Calculating Expected Credit Loss Across Bond Ratings

Summary

The document shows how to calculate a portfolio’s one-year expected credit loss when it contains bonds with different ratings, default probabilities, and recovery rates. For each bond group, it multiplies exposure at default by probability of default and loss given default, where loss given default is one minus the recovery rate. It then adds the group-level expected losses to obtain the portfolio total.

The example applies this method to A-rated and BBB-rated bonds and reports a total expected loss of $0.77 million. The calculation uses the stated exposures, default probabilities, and recovery assumptions. It treats the groups’ expected losses additively; their independence is not needed to calculate the mean loss, though it would matter for analyzing the distribution of portfolio losses or the probability of extreme outcomes. The result is an expectation, not a forecast of the realized loss in any particular year. The document does not address uncertainty in the inputs, changes in exposure, or dependence between defaults.

Key ideas

• Expected credit loss is calculated as probability of default multiplied by loss given default and exposure at default.
• Loss given default equals one minus the recovery rate.
• Calculate expected loss separately for each bond group and add the results.
• The portfolio expected loss is an average measure and does not describe the range of possible realized losses.

Tags

# Calculation Expecting Credit Loss from a Portfolio


# Calculation Expecting Credit Loss from a Portfolio












I have the following question:

An investor holds a portfolio of 50 million dollars. This portfolio consists of 'A' rated bonds (30 million dollars) and 'BBB' rated bonds (20 million dollars). Assume that the one-year probabilities of default for 'A' rated and 'BBB' rated bonds are 3 and 5 percent, respectively, and that they are independent. If the recovery value for 'A' rated bonds in the event of default is 70% and the recovery value for 'BBB' rated bonds is 50%, what is the one-year expected credit loss from this portfolio?

How is this calculated with two differently rated bonds?

## Answer by alexbougias (score 2, accepted)

https://quant.stackexchange.com/a/59943

The expected loss (in dollars) is defined as

$$ \mathbb{E} (L)= \underbrace{PD}_{\text{default probability }} \times \underbrace{LGD}_{\text{loss given default }} \times \underbrace{EAD}_{\text{exposure at default}}$$

For your portfolio, the expected credit loss is \begin{aligned} \mathbb{E} (L_{portfolio}) & {} = \mathbb{E} (L_{A})+\mathbb{E} (L_{BBB}) \\ &{} = PD_A \times LGD_A \times EAD_A+ PD_{BBB} \times LGD_{BBB} \times EAD_{BBB} \\ & {} = 0.03 \times 0.30 \times $30m + 0.05 \times 0.50 \times \\\$ 20m \\ & {} = $0.77mn \\ \end{aligned}

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.