Value‐at‐Risk

Abstract

Abstract The Value at Risk (VaR) on a portfolio is the maximum loss we might expect over a given period, at a given level of confidence. It is therefore defined over two parameters – the period concerned, usually known as the holding period, and the confidence level – whose values are arbitrarily chosen. The VaR is a relatively recent risk measure whose roots go back to Baumol, who suggested a risk measure equal to μ – k σ, where μ and σ are the mean and standard deviation of the distribution concerned, and k is a subjective parameter that reflects the user's attitude to risk. The term value at risk only came into widespread use much later. The notion itself lay dormant for nearly 30 years, and then shot to prominence in the early to mid 1990s as the centerpiece of the risk measurement models developed by leading securities firms. The most notable of these, Morgan's Risk‐Metrics model, was made public in October 1994, and gave rise to a widespread debate on the merits, and otherwise, of VaR. Since then, there have been major improvements in the methods used to estimate VaR, and VaR methodologies have been applied to other forms of financial risk besides the market risks for which it was first developed.