Downside risk

While the term Downside risk is frequently applied, often quite loosely, to a number of different measures of financial risk associated with losses, the statistic below-target semi deviation or simply target semi deviation (TSV) has become the industry standard.

Examples

• Value at Risk
• Average value at risk
• Semi-deviation defined by

$SD(X)=\left(\mathbb {E} [(X-\mathbb {E} [X])^{2}1_{\{X\leq \mathbb {E} [X]\}}\right)^{\frac {1}{2}}$

where $1_{\{X\leq \mathbb {E} [X]\}}$ is an indicator function, i.e. $1_{\{X\leq \mathbb {E} [X]\}}={\begin{cases}1&{\text{if }}X\leq \mathbb {E} [X]\\0&{\text{else}}\end{cases}}$

History

Since the early 1980's when Dr. Frank Sortino developed formal definition of downside risk as a better measure of investment risk than standard deviation this term has become the industry standard for risk management.

See also

• Sortino ratio