This is the beginning of Module 3. In Module 3, we're going to focus on credit portfolio management. We have spent Module 1 and 2 for the most part looking at single names, single loans. One loan, one obligor, one borrower, one counterparty. Now we're going to step back and look at in terms of a portfolio of exposures and portfolio of themes. In Lesson 1, we looked at some basic portfolio concepts, essential concepts in managing portfolio risk. That includes correlation and concentration, unexpected loss of the entire portfolio. We'll take a peek a little bit more in-depth about how the concept of unexpected loss, it's what bank regulators look at in determining a capital requirement for a bank, for the credit risk in the portfolio. Then we'll talk about credit value at risk. Remember, this is credit deterioration and then we can now come up with a value, a metric, and very similar to a market value at risk. For those of you who are familiar with market value at risk, what we try to measure there is that within a certain confidence level, within a certain probability, what is the most that we can lose in the value of a market portfolio of trading assets? We try to translate that into the world of credit and the world of credit would say, because of credit deterioration, what can we lose the most within a certain confidence in terms of the market value of trading of credit assets, whether they're loans or bonds? What is the most we can lose, not default, but as a result of deterioration, credit spreads increases? When credit spreads increases, then bond prices go down. What is the most that we lose? That's the concept of credit value. I will go back and look at that a little bit more in-depth. Credit portfolio management. Here's a balance sheet. This is not the balance sheet of a company, this is the balance sheet of a financial institution. In that financial institution, it can be insurance company, it could be a bank, it could be a fund, it has a portfolio of credit exposures, loans, bonds, commitments, counterparty trading exposures. How does it manage that exposure, that collection, that aggregation of exposures on an ongoing basis? It can calculate expected loss for the entire portfolio, and then it also can calculate unexpected loss. Then for a bank, as we have mentioned, the expected loss is going to help us determine a credit provision, a loan loss reserve. On average, how much is the bank going to lose as a result of credit risks in each year, the average? The unexpected loss is going to be what's the worst that it could lose in certain probability because of credit risk? Here, this is on average. Let's think of that is on average, what it can lose for a year, and then what we're going to do is going to take a charge to earning. We're going to predict on average what our losses could be in the portfolio and then we're going to take a charge to earnings, and that's my loan loss allowance and my credit provisions that we see on bank accounting statements. The unexpected loss is that when I look at that portfolio, I look at the worst-case scenario. In theory, it's with 99 percent probability, what's the worst I could lose in this portfolio? I'm going to have capital, I need capital to absorb that loss. If I have a loan portfolio of a billion dollars and if I say the worst-case scenario, its unexpected loss, not the average loss, is that it's going to be $100 million loss, then bank regulators will say, "You need 100 million to absorb that once in a 100-year type of event." A catastrophic type of loss. This is what regulators want to see in terms of the credit risk and how do we absorb that once Armageddon situation type of loss on that balance sheet. Portfolio risk is our next step beyond looking at each name, each exposure, expected loss, probability default, rating. Now I step back, and look at the entire portfolio. The purpose of portfolio management, we want to look at the expected loss of the entire portfolio by all products and categories of risk, including not just loan upstanding, but commitments, revolving credit commitments, letters of credit, counterparties, trading exposures as well. Then we're going to try to use that benchmark for expected loss to calculate my loan loss allowances. Then we're going to need to use that as a basis to go one step further and calculate the unexpected loss in the portfolio as well. Keep in mind, expected loss is a function of [inaudible]. Expected loss is also a function of tenor. It's a function of whether if one year out, five years out, or 10 years, as much it is as a function of the rating itself is a rating. Here is a hypothetical example. This is a hypothetical example. I have a portfolio. I have eight loans in the portfolio. For the eight loans in the portfolio, in the first column, is the outstanding. This is the outstanding. These are loan outstandings. This is in millions and I have 1.1 billion total outstandings. The second column, credit analysts will have done an analysis of the loan. Regardless of whether it's secured us unsecure at that point time is really about coming up with a rating. Credit analysts will come up with that rating, and then we'll map that into a probability of default. Again, this is hypothetical. We now have our PD. Then for each loan, I'll look at the type of support collateral guarantor. I can look at whether it's senior or junior and I can calculate my LGD. The lower the LGD, the more likely that the loan has been collateralized, the higher the LGD, the more likely that the loan could be subordinated. In this example, if the LGD is five percent, that's going to mean that it's a collateralized loan. The LGD at 75 percent is going to suggest that the loan is subordinated. The LGD at 35 percent It's going to suggest to me that that loan is senior and unsecured. This is hypothetical, so we come up with the