coherent risk measure
- Thread starter ajsa
- Start date
Hi ajsa,
According to Dowd, "X and Y represent any two portfolios’ P/L (or future values, or more loosely, the two portfolios themselves), and let rho(.) be measure of risk over a chosen horizon."
such that monotocity means "that a random cash flow or future value Y that is always greater than X should have a lower risk: this makes sense, because it means that less has to be added to Y than to X to make it acceptable, and the amount to be added is the risk measure."
But it is often confused with the notion of greater risk implies greater returns, so many questions even get this wrong:
http://forum.bionicturtle.com/viewthread/1946/
(even Wilmott's book has it confused with high risk/high return)
David
According to Dowd, "X and Y represent any two portfolios’ P/L (or future values, or more loosely, the two portfolios themselves), and let rho(.) be measure of risk over a chosen horizon."
such that monotocity means "that a random cash flow or future value Y that is always greater than X should have a lower risk: this makes sense, because it means that less has to be added to Y than to X to make it acceptable, and the amount to be added is the risk measure."
But it is often confused with the notion of greater risk implies greater returns, so many questions even get this wrong:
http://forum.bionicturtle.com/viewthread/1946/
(even Wilmott's book has it confused with high risk/high return)
David
Hi asja,
Because VaR is a quantile (e.g., median) and not an average (that's why ES can be sub-additive: it's a conditional *average*), aggregation can produce quirky results. VaR is subadditive for so-called elliptical distributions (superclass of normal; so VaR is subadditive for normal), it's just sometimes not other non-eliptical distr.
The best way to see (IMO) is with an example ... I assume you saw my example taken straight from Dowd:
http://www.bionicturtle.com/premium/spreadsheet/5.d.1._expected_shortfall/
...the case of two/three bonds which demonstrates VaR isn't SA...
David
Because VaR is a quantile (e.g., median) and not an average (that's why ES can be sub-additive: it's a conditional *average*), aggregation can produce quirky results. VaR is subadditive for so-called elliptical distributions (superclass of normal; so VaR is subadditive for normal), it's just sometimes not other non-eliptical distr.
The best way to see (IMO) is with an example ... I assume you saw my example taken straight from Dowd:
http://www.bionicturtle.com/premium/spreadsheet/5.d.1._expected_shortfall/
...the case of two/three bonds which demonstrates VaR isn't SA...
David
Ajsa
I only know that VaR is coherent if the distribution is elliptical (incl. normal). The authors i've read seem to imply VaR meets the other 3, but (i) i've not tested it and (ii) as it doesn't necessarily follow from that statement i do know, I really don't know...David
I only know that VaR is coherent if the distribution is elliptical (incl. normal). The authors i've read seem to imply VaR meets the other 3, but (i) i've not tested it and (ii) as it doesn't necessarily follow from that statement i do know, I really don't know...David
