returns the downside deviation, defined as the square root of the downside variance.
returns the downside variance, defined as $$ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N} \theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} $$, where $ \theta $ = 0 if x > 0 and $ \theta $ =1 if x <0
gaussian-assumption Expected Shortfall at a given percentile Assuming a gaussian distribution it returns the expected loss in case that the loss exceeded a VaR threshold,
$$ \mathrm{E}\left[ x ;|; x < \mathrm{VaR}(p) \right], $$
that is the average of observations below the given percentile $ p $. Also know as conditional value-at-risk.
See Artzner, Delbaen, Eber and Heath, "Coherent measures of risk", Mathematical Finance 9 (1999)
gaussian-assumption Average Shortfall (averaged shortfallness)