# skfolio.measures.value_at_risk ### skfolio.measures.value_at_risk(returns, beta=0.95, sample_weight=None) Compute the historical value at risk (VaR). The VaR is the smallest loss exceeded with probability at most $1 - \beta$. It is the lower $\beta$-quantile of the empirical loss distribution $F_L$: $$ \mathrm{VaR}_{\beta} = \inf\{\ell \in \mathbb{R} : F_L(\ell) \geq \beta\} $$ With `sample_weight`, $F_L$ is the weighted empirical distribution function. * **Parameters:** **returns** *ndarray of shape (n_observations,) or (n_observations, n_assets)* : Array of return values. **beta** *float, default=0.95* : The VaR confidence level. Must be between 0 and 1. The endpoints select the best and worst usable returns, respectively; zero-weight observations are excluded. **sample_weight** *ndarray of shape (n_observations,), optional* : Sample weights for each observation. If None, equal weights are assumed. * **Returns:** **value** *float or ndarray of shape (n_assets,)* : Value at Risk. If `returns` is a 1D-array, the result is a float. If `returns` is a 2D-array, the result is a ndarray of shape (n_assets,). ### Notes With $n$ equally weighted observations and an integer $k = (1 - \beta) n$, the VaR is the $(k+1)$-th largest loss and the CVaR is the mean of the $k$ largest losses. For example, with 100 observations and `beta=0.95`, the VaR is the sixth largest loss. NaN handling: NaN returns are excluded from each column’s calculation. Remaining sample weights are rescaled to sum to one. The result is NaN if no observations or no positive weight remain. ### References * **[1]** “Conditional value-at-risk for general loss distributions”, Journal of Banking & Finance, Rockafellar & Uryasev (2002) * **[2]** “Quantitative Risk Management: Concepts, Techniques and Tools”, Princeton University Press, McNeil, Frey & Embrechts (2015)