### Credit Risk – Default Probability and Loss Severity

The credit risk is the risk of loss resulting from a borrower’s (debt issuer) failure to make full and timely payments of interest and/or principal. Credit risk is made up of 2 components:

1. Default risk or default probability: Probability that a borrower defaults in accordance with the terms of the debt security.
2. Loss severity or loss given default: The portion of a bond’s value including unpaid interest an investor loses in the event of default.

## Expected Loss

The credit risk is reflected in the distribution of potential losses that may arise if the investor is not paid in full and on time. It is often preferred to summarize the risk with a single default probability and loss severity to simply focus on the expected loss:

$$\text{Expected loss = Default probability} × \text{Loss given default}$$

The loss severity could be expressed as either a monetary amount (i.e., $250,000) or as a percentage of the principal amount (i.e., 35%). The loss severity, or loss given default, is also expressed as (1 – Recovery rate), where the recovery rate is described as the percentage of the principal amount recovered in the event of default. ## Question An analyst estimates that a bond issue has a 20% probability of default over the next year and the recovery rate in the event of default is 80%. If a firm holds$1 million worth of this bond issue, then the expected loss is closest to:

A. $160,000 B.$40,000

C. $640,000 Solution The correct answer is A. Expected loss = Default probability × Loss given default Loss given default = (1 – Recovery rate) = 1 – 80% = 20% Expected loss = 20% × 20% = 4% In dollar amount:$1 million × 4% = \$40,000

Describe default probability and loss severity as components of credit risk

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