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ERM Exam Old Advanced Finance and Enterprise Risk Management (ERM) Forum

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  #141  
Old 03-12-2018, 09:46 AM
Actuary9914 Actuary9914 is offline
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For XL reinsurance, the material states that the reinsurer may require the cedent to co participate in losses above the retention so they have skin in the game.

Technically, wouldn't this be the same as pro-rata surplus share? Are there any differences between the two?
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  #142  
Old 03-12-2018, 10:17 AM
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Eddie Smith
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For XL reinsurance, the material states that the reinsurer may require the cedent to co participate in losses above the retention so they have skin in the game.

Technically, wouldn't this be the same as pro-rata surplus share? Are there any differences between the two?
The critical difference is that XL agreements usually focus on aggregate losses, so they are "non-proportionate" to individual risks. Surplus share is technically a form of proportional reinsurance. Even though the proportion varies by risk, it's still defined in terms of specific risks in advance.

XL losses can really only be known after the fact. With surplus share, you know in advance what % of each individual risk is ceded. With XL, the reinsurer's share in dollars isn't really known until after the loss occurs. The cedant's share in dollars (if there is a coinsurance % on excess losses) isn't known in advance either.

That said, you can also define XL on a per risk basis, and you can certainly begin to blur the lines just depending on the specifics of the agreement.
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  #143  
Old 03-12-2018, 12:47 PM
MySpaceTom MySpaceTom is offline
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The SOA... "encourages all students to read through the entire case study to gain an overview of the corporation". However, each extension only cites a specific grouping of pages.

Does anyone else plan on (or recommend) reading through the entire thing? Or, is this just filling your brain with unnecessary information?
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  #144  
Old 03-12-2018, 01:53 PM
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Eddie Smith
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Originally Posted by MySpaceTom View Post
The SOA... "encourages all students to read through the entire case study to gain an overview of the corporation". However, each extension only cites a specific grouping of pages.

Does anyone else plan on (or recommend) reading through the entire thing? Or, is this just filling your brain with unnecessary information?
The entire case study is an enormous document, so feel free to flip through it out of curiosity, but I would only focus your study time on your specific extension since the SOA explicitly says to do that. Spending too much time in the other extensions and can even hurt you to the extent that it disorients you from the key information in your specific extension's section. For example, the general insurance section is a collection of more summarized points from the other 5 extensions. It has much less detail than any of the other extension-specific sections but also overlap.
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  #145  
Old 03-13-2018, 11:36 PM
manu652 manu652 is offline
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Hi,

I feel confused about the "Total exposure" mentioned in ERM-103-12 Box A. The material said it is a coherent risk measure without telling more details about it. Does anyone know its definition (or is it just some generic concept)?

Thanks
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  #146  
Old 03-14-2018, 12:32 AM
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Hi,

I feel confused about the "Total exposure" mentioned in ERM-103-12 Box A. The material said it is a coherent risk measure without telling more details about it. Does anyone know its definition (or is it just some generic concept)?

Thanks
Good question! A "coherent" risk measure is one that satisifies these four properties (positive homogeneity, sub-additivity, translation invariance, and monotonicity).

But that's the technical definition. We've said that anything that satisfies these four things is coherent. But what is really meant by this is that, if a risk measure is coherent, we think it should behave in a manner that we think is reasonable. But, since 'being reasonable' is a very qualitative criteria, all our readings say "A measure is coherent if it has these four properties." The closest thing to a qualitative definition I've seen is that a coherent risk measure is a "good risk measure."

For example, we think it's reasonable that risks should diversify, or at least not make the overall risk worse when added together in a portfolio. This is the sub-additivity property. VaR famously fails this test, because you can design scenarios in which VaR(A+B) > VaR(A) + VaR(B), which means that simply grouping two risks together make the risk greater than the sum of the parts - that is, we have negative diversification. We think that doesn't make sense, so we say it is not "coherent."

No one will define it like this, and we never get readings that say it this way, but if I had to describe it to someone outside of the actuarial world, I would say "A coherent risk measure is one that makes logical sense." Adding cash to the portfolio helps, bigger portfolio have bigger risks, etc.

Hopefully that helps! We don't have any hard definitions outside of the necessity to meet these four criteria, but I hope that will explain a little more of the "why" behind this term.
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  #147  
Old 03-14-2018, 09:28 AM
Actuary9914 Actuary9914 is offline
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In VAR, chapter 7, formula 7.38:

I understand that the first two terms must be constant at the optimal portfolio, but is it really true that term 1 = term 2?

Wouldn't that imply that Marginal Var (i) = Beta (i)?
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  #148  
Old 03-14-2018, 10:10 AM
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Eddie Smith
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Originally Posted by manu652 View Post
Hi,

I feel confused about the "Total exposure" mentioned in ERM-103-12 Box A. The material said it is a coherent risk measure without telling more details about it. Does anyone know its definition (or is it just some generic concept)?

Thanks
As Paul noted, a coherent risk measure is really a statistical definition defined in terms of 4 criteria. The most plain English interpretation of "coherent" is "consistent" or "internally consistent" in the context of risk measures. The criterion that tends to gets the most attention in risk modeling is the sub-addivity property, which Paul described above. In formula form, a risk measure (RM) is sub-additive if RM(X+Y) < RM(X) + RM(Y).

Sub-addivity is extremely important in most financial and insurance risk management applications because we want to reduce overall risk by pooling individual risks that aren't perfectly correlated. VaR fails the sub-addivity property if risks have jointly fat tails (i.e. any degree of tail dependence). In plain English, many financial and insurance risks become worse together when things start going badly in the tail. VaR is blind to what happens beyond the VaR percentile, so it misses this behavior entirely.

