VaR - It refers to the maximum potential loss which shall not be exceeded during a specified period of time with a given probability level.
Example - our portfolio would not lose more than, say 10% with a probability of
VaR requires two parameters
1. confidence level
2. Time Horizon
Types of VaR calculations
- unconditional VaR, based on the unconditional distribution of the underlying risk factors; and
- conditional VaR, which assumes that the relevant distribution and/or parameters could change over time.
Choosing VaR
A financial institution monitoring the daily activities of its traders is likely to use 95% confidence level.
When dealing with capital requirements, supervisory authorities usually adopt a 99%confidence level.
On the other hand, the Basel Committee on Banking Supervision (BCBS) sets the confidence level at a remarkably high 99.9%
There are two main methodologies for VaR calculation:
- parametric method, which uses a specific parametric distribution function like a normal distribution or a t-distribution; and
- non-parametric or historical method, which uses the empirical distribution obtained directly from the historical data
- unconditional VaR, based on the unconditional distribution of the underlying risk factors; and
While assuming stationarity may not always be wrong as there are periods in which underlying risk factors are stable, over longer time horizons, that assumption does not hold. As such, we distinguish between two additional types of calculations:
- conditional VaR, which assumes that the relevant distribution and/or parameters could change over time.
Criticism of VaR
1. Liquidity risk.
2. Model risk.
3. Quantiles of distributions do not tell us the whole story.
4. Lack of subadditivity