quantlab.portfolio.base.CovarianceEstimate

class quantlab.portfolio.base.CovarianceEstimate(symbols, covariance)

Bases: object

A covariance estimator’s covariance of returns at one bar, over the symbols it covers.

The dense quantlab.risk.base.ReturnCovariance: it has no factor form and no risk factors (LowRankCovarianceEstimate is the low-rank one).

Attributes:

symbolsnp.ndarray

The symbols the estimate covers, the order of covariance’s rows and columns; a symbol with too little history is left out.

covariancenp.ndarray

The dense [n, n] covariance matrix.

Examples

>>> estimate = CovarianceEstimate(
...     symbols=np.array(["AAA", "BBB"]),
...     covariance=np.array([[0.04, 0.01], [0.01, 0.09]]),
... )
>>> estimate.variance
array([0.04, 0.09])
>>> estimate.factor_form() is None
True

factor_exposure(name, symbols)

Refuse: a dense estimate has no risk factors.

A factor risk model’s FactorRiskForecast answers with its column of B (ReturnCovariance.factor_exposure).

Raises:

ValueError

Always.

Examples

>>> estimate.factor_exposure("market", np.array(["AAA"]))
Traceback (most recent call last):
...
ValueError: the covariance estimate has no risk factors, so no exposure to 'market'

factor_form()

Return the factor form of the covariance, or None when it has none.

A dense estimate has none. A factor risk model’s FactorRiskForecast returns (exposures, factor_covariance, specific_variance), from which an optimiser builds a low-rank risk term instead of the dense one.

Examples

>>> estimate.factor_form() is None
True

scaled(factor)

Return the estimate with every entry multiplied by factor.

Variance is linear in time, so a one-bar covariance times n is the covariance of n-bar returns.

Examples

>>> estimate.scaled(5).variance
array([0.2 , 0.45])

subset(rows)

Return the estimate over the symbols at positions rows, in that order.

Examples

>>> estimate.subset(np.array([1])).symbols.tolist()
['BBB']

property variance

Each covered symbol’s variance, the covariance’s diagonal.

Examples

>>> estimate.variance
array([0.04, 0.09])