LGD. Then for each loan, I'm going to calculate the expected loss. Very simple. Probability default times the loss given default times the outstanding, I have my expected loss for each loan. I sum that up. For my hypothetical portfolio at 1.125 billion, I now have an expected loss of 5.3 million. That's how much I expect to lose in that portfolio. I hope to compensate for that by having a net interest earn in LIBOR plus credit spread, that's going to exceed five million. I want to make sure that when I price these loans in each case, that my earnings, my credit spread is going to be higher than five million or more specifically, my credit spread is going to be higher than 47 basis points. This is a hypothetical example. It's a very typical example of how a portfolio is measured. Then from period to period, companies evolve, deteriorate, get better. We will change the default probability from period to period. As an aside, I'll say this very quickly, many banks in the first quarter of 2020, they increased their loan loss reserves, mostly because default rates increase. Default rates increase, therefore they expected loss increase, and so we would increase our loan loss reserve. Now, they also increased for other factors, but there had to be a very important factor as we're going into the pandemic in the first quarter of March 2020. By the time we get to the fourth quarter and we see some recovery in the economy, we see some resumption of economic activity, then the default probabilities have come down, the expected losses come down and then banks actually can reduce their loan loss reserves. This is done on an ongoing basis. We don't do it once a year, on occasionally, on an ongoing basis. We're looking at the rating of each of these loans after having done the analysis and then map that into a default probability, and then actually do the calculations for expected loss. What we don't have here and this is where it gets complicated. What we don't have here is now we haven't looked at correlations and we haven't looked at unexpected loss. We haven't looked at and we got to make sure that did we look at these default probabilities based on tenure and not just on credit ratings as well? Did we look at the unexpected loss? Then we take into consideration correlation and concentration. That's where it gets a little bit more complicated, when we start talking about how do we analyze these different types of portfolio risk. Portfolio management includes looking at the portfolio. This balance sheet, again, it is not a corporate, it is the financial institution that's involved with having credit risk on its balance sheet, lenders, investors, lenders investments and bond portfolios and loan portfolios, loan commitments. Here's my checklist. If I'm looking at a portfolio, I want to make sure I'm looking at overall default in recovery risks, I need to look at concentration, I need to look at correlation, I also need to look at incremental and marginal risk. What that means is that to what extent my next loan is going to have impact on the overall portfolio? How is it going to change the concentrations and correlation? I have a loan portfolio that's 500 million and if I add another loan, how's it going to change the look of the portfolio? Is it going to make it more risky? Is it going to make it less risky? Is it going to make it more concentrated? Is it going to make it less concentrated? Pricing risks, of course, that goes back to what we've been talking about all along. Got makes sure that we are compensated for the expected loss in the portfolio. This is out of the scope of the course, what financial institutions also have to make is how are we going to fund that loan portfolio? That's what relates to liquidity risk. That's not in the agenda here. Well, financial institutions are very much very sensitive about I've got a loan portfolio I'd have to fund it, how do I fund it? How do I make sure that I have the funding in place to be able to support that? Then the last thing here is that what is the capital requirement whether insurance company or a bank or a broker, dealer? I need a certain amount of capital to absorb, not the average loss, not the expected loss, but the unexpected loss. The worst-case scenario, that once in a 100-year event that could be so imploding, what is that? How much can we lose and could the bank survive that worst-case scenario? That's what we call the capital requirement. Let's go back and talk about this unexpected loss. We have the expected loss, so there's an unexpected loss. The unexpected loss accounts for losses beyond the expected. It's related to historical volatility in the default probability or default frequency. Very simplistic presentation of this is that for a loan, I have come up with a rating I now have a probability default. Based on that probability default, that wasn't average, remember we looked at default frequencies and that was an average over 40 years. But in some years, a probability default can be much higher and some years it could be lower over that 44-year period we looked at in a modus example. That wasn't average. Some years for the one-year loan, five-year loan, the probability of default frequency was much higher. What I need to do now is look at what is the variance in probability default in each year, for each rating? If on average, if it's a single B, and if on average the probability of default or a default frequency was 0.5 percent. Well, in some years it could have gone to two percent, some years had gone down to zero percent. What's the variance in terms of that probability default? I'm paying attention at the peak. How high did that default frequency go for certain ratings? How high? I'm going to use that as a basis of calculating my unexpected loss. Now, I'm presenting this in very simplistic facts. What were trying to do here is just