Variance-covariance method
Also known as the parametric method, the variance-covariance method assumes that gains and losses follow a normal distribution and expresses potential losses as events measured in standard deviations from the mean. So, rather than rely solely on historical data, this statistical model will assume wins and losses along a normal distribution pattern, also known as a bell curve, on which the historical patterns are overlain to model possible outcomes.
Monte Carlo method
You can also use a Monte Carlo simulation to model the value at risk of a given investment or portfolio. Using computational models, random possible projected returns are simulated hundreds or thousands of times and the results are then used to calculate the value at risk according to the worst-case scenarios.
Components of value at risk
Value at risk calculations can be very complicated, but they have just a few major components:
- Time horizon. The time horizon influences how sensitive the VaR is to market movements, and can be any range of time that you want to examine.
- Confidence level. Expressed as a percentage, the confidence level is how certain the model is about the outcome. For example, a 95% confidence level with a VaR says that there's a 5% chance that the loss will exceed the calculated VaR, but a 95% chance that it will be within the model.
- Volatility estimation. You have to know how much uncertainty to include in your model; that's where the volatility estimation comes in. This is often determined by other statistical models.
- Return distribution. Often, a normal distribution (a bell-shaped curve) is assumed with VaRs, but any kind of return distribution can be possible in a model – and more importantly, in real life.