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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def information_ratio(rets, bm_rets, scale=None, expanding=False):
 """Information ratio, a common measure of manager efficiency, evaluates excess returns over a benchmark versus tracking error. :param rets: period returns :param bm_rets: periodic benchmark returns (not annualized) :param scale: None or the scale to be used for annualization :param expanding: :return: """

    scale = _resolve_periods_in_year(scale, rets)
    rets_ann = returns_annualized(rets, scale=scale, expanding=expanding)
    bm_rets_ann = returns_annualized(rets, scale=scale, expanding=expanding)
    tracking_error_ann = std_annualized((rets - bm_rets), scale=scale, expanding=expanding)
    return (rets_ann - bm_rets_ann) / tracking_error_ann