Credit risk can be defined as the risk of losses generated by a change in the counterpart’s ability to perform its obligations.

It is a short definition that requires a quite long explanation.

Let’s start by analysing the keywords contained in the above definition.

Credit risk can be defined as the risk of losses generated by a change in the counterpart’s ability to perform its obligations.

when a financial institution grants a credit to an entity (it can be private, public, financial or non-financial) two main obligations arise, one for each part. The lender promises to credit the agreed amount of money to the borrower, while the borrower promises to repay its debt to the lender (plus interests).

Counterpart’s ability:
the borrower must be able to fulfil its obligations at each deadline. Every time a payment is due it needs a certain amount of money to pay the lender.

Risk of losses:
If the borrower doesn’t have the needed funds to perform the due payments, the financial institution won’t receive the money and will incur in a loss.

Before granting a credit the financial institution must be sure that the borrower will be able to meet its obligations in the future. The institution performs a risk assessment on the potential borrower, it basically conducts a series of analysis aimed to estimate the risk that the borrower’s ability to pay will deteriorate.

The word “change” is key to understand Credit risk. A bank cannot be hundred per cent sure that the ability to pay of its clients will remain untouched for all the duration of the loan, it simply cannot see into the future of its clients.

The bank makes an assessment of all the factors that can affect the borrowers ability to repay their loans, an event that generates a change.

The worst scenario occurs when the borrower’s creditworthiness changes so much that it becomes impossible to honour its debt and it becomes insolvent (borrower’s default).

As matter of facts, every time a bank creates a loan, it estimates the amount of money that can be lost in case of default of the borrower.

The main purpose of the Credit risk is the estimation of the potential losses generated by a default of the borrower, the so called Expected Loss.

I am now going to illustrate how credit risk and real economy interacts in practice using two pseudo-real examples.
The first one to clarify Expected Loss and the second to show the real effect of EL for the private non-financial sector.

To build the first example I introduce Mr. X and Bank A.

Bank A is, guess what, a bank.

Mr. X holds a mortgage with Bank A of 100.

The mortgage is backed by a real estate asset valued 120.

The Expected Loss (I will call it EL from now on) represents the sum of money that a bank is expected to lose on a given exposition, with a given probability and within a given period of time (usually one year).

In our example the bank exposition, with Mr. X, is 100, which in turn corresponds to the debt that Mr. X has with Bank A.

EL is calculated as product of three different components: PD, LGD and EAD.


Let me explain what each component is:

PD = Probability of Default.

It is the probability that Mr. X will not be able to fulfil its obligation (for instance, not be able to pay interest or principal when they come due) with Bank A within a given period of time.

EAD = Exposure at Default.

It is the outstanding of the Bank A toward Mr. X at the point in time when X goes in default.

In our example, EAD = 100

LGD = Loss Given Default.

It is net loss that the bank can lose if Mr. X goes into default. Back to our case, we know Mr. X has a debt of 100, if he defaults today his exposure at default is 100.

Does this mean that the Bank will lose all 100? It depends on the LGD value.
We also know that the mortgage is backed by a real assets valued 120. When the mortgage holder defaults tha bank takes possesion of the asset and presumably put it on sale.
Let’s say that the bank realises 90 from the asset sale, this 90 is a positive cash flow that decurts the pending loss deriving from Mr. X’s default.
The net loss is then, the 100 defaulted exposure minus the recovered 90. Of the initial 100 exposure the bank has recovered 90.

Bank A’s recovery rate:

RR = 90 / 100 = 0.9

How much is the loss given default?

We take the net loss and divide it by the exposure at default:

LGD = (100 - 90) / 100 = 0.1

which is equivalent to:

LGD = 1 - RR = 1 - (0.9) = 0.1

Can LGD be negative?

It can happen, this means that the bank managed to recover more that the actual exposure at default.

I gave you a basic explanation of what PD, EAD and LGD are, in practice banks estimate each component with more or less complicated statistical models (I will deal with them in the future)

There are formal rules that lead the banks throughout the EL assessment; the main framework in place today is the Basel Accord. The accord contains rules and prescriptions that the adhering banks has to follow when estimating PD, LGD and EAD.

From now I will focus more on the Probability of Default since it is the dominant component of the Expected Loss.

PD is the primary component when determining the EL. All banks adhering to the Basel agreement are required to estimate a specific PD for each exposure class included in their portfolio (there are limited exceptions to this rule).
The Basel agreement stipulates three approaches for estimating the EL components: Standardised, Internal Rating Based Foundation and Internal Rating Based Advanced.

