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Distance to Default Is Measured in Standard Deviations

Article Quant Q&A · Author: balteo
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Summary

The document clarifies that distance to default is expressed in standard deviations, not in units of time such as years. It describes the measure as a firm’s distance from a default threshold in a statistical framework, so a larger positive value indicates greater separation from that threshold under the model’s assumptions.

The answer converts distance to default into a default probability by applying the standard normal cumulative distribution function to its negative. For the stated value of 2.978, it reports an estimated 0.15% probability of default over the next period and explains that the calculation is single-tailed. That probability depends on the model and on what “next period” represents; the document does not define the period length or discuss estimation assumptions, calibration, or alternative default-risk models.

Key ideas

  • Distance to default is expressed in standard deviations rather than years.
  • The answer maps distance to default to probability using the standard normal cumulative distribution function.
  • The conversion uses the negative of the distance to default and treats default as a single-tailed event.
  • The stated probability applies to the next period, whose duration is not specified in the document.
  • Interpreting the probability depends on the assumptions of the model used to estimate distance to default.

Tags

Fixed incomeRisk managementStatistics
Full text
# What is the unit of the Distance to Default measure?


# What is the unit of the Distance to Default measure?












I read in a book that the distance to default of a company is "2.978". Can anyone please tell me what is the unit implied behind this measure? Are they "years" for instance?

## Answer by Richard Herron (score 10, accepted)

https://quant.stackexchange.com/a/1289

Distance to default $DD$ should be measured in standard deviations. You convert this into a probability $p_{default}$ using the normal CDF: $p_{default} = N(-DD)$. So if $DD = 2.978$ then the firm is about 3 standard deviations from default and has a $\frac{1 - 0.997}{2} = 0.0015 = 0.15 \%$ chance of defaulting in the next period. I divided by two because this is a single-tailed test.

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