rate * 100
    return percent


if __name__ == '__main__':
    import doctest
    doctest.testmod(verbose=True, exclude_empty=True)

Answer 2

Formula

D = len(ann_return)
ann_return.add(1).prod() ** (12 / D) - 1