returns the downside deviation, defined as the square root of the downside variance.
returns the variance of observations below 0.0, $$ \frac{N}{N-1} \mathrm{E}\left[ x^2 ;|; x < 0\right]. $$
expected shortfall at a given percentile 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)
returns the semi deviation, defined as the square root of the semi variance.
returns the variance of observations below the mean, $$ \frac{N}{N-1} \mathrm{E}\left[ (x-\langle x \rangle)^2 ;|; x < \langle x \rangle \right]. $$
See Markowitz (1959).
averaged shortfallness, defined as $$ \mathrm{E}\left[ t-x ;|; x<t \right] $$