Downside risk: Difference between revisions
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'''Downside risk''' is the [[financial risk]] associated with losses. That is, the risk of difference between the actual return and the expected return (when the actual return is less), or the uncertainty of that return.<ref>{{cite book|title=Quantitative risk management: concepts, techniques and tools|first1=Alexander J.|last1=McNeil|first2=Rüdiger|last2=Frey|first3=Paul|last3=Embrechts|publisher=Princeton University Press|year=2005|isbn=9780691122557|pages=2–3}}</ref><ref>{{cite book|title= |
'''Downside risk''' is the [[financial risk]] associated with losses. That is, the risk of difference between the actual return and the expected return (when the actual return is less), or the uncertainty of that return.<ref>{{cite book|title=Quantitative risk management: concepts, techniques and tools|first1=Alexander J.|last1=McNeil|first2=Rüdiger|last2=Frey|first3=Paul|last3=Embrechts|publisher=Princeton University Press|year=2005|isbn=9780691122557|pages=2–3}}</ref><ref>{{cite book|title= |
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: <math>SD(X) = \left(\mathbb{E}[(X - \mathbb{E}[X])^2 1_{\{X \leq \mathbb{E}[X]\}}\right)^{\frac{1}{2}}</math> |
: <math>SD(X) = \left(\mathbb{E}[(X - \mathbb{E}[X])^2 1_{\{X \leq \mathbb{E}[X]\}}\right)^{\frac{1}{2}}</math> |
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: where <math>1_{\{X \leq \mathbb{E}[X]\}}</math> is an [[indicator function]], i.e. <math>1_{\{X \leq \mathbb{E}[X |
: where <math>1_{\{X \leq \mathbb{E}[X]\}}</math> is an [[indicator function]], i.e. <math>1_{\{X \leq \mathbb{E}[X\}} = \begin{cases}1 & \text{if } X \leq \mathbb{E}[X]\\ 0 & \text{else}\end{cases}</math> |
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== History == |
== History == |
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Revision as of 04:16, 16 February 2012
Downside risk is the financial risk associated with losses. That is, the risk of difference between the actual return and the expected return (when the actual return is less), or the uncertainty of that return.[1]<ref>{{cite book|title=
- where is an indicator function, i.e.
![{\displaystyle SD(X)=\left(\mathbb {E} [(X-\mathbb {E} [X])^{2}1_{\{X\leq \mathbb {E} [X]\}}\right)^{\frac {1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34d2f0378035113892c38c2ad7cb4b02cacff6dd)
![{\displaystyle 1_{\{X\leq \mathbb {E} [X]\}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1782abaed59b0f989a1fe2be67c8c895be18697)
![{\displaystyle 1_{\{X\leq \mathbb {E} [X\}}={\begin{cases}1&{\text{if }}X\leq \mathbb {E} [X]\\0&{\text{else}}\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5ee8257472bf4f79ee0261ffbb8e832e8ec1806c)
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
References
- ^ McNeil, Alexander J.; Frey, Rüdiger; Embrechts, Paul (2005). Quantitative risk management: concepts, techniques and tools. Princeton University Press. pp. 2–3. ISBN 9780691122557.
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