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fynance.algorithms.allocation.MVP

fynance.algorithms.allocation.MVP(X, normalize=False)

Get weights of the Minimum Variance Portfolio allocation.

Parameters:
X : array_like

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

normalize : boolean, optional

If True normalize the weigths such that \(0 \leq w_i \leq 1\) and \(\sum_{i=1}^{N} w_i = 1\), \(\forall i\). Default is False.

Returns:
array_like

Vector of weights to apply to the assets.

See also

HRP

Notes

The vector of weights noted \(w\) that minimize the portfolio variance [4] is define as below:

\[\begin{split}w = \frac{\Omega^{-1} e}{e' \Omega^{-1} e} \\\end{split}\]
\[\text{With } \sum_{i=1}^{N} w_i = 1\]

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

References

[4]https://breakingdownfinance.com/finance-topics/modern-portfolio-theory/minimum-variance-portfolio/