yabte.utilities.portopt

Minimum Variance

Calculate portfolio weights by minimizing variance.

That is to minimize the following expression subject to various constraints.

\[\frac{1}{2} w' \Sigma w\]

Typical constraints are achieving a target return, i.e. \(w' \mu = r\), and that all weights sum to one, i.e. \(\Sigma_i w_i = 1\).

yabte.utilities.portopt.minimum_variance.minimum_variance(Sigma: ndarray, mu: ndarray, r: float) → ndarray

Calculate weights using Lagrangian multipliers and algebraic closed form solution.

yabte.utilities.portopt.minimum_variance.minimum_variance_numeric(Sigma: ndarray, mu: ndarray, r: float) → ndarray

Calculate weights using Lagrangian multipliers and numeric solution (using scipy’s root function).

yabte.utilities.portopt.minimum_variance.minimum_variance_numeric_slsqp(Sigma: ndarray, mu: ndarray, r: float) → ndarray

Calculate weights using Lagrangian multipliers and numeric solution (using scipy’s minimize function).

Inverse Variance

Calculate portfolio weights by inverting variance.

That is,

\[w = \frac{\sigma^{-1}}{1'\sigma^{-1}}\]

where \(\sigma^2 = diag(\Sigma)\).

yabte.utilities.portopt.inverse_volatility.inverse_volatility(cov: ndarray) → ndarray

Calculate weights using inverse variance.

Hierarchical Risk Parity

Calculate portfolio weights with hierarchical risk parity.

That is to employ hierarchical tree clustering on the correlation distance matrix and quasi-diagonalisation followed by recursive bisection to determine the weights. See [LP] for further details.

References

[LP]

López de Prado, M. (2016). Building Diversified Portfolios that Outperform Out of Sample. The Journal of Portfolio Management, 42(4), 59–69. https://doi.org/10.3905/jpm.2016.42.4.059

yabte.utilities.portopt.hierarchical_risk_parity.hrp(corr: DataFrame, sigma: ndarray) → ndarray

Calculate weights using hierarchical risk parity and scipy’s linkage/to_tree functions.