Hello,i have calculated historical equity correlation for the iTRAXX firms. The average is 40%.It is much higher than implied correlation. (tranche 0-3 has 23% implied corr).Does anyone has reference or can explain this?Thanks!

On how many years did you calculate historical equity correlation ?

3 years

QuoteOriginally posted by: DiceManHello,i have calculated historical equity correlation for the iTRAXX firms. The average is 40%.It is much higher than implied correlation. (tranche 0-3 has 23% implied corr).Does anyone has reference or can explain this?Thanks!Future expectations are different from historicals. Then add risk premium. Then add a very rough model...The implied equity vols aren't equal to the historicals either (they are currently lower)

QuoteOriginally posted by: karstenQuoteOriginally posted by: DiceManHello,i have calculated historical equity correlation for the iTRAXX firms. The average is 40%.It is much higher than implied correlation. (tranche 0-3 has 23% implied corr).Does anyone has reference or can explain this?Thanks!Future expectations are different from historicals. Then add risk premium. Then add a very rough model...The implied equity vols aren't equal to the historicals either (they are currently lower)ok, but in the first place* why would equity correlation be closely related to correlation used for CSO?* why do you compare CSO corr. with average equity corr.? Maybe only average of equities with low/high spreads should be used... or whatever else....one of the reason why there is no widely accepted model is that we can not answer these question precisely enough.

QuoteOriginally posted by: hojdardok, but in the first place* why would equity correlation be closely related to correlation used for CSO?* why do you compare CSO corr. with average equity corr.? Maybe only average of equities with low/high spreads should be used... or whatever else....Actually, they could be the same. Once we have made the Gaussian copula assumption then we assume the gaussian structure comes from a set of diffusion processes with the same correlation structure. Each of these diffusions also underlies a structural model for the equity. The equities will necessarily have the same correlations as the diffusions that drive them. So once you accept the Gaussian copula and a diffusive structural model then it seems to me you have good theoretical reasons to use your equity correlations as copula correlations. Regards,Karsten

QuoteOriginally posted by: karstenQuoteOriginally posted by: hojdardok, but in the first place* why would equity correlation be closely related to correlation used for CSO?* why do you compare CSO corr. with average equity corr.? Maybe only average of equities with low/high spreads should be used... or whatever else....Actually, they could be the same. Once we have made the Gaussian copula assumption then we assume the gaussian structure comes from a set of diffusion processes with the same correlation structure. Each of these diffusions also underlies a structural model for the equity. The equities will necessarily have the same correlations as the diffusions that drive them. So once you accept the Gaussian copula and a diffusive structural model then it seems to me you have good theoretical reasons to use your equity correlations as copula correlations. Regards,KarstenStructural models are usually working with asset values which are made of equity AND debt.Hence correlations between assets and equities can't be equal in general. This is true especially in distressed economic conditions - and these are conditions in which you are interested when pricing correlation products. Note that in these conditions the equity option on firm's asset (striked at the debt value) has delta close to zero and thus assets are close to independent of equity.Also leverage plays its role by making debts (read assets) of two companies more correlated (but not that of equities). In fact this is similar to the first argument because leverage goes up with decreasing equity value (and decreasing option delta).Regards,Dan

QuoteOriginally posted by: hojdardStructural models are usually working with asset values which are made of equity AND debt.Hence correlations between assets and equities can't be equal in general. This is true especially in distressed economic conditions - and these are conditions in which you are interested when pricing correlation products. Note that in these conditions the equity option on firm's asset (striked at the debt value) has delta close to zero and thus assets are close to independent of equity.Also leverage plays its role by making debts (read assets) of two companies more correlated (but not that of equities). In fact this is similar to the first argument because leverage goes up with decreasing equity value (and decreasing option delta).Regards,DanHi Dan,I don't disagree that in practise it is not a good idea to just plug equity correlations into your copula model. Perhaps I should have been slightly more specific. What I am saying is that if you accept the gaussian copula model then you are restricted to working with diffusion driven asset processes. Now if you work with any ***single factor*** structural model (and lots of people do e.g. CreditGrades, HW 2000, etc) then equity and debt not only can be - they will be perfectly correlated. in fact, ***all*** derivatives (e.g. debt,equity, converts, one touch himalayan blah, blah, blah) are perfectly correlated. In that case, the equity correlation structure is the ***only*** theoretically consistent thing to use for your copula. And yes, you shouldn't be using a single factor structural model - but then you shouldn't be using the simple gaussian copula either. It's all wrong, wrong, wrong.Also, I don't agree with your characterization of the relationship between equity and debt as a company becomes distressed. As credit quality declines, the correlation between equity and debt actually increases. The reason for this is that as one approaches default, the value of the equity becomes driven more and more by changes in the probability of default (just like the debt). This is because non-default becomes increasingly less likely and therefore changes in the outlook for potential returns to equity (which do not affect the payoff of debt) become weighted by increasingly vanishing probabilities. I think a good multi-factor model ought to capture this.Finally, I am not sure why you say that leverage causes companies to become more correlated. I would think they would become less correlated as they become more and more driven by their own ideosyncratic risks and less and less by market effects like changing risk premia. (From a Markowitz perspective, this would also explain why risk premia have been observed to be much lower in junk than in high grade debt). I could be wrong - I haven't tried to quantify this. It's just what I think I observe. Regards,Karsten

karsten, why on earth do you think that a Merton type structural model is a reasonable assumption to reality? You don"t need a model linking equity and credit to justify a copula model for the joint default distribution. The only point where you would need it, is to justify that equity correlations can indeed be used as proxy for asset correlations in a Gaussian copula model. Clearly, the market tells you that this assumption is invalid. Whether or not the Gaussian copula assumption makes sense is a separate problem.

