fynance.algorithms.allocation.MVP_uc

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

Get weights of the Minimum Variance Portfolio under constraints.

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 variance of the portfolio.

Notes

Weights of Minimum Variance Portfolio verify the following problem:

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

Where \(\Omega\) is the variance-covariance matrix of X and \(e\) a vector of ones.