Value at Risk

Abstract

The main business of banks and insurance companies is risk. Banks and financial institutions lend money, running the risk of losing the lended amount, and they borrow “short money” having less risk but higher expected rates of return. Insurance companies on the other hand earn a risk premium for guaranteeing indemnifification for a negative outcome of a certain event. The evaluation of risk is essential for both kinds of business. During the 1990’s there has been established a measure for risk in finance theory as well as in practice, the Value at Risk, VaR. It was mainly popularized by J.P. Morgan’s RiskMetrics, a database supplying the essential statistical data to calculate the VaR of derivatives. In the context of finance Value at Risk is an estimate, with a given degree of confidence, of how much one can lose from a portfolio over a given time horizon. The portfolio can be that of a single trader, or it can be the portfolio of the whole bank. As a downside risk measure, Value at Risk concentrates on low probability events that occur in the lower tail of a distribution. In establishing a theoretical construct for VaR, Jorion [10] first defines the critical end of period portfolio value as the worst possible end-of-period portfolio value with a pre-determined confidence level “1− α” (e.g., 99%) These worst values should not be encountered more than α percent of the time. For example, a Value at Risk estimate of 1 million dollars at the 99% level of confidence implies that portfolio losses should not exceed 1 million dollars more than 1% of the time over the given holding period [10]. Currently, Value at Risk is being embraced by corporate risk managers as an important tool in the overall risk management process. Initial interest in VaR, however, stemmed from its potential applications as a regulatory tool. In the wake of several financial disasters involving the trading of derivatives products, such as the Barrings Bank collapse (see [10], regulatory agencies such as