# Week 2: Approaching Credit Risk

### Week 2: Approaching Credit Risk

#### Summaries

• Week 2: Approaching Credit Risk > Lesson 1: The Standardized Approach > Video Lesson
• Week 2: Approaching Credit Risk > Lesson 2: Internal-Rating Based Approaches > Video Lesson
• Week 2: Approaching Credit Risk > Lesson 3: An Introduction to R > Video Lesson
• Week 2: Approaching Credit Risk > Summary > Video
• Week 2: Approaching Credit Risk > The Sofa > The 2014 Sofa
• Week 2: Approaching Credit Risk > The Sofa > The 2015 Sofa

#### Week 2: Approaching Credit Risk > Lesson 1: The Standardized Approach > Video Lesson

• Or, to be more exact, we analyze in some little detail the standardized approach that, as you know, is the simplest approach banks can use to assess and hedge credit risk, under the Basel framework.
• Risk-weighted Assets are a very important quantity in risk management.
• In basic terms, that are a weighted sum of on-balance and off-balance sheet items, which are weighted using some specific risk weights.
• The credit equivalent amount is a measure used to quantify credit risk for off-balance sheet instruments, such as interest rate derivatives.
• The goal of the credit equivalent amount is therefore to translate the value of off-balance sheet items into risk equivalent credits.
• In this case, their principal amounts are multiplied by specific risk weights, which depend on the nature of the different items.
• In this case we sum the products of credit equivalent amounts and risk weights.
• We cannot enter into much detail in this introductory course to credit risk management.
• In the Standardized Approach, risk weights are set by the regulator and banks are simply required to compute their RWA using the previous formula.
• Risk weights are defined for classes of items, ordered according to credit ratings.
• As said in Week 1, capital requirements for credit risk are then equal to 8% of RWA.
• How do the risk weights look like? The table you can see on your screen contains an example of risk weights under the standardized approach.
• Looking at the table, we see that a BBB-rated government bond has a risk weight of 50%, or 0.5.
• A loan to a AAA-rated corporation has a risk weight of 20%, and so on.
• Notice the following: very often the risk weight for unrated items is lower than that of worst rated items.
• In the documents regulators publish periodically, we can find many other and different risk weights.
• For residential mortgages, the risk weight is usually around 35%. Ok, let’s consider an application.
• What is the value of our RWA? What is our capital requirement for credit risk? Ok, we start from the loans to A-rated corporations.
• What is the risk weight? Going back to the previous table, we discover that the risk weight for A-rated corporations is 50%, or 0.5 in decimals.
• In this case, the risk weight for AA bonds is 0%. Hence 10 times 0 is 0.
• Finally we have 60 million euros times 0.35, the risk weight for residential mortgages.
• Obviously the computation in real life includes many more items, often very difficult to assess precisely, by the idea is exactly the same! What are the capital requirements for credit risk in this case? We simply multiply 81 by 0.08, or 8%. The result is 6.48.
• Well done, risk managers! Ok we are done for the moment.

#### Week 2: Approaching Credit Risk > Lesson 2: Internal-Rating Based Approaches > Video Lesson

• The foundation Internal-rating based approach, and the advanced internal rating-based approach.
• It’s essentially a list of definitions and laws, so – I know- nothing very exciting, but it is something that we have to know, in order to correctly approach credit risk.
• What is the main difference between these two approaches? The main difference is that, under the Foundation IRB, banks are supposed to compute a quantity called PD, probability of default, and they are free to compute this quantity using the method they like, and we will see some methods in Week 4, 5, and 6.
• Now, banks have the possibility of choosing between the foundation and the advanced approach, within the IRB class.
• Typically banks choose this approach, if they don’t have very complex research units, because under this approach they simply have to compute the probability of default, and then all formulas are provided by the regulator.
• So you see the difference between the standardized approach, in which everything is provided by the regulator, and banks simply have to make – if you want – silly computations.
• In the Foundation IRB approach, compute the PD, which is much more sophisticated than, for example, the computations you can have under the standardized approach, but once they have this guy, they just plug in the probability of default within some formula, which is provided by the BCBS, and that’s it.
• Under the Advanced IRB approach, on the contrary, banks have much more freedom: they can compute many different quantities, and on the platform you will find the definition of all these quantities.
• These quantities are essentially computed through proprietary models, and once they have these quantities, they can compute the RWA.
• Under the Advanced approach, banks are free to compute more quantities, this is much more difficult, but for banks – we will see – that has obviously some advantages, in terms of the capital they have to keep in terms of capital requirements, and RWA, 8%….

