Volume 3 — Valuation and Risk Metrics © Copyright 2002, CCRO. All rights reserved. 12 approach is that it is computationally intensive and time consuming, entailing revaluation of the portfolio under each scenario. Historical Analysis: In the historical methodology, VaR is estimated by taking actual historical rates and revaluing positions for each change in the market. Assuming a complete pricing algorithm is used, the method is accurate for all instruments. The methodology provides a full distribution of potential portfolio values rather than just a specific percentile. The user need not make distributional assumptions, although parameter fitting may be performed on the resulting distribution. Tail risk is incorporated but only if the historical data set includes the tail events. Historical analysis is faster than Monte Carlo simulation because fewer scenarios are used, although it is still somewhat computationally intensive and time consuming. A disadvantage is that a significant daily rate history is required, and sampling far back can create problems if the data are irrelevant to current conditions (for example, if currencies have been devalued). Similarly, scaling far into the future can be difficult. An additional disadvantage is that the results are harder to verify at high confidence levels (99% and beyond). Table 1 compares the attributes of the three methodologies for calculating VaR. Table 1. Comparison of Attributes of Methods for Calculating Value at Risk Methodology Attributes Volatility Considered Correlation Considered Optionality Considered Probability Considered Assumes Distribution Estimation Speed Prices Used Parametric, closed form, or variance/ covariance Yes Yes Not usually but approxi- mately considered Yes Yes Fast Current forward prices Monte Carlo Yes Yes Yes Yes Generally assumed Very slow Simulated forward prices Historical Implicitly Implicitly Yes Implicitly No Slow Historical set of forward prices Clearly, each methodology has its strengths and weaknesses. One may be better suited than another based on the desired processing time, system capabilities, intended use, portfolio makeup, and other factors. Each company should determine the most appropriate one for its business. The appropriateness of a methodology chosen by a given company must be consistent with the nature and structure of its portfolio. The robustness and validity of the methodology must be established through a process of back-testing (described below). Any changes to a given methodology must be well documented and substantiated through a systematic analysis of the new methodology in contrast to the old. All material impacts on the measured levels of risk must be recorded. Holding Period The holding period is the time over which the variability in the value of a portfolio or estimated earnings from an economic activity is assessed. During the holding period, changes in the