factor_cov

Defined in fynance.portfolio.covariance

factor_cov(X, n_factors=3)

Statistical factor-model covariance (low-rank + diagonal).

Eigendecomposes the (population) sample covariance and keeps the k = min(n_factors, N) largest eigenpairs as a common (systematic) component \(B B^\top\) with loadings \(B = V_k \text{diag}(\sqrt{l_k})\); the remainder of each asset’s variance is kept as an idiosyncratic diagonal term. The result is positive semi-definite by construction and matches the sample covariance’s diagonal (total variance) exactly.

Parameters:

Xarray_like

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

n_factorsint, optional

Number of factors to keep, clipped to N. Default 3.

Returns:

np.ndarray

Symmetric (N, N) covariance matrix, B @ B.T + diag(idio).

Examples

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> X = rng.standard_normal((100, 5))
>>> S = factor_cov(X, n_factors=2)
>>> S.shape
(5, 5)
>>> bool(np.all(np.linalg.eigvalsh(S) >= -1e-10))
True