What is the unit behind Distance to Default?

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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?
Thanks in advance,
Julien.

 

[David Harper CFA FRM]

Hi Julien,

Distance to default, as often expressed (eg, 2.978), is a unitless standard deviation. In the specific case of Merton Model, it is the unitless standard deviation of a unit normal and is therefore a z-score (see http://en.wikipedia.org/wiki/Standard_score). So, in this typical case, the interpretation of 2.9 is something like "in the future [end of period], the default threshold will be 2.9 standard deviations below the expected asset value."

A bit more nuance: just as it is possible to express a standard deviation in dollar terms, you sometimes see DD = [$future firm value - $default threshold]/[$future firm value * %volatility]. This is the same idea but from a different perspective and technically this DD is the standard deviation of a lognormal distribution, so as a general case the DD is a standard deviation but not necessarily of a normal distribution.

Hope that helps, David