Talk:Coherent risk measure

Latest comment: 12 years ago by Zfeinst in topic External link: The Case for Incoherence

Monotonicity

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Monotonicity
 

That is, if portfolio   has better values than portfolio   under all scenarios then the risk of   should be bigger than the risk of  : more profit, more risk.[1]


That is wrong. If all scenarios are worse the risk measure should be higher, not lower, as stated. See for that: http://www.math.ethz.ch/~delbaen/ftp/preprints/CoherentMF.pdf page 7 —Preceding unsigned comment added by 91.34.52.136 (talk) 13:58, 29 March 2010 (UTC)Reply

91.34.52.136 (talk) 13:58, 29 March 2010 (UTC)Reply

Agreed! Smc2911 (talk) 07:09, 28 April 2010 (UTC)Reply

Here is another reference: Convex measures of risk and trading constraints

Smc2911 (talk) 07:14, 28 April 2010 (UTC)Reply

References

  1. ^ Wilmott P. (2006) Quantitative Finance, Wiley, 2nd. Ed., Vol. 1, p. 342.

Incohorent risk measure

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The page gives no clue what X and Y are.

The reader wants to assume these are securities or investments, so that \rho(X) is the risk of X. But then we have:

"Monotonicity

   \rho(X) \leq \rho(Y) whenever Y \leq X "

So X can't be an investment: one investment is not less than another. Unless we have some ordering of investments which is not explained and is totally mysterious. Nor can X be the value of a particular investment, since the risk of an investment (if \rho is indeed risk) is not a function of the value of that investment.

This article might make sense to someone who is familiar with the broader subject matter, serving to remind them of something they already know, or providing details about something they understand generally.

But it offers nothing but confusion and mystery to the non-expert reader who wants to know what a coherent risk measure is.

Joaquin

Third rule

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I don't understand the third rule, translational invariance. What is d?

Shouldn't the fourth rule be called 'linearity' not 'homogeneity'?

Clarification of , , and

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The monotonicity axiom is confusing if you don't know what   represents. Is   an antitone function? Seems to me that if   and   represent the value of a risky item, and   is a risk-quantification measure, then monotonicity should be:
if   then  
That is, a highly priced item is considered riskier (note the reversal of the implication as well).
--203.185.215.144 23:44, 28 February 2007 (UTC) GregReply

With   and  representing (future) values of a risky portfolio, the monotonicity axiom is exactly the opposite:
if   then  ,
meaning if   portfolio value is higher than   portfolio value for every possible outcome (state of the world), then its risk (identified with the cash amount that has to be added to the portfolio to become acceptable) should be smaller. Just check Artzner et al. I will correct this if nobody has any objections. -- Zsolt Tulassay 15:09, 15 June 2007 (UTC)Reply

Non-coherance of VaR

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Could someone add an example illustrating this as it's not immediately obvious. An example would be of great benefit in my opinion —Preceding unsigned comment added by Red.devil.ade (talkcontribs) 09:30, 18 February 2009 (UTC)Reply

Translation invariance, which sign?

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Shouldn't it be +a instead of -a after the equality? Like this:

Translation invariance
 

For instance top page 7 in this article suggests the same:

http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.3340v1.pdf

Or am I wrong? —Preceding unsigned comment added by MVjensen (talkcontribs) 11:02, 12 November 2009 (UTC)Reply


I have now changed the sign, since noone commented on this discussion.

MVjensen (talk) 20:40, 7 December 2009 (UTC)Reply

The negative sign is correct because the risk is reduced when you add cash.

91.34.52.136 (talk) 13:55, 29 March 2010 (UTC)Reply


There is indeed some confusion around about the minus sign. This relates to two differnt schools (a) the insureance people: they consider a sochastic variable representing the losses (so higher is worse) and (b) asset managers, they consider the distribution of returns (so lower values are worse). This page is written in the paradigm (b) ... maybe worth to clarify this? Is it ok to do so? Phdb (talk) 14:22, 12 August 2011 (UTC)Reply

Other non-coherent measures than VaR

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There are many other risk measures that are not cohrent (eg. VAR, standard deviation, etc.). Ok to write a small text about them too? Phdb (talk) 14:22, 12 August 2011 (UTC)Reply

I think a small text about them would be ok, though it should more be just to comment that other types of risk measures exist. I would not suggest using standard deviation (or variance) since they are not actually risk measures. Zfeinst (talk) 17:34, 12 August 2011 (UTC)Reply

External link: The Case for Incoherence

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In external links there is the page

Glyn Holton: The Case for Incoherence

given. I just read this blog post and the initial example is misinterpreted (which gives rise, I feel, to an incorrect conclusion). I would propose removing this link for this reason.

The example (from the post) to which I am referring states: There are three wells, one or more of which may be poisoned. Should you drink from just one well or from all three?

In the post, it argues of course you drink from just 1; I agree. However, the author (Glyn Holton) goes from this to stating that subadditivity was violated, which is incorrect. Subadditivity would say

 

which can trivially be satisfied by situations where   for all wells. In fact, the "return" of drinking from all 3 wells is worse than the "return" of drinking from just 1 well with probability 1 (death certain unless all wells clean vs. death certain only in subset of those cases). Therefore by monotonicity we have that   for all wells.

Am I missing something? Does anyone object to removing the link? Thanks. Zfeinst (talk) 04:06, 12 March 2012 (UTC)Reply