In the last chapters, we introduced customer-centricity and risk management as the cornerstones of a modern business strategy. To make these strategies actionable, financial institutions need tools that connect risk with pricing and profitability. Two such tools are risk appetite and relationship pricing.
Before we explore them in detail, we must first establish a common foundation: the concept of Risk-Adjusted Return on Capital (RAROC). RAROC connects risk, expected return, and capital requirements into one framework. It allows financial institutions to accelerate loan approvals, strengthen transparency, and make informed pricing decisions.
This first part introduces the basic building blocks—Probability of Default (PD), Loss Given Default (LGD), and Exposure at Default (EAD)—and explains how they combine into Expected Loss (EL) and Unexpected Loss (UL). In the next article, we will apply these findings to RAROC, risk appetite, and relationship pricing.
Quantifying Credit Risk: Three Variables
Credit risk can be broken into three measurable factors:
1. Probability of Default (PD)
The likelihood that a borrower will default within a given timeframe, usually one year.
Example
- A PD of 5% means that, out of 20 similar loans, on average, one will default in the next 12 months.
Note
- PDs are derived from rating models, which we will explore separately.
2. Loss Given Default (LGD)
The share of the exposure that the bank loses if default occurs.
Driven by recoveries, such as collateral sales.
Example: If a borrower defaults on $5,000 and collateral recovers $3,000, the LGD is 40%.
3. Exposure at Default (EAD)
The amount outstanding when default occurs.
For credit lines, the EAD is often close to the full limit.
For amortizing loans, the EAD depends on when in the loan’s life the default occurs.
Expected Loss: The Cost of Doing Business
The formula is simple:
Expected Loss (EL) = PD × LGD × EAD
Think of EL as the insurance premium of lending. It represents the average credit cost that institutions must provision for.
Example:
A loan of $10,000 with PD = 5%, LGD = 40%, and EAD = 50% ($5,000) has an EL of $100.
This is the average expected loss across many similar loans.
At the portfolio level, expected losses balance out:
If 100 loans each have an EL of $100, the portfolio EL is $10,000.
Some loans will not default (loss = $0), others will default (loss = $2,000 each). On average, across many loans, the expected and realized losses converge.
Portfolio Exercises
To better illustrate the concepts, consider a portfolio of 100 loans, each $10,000, four-year amortizing, with PD = 5%, LGD = 40%, and EAD = 50%. Collateral averages $3,000 per loan.
1. Expected Loss of an Individual Loan
$10,000 × 5% × 50% × 40% = $100
2. Loss if One Loan Actually Defaults
With $5,000 outstanding and $3,000 recovered, the loss is $2,000.
3. Expected Loss of the Portfolio
$100 × 100 loans = $10,000.
4. How Many Loans Are Expected to Default?
With PD = 5%, we expect 5 loans to default.
Actual loss = 5 × $2,000 = $10,000.
5. What if Only 4 Loans Default (4%)?
Actual loss = 4 × $2,000 = $8,000.
Since provisions were $10,000, the bank shows a $2,000 surplus.
6. What if 6 Loans Default (6%)?
Actual loss = 6 × $2,000 = $12,000.
The $2,000 excess above provisions must be covered by equity.
Unexpected Loss: Why Equity Matters
While expected loss is provisioned for, unexpected loss (UL) represents the variability around the average. Some years, defaults will be below expectation, other years far above.
Unexpected loss is measured by simulating many scenarios (e.g., Monte Carlo simulations).
The distribution of losses is skewed: the upside is capped (zero defaults), but the downside is large (many defaults possible).
To remain solvent, banks must hold capital sufficient to absorb these unexpected losses.
Using regulatory approaches (e.g., Basel framework), we calculate both:
Expected Loss (EL): $100
Unexpected Loss (UL): $966.46
Total Economic Capital: $1,066.49 for the $10,000 loan (at 99.9% confidence).
This capital requirement ensures that the bank, in theory, only defaults once in 1,000 years.
What’s Next in the Series
With this introduction, we now understand how to quantify credit risk and determine the equity capital needed to support exposures. This foundation leads directly into RAROC (Risk-Adjusted Return on Capital), which uses these calculations to evaluate profitability.
In the next article, we will expand on RAROC and explain how it underpins two essential concepts: risk appetite and relationship pricing. These tools bring transparency, speed, and flexibility to credit decision-making and are critical for modern financial institutions.
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