MVP_uc¶

Defined in fynance.algorithms.allocation

MVP_uc(X, w0=None, up_bound=1., low_bound=0.)[source]

Get weights of the Minimum Variance Portfolio under constraints.

Numerical (SLSQP) Markowitz allocation that minimizes portfolio variance subject to box constraints on each weight, in addition to the sum-to-one constraint. Use this variant whenever short selling must be excluded or per-asset caps need to be enforced; use MVP for the unconstrained closed-form solution.

Parameters:

Xarray_like: Each column is a series of price or return’s asset.
w0array_like, optional: Initial weights to maximize.
up_bound, low_boundfloat, 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.