fynance.algorithms.allocation.ERC

fynance.algorithms.allocation.ERC(X, w0=None, up_bound=1.0, low_bound=0.0)

Get weights of Equal Risk Contribution portfolio allocation.

Parameters:

X : array_like

Each column is a series of price or return’s asset.

w0 : array_like, optional

Initial weights to maximize.

up_bound, low_bound : float, optional

Respectively maximum and minimum values of weights, such that low_bound \(\leq w_i \leq\) up_bound \(\forall i\). Default is 0 and 1.

Returns:

array_like

Weights that minimize the Equal Risk Contribution portfolio.

Notes

Weights of Equal Risk Contribution, as described by S. Maillard, T. Roncalli and J. Teiletche [1], verify the following problem:

\[\begin{split}w = \text{arg min } f(w) \\ u.c. \begin{cases}w'e = 1 \\ 0 \leq w_i \leq 1 \\ \end{cases}\end{split}\]

With:

\[f(w) = N \sum_{i=1}^{N}w_i^2 (\Omega w)_i^2 - \sum_{i,j=1}^{N} w_i w_j (\Omega w)_i (\Omega w)_j\]

Where \(\Omega\) is the variance-covariance matrix of X and \(N\) the number of assets.

References

[1]	http://thierry-roncalli.com/download/erc-slides.pdf