QuoteOriginally posted by: complexitykarsten, why on earth do you think that a Merton type structural model is a reasonable assumption to reality? You don"t need a model linking equity and credit to justify a copula model for the joint default distribution. The only point where you would need it, is to justify that equity correlations can indeed be used as proxy for asset correlations in a Gaussian copula model. Clearly, the market tells you that this assumption is invalid. Whether or not the Gaussian copula assumption makes sense is a separate problem.Strong words. Presumably some kind of structural model underlies the relationship between equity and credit. If that's not relevant to your trading then feel free to ignore it. Not everyone has the same goals as you.Karsten

QuoteHi Dan,I don't disagree that in practise it is not a good idea to just plug equity correlations into your copula model. Perhaps I should have been slightly more specific. What I am saying is that if you accept the gaussian copula model then you are restricted to working with diffusion driven asset processes. Now if you work with any ***single factor*** structural model (and lots of people do e.g. CreditGrades, HW 2000, etc) then equity and debt not only can be - they will be perfectly correlated. in fact, ***all*** derivatives (e.g. debt,equity, converts, one touch himalayan blah, blah, blah) are perfectly correlated. In that case, the equity correlation structure is the ***only*** theoretically consistent thing to use for your copula. Dear Karsten,you need not to be that categorical by saying "equity correlation structure is the ***only*** theoretically consistent thing to use for your copula" .It is not quite true, there are other equally "consistent" copula models beyond the structural framework.Reduced form models are consistent with normal copula (they may not be equally transparent, but they are consistent), as well as recent work by Geisecke on successive defaults (which is a structural model, but has features of the intensity based ones. There your normal copula will define dependence between debts, whereas assets could assumed well to be independent conditioned on debts). They are all consistent. And all not quite right. (I would even say that structural interpretation of the gaussian copula is less consistent, than the other ones. For example, currently used factor model is not even a dynamic model, even though is used as such for tranche pricing. If you write carefully down the mechanism of the standard version of it, you will see that it cannot tell you when exactly a default happens, only whether it has happened before some predefined time T. In other words, the standard normal copula model is using the classical Merton's model, as opposed to its dynamic analog the first hitting time model (where one should look at the minium of the value process, not just its final value). So by definition you should not be able to to tell the exact default times. But none the less the model is used to somehow output those and to figure out who default first or second. And you can check that this cannot be done in a consistent manner, unless you are taking into account the joint distribution of the miniums of the correlated brownian motions, or whatever underlying processes you have. And it is not something people would do, because of the computational complexity.)But I do understand that the structural models appeal by their apparent simplicity and the link between the credit events and the economic fundamentals. However one needs to be wary when he grounds his modeling on a whole bunch of simplifying assumptions. Because then you won't even notice how your model will start to produce wrong numbers (especially if there are no many benchmarks)For example, using equity correlation instead of asset could produce quite different results. People have done numerous analysis on that (taking into account firms' debt reports) and it appears those pairwise correlation numbers may differ not only in magnitude (up to 10 times), but also in sign!There are a lot of other things, that factor structural models ignore or twist, what also needs to be accepted with caution.The bottom line is that there are no such thing as "the only true" model, and one just chooses what model he wants to believe in. In the end of the day the truth about all the models is that all of them are wrong(!) (when compared to reality), however some could be useful (if properly used).QuoteFinally, I am not sure why you say that leverage causes companies to become more correlated. I would think they would become less correlated as they become more and more driven by their own ideosyncratic risks and less and less by market effects like changing risk premia. (From a Markowitz perspective, this would also explain why risk premia have been observed to be much lower in junk than in high grade debt). I could be wrong - I haven't tried to quantify this. It's just what I think I observe. Regards,KarstenRisk premium theoretically has nothing to do with the asset correlation of firms. Risk premia are just changes in the drift when we switch to the risk neutral world. Correlation, by Girsanov's theorem, is invariant under a measure change. In real world things are slightly more complicated, but risk premium being low is not an evidence that correlation to market factor is low.Besides, some empirical studies show that in distressed times firms (especially the highly leveraged ones) are significantly more(!) correlated. In some sense that supports the argument by hojdard. I understand that, since much depends on the model those fellows used for their empirical analysis, everybody decides for himself whether to trust those results or not. But the point is that correlation of defaults and assets could be quite different through time (depending on many factors, e.g. economic cycle) Therefore to use historical correlation from a certain period of time, even if you somehow have obtained the right asset correlation (not just that of equities) could be wrong, especially for senior tranches (because those guys are gonna be under stress only if things are really bad in the economy, meaning that for those products it could make more sense to use correlations conditioned on that situation)Regards.