understand the concept of default probability in terms of the average default probability of default frequency. Then what's the worse? How high can it go? A singular name on average might default 4-5 percent of the time but in some years it might go to three percent. Some years it might go down to zero percent, so how high can it go? That's why I want to do an account for unexpected loss. Basel III, which is bank regulation guidance for banks around the world. Basel III says that unexpected loss is a result of a calculation. So what Basel III says, "What is the worst that you can lose in that loan portfolio or in your credit exposure with 99.9 percent confidence?" The statisticians. What Basel says is that let's assume that the distribution of losses as it relates to probability fault is a normal distribution. That's an assumption, and then what we're going to do is that we're going to look at that in terms of a normal distribution. Based on that probability result, how high can it go and then how low can it go? I'm worried about the high. How high can a probability of default go with 99.9 percent for that particular rating? I'm looking at a single AMA, I see the average is 0.5 percent. But with 99.99 percent probability, how high can that probability of default for a single AMA go? Then we're going to multiply that by the LGD and that's going to determine what my unexpected loss would be. For the most part, for AMA and for a portfolio, our loss is going to be right around the expected loss. But Basel says, "I'm not worried about the expected loss. I want to look at the worst-case scenario, and then do you have enough capital to support that?" Do you have enough capital to support that amount of loss in a single year? That's the capital requirement and it goes back to the portfolio. The unexpected loss on a name by name basis and then in aggregate, the unexpected loss for the entire portfolio. There is something that does go into the consideration, correlation in terms of default probabilities. Remember we talked about two names, a and b can both half a default probability. But if they are very highly correlated, then one name goes into default, then another name can go into default. If one name goes into default another name can go to default if there's a high correlation. Basel III requires that banks, when they do their calculation of this concept of unexpected loss, that they must take correlation into consideration. That's very complex. It's a little bit out of the scope at this particular course, but it does say that you've got to take correlation into consideration. If obligors are names of highly correlated, then our default probabilities are not understated. Our default probabilities could be understated in terms of looking at a name from [inaudible] We now go into other aspects of concentration risk and I'm going to return to correlation risks. Concentration risk is what it is. It's measured based on individual loans or groupings of loans by industries, currencies, or geographies. I want to know in my loan portfolio, how much of it is concentrated in airlines? How much of it is concentrated in oil and gas? How much of it is concentrated in consumer and retail product companies? I try to measure concentration. We know that too much concentration in a vulnerable industry is not a good thing. Concentration leads to high correlation as well and so are there ways for us to measure concentration? Many banks will look at this one, many portfolio managers, and they'll say anything that's more than 10 percent in an industry. Anything that's more than 10 percent for a particular country might be too excessively concentrated. Different banks and different portfolio and risk managers may have different ideas about what constitutes concentration. I'm using a benchmark say, I've got a portfolio of corporate names and bars and credit exposures. Any one industry that's above 10 percent could be my benchmark of what I ever call excess concentration. We can also use what is called a Herfindahl-Hirschman Index. I introduced that as a HHI index. It is an index between zero and 100 percent. We can do this calculation. If there is a loan, it's only one loan in the portfolio then the HHI index is 100 percent. If there are 100 loans in the portfolio and if each one has one percent of the total exposure, then the HHI index would equal to one percent. The higher the HHI index, the more heavily concentrated the loan. We can use that index to measure to what extent is the portfolio becoming more concentrated from year to year. In the example above, I have seven loans in the portfolio, and I want to measure concentration. The HHI index based on the HHI formula would say that it's 21 percent HHI index. What I would do is, I'll measure that against other firms, other banks, other portfolios, or I'll measure that in terms of trends from period to period. Now, I can eyeball this. I eyeball this, I see 15 percent, 10 percent, 11 percent, 12 percent, 37 percent, anything that's above 10 percent. But I also can use a metric so as I measure concentration from period to period. It is called a Herfindahl-Hirschman Index. It is one way of being able to assess concentration, whether it's increasing or decreasing from period to period. Correlation risks. Concentration can lead to correlation risks. Correlation is looking at the loans in the portfolio and determining whether they will default at the same time. It could be loans in different industries, different geographies, and different countries. They could be seemingly very independent loans. What is the probability that all the loans or large groups of loans will default at once? This is a very simplistic portfolio. More complicated portfolios would include a bank loan portfolio. It could be loans that are in certain countries, loans that are in certain states, loans in