#### Week 2: Approaching Credit Risk > Lesson 3: An Introduction to R > Video Lesson

• We will see some basic commands of this new software, and we will see how we can compute very basic quantities.
• If you need to store a given quantity into a variable, because you need to use it over and over again, you simply type something like: x=5.
• To see the content of a variable, you can type the name of the variable and press “enter” or “return”, or you can use functions like “print”.
• In R Studio, all the variables you have defined in the present session are given in the “Environment” space.
• Another way of creating variables is using the arrow “<-“.
• Once you have defined a variable, you can work with it in any operation.
• Notice that in typing x equal to c 2, 3 and so on, we have overwritten the old value of x. Now x is no longer equal to 5, but it is a vector.
• To compute the sum of all the elements in the vector.
• If we want to store this information in a new variable s, we can simply type s=sum(x).
• When you apply some specific operations, like the power operation or the square root, to a vector, R performs this task element by element within the vector.
• To select one specific element within a vector, we can use the square brackets.
• R possesses many useful functions to create special vectors.
• The function “length” tells us the length of a vector, that is the number of elements it contains.
• Sometimes it may be useful to substitute a single element within a vector.
• Just select the element you want to change, and assign the new value, as you can see on screen.
• With vectors we can also perform very useful logical operations.
• This command checks for the values, within vector u, that are strictly smaller than 8.
• Can you see what I am doing now? To delete a variable, we can use the command remove, or rm().
• The command is “plot”, and the names of the variables.
• Generating 100 observations from a standard Normal distribution, with mean 0 and standard deviation 1, is extremely simple.
• Easy, isn’t it? If you prefer a Gaussian distribution with mean 5 and standard deviation 2, the command slightly changes.
• We can plot another histogram, we can compute the mean, the standard deviation, the median, and so on.
• To read the help guide about the use of a specific function, just type ? and the name of the function.
• As you will see in the R manual, we can perform many other operations with vectors and variables.
• With vectors, we can sum them, we can multiply them element-wise, but we can also perform linear algebra computations.

#### Week 2: Approaching Credit Risk > Summary > Video

• We have seen that we have three major approaches: the standardized approach, and the two internal-rating based approaches, that is to say the Foundation and the Advanced internal-rating based approach.
• Ok, in any case, what we have said is that in the Standardized approach the risk weights are provided by the regulator, and the standardized approach is essentially meant for small banks, that do not have the money to invest in internal models, or banks that do not meet the minimum requirements for the internal-rating based approach.
• For what concerns the internal-rating based approach, we have seen together that there are some parameters, some functions, and some minimum requirements, that have to be taken into consideration by banks, when developing their approaches.
• Next week we will start introducing the Value-at-Risk, then we will introduce credit ratings in Week 4, and from that point on, we will really enter into the real modeling of credit risk.
• For the moment, I just want you to understand the big picture, which is behind credit risk management, and then we will introduce more and more details to fill in all the gaps.

