financial.value_at_risk

Value at Risk (VaR) via historical simulation.

References: - https://en.wikipedia.org/wiki/Value_at_risk - https://www.investopedia.com/terms/v/var.asp

Value at Risk measures the maximum loss a portfolio can suffer over a given period at a chosen confidence level. Historical simulation is a non-parametric method: it reuses the observed returns and reads the quantile from the empirical distribution, so no assumption is made about the shape of the loss distribution. The result is the negative of the corresponding return quantile, i.e. a positive loss magnitude when the tail of the distribution contains losses.

Functions

_linear_interpolated_quantile(→ float)

Linear interpolation between the closest ranks (NumPy default, type 7).

value_at_risk(→ float)

Calculate the historical-simulation Value at Risk of a portfolio.

Module Contents

financial.value_at_risk._linear_interpolated_quantile(sorted_values: collections.abc.Sequence[float], quantile: float) → float

Linear interpolation between the closest ranks (NumPy default, type 7).

>>> _linear_interpolated_quantile([-10.0, -5.0, -2.0, 1.0, 4.0], 0.05)
-9.0
>>> _linear_interpolated_quantile([1.0, 2.0, 3.0], 1.0)
3.0
financial.value_at_risk.value_at_risk(returns: collections.abc.Sequence[float], confidence_level: float = 0.95) → float

Calculate the historical-simulation Value at Risk of a portfolio.

The confidence level is the probability that the loss will not exceed the returned value. The default of 0.95 means that 95% of the observed returns are better (higher) than the VaR threshold, and the remaining 5% are worse.

Examples: >>> value_at_risk([-10, -5, -2, 1, 4], 0.95) 9.0 >>> value_at_risk([-2, -1, 0, 1, 2, 3], 0.90) 1.5 >>> value_at_risk([5, 10, 15], 0.75) -7.5 >>> value_at_risk([], 0.95) Traceback (most recent call last): … ValueError: returns must not be empty >>> value_at_risk([-1, 0, 1], 1.0) Traceback (most recent call last): … ValueError: confidence_level must be strictly between 0 and 1 >>> value_at_risk([-1, float(“nan”), 1], 0.95) Traceback (most recent call last): … ValueError: returns must contain only finite numbers

Time complexity: O(n log n), where n = len(returns), for sorting. Space complexity: O(n) for the sorted copy.