PFE

[Kavita.bhangdia]

Hi All,
Gregory mentions that difference between VaR and PFE is that PFE is associated with the gain ( right tail), whereas VaR is associated with the loss ( Left tail).

But since right and left tail are mirror images in normal distribution, numerically VaR and PFE should be equal for a give confidence..

Please correct me if I am wrong..

Thanks,
Kavita

 

[ShaktiRathore]

Hi,
Var and PFE are different concepts while PFE is used to calculate the potential future exposure in the credit contract that is whats is the maximum exposure that the counterparty can have in a contract at a given confidence level whereas the Var deals with the maximum loss that a portfolio can suffer i.e. maximum negative return of portfolio at a given confidence level. maximum negative return of Var and the maximum exposure of the PFE are similar except that we calculate the maximum exposure from the right tail of the exposure distribution whereas we calculate the maximum negative return from the left tail of the return distribution of the portfolio.
Var = z1*sigma(Portfolio returns)
PFE=z2*sigma(Exposure to counterparty)
Yes you are correct upto a point that is for identical confidences the values of the normal deviate z should be the same numerically z1=z2 but the values of Var and PFE can differ based on the the different volatilities of the exposure(sigma(Exposure to counterparty)) and the Portfolio returns(sigma(Portfolio returns)).THerefore the VaR and PFE need not equal numerically.
What is sam

 

[David Harper CFA FRM]

@Kavita.bhangdia In addition to @ShaktiRathore 's point, there is also: it is true but only if the distribution is normal and the mean is zero. Just to tweak the standard normal, for example, say the drift (mean) is +0.2 and the volatility is 1.0. Absolute 95% VaR = -0.2 + 1*1.645 = 1.45; i.e., with positive drift, you'd expect to lose 0.2 less than 1.645. But the 95% PFE = +0.2 + 1*1.645 = 1.845. More realistically, while daily market VaR often can be approximated fairly with normal returns, PFE is based on a longer horizon where the credit exposure profiles are really never normal. VaR and PFE have one thing in common: they are both statistical quantiles of a distribution. Thanks,

 

[Kavita.bhangdia]

Thanks!