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78 lines
2.7 KiB
Python
78 lines
2.7 KiB
Python
"""
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The ``objective_functions`` module provides optimisation objectives, including the actual
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objective functions called by the ``EfficientFrontier`` object's optimisation methods.
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These methods are primarily designed for internal use during optimisation (via
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scipy.optimize), and each requires a certain signature (which is why they have not been
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factored into a class). For obvious reasons, any objective function must accept ``weights``
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as an argument, and must also have at least one of ``expected_returns`` or ``cov_matrix``.
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Because scipy.optimize only minimises, any objectives that we want to maximise must be
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made negative.
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Currently implemented:
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- negative mean return
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- (regularised) negative Sharpe ratio
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- (regularised) volatility
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"""
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import numpy as np
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def negative_mean_return(weights, expected_returns):
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"""
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Calculate the negative mean return of a portfolio
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:param weights: asset weights of the portfolio
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:type weights: np.ndarray
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:param expected_returns: expected return of each asset
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:type expected_returns: pd.Series
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:return: negative mean return
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:rtype: float
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"""
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return -weights.dot(expected_returns)
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def negative_sharpe(
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weights, expected_returns, cov_matrix, gamma=0, risk_free_rate=0.02
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):
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"""
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Calculate the negative Sharpe ratio of a portfolio
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:param weights: asset weights of the portfolio
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:type weights: np.ndarray
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:param expected_returns: expected return of each asset
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:type expected_returns: pd.Series
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:param cov_matrix: the covariance matrix of asset returns
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:type cov_matrix: pd.DataFrame
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:param gamma: L2 regularisation parameter, defaults to 0. Increase if you want more
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non-negligible weights
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:type gamma: float, optional
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:param risk_free_rate: risk-free rate of borrowing/lending, defaults to 0.02
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:type risk_free_rate: float, optional
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:return: negative Sharpe ratio
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:rtype: float
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"""
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mu = weights.dot(expected_returns)
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sigma = np.sqrt(np.dot(weights, np.dot(cov_matrix, weights.T)))
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L2_reg = gamma * (weights ** 2).sum()
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return -(mu - risk_free_rate) / sigma + L2_reg
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def volatility(weights, cov_matrix, gamma=0):
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"""
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Calculate the volatility of a portfolio
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:param weights: asset weights of the portfolio
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:type weights: np.ndarray
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:param cov_matrix: the covariance matrix of asset returns
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:type cov_matrix: pd.DataFrame
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:param gamma: L2 regularisation parameter, defaults to 0. Increase if you want more
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non-negligible weights
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:type gamma: float, optional
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:return: portfolio volatility
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:rtype: float
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"""
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L2_reg = gamma * (weights ** 2).sum()
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return np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights))) + L2_reg
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