Loss Given Default (LGD) Calculator

1. What is the Loss Given Default (LGD) Calculator?

Definition: This calculator computes the loss given default ($ LGD $), the amount of money an investor is likely to lose if a borrower defaults, based on recovery rate, loss severity, and expected exposure.

Purpose: Helps investors and risk managers assess potential losses in credit investments, aiding in risk assessment and loan pricing.

2. How Does the Calculator Work?

The calculator follows a three-step process to compute the LGD:

Formulas:

$ LS = 1 - RR $

$ RR = 1 - LS $

$ LGD = EE \times LS $

$ LGD = EE \times (1 - RR) $

Where:

$ LGD $: Loss Given Default (dollars)
$ RR $: Recovery Rate (decimal)
$ LS $: Loss Severity (decimal)
$ EE $: Expected Exposure (dollars)

Steps:

Step 1: Determine recovery rate or loss severity. Input one value (e.g., $ RR $ or $ LS $); the other is calculated as $ LS = 1 - RR $ or $ RR = 1 - LS $.
Step 2: Determine expected exposure. Input the amount of investment ($ EE $).
Step 3: Calculate LGD. Compute $ LGD = EE \times LS $ or $ LGD = EE \times (1 - RR) $.

3. Importance of Loss Given Default Calculation

Calculating LGD is crucial for:

Risk Assessment: Quantifies potential loss in case of default, critical for credit risk modeling.
Loan Pricing: Helps lenders set interest rates to compensate for expected losses.
Portfolio Management: Assists in balancing risk across credit investments.

4. Using the Calculator

Example (Company Alpha): $ RR = 80\% $, $ EE = \$1,000,000 $:

Step 1: $ RR = 0.80 $, $ LS = 1 - 0.80 = 0.20 $ (20%).
Step 2: $ EE = \$1,000,000 $.
Step 3: $ LGD = 1,000,000 \times 0.20 = \$200,000 $.
Results: $ RR = 80.00\% $, $ LS = 20.00\% $, $ LGD = \$200,000.00 $.

An LGD of $200,000 indicates a 20% loss on a $1,000,000 exposure if Company Alpha defaults.

Example 2: $ LS = 40\% $, $ EE = \$500,000 $:

Step 1: $ LS = 0.40 $, $ RR = 1 - 0.40 = 0.60 $ (60%).
Step 2: $ EE = \$500,000 $.
Step 3: $ LGD = 500,000 \times 0.40 = \$200,000 $.
Results: $ RR = 60.00\% $, $ LS = 40.00\% $, $ LGD = \$200,000.00 $.

An LGD of $200,000 reflects a 40% loss on a $500,000 exposure.

Example 3: $ RR = 90\% $, $ EE = \$2,000,000 $:

Step 1: $ RR = 0.90 $, $ LS = 1 - 0.90 = 0.10 $ (10%).
Step 2: $ EE = \$2,000,000 $.
Step 3: $ LGD = 2,000,000 \times 0.10 = \$200,000 $.
Results: $ RR = 90.00\% $, $ LS = 10.00\% $, $ LGD = \$200,000.00 $.

An LGD of $200,000 indicates a 10% loss on a $2,000,000 exposure, suggesting high recovery potential.

5. Frequently Asked Questions (FAQ)

Q: What does LGD represent?
A: LGD is the portion of an exposure lost if a borrower defaults, after accounting for recovery.

Q: Why input only one of recovery rate or loss severity?
A: They are inversely related ($ RR + LS = 1 $), so providing one calculates the other, ensuring consistency.

Q: Can LGD exceed expected exposure?
A: No, LGD is capped at $ EE $ since $ LS \leq 1 $.