Volume 3 — Valuation and Risk Metrics © Copyright 2002, CCRO. All rights reserved. 13 market prices of the commodities or other variables underlying the portfolio or activity drive corresponding changes in the value or earnings estimates that were used at the beginning of the holding period. The holding period can vary for different components of the portfolio of positions or types of economic activity. In the case of VaR, the holding period generally should be representative of the time it would take to liquidate the portfolio hence, it is also called the liquidation period. Another interpretation of the holding period is that it is the length of time that would pass while strategies are employed and actions taken to remove the variability in the value or earnings (i.e., to render the portfolio of positions or economic activity risk-free). The VaR for a given portfolio increases as holding periods are increased. The holding period can correspond to any period deemed relevant to managing a commercial activity. Different companies may have variations of these general examples depending on the specifics of their business. To provide clarity, the management rationale for the holding period selected should be disclosed. When a company calculates VaR over a one-day holding period, the metric is commonly referred to as the daily earnings at risk. Daily earnings at risk (DEaR) provides a measure of the market risk of the portfolio of positions. It is most appropriate for positions and portfolios where markets are very liquid and sufficiently deep to permit either liquidation or the placement of effective hedging strategies to mitigate the market or price risk in a very short period (one day or less). It is also a reasonable measure of risk when the trading strategies are such that the portfolio composition changes significantly day by day. For proprietary trading, VaR and DEaR would be the same valuation. Confidence Level The confidence level is a measure of the degree of confidence, or equivalently the probability that is associated with the set of outcomes, for a random variable (or a stochastic process) of interest. A confidence level of  is defined as the probability that, given the underlying distribution of the random variable (or process), the set of possible outcomes will lie in a range greater than or equal to a predetermined value. Equivalently, a confidence level of (1 — ) is defined as the probability that the set of outcomes will lie in a range less than or equal to a predetermined value. For example, a confidence level of 5% is used to assess the set of possible outcomes and assign a probability of 1 in 20 that the actual outcome will lie below a predetermined value, the latter being a function of the underlying distribution and the level of confidence being used. Alternatively, a confidence level of 95% is used to assess the set of possible outcomes and assign a probability of 19 out of 20 that the actual outcome will lie above the predetermined value. VaR is typically used to measure downside risk. Thus, when a confidence level such as 5% is mentioned in a VaR discussion without qualification, it is generally understood that it applies only to the left-hand tail of the distribution. However, it is also possible to use the VaR framework to measure upside potential. Thus, VaR can be computed using either a one-tailed or two-tailed confidence level. With a one-tailed confidence level, VaR is the point where the negative change in cash flows will be larger only 5% of the time, assuming a 95% confidence level (see Figure 1a). With a two-tailed confidence level, VaR is the point where the positive