Everything that's not linear. For example, options are thought of as nonlinear exposures, because they respond differently to changes in the value of the underlying instrument depending on whether they are in-the-money, at-the-money, or out-of-the-money.
I think of stress testing as measure of risk exposure that's complementary to VaR. Stress testing is a measure of potential loss as a result of a plausible event in an abnormal market environment. Two types of stress testing are popular. The first is based on economic scenarios. Pretend your portfolio experiences the 1987 or 1997 stock market crash again. The second is "matrix" based. Change a bunch of assumptions about correlations and variances and see what happens. Neither is statistical in nature, in contrast to VaR. That is, you don't know the probability of any particular scenario.
Backtesting is a statistical process for validating the accuracy of a VaR model. Banking regulators require backtesting for banks that use VaR for regulatory capital. It involves a comparison between the number of times the VaR model under-predicts the subsequent day's loss, versus the number of time such an under-prediction is expected. If losses exceeding VaR have a 1 in 100 chance of ocurring, then we expect to see 2 or 3 of those in a year. There is a lot of debate about whether backtesting is meaningful, because it is difficult to validate a model based on a few extreme events - not enough data.
Love-hate, I think. Love first. Banking regulators internationally have agreed to allow banks to use VaR models to calculate regulatory capital. Don't ask why banks have minimum capital set by regulators, as that is a different FAQ. In the USA, the securities regulator allows corporates to use VaR to express their exposure to market risk in their annual and quarterly regulatory public financial filings. Now hate. Regulators aren't sure that VaR is the "right" measure of risk? Nor are they sure how much weight should be given to it in risk management. They really aren't sure whether VaR should be extended to the measurement of other kinds of risk, such as credit risk.
It is the period of history that is used to collect data used in the computation of VaR. This is important, because if the data is inappropriate for the forecast, the forecast is no good.
Excellent question. A precise answer isn't possible yet. This is troublesome, as one hopes that it is being used in ways that are consistent with the concept of shareholder wealth maximization, but we can't be sure.
Pet peeve coming up. While VaR is an estimate of a percentile of the loss distribution, it is commonly referred to as a confidence level. This is because we say, we are 99% confident that the loss will not exceed $XX. It's more exact to refer to VaR as a percentile estimate. Because VaR is a statistical estimate, it is an uncertain amount itself, and that uncertainty can be encapsulated in a statistical concept called a confidence interval - I am 95% sure that the VaR actually lies between $AA and $BB. It's too confusing to talk about a confidence interval around a confidence level.
The use of VaR for non-financial firms is still evolving. Currently it is mostly focused on either VaR for derivatives and hedging instruments only or VaR for cash flows, i.e., EaR.
Accuracy is in the eye of the beholder. A general answer to this question is not possible, because it will depend on the nature of the portfolio and the data used in the estimation of VaR. Several studies comparing methodologies were conducted a few years back, typically with linear portfolios, either equities or fx. These tended to show that the variance-covariance approach was better when short histories of market prices were used, because Monte Carlo and Historical Simulation would under estimate the 99th percentile. With longer histories MC and HC were equal to or better than VCV. But I don't recommend you generalizing from these studies, because of their limited scope. Because of this, it is very important to have an estimate of precision for every VaR estimate (A confidence interval).
I know that one major bank uses 500 simulations for its Monte Carlo VaR. Again, the answer depends on the complexity of the portfolio. Linear instruments, fewer simulations. But MC has its own peculiarities that affect accuracy. For example, some MC routines use "variance reduction." These are "tricks" used to improve accuracy for a given simulation size. With variance reduction techniques (e.g., Antithetic Variates), the fewer simulations needed for a given accuracy. Remember that underlying every MC is some distribution from which observations of market rates are sampled. So assumptions about the distribution and shortcuts taken to reduce the "dimensionality" of the distribution will also have a cost in accuracy which should require more simulations for a given level of accuracy.
I know this is really two questions. The underlying question really is, what percentile of the return distribution gives me better information about risk exposure? If the portfolio return distribution were normally distributed, it wouldn't matter, because every percentile is expressible as a constant times the standard deviation of the return, the standard deviation being the only real information you need for risk assessment in the normal distribution case. The trade-off between choice of percentiles in the real world in which we live is really about accuracy. It is more difficult to accurately estimate a point farther out in the tail of the distribution of returns, because there is less observable data to use in the estimation. However, you may wish to look farther out in the tail if you believe that your portfolio return distribution is more "fat-tailed" (you may think of it as when the ratio: 99 percentile/95 percentile is greater than if the ratio were calculated for a normally distributed return distribution). If there's more going on out there in the tail, you may want to focus on it more. However, simply because 99th percentile VaR yields a bigger VaR does not mean that using a 99th percentile rather than a 95th percentile VaR is a more conservative of a measure of risk. All it means is that you are looking at a point farther out in the tail and calling that your risk exposure. Whether you use 95 or 99, you are generating an estimate of risk from the same distribution of returns.
The standard time horizon (that period over which the VaR forecast is made) is one day for most financial businesses with active trading portfolios. The logic for this horizon is that it would take less than one day to either exit or hedge out all the market risk in any position, so that's really how long is the exposure. This reasoning suggests that the horizon should be tuned to the interval to close out the market exposure. This is a bit simplified, because it ignores liquidity issues (large positions may take longer to exit, simply because they are large), differences among portfolio instruments (it is not reasonable to employ a one day horizon for some positions and a multi-day horizon for others, and then to aggregate them for portfolio VaR calculations), and consistency with credit VaR calculations (typically using a much longer horizon, thereby making aggregation complicated - ignoring all the other theoretical issues in aggregating credit and market risk). These two problems have no completely satisfactory solutions. So, it may be best to identify a singly horizon that best fits the portfolio's characteristics and use that for everything when calculating VaR.
Unfortunately, the term is not used consistently by all authors. Conditional value at risk (cvar) is most often used to refer to a measure of the risk of loss beyond the VaR. I.e., if the VaR of a portfolio is DM 5,000, then what is the expected loss beyond DM 5,000 (or "mean excess loss"), given that an observed loss is greater than the VaR. However, some use the term to mean the estimation of VaR from "conditional" asset return distributions (a conditional distribution is one that takes into account changes in the shape of the distributions through time).
There are many considerations, if capital is to be based on VaR. VaR doesn't tell you how big your losses could be on a bad day, it only defines what distingishes a bad day from other days. If you have two portfolios with exposures to risks of different markets, but the portfolios nevertheless have the same VaR, then it may be wrong to keep the same capital against each portfolio, because one may have much worse performance given a VaR exceedance day. Also, since VaR looks at only a particular forecast horizon, and a bad economic environment may extend beyond that horizon, the relationship between VaR and a business-continuity-threatening type of market event is murky at best. Finally, the relationship between the amount of risk taken and the amount of capital to be held may come down to the nature of the trading and the risk appetite of the "owners" of the capital. If the portfolio has significant nonlinear risks, then the relation between the capital and VaR is even more difficult to judge, as it is sometimes the case that the nonlinearities are greatest beyond the VaR (e.g., in a trading book, with a portfolio of barrier options, where the barriers are not hit within the set of market moves resulting in the VaR). I could go on, for example, the relationship between VaR and the cost of capital under the investment rule of shareholder wealth maximization is not clear - whereas if it were clear, then we could deduce the amount of capital just sufficient to support a given level of risk. And, the impact of VaR-based capital requirements on the incentives of those taking the risks is not all all clear. Having said all that, which should be pretty discouraging, I will hazard that a one day VaR equal to about 3% of the trading capital is a pretty good sized risk in a normal environment.