Expected Credit losses method for loan portfolio modelling

This is part of the series of posts, explaining the valuation on NPL portfolios. In this post I am describing how modelling process of the future credit losses. So, let’s start.

Overview

The Expected Credit losses method uses three parameters and each of the parameters is modeled separately with different inputs (economic indicators, portfolio inputs). For each individual account, the expected loss during the course of next 12 months can be formulated as:

Credit Loss Projections = Exposure at Default * Probability of Default * Losses Given Default

Or

CLP = EAD * PD * LGD

This modeling methodology is in line with Basel framework but, also, has following advantages over traditional methods for loss forecasting. (Quoting from another blog).

1. The account-level modeling practice provides a distinct risk profiling for each individual borrower.

2. Each risk parameter is driven by a separate set of economic factors independently, allowing a more dynamic view of economic impacts

3. The modeling methodology is in line with statistical techniques prevailing in the consumer lending arena and intuitively adoptable by most model developers.

4. Since this methodology heavily relies on statistical modeling concepts, the loss estimation is subjected to specific statistical assumptions on distributions and functional forms.

Source: Yet another Blog in Statistical Computing

Here we see the value of Loan assessment exercise we have done in the previous step, because with these inputs we have increased the model’s predictive power, as we managed to:

1. Collect data — Got a history of ratings, found the amount of data which were missing and avoided sample biases

2. Analyse Data — Reconsolidated them in a common format that could be used in our models (floating rate, amortization vs bullets, default rating)

3. Get historical performance — Constructed statistical relationships between performance and macroeconomic factors that allowed for a better predictive power to the model.

4. Make collateral analysis — Categorized them and made forward looking value curves using 3rd party data to get a better picture of the future liquidation value (e.g. Real estate value increase/decrease relative to GDP growth)

5. Understand Loan and country specific factors — Got findings that could be used in the model such as recovery timeline, treatment of modified loans, unsecured recovery assumptions

Now, wearing the quantitative hat, let’s look each of the parameters separately.

EAD — Exposure at default

That might be the easiest of the three; it is the entire funded balance. However, if applicable, it should include an additional amount as an assessment of future draws on existing commitments of the bank to the borrower.

eg. EAD = 100% of the current balance +10% of unfunded commitment

Regarding the amortization, we can take an average, and then we work with scenario (Base case, Worst case). Having the information from the loan review, we can double check the validity using historic data points.

For the balance given from the bank, adjustments might be required for any defaulted loan that was not presented in this category (e.g. it was presented rescheduled).

PD — Probability of default

Here, we are heading to more “black box calculation” and the best we can do is to describe the process used by Blackrock, adjusted to a corporate loan portfolio.

To determine the default rates, Blackrock used a regression based model that associated bank’s ratings to their Master ratings, and to defaults probabilities.

Using outcomes of the loan review exercise and past experience, they mapped bank’s rating to a master rating (e.g. may be the C-Rest could be a default in real life) after they have cleaned, homogenized and having taken out any possible sample bias.

Therefore, now, there is an association of bank’s rating with a rating that we can use in the model. However, the need still exists for understanding how outside economic factors affect the rating downgrade and consequently the PD.

We use the initial master rating and the factor with the highest correlation, which is unemployment rate. Using three main variables, we can model the PD.

• Initial Rating (+ positive sign) — Starting point and best sort term prediction factor to default
• Unemployment rate annual change (+ positive sign) — Highest correlation factor in a regression with default
• Rating * Time since rating (- negative sign) — Reflections of the diminishing predictive power of the starting rating for the future forecast (the negative sign shows this diminishing effect)

Going to PD is done through a formula taking into account the above mentioned factors. This is truly black box, and I am not aware of the weighting of each factor but just a simple indicative formula that was given to the Bank of Greece.

PD = 1 / (1 + e^(a+b’X))

LGD — Losses given default

Here, we must predict, what would be the recovery value for each year for the defaulted loans. Knowing the recovery value in year 0, we need to predict a floor (i.e the minimum cash, we expect to get) and secondarily, how the value of the collaterals will change through time.

Therefore, having mapped the loans with the type of collateral, they have (eg. Loan X has 50% cash deposit, 50% real estate), we can predict recovery value when loan x defaults after y years)

So the whole process is:

1. Collect collateral data and link them to loans

Get data from the bank (in the form of a data tape) and assign them to each loan, there are a lot of issues that can arise but I might discuss in another post.

2. Rebase collateral values to date 0

Use a specialized index to rebase them at time 0 (If applicable e.g. cash value is the same), making adjustment across all the loans. Else, if there are few and of high worth, you can do new valuations for each of them, or a combination of the two.

3. Forward value adjustment and recovery timeline

For recovery lag, we use the experience from loan review, as the legal framework is different in each country, and use it in case of default. For adjusting collateral valuing, we use an index (e.g. Central bank’s real estate index projection).

4. Collateral haircuts

For each type of tangible collateral (i.e real estate, cash, inventory) when liquidated, the real recovery value is lower due to legal and administrative fees. Therefore, using past cases from the loan reviews and 3rd party opinions (i.e. layers, liquidators), for each type of collateral haircut factor should be assigned to get a table like this one.

So, the Final haircut would be:

Liquidation haircut = Re-Based bank Market value x (1 — Overvaluation discount) x (1 — total expected liquidation, enforcement cost, preferential claims)

5. Assign realizable value to exposure

Finally, we assign the floor recovery value to each loan and with that we have all the factors of the formula to calculate Credit losses projections.

Closing

Of course, like every valuation, it is harder than it sounds. This method is very time consuming and experience plays a crucial part. The process described need cooperation of the bank, therefore is not always used and it is usually for the final stage of the negotiations.