CAR

[higaurav]

Hi David,

In this Question, why do we reduce 1 from 5.175 while calculating CAR..pls explain.

The annual credit volatility of an asset is 15%. What is 1-year credit at risk (CAR) on a 95% confidence level for a notional of $1 million? (Note: when the mean is 0 and the standard deviation of ln(x) is 1.0, the cumulative lognormal distribution at 5.175 equals 0.95.)

Rgrds,
OM

 

[David Harper CFA FRM]

Hi OM,

Because the mean of standard lognormal is *roughly* 1.0; i.e., LN(0) = 1.0.
So, under a credit distribution, it is treating the distance from 0.0 to 1.0 as the gain/profit (or arguably, the expected loss).

Analogous to, when we use the normal with -1.645, we implicitly mean: -1.645(vol) - (mean of 0) = -.1645 to get the distance from the zero. but the lognormal is not symmetric around 0, so we really want the standard deviations "to the right of 1.0."

However, this application dropped off the 2008 FRM when de Servigny Ch 6 was dropped...

David