# Difference between VaR and credit VaR?

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

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.

I would like to bring this topic back to life as I believe it calls for some further explanation and disambiguation of definitions.

VaR - Value at Risk - is a statistical technique which, given some parameters (horizon, confidence interval, look-back period) and estimation methodology, attempts to forecast the worst possible loss of my portfolio (with a given confidence) at any given horizon. So, for example having a portfolio on which I calculate a 99% 1-day VaR and found it to be 100k, the results could be interpreted as following, at any given one day, with 99% certainty, my portfolio is not expected to loose more than 100k.

Typically, how this is done is, by decomposing all assets of the portfolio into relevant risk factors (factors relevant for its valuation) and simulating their behavior, re-value the entire portfolio. Such factors can be swap curves, FX rates, credit spreads, equity prices, equity indices, implied volatily etc. This approach as it is evident, concerns market risk factors and how they on a day-to-day affect the performance of the portfolio.

Credit VaR - this statistical technique (various implementations and methodologies) provides a measure of the portfolio's risk given changes in the value of debt caused by counterparty default or deterioration of that counterparty's credit worthiness. Furthermore, intra-portfolio asset correlation is an important aspect here (a lot of discussion can be made around this topic and various methodologies have been developed). As it is evident, this type of technique most closely concerns debt portfolio with longer horizons.