var¶

Defined in fynance.metrics

var(X, alpha=0.05, method='historical')[source]

Value-at-Risk of a price/equity curve’s per-period returns.

The loss quantile at confidence level 1 - alpha: with probability alpha, a period’s return falls below -VaR. Reported as a positive number (the magnitude of the loss quantile), following the usual risk-desk convention.

Parameters:

Xarray_like: Time-series of price, performance or index (a single curve).
alphafloat, optional: Tail probability, in (0, 1). Default is 0.05 (95% VaR).
method{‘historical’, ‘gaussian’, ‘cornish_fisher’}, optional: Estimation method. Default is ‘historical’.

Returns:

float: Value-at-Risk, positive for a typical loss-bearing distribution.

See also

cvar, cdar, roll_var, tail_dependence

Notes

Let \(R\) be the per-period returns of X (see _returns_from_prices) and \(n\) their count.

method='historical': the empirical quantile, taken as the k-th smallest observed return (_tail_k, k = max(1, floor(alpha n))) — an actually realized scenario, no interpolation between two observations.
method='gaussian': \(VaR = -(\mu + \sigma z_\alpha)\) with \(z_\alpha = \Phi^{-1}(\alpha)\) the standard normal quantile, \(\mu, \sigma\) the sample mean/std of \(R\).
method='cornish_fisher': as 'gaussian' but with \(z_\alpha\) replaced by the Cornish-Fisher expansion [1] that corrects for sample skewness \(s\) and excess kurtosis \(k\):

\[z_{CF} = z + \frac{z^2 - 1}{6}s + \frac{z^3 - 3z}{24}k - \frac{2z^3 - 5z}{36}s^2\]

Reduces to the Gaussian quantile when \(s = k = 0\).

References

[1]

Favre, L., and Galeano, J.-A., 2002, Mean-Modified Value-at-Risk Optimization with Hedge Funds, Journal of Alternative Investments.

Examples

>>> import numpy as np
>>> X = np.array([100., 99., 103., 95., 101., 98., 104., 90., 108., 97.,
...                102.])
>>> round(var(X, alpha=0.2, method='historical'), 4)
0.1019
>>> round(var(X, alpha=0.2, method='gaussian'), 4)
0.0723