As an example, you could find VaR from the lognormal distribution function. Analytical Set up a model, find the simultaneous distribution and fit the model to the data. A portfolio’s distribution can be determined by 3 methods: 1. The parametric approach is based on the assumption of a certain distribution. However, this will only work if the future looks sufficiently like the past. The non-parametric approach is very simple and it’s an advantage that we don’t have any distribution assumptions. The ES estimate is thus the average of all L_i that surpasses VaR. S is the current size of the position in some asset and ^q( α) is the estimated upper α-quantile of the return distribution. A guy called Nassim Taleb also once testified in Congress asking for the banning of VaR. In 2008 in Global Association of Risk Professionals Review, Einhorn compared VaR to “ an airbag that works all the time, except when you have a car accident” and that it is potentially catastrophic when its use creates a false sense of security among executives. VaR is often measured daily, and because it is a very short-term measure, it assumes that tomorrow will be more or less like today. Another way of thinking of this is to say that VaR is the boundary between “normal” market days and extreme events, making it terrible to use during or close to a financial crisis. That seems inappropriate for a risk measure. It is a quantile measure and actually a value depicting the best of the worst case scenarios, thus underestimating the potential losses. The biggest con is the uncertainty of what will happen if the VaR measure is exceeded - if we end up “in the last 5%” - and this makes VaR a questionable metric for risk management. A typical conclusion is then that “ with 95% probability, the investor will not lose more than VaR(α = 0.95)”. This is the most essential part and I will return to this later on. Lastly, the probability distribution has to be identified.
For active traders it will mostly be a one-day VaR. Common levels are 1%-5%, but higher quantiles might be used on trading floors of investment banks for daily risk assessments, while the lower quantiles might be applied in long-run risk analysis for pension funds. First, the quantile α has to be specified. When computing VaR, three steps have to be considered. Which simply means that we, with probability α, won’t lose more than VaR( α). If L is a loss distribution or potential loss with some horizon T and a continous distribution function F_L, then the VaR( α, T) measure is given by: The risk that VaR measured did not include the biggest risk of all the possibility of a financial crisis. This widespread reliance on VaR has shown to be a mistake. The Basel Committe even said that banks could rely on their own internal VaR calculation to set their capital requirements. In the 90s, the SEC ruled that firms had to include a quantitative measure of market risk in their financial statements, and VaR became the main tool for doing so. Risk managers use VaR to measure and control the level of financial risk exposure, which can be within the firm, a portfolio consisting of any type of asset or a specific position and thus be used to gauge the asset value needed to cover possible losses. It is a measure for what the maximum expected loss is, given some 1 - α% probability and some time horizon T.
VaR is a single measure of market risk, meaning changes in asset value, and is conceived to help the actual decision about taking a risk. The most common risk measure in finance after volatility is VaR.
we are interested in the tail of the distribution of possible losses. First, we will be interested in looking at scenarios with big losses, i.e.