# Difference between VaR and credit VaR?

Quick question: is there a difference between credit VaR and VaR or are they the same thing?

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They are different metrics.

As I understand it:

• Market risk VaR is a not a coherent risk measure, because it is not subadditive.

• Market returns are generally considered on a shorter time horizon relative to credit returns, which has implications for expected return drift (namely, credit return drift is likely more substantial, as credit is longer dated).

• Credit return distributions are also considerably more skewed.

Credit VaR effectively subtracts the expected portfolio value from a confidence cutoff value (often something like from 95 to 99.9 percentile). I.e. it is the value at the confidence cutoff less then expected value of the tail region for which it is the right bound. Malz has a bit more on credit risk VaR in Chapter 6.9.1 a

Somewhat Related (and confusing, since a few resources I have seen have referred to CVaR as either credit and conditional VaR):

Conditional VaR (or expected shortfall) is $\frac{\int_{-\infty}^c f(x) x \, \mathrm{d}x}{\mathbb{P}\{x \le c\}}$

where $c$ denotes the value threshold that corresponds to the percentile of interest. It is coherent.

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