Note in the case of elliptical distributions (a.k.a. normal or Gaussian) VaR actually satisfies sub-addivity making it a coherent risk measure in that specific situation. This is because joint elliptical distributions have zero tail dependence, so with normal and jointly normal risk variables, VaR(X+Y) < VaR(X) + VaR(Y). It's worth emphasizing that some risks are elliptical, so VaR may be totally fine for those. For example, high volume manufacturing assembly errors may be normal. Or small clerical mistakes, etc. So VaR can actually be coherent if the risks are truly elliptical with zero tail dependence in reality (i.e. the joint tail behavior is irrelevant).

But again, that's rarely the case for most of the financial and insurance risks that we worry about under ERM. Even if a specific risk has a marginal normal distribution, it may have a very non-normal joint distribution with other risks. For example, routine clerical errors may be normal, but when mixed with operational risks (management/system failures, etc.), the joint tail could be pretty ugly.
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Last edited by E; 03-14-2018 at 10:17 AM..
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  #149  
Old 03-14-2018, 12:16 PM
manu652 manu652 is offline
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Quote:
Originally Posted by PaulP View Post
Good question! A "coherent" risk measure is one that satisifies these four properties (positive homogeneity, sub-additivity, translation invariance, and monotonicity).

But that's the technical definition. We've said that anything that satisfies these four things is coherent. But what is really meant by this is that, if a risk measure is coherent, we think it should behave in a manner that we think is reasonable. But, since 'being reasonable' is a very qualitative criteria, all our readings say "A measure is coherent if it has these four properties." The closest thing to a qualitative definition I've seen is that a coherent risk measure is a "good risk measure."

For example, we think it's reasonable that risks should diversify, or at least not make the overall risk worse when added together in a portfolio. This is the sub-additivity property. VaR famously fails this test, because you can design scenarios in which VaR(A+B) > VaR(A) + VaR(B), which means that simply grouping two risks together make the risk greater than the sum of the parts - that is, we have negative diversification. We think that doesn't make sense, so we say it is not "coherent."

No one will define it like this, and we never get readings that say it this way, but if I had to describe it to someone outside of the actuarial world, I would say "A coherent risk measure is one that makes logical sense." Adding cash to the portfolio helps, bigger portfolio have bigger risks, etc.

Hopefully that helps! We don't have any hard definitions outside of the necessity to meet these four criteria, but I hope that will explain a little more of the "why" behind this term.
Quote:
Originally Posted by E View Post
As Paul noted, a coherent risk measure is really a statistical definition defined in terms of 4 criteria. The most plain English interpretation of "coherent" is "consistent" or "internally consistent" in the context of risk measures. The criterion that tends to gets the most attention in risk modeling is the sub-addivity property, which Paul described above. In formula form, a risk measure (RM) is sub-additive if RM(X+Y) < RM(X) + RM(Y).

Sub-addivity is extremely important in most financial and insurance risk management applications because we want to reduce overall risk by pooling individual risks that aren't perfectly correlated. VaR fails the sub-addivity property if risks have jointly fat tails (i.e. any degree of tail dependence). In plain English, many financial and insurance risks become worse together when things start going badly in the tail. VaR is blind to what happens beyond the VaR percentile, so it misses this behavior entirely.

Note in the case of elliptical distributions (a.k.a. normal or Gaussian) VaR actually satisfies sub-addivity making it a coherent risk measure in that specific situation. This is because joint elliptical distributions have zero tail dependence, so with normal and jointly normal risk variables, VaR(X+Y) < VaR(X) + VaR(Y). It's worth emphasizing that some risks are elliptical, so VaR may be totally fine for those. For example, high volume manufacturing assembly errors may be normal. Or small clerical mistakes, etc. So VaR can actually be coherent if the risks are truly elliptical with zero tail dependence in reality (i.e. the joint tail behavior is irrelevant).

But again, that's rarely the case for most of the financial and insurance risks that we worry about under ERM. Even if a specific risk has a marginal normal distribution, it may have a very non-normal joint distribution with other risks. For example, routine clerical errors may be normal, but when mixed with operational risks (management/system failures, etc.), the joint tail could be pretty ugly.
Thank you! That explains a lot, but that was not I originally asked.. I was not asking about the definition of "coherent risk measure", instead I was asking about the definition of "Total exposure" as a risk measure listed in Box A. I understand other risk measure listed there, like VAR and Expected shortfall, may or may not be a coherent risk measure.

My apologize for the ambiguity in my question. I just feel "Total exposure" is not well defined in 103-12 nor any other materials, so maybe it is just an "ideal/perfect risk measure" we desire but does not exist in practice?

Last edited by manu652; 03-14-2018 at 12:19 PM..
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  #150  
Old 03-14-2018, 12:34 PM
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Eddie Smith
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Originally Posted by manu652 View Post
Thank you! That explains a lot, but that was not I originally asked.. I was not asking about the definition of "coherent risk measure", instead I was asking about the definition of "Total exposure" as a risk measure listed in Box A. I understand other risk measure listed there, like VAR and Expected shortfall, may or may not be a coherent risk measure.

My apologize for the ambiguity in my question. I just feel "Total exposure" is not well defined in 103-12 nor any other materials, so maybe it is just an "ideal/perfect risk measure" we desire but does not exist in practice?
Sorry for misunderstanding! You are right that ERM-103 doesn't define "total exposure" well, but they are most likely talking about the total exposure to loss. Suppose you have 1M invested in corporate bonds. Your total exposure to credit risk (loss due to defaults) is 1M. This would be a pretty extreme risk measure that doesn't reflect the probability of default, but it still might be meaningful at a high level. This concept is also related to other similarly named things on the syllabus like "current exposure" and "potential exposure," which measure the current MV impact of losses due to credit defaults. Fundamentally, your expected losses are just a weighted average of your total exposure.
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