#### Previous topic

fynance.algorithms.allocation.MVP

#### Next topic

fynance.algorithms.allocation.rolling_allocation

# 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. 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.