a certain industry. What's the probability that they're both one group of loans, one set of loans that default at the same time? What's the probability that we'll have clusters of default? How does that correlation have impact, not only the probability that large groups of loans could all default at once but also in terms of calculating unexpected loss in the portfolio? The more highly correlated that the loans are in the portfolio, then, therefore, the higher the losses or the unexpected worst-case losses that we would expect to see in the portfolio. There are different ways of approaching this. I think the most important is to identify and understand what is correlation risk, we more specifically call it default correlation. How do these loans in terms of how are they interrelated, how are they related? Are there factors that influence one set of loans and also influence a 2nd set which will contribute to large clusters that default at the same time? Once you understand what we're trying to get at, then we try to quantify that. Now, we can look at that in terms of loans in the same industry or the more highlighted could be kept default correlations that are high, loans that might be subject or influenced by the same factors. Two companies, two sets of loans that are in two different industries may be influenced or may be susceptible to some of the same factors as well. We could consider that there are a lot of situations last year that companies and very different airlines, travel and hospitality, entertainment industries have very different loans, different companies, but they're all susceptible to some of the same factors which could contribute to clusters of default. Portfolio managers understand what correlation is. Sometimes they struggle with how to actually quantify it. Now, we're not going to spend that much time in this particular course to try and just go through some of the history of how risk managers have had tried to quantify and address it. There is the Basel III when it relates to bank regulation. [inaudible] three has an approach as well. As I had mentioned that to calculate the capital requirements for a loan portfolio, it calculates unexpected loss, and then it adjust that for correlation, makes certain assumptions and adjust for correlation. The performance, let's summarize it without going too far in that, because that's beyond the scope of what we're trying to cover in this session. The performance of individual loans can be correlated. Defaults on certain individual loans can occur at the same time, if they are highly correlated. Then if the probability of default can be derived or determined and if expected loss and unexpected loss are calculated, then how do we adjust those calculations for correlation. That's the objective here. Whatever model, assumption or approach that we use, we're trying to treat objective of adjusting for portfolio default correlation. Risk managers try to find the most effective method to address that correlation. Now, one quick example of the impact of correlation. Let's just make a simple example. I have Loan 1 and then I have Loan 5. Let's assume that we're looking at them independently. This loan has a probability default of 0.5 percent. This loan has a probability default of 2.0 percent. If they are highly correlated, and if therefore the default probabilities are highly correlated, then what's the probability if they are 100 percent correlated and what's the probability that they will default at the same time? What that means here is that they have independent problems, 0.5 percent and 2.0 percent. If they're 100 percent correlated, that means that Loan 5 defaults, Loan 1 is going to correlate no matter what to default probabilities for Loan 1 is. That means that if they are 100 percent correlated, that means that if Loan 5 defaults, Loan 1 will default also, which means, I might have to adjust this default probability to reflect the same default probability of Loan 5. So 0.5 percent default probability is understated, I might need to adjust it to 2.0 percent to account for 100 percent correlation with Loan 5. I guess more complicated because in my portfolio here I have seven loans and I have over 40 possible pairings and a large number for it. I can have millions of possible pairings. I'm explaining the challenge in dealing with correlation, but we tried to at least acknowledge it and then try to come up with suitable methodology to at least account for the correlation. I don't want to ignore it, I want to understand what the possible impact could be. In this case here, going back to the same hypothetical portfolio, if performance correlations are not among the pairs of loan assets, can we assume that default correlations are similar with this example that we just used? How should we adjust the model in terms of calculating unexpected loss to account for all the different loan pairs, and then, how do we approach default correlations in terms of a distribution tail? You remember it? Then basil 3 computation, it looks at the expected loss and it looks at a normal distribution around the expected loss. It can calculate the unexpected loss based on volatility or variance and probabilities of default, and then also calculate the unexpected loss so that there's the notion that the more highly correlated or the more impact of correlation on the portfolio, the fatter the distribution in my distribution, not portfolio losses. Correlation will increase my unexpected loss. Once we understand those principles, we have to adjust on what model or approach we're going to do to account for that. That's beyond the scope of this, but I think that's important to understand. Let's not ignore correlation and let's understand the complications that are introduced by correlation as you try to calculate expected loss and unexpected loss in the portfolio.
