CreditGuy, that's one of those emails that probably sounds the way you wanted it to out loud, but in text, without any tone it may be misinterpreted.If you mean that I should be posting other people's research in order to be balanced... I'm afraid I can't do that. This research is not academic research for public distribution. If someone else wants to post it here, perhaps someone from Bear than that would be good, but I just can't do it.If you mean than as I have been as helpful as possible, and deserve to be able to see what everyone else is saying... Perhaps you're right, but I've seen this particular piece, so not to worry.BTW: I'm speaking on Base Correlation in Madrid tomorrow, is anyone going?RegardsLee

Leeyep -- see you there ; looking at the agenda seems to be some very interesting work being reported on.Mark

Just had some thoughts on ATM Correlation. Basically, I think that the ATM point could also be defined in many other ways. No one really expects loss levels consistent with the risk neutral measure. So, maybe the market consesnsus of the ATM point is not equivalent with the risk neutral expected loss of the portfolio. I'll expand on this in a couple of days, when I'm back from Europe.

Interesting.. I agree that one expected loss is not necessarily the point that is most interesting (that is the point where correlation is most static ?), but I can't get away from the fact that it is a function of expected loss somehow. I did consider the inflexion point of the loss distribution.Interested to hear your thoughts...RegardsLee

I'm very interested in this concept of base corr. I've read through the documents, especially through the equations in the spreadsheet guide, but I still have a question. It relates to one someone asked in the beginning of this discussion. How can I calculate the expected loss of a tranche given only the spread? From the eqs. in the notes we have:E[Tranche Loss] = spread * RiskyDuration * Tranche sizeHowever we need the correlation to calculate the RiskyDuration. We need it for the expected survival. Any thoughts on that? Lee? Thanks in advance.Fodao

fodao, expected loss is independent of correlation. Correlation changes the shape of the loss distribution but not its mean. To illustrate, a 0%-100% tranche on some index portfolio is the same as a position in the index swap. Clearly, you can price the swap without any correlation assumptions.

hey , im glad you brought that up as well, fodao, this is the question that i brought up a while ago. expected *tranche* loss is does depend on correlation, even though expected underlying pool loss is independent of correlation. so i think the question still stands. cheers

As CompleteQuant said the expected loss of a TRANCHE definitely depends on correlation while the whole portfolio expected loss doesn't.However I think the answer is the following: Let's say we want to bootstrap the base corr. We are given the spreads1 for the equity tranche [0, K1]. In this case the base corr is equal to the implied corr. Let's call it rho1. Now we want to find the base corr for [0, K2]. We have:E[0, K2] = E[0, K1] + E[K1, K2]We have the market spread s2 for the tranche [K1, K2]. How can we find rho2, the base corr for [0, K2]? I think we assume that E[0, K2] and E[K1, K2] are implied functions of rho2 and, given s2 and E[0, K1], we can calculate its value. Comments?

CompleteQuant and fodao,The information you have is the spread of the tranche. The process of obtaining the correlation and hence the expected loss of the portfolio is an iterative process. Using the base correlation model from JPMorgan (see earlier in this thread) if you have the spreads on the tranches you can solve for the correlations/expected loss of the tranche. This process also works the other way where if you have the correlations you can obtain the spread on that tranche. This is particularly useful for the offmarket tranches by interpolating along the base correlation curve to back out tranche spreads. There needs to be some price discovery - you cant get tranche prices if all you have is the index level...

Another way perhaps...The expected loss for a tranche depends on correlation only if your starting point is the porfolio spread or default probability.If I tell you an instrument has an expected loss, and that you will need to be paid a spread to bear that expected loss, what more do you need to know?The reason, I think, that this gets so confusing is that models rarely split the process into two parts (correlation to expected loss per tranche, expected loss to spread).[Edit: I agree though that the documentation doesn't help this]Perhaps that helps...RegardsLee

Lee, If you give me the expected loss for the tranche and the spread I totally agree that you don't need the correlation. But I thought that you could only get the spread from the market. Are there also quotes for expected losses for each liquid tranche?

Sorry, what I meant was...Imagine there is an instrument where there is a (fixed but unknown) expected loss, and you need to be paid a spread to bear that loss. Then those things are related. They are related without you particularly needing to know about the nature of the instrument (or whether it is a product which is sensitive to correlation). Hence you can move from expected loss to spread and from spread to expected loss. If they are related you can go backwards as well as forwards.Another prompting question: If I tell you that there is an asset A and an asset B, with spreads, and notionals. What do you need to know to calculate expected losses?If I tell you that asset A is a portfolio and asset B is a tranche of a portfolio, what is it about asset B that makes you need correlation and about correlation A that makes you not care?RegardsLee

Yes they are related, but it doesn't mean that the expected loss is completely determined by the spread. There are other variables that come in.Given assets A and B with spreads and notionals I need to know what is their composition and their capital structure to calculate the expected loss and the correlation might be important. If A is a portfolio of defaultable instruments, only the marginal default probab. is taken into account to calculate the exp. loss, therefore corr. is not an issue. If B is a portfolio tranche, we only have losses when the total portfolio loss is above a threshold, therefore now the corr. becomes important.If corr wasn't important for the exp loss of B, the curves of Exp loss for CDO tranches as a function of corr. would be flat and we know that this is not true.

hi allindeed, the tranche loss depends on correlation because of the tranching (attachment, exhaustion).i like your way of expressing it, fodao. Rephrasing you:E(0,K2;rho2) = E(0,K1;rho1)+ E(K1,K2;rho2) (1)There is a bit of an inconsistency here, if you want to call it that, since the two terms on the rhs are computed at different rho's. More practically, perhaps it is just an assumption/simplification of the model.I think another inconsistency/simplification being made here is that the relation (1) between expected losses is only being applied at ONE payment date, presumably the maturity of the tranche. But the spread of the tranche is a function of expected tranche losses at all payment dates up to maturity. Even if you satisfy (1) at maturity, its not guaranteed to hold at earlier dates is it?Im starting to think maybe this isnt a trivial point..

QuoteOriginally posted by: leemcgIf I tell you an instrument has an expected loss, and that you will need to be paid a spread to bear that expected loss, what more do you need to know?Lee, I would argue that you also need to know the timing of those losses. Two assets with the same expected loss can have different risky durations, requiring different spreads as compensation.For tranches, a correlation along with the attachment points would be needed to calculate the expected loss over time. However, if you're already calculating the premium leg along with the protection leg, this is a non-issue.