Value at Risk - Definition of VaR
5 important questions on Value at Risk - Definition of VaR
1. How do you choose the time horizon for the VaR calculation?
2. Give some typical time horizons.
The choice of the time horizon should reflect the time period over which a financial institution is committed to hold its portfolio. This period may be affected by contractual and legal constraints and/or liquidity considerations.
Typical time horizons are: 5 years, 1 year, 1 month, 10 days and 1 day.
Let mu be the mean of the loss distribution. Define the mean-VaR.
Why do we use the mean-VaR in credit risk management?
VaR(mean) = VaR(a) - mu
a = alpha
We use the mean-VaR in credit risk management to determine economic capital against losses in loans.
When do we say that the mean-VaR is the daily earnings at risk in risk assessment?
When we consider a 1-day time horizon.
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Suppose that the loss distribution FL is normal with mean mu and standard deviation sigma. We fix a (alpha) in the interval (0,1). Denote the VaR and the mean-VaR.
VaR = mu + sig*phi^-1(a)
mean-VaR = sig*phi^-1(a)
phi^-1(a) is the a-quantile of a standard normal distribution.
In what theoretical situations is the VaR a coherent measure?
The VaR is coherent in the case of elliptical distributions. The normal distribution is a special case of elleptical distribution. This means that the VaR of a portfolio created with independent 'normal' investments is subadditive.
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