#### Week 2: Approaching Credit Risk > The Sofa > The 2014 Sofa

• Together with my assistants, Tamara and Mitchell, I have selected some of your questions, and I will now try to give an answer.
• The question of Rachel is the following: to what extent do the course coordinators feel like the general principles of Basel II and III were and are followed in practice? So, officially the principles of Basel II and Basel III were and are followed.
• My personal idea is that, especially at the very beginning of Basel II, there was a lot improvisation, because people were not aware of all these new statistical tools they had to use.
• So you will see during this course that there is somehow a difference between the principles of the basel framework – that are totally correct and I would say that no one could disagree about those principles – and the way in which they are really implemented.
• There was no name for that question, and it is the following: does Basel II only affect banks? Are companies immune? Obviously the answer is no.
• So…companies -even if they are not banks- are affected by Basel II and Basel III, both directly and indirectly.
• If you are a company, and you go to a bank and you want to borrow some money from the bank, obviously you are subject to the credit evaluation of the bank, so the banks will assess your creditworthiness using the rules that are imposed by the Basel framework.
• If you are a company and your shares are traded on the market, or you are issuing bonds, in that case again you are subject to the Basel framework.
• If you ask me if the small ice-cream shop at the corner is subject to Basel directly in the assessment of the creditworthiness or in assessing the risk of its suppliers and vendors, I would say no.
• Edward asks: how does one manage the risk of unknown scenarios? This is a very good point.
• All the techniques we will see together, and in general all the techniques you may use in risk management, rely on one strong assumption, that is to say that you can always quantify the probability of an event.
• It can be a very very small probability, almost 0, but the idea is that you can always quantify that probability, that you can always express a probability belief about an event.
• Now, what happens if you cannot express that probability? Then you enter in a field that economists call Knightian uncertainty, from the name of Frank Knight, and that is to say you are in the field in which there are scenarios you are not even able to imagine, or that you cannot take into consideration in your actual assessment of risk.
• Would you have expected something like the web, like internet, that is to say the infrastructure that is allowing you to watch me speaking on my sofa? No. So, for example, there are many scenarios that can come up from science, from research, that we cannot even imagine at this very moment.
• This is very important, because it allows us to understand that, in order to be a very good risk manager, you surely need knowledge, you must be able to compute very often the most cumbersome quantities, you must be able to give an interpretation to these numbers, you must know the points of strength and the points of weakness of these numbers, but you also need to be humble.
• In the best situation, they are a sufficient approximation of the truth, but you always have to keep in mind that bad things can happen, and you cannot completely sterilise risk.
• There is a very strong discussion among scholars and practitioners with respect to this fact, that is to say that the past is not an optimal predictor of the future.
• Then there is a question of Xenu about emotional risk, and in speaking about emotional risk Xenu refers to the tendency of people to put money in the system at good times, and withdraw it at bad times.
• The idea is that, when you consider all investors, the great majority of investors – and I am speaking about small investors, not large institutional investors, banks and so on, but think about me, think about any other small investor… Very often what is observed on the market is that these investors behave like sheep, meaning that it is like they move in herds.
• Now, this effect is not taken into consideration directly and officially in the Basel framework, because it is very difficult to quantify such a behaviour.
• At the same time, the most recent econometric literature shows that inflation, and to be more precise inflation volatility and excessive inflation have a rather non-trivial impact on credit spreads.
• A lot of countries have a system in which it is very easy for students to borrow money from the government to pay for their education.
• How can the state be sure to get that money back? Ok the state cannot be sure about the possibility of getting its money back.
• You can lend your money to a AAA company, you can lend your money to a AAA country, the probability of default, the probability of losing money will be extremely low, very close to 0, but there is always a very very very small probability of default, and probability of losing money.
• So it is giving the opportunity to a student to lend money at very convenient rates and essentially with no pledge, it is doing that not to get the money back, but because it is investing in education, because they think that having educated people is very important for the economy, is very important for the society, it’s very important for the country.
• In that case, it is not really considering the possibility of getting money back what moves the government in allowing students to get money, not for free but at very convenient rates, and almost with no pledge.

#### Week 2: Approaching Credit Risk > The Sofa > The 2015 Sofa

• This week I have selected 3 questions from the course forum, and I would like to ask you to keep on posting your questions, because I think it is very interesting to see your point of view, to know your doubts, and to know your questions.
• William asks me: “Do you think it is necessary to introduce the concept of risk in younger generations? How can we do so?”.
• We need to teach people how to deal with randomness, how to deal with risk, and how to quantify risk.
• Claudio asks: “Do you think that the tightening by banks on residential mortgages and stricter requirements are direct consequence of the Basel III regulations?”.
• After this first period – and that can be condemned! – banks have preferred to have an easy life, by getting easy money from the central banks, at very convenient interest rates, and investing that money in, essentially, government bonds.
• What is Basel 4? And are we covering Basel 4 in this course? This is another nice question.
• Quite recently, the BCBS has released a consultative document that has bee called – unofficially – Basel 4.
• Not from the side of the Basel Committee, but essentially from the side of consulting companies.
• In this new document, the Basel Committee essentially proposes some modifications of Basel III.
• A more transparent disclosure of reserves for banks, and a better exchange of information on the market.
• It’s the point that, in this new Basel 4…in this Basel 4, the Basel Committee is essentially proposing to favor more standardized approaches, simpler approaches to risk – so, for example, in the case of credit risk, that would be the standardized approach, with respect to other approaches, for example the IRB ones.
• Why this? We can see essentially two goals for the Basel Committee.
• From the other, there is also the desire of limiting, of constraining the natural desire of banks to reduce their capital requirements by using fancy models that are very nice from a mathematical point of view – I do love them, I teach them to my students in the Master Applied Mathematics here at TU Delft, but these models sometimes are quite tricky, and it can be difficult to assess the intrinsic risk, what we can call the model risk of these approaches.
• Model risk is essentially the risk that the model you are using to identify, to assess and to hedge risks is not correct.
• So I think this idea of moving towards a more conservative approach, and towards a simpler approach like the standardized one is surely not a bad idea.
• Are we covering Basel 4 in this course? The answer is no, because the vagueness about Basel 4 is still very large.
• Also for Basel III, in the next months, in the next years, we can see changes, so you can imagine for Basel 4.
• Probably, it is too early, at this moment, to consider Basel 4.
• Who knows, maybe Basel 4 will be part of next year course.