ledoit_wolf¶

Defined in fynance.portfolio.covariance

ledoit_wolf(X, target='const_corr')[source]

Ledoit-Wolf linear shrinkage covariance estimator.

Closed-form convex combination \((1 - \delta) S + \delta F\) of the sample covariance \(S\) and a low-variance target \(F\), with the shrinkage intensity \(\delta \in [0, 1]\) chosen to minimize the asymptotic expected Frobenius loss. Well conditioned even when \(N\) is comparable to or larger than \(T\) (where the plain sample covariance is singular or ill-conditioned).

Parameters:

Xarray_like

Returns panel, shape (T,) or (T, N).

target{‘const_corr’, ‘identity’, ‘diag’}, optional

Shrinkage target:

'const_corr' — constant-correlation matrix built from the mean off-diagonal correlation (Ledoit & Wolf, 2004b).
'identity' — mean-variance scaled identity (Ledoit & Wolf, 2004a).
'diag' — diag(S), i.e. shrink off-diagonal entries only.

Default 'const_corr'.

Returns:

np.ndarray: Symmetric (N, N) shrunk covariance matrix.

References

[1]

O. Ledoit, M. Wolf, “A well-conditioned estimator for large-dimensional covariance matrices”, Journal of Multivariate Analysis, 88(2), 2004, 365-411.

[2]

O. Ledoit, M. Wolf, “Honey, I shrunk the sample covariance matrix”, The Journal of Portfolio Management, 30(4), 2004, 110-119.

Examples

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> X = rng.standard_normal((50, 4))
>>> S = ledoit_wolf(X)
>>> S.shape
(4, 4)
>>> bool(np.allclose(S, S.T))
True