 Hi everyone, it's MJ and in this video I want to talk about credit portfolio models now This is just very quickly gonna be an overview We're not gonna get into too much detail instead what I'm gonna be doing for students who want to know a little bit more I will be attaching PDF documents of these models and you can have a little bit of a deeper dive So just y'all just to manage expectations. We are giving just a quick overview here Before the previous models that we've looked at specifically the structural models of the Merton All the migration models of Yarrow. We were looking at the probability of a single bond Defaulting what we want to do now is we want to consider a portfolio of bonds And essentially we will be using the value at risk framework and just a quick reminder If you haven't watched the market risk course value at risk Essentially is a statement about risk and it captures three dimensions of risk the frequency the severity and the duration of the total risk portfolio and an example is saying like there is a 95% chance that we won't lose more than a hundred million over the next ten days ten days is the duration hundred million is the minimum severity and 95% you can think of as the confidence Which is a little bit of also a little bit connected to to frequency now? Value at risk is very much a framework not necessarily a model on its own so a lot of different models can be used to calculate the value at risk and What we're going to be using the value at risk for for in this video is for a bond Portfolio and the big thing about a portfolio is that we must take into consideration Correlation so we must look at correlation How are these bonds connected? Is there any benefit and diversification or are we just you know opening ourselves up to a lot of? Concentration so this is very much like I say gonna be just a quick overview of the various approaches to create credit portfolio models So the first one I want to talk about is the multivariate structural model so you can take the Merton or the KMV approach which we spoke about earlier and You can extend them for a whole bunch of a whole bunch of bonds and in this situation You might use the multivariate t distribution with a correlation matrix Or you can even be a little bit fancy and use a copula which will allow the correlations to change And I'll try putting the appendix in time I'll try adding a whole bunch of information about copulas and multivariate Distribution so those of you who are interested in the maths can go through it Then we also going to be looking at this idea of the multivariate migration model again This was the Yarrow model, but you can now extend it and a model that is famous for it using the migration approach To extend it to a bond portfolio is something known as the credit metric model and for this model I have attached the PDF and I will be including quite a few of the graphics that I found in that PDF in this video So I don't actually show two to them to you right now the first one I find very very interesting because when we when we did this whole course on market risk Remember we challenged this assumption of normality of market Market risk and market returns and we said that it was very much a simplified approach because we you know the math It makes the maths quite easy Credit risk especially in this credit metric document. They're identifying that okay No hold on this this normal assumption is actually wrong and credit risks are actually They actually have this this idea where they are negatively skewed Which means most of the time they're going to be you know Generate a gain, but they also have these fat tails. You can see over here. You've got these fat tails of losses So they understand that the models need to incorporate Distributions that are a lot more complicated than the normal of course Of course the normal keeps popping up no matter where even when people are aware of it And you kind of see this model all this graphic that they had further down in the paper chalk 5.2 Where they're looking at the bonds with the different credit rating agencies And they say this is how the price moves and you can see they very much have got the normal distribution Along a whole bunch of values, so they still they're still Reverb back to it, but it is quite quite interesting to see that they do acknowledge Like I say I would say that this is not only just the distribution of credit returns But also of market returns. It's just we use this normal for more of a simplicity But like I said, we talk about that in the market risk course Coming back to to credit risk We can use also a whole bunch of actuarial models and there's a whole bunch out there Another PDF that I will be attaching is the credit risk plus model which was developed in the late 90s It kind of uses the Poisson distribution And I mean this is the whole idea is actuarial science has created a lot of beautiful risk models to deal with Mortality and you know various other insurance whether a short-term claims and pensions and all of those things And that's the thing is that if you have enough data with credit risk You can very comfortably use the actuarial models You could even build a ruin theory model and take all of these things into consideration so You can use the actuarial models if you have the data and if like we said in the previous video You're comfortable with the assumption that the future can be predicted by the past returns And like we said that very much is the case with actuarial risks like mortality and morbidity However, it's not necessarily the case when it comes to asset managers performances Specifically in the speculative realm of the hedge funds But like I said, there are lots of different approaches You can even build up survival models with the Goomba copula You can even build something called a common shock model with the Marshall Olken copula So there are a whole bunch of different approaches and I think The big thing with credit risk Well, this was one of the things that that kind of caused a little bit of the world financial crisis was that these models were incredibly Difficult and sophisticated and complicated but their Achilles heel was their dependency on getting correlation correct and a lot of the times they were using The normal copula which didn't allow the correlation To change in such an extreme way as what we observe So it's much better to use the Goomba or the Marshall Olken copula Instead of the normal one, but like I said, it's probably the big Achilles heel of all of these portfolio models Whether it be credit whether it be market or whether it even be a total portfolio where you're combining market and credit together It's trying to get correlation correct is incredibly difficult Then there's also the the economists they've come up with a whole bunch of various models You know models that look at what is the impact of interest rate and inflation on the probabilities of of default So like I said, there are there's lots and lots of different approaches to credit risk This course very much just wants to give an overview look at the principles Look at some of the drawbacks to some of the common ones But this is almost an inexhaustible topic because new models are popping up every single day And of course when you're dealing with a portfolio, you do need to look at the recovery rates and recovery rates like I said is The portfolio model not only needs to tell us how many bonds are going to default But we also need to know what is the loss for each of them and you can think of recovery rates as The the inverse of a loss distribution So we will take the same approach as a loss distribution So loss is saying how much we lost from this event happening recovery rate is is essentially saying Given the maximum loss, how much were we still able to to recover? So they're very very similar But one thing that you need to understand, especially when it comes to say credit risk and how it's different to insurance risks Is that the distributions that we fit will be different? So remember with the loss distributions, it was very much the log normal or the exponential It was these, you know, positively fat-tailed distributions Whereas what we can see specifically with credit risk is you have the the beta distribution Which could be used in some situations for for loss distributions But we're going to see that it fits much better with With the credit risk and it will allow for the different types of bonds. So you can see senior unsecured There's quite a good chance that you're going to get the majority Sorry about that There is quite a big chance that you're going to get the majority of your your bond value back Whereas if it's say a junior bond, you can see that you're only going to be recovering a very very small amount 10% if not less So also important to understand that the seniority of the class is also going to have an impact On the bonds recovery rate But at the end of the day, all of these different models are trying to do the same thing And they're trying to calculate the value at risk due to credit And you can see they will so this is one that's coming back to credit metrics, which is the migration portfolio approach You're looking at exposure You're looking at a whole bunch of different factors You're looking at correlations But at the end of the day, you want to say, okay What is the portfolio value at risk due to the credit risk that I have taken out? Anyway, this has very very much been an overview of the portfolio models I will be attaching some PDFs So that you can go and look at the credit metrics and the credit risk plus in more detail And like I say in time, I will be adding an appendix trying to explain copulas And I'll be doing it in a very general way, but you can then apply it to the credit risk approach Other than that, thanks so much for watching and I'll see you guys in the next video. Cheers