# 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?

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## 1 Answer

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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Thanks for your reply RichardH. Then what is the unit for the "next period"? – balteo Jun 6 '11 at 20:00
@balteo -- I don't know your data source, but I expect that it should be on an annual basis, because this is how firms report debt liabilities (i.e., they report debt liabilities due in the next year). – Richard Herron Jun 6 '11 at 21:28
thanks a lot! – balteo Jun 7 '11 at 8:12