Information ratio in

[lsyi...@gmail.com]

Hi there

I just found the definition/formula of information ratio in zipline seems not consistent.

As in investopia and wikipeida, it should be defined as the ratio between (portfolio returns - benchmark returns) and standard deviation of (portfolio returns - benchmark returns)

Rp = Return of the portfolio
Ri = Return of the index or benchmark
Sp-i = Tracking error (standard deviation of the difference between returns of the portfolio and the returns of the index)

In zipline/finance/risk/risk.py, the information_ratio function is formulated accordingly. 

def information_ratio(algorithm_returns, benchmark_returns):

    """

    http://en.wikipedia.org/wiki/Information_ratio

    Args:

        algorithm_returns (np.array-like):

            All returns during algorithm lifetime.

        benchmark_returns (np.array-like):

            All benchmark returns during algo lifetime.

    Returns:

        float. Information ratio.

    """

    relative_returns = algorithm_returns - benchmark_returns

    relative_deviation = relative_returns.std(ddof=1)

    if zp_math.tolerant_equals(relative_deviation, 0) or \

       np.isnan(relative_deviation):

        return 0.0

    return np.mean(relative_returns) / relative_deviation

But this function is not imported elsewhere

However, in both risk/cumulative.py, and risk/period.py, a information_ratio function is defined and it uses the algorithm volatility instead as the denominator. 

def information_ratio(algo_volatility, algorithm_return, benchmark_return):

    """

    http://en.wikipedia.org/wiki/Information_ratio

    Args:

        algorithm_returns (np.array-like):

            All returns during algorithm lifetime.

        benchmark_returns (np.array-like):

            All benchmark returns during algo lifetime.

    Returns:

        float. Information ratio.

    """

    if zp_math.tolerant_equals(algo_volatility, 0):

        return np.nan

    # The square of the annualization factor is in the volatility,

    # because the volatility is also annualized,

    # i.e. the sqrt(annual factor) is in the volatility's numerator.

    # So to have the the correct annualization factor for the

    # Sharpe value's numerator, which should be the sqrt(annual factor).

    # The square of the sqrt of the annual factor, i.e. the annual factor

    # itself, is needed in the numerator to factor out the division by

    # its square root.

    return (algorithm_return - benchmark_return) / algo_volatility

Any reasoning behind this ?

[Joe Jevnik]

Hey, I don't have an answer yet but I just wanted to let you know that we are looking into this.