Standardised: the bank does not directly estimate the EL components but exploits those specified by the regulations (it is used in very few cases today).

Internal Rating Based Foundation: the bank estimates internally only the PD while taking LGD and EAD stated in the regulation.

Internal Rating Based Advanced: the bank estimates internally all three components, PD, LGD and EAD.

Today all the major financial institutions utilizes the approach Foundation or Advanced, and if we look closely to the share of the private non-financial sector which directly or indirectly depends on the credit policies of these institutes, one can see that a large part of our real economy depends of the credit risk model developed by those banks. Households, small medium enterprises, large corporate and even sovereign governments are directly affected by the EL estimates of the credit institutions.

EL plays a key role in the credit market in two different circumstances: acceptance on new credit applications and pricing of existing credits.

Almost all the models through which a bank grants a loan and/or asses the interest rate to be applied on a loan are risk based, thus they directly depend on the EL estimate and thus on the PDs (and LGDs).

PD estimates are generated by a statistical model whose input variables are a set of demographic, economic and financial factors, and the output is a probability (a number between 0 and 100). This probability represents the score that the bank assigns to each customer (both new and existing), the closer is the PD to 0 the higher is the customer’s score.

Let me introduce the second pseudo-real example.

Bank A has implemented a PD model for new mortgages applications with these characteristics:

PD = household income + household employment status + household credit records.

Household income, employment status and credit records are the input variables. The variable selection as well as the determination of corresponding weights for each PD model is performed by exploiting a statistical model (or more than one if needed). I am not going through the statistical model in this introduction, it will be part of another section (not yet completed). Here I just deal with PDs in a qualitative manner.

The case.

Mr. X and Mr. Y desire to buy an apartment, they walk in to the bank and are both granted a new mortgage loan.

Mr. Z also wants to obtain a mortgage but when he goes to the same bank but he is refused the loan.

Mr. X has been granted a floating interest rate of 3.1% while Mr. Y received 4.2%.


Why have Mr. X and Mr. Y been granted the mortgage while Mr. Z has not?

Why has Mr. X received a lower interest rate compared to Mr. Y (3.1% vs 4.2%)?


The answer to these questions lied in the PD model.

Let’s take a look to input factor to the PD model for each counterpart.


Mr. X’s household is composed of two adults and a child, both adults are full time employed, medium high salary and never registered any payment remark.

Mr. Y’s household is composed of just two adults, he works full time and his wife is part-time employed, medium salary and no payment remarks.

Mr. Z’s household consists of two adults and two children, both adults are full time employed, medium high salary but in the last 12 months they have miss three payment deadlines (car loan 10dd, TV installment 12dd and tax payment 54dd)

The input factors have a different weight for each individual depending of the value that each individual support on the input factors of the PD model (household income, household employment status, household credit records).

For instance, the input variable household income will weight more for a subject with 100 income compared to a one with 10000 income.

From the example we can see that both the acceptance of a new loan by the bank and the price of it (interest rate applied) depends of the PD.


Whether you are granted a loan or not depends on your PD.

The interest rate you pay on a loan depends on your PD.

Acceptance and Pricing are risk based.

If we go back to the Expected Loss definition, we can now analyse what would happen to the bank A if Mr. X goes into default; following the Basel definition of default, Mr. X is in default if he delays a payment for more than 90 days.

Mr. X’s PD is 3.1% (probability that Mr. X will go into default within the next 12 months = 3.1%).

Mr. X’s LGD is 45% (we assign a fixed value to LGD, if X goes in default the bank expects to lose 45% of the outstanding with Mr. X).

Mr. X’s EAD = 100$ (Mr. X’s outstanding at the time of default).

Mr. X’s EL is then calculated as follows:

EL = 3.1% * 45% * 100$ = 1.395$

The quantity 1.395 is the amount the bank A is expected to lose in case X defaults.

If we aggregate the same calculation per portfolio level, we obtain the EL estimate for Retail, SME, Large Corporate, and Sovereign and so on.

This is a very important quantity since it will directly affect both the Regulatory Capital Requirement and the Risk Capital of the bank.

The Core Tier 1 ratio for instance, which is extensively used today in those pointless stress tests made by the EBA (European Banking Authority) is calculated as the ratio of core equity capital and risk weighted asset (where the latter is a direct function of the EL and the PD).

Another important indicator, also used in the EBA stress tests is the NPL (Non-Performing Loans) ratio. This is the ratio of the “bad” loans divided by the sum of all the loans. The higher is the NPL of a portfolio, the higher must the PD estimate of the bank for that segment be.


More to follow on these topics…