# Using Built-In Measures¶

The real time-saver is the built-in measures in frds.measures.

For example, Kritzman, Li, Page, and Rigobon (2010) propose an Absorption Ratio that measures the fraction of the total variance of a set of asset returns explained or absorbed by a fixed number of eigenvectors. It captures the extent to which markets are unified or tightly coupled.

Example: Absorption Ratio
>>> import numpy as np
>>> from frds.measures import absorption_ratio # (1)
>>> data = np.array( # (2)
...             [
...                 [0.015, 0.031, 0.007, 0.034, 0.014, 0.011],
...                 [0.012, 0.063, 0.027, 0.023, 0.073, 0.055],
...                 [0.072, 0.043, 0.097, 0.078, 0.036, 0.083],
...             ]
...         )
>>> absorption_ratio(data, fraction_eigenvectors=0.2)
0.7746543307660252

1. absorption_ratio function can also be imported using:

from frds.measures.bank import absorption_ratio


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2. Hypothetical 6 daily returns of 3 assets.

Another example, Distress Insurance Premium (DIP) proposed by Huang, Zhou, and Zhu (2009) as a systemic risk measure of a hypothetical insurance premium against a systemic financial distress, defined as total losses that exceed a given threshold, say 15%, of total bank liabilities.

>>> from frds.measures import distress_insurance_premium
>>> # hypothetical implied default probabilities of 6 banks
>>> default_probabilities = np.array([0.02, 0.10, 0.03, 0.20, 0.50, 0.15]
>>> correlations = np.array(
...     [
...         [ 1.000, -0.126, -0.637, 0.174,  0.469,  0.283],
...         [-0.126,  1.000,  0.294, 0.674,  0.150,  0.053],
...         [-0.637,  0.294,  1.000, 0.073, -0.658, -0.085],
...         [ 0.174,  0.674,  0.073, 1.000,  0.248,  0.508],
...         [ 0.469,  0.150, -0.658, 0.248,  1.000, -0.370],
...         [ 0.283,  0.053, -0.085, 0.508, -0.370,  1.000],
...     ]
... )