Credit Risk – Default Probability and Loss Severity

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

• default risk or default probability: probability that a borrower will violate the terms of the debt security;
• loss severity or loss given default: the portion of the value of a bond, including unpaid interest, an investor loses in the event of default.

Expected Loss

Credit risk is reflected in the distribution of potential losses that may arise if an investor is not paid in full and on time. It is common practice to summarize the risk with a single default probability and loss severity so as to simply focus on the expected loss:

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

Loss Severity

Loss severity could be expressed either as a monetary amount (e.g., $250,000) or as a percentage of the principal amount (e.g., 35%). In addition, 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:

1. $40,000
2. $160,000
3. $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