fynance.algorithms.allocation.MDP

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

Get weights of Maximum Diversified 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 maximize the diversified ratio of the portfolio.

See also

diversified_ratio

Notes

Weights of Maximum Diversification Portfolio, as described by Y. Choueifaty and Y. Coignard [5], verify the following problem:

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

Where \(D(w)\) is the diversified ratio of portfolio weighted by w.

References

[5]	Choueifaty, Y., and Coignard, Y., 2008, Toward Maximum Diversification.