We use the value-at-risk approach to derive quantitative measures for our trading book market risks under normal market conditions.
For a given portfolio , value-at-risk measures the potential future loss (in terms of market value) that, under normal market conditions, will not be exceeded in a defined period and with a defined confidence level . The value-at-risk measure enables us to apply a constant and uniform measure across all of our trading businesses and products. It also facilitates comparisons of our market risk estimates both over time and against our actual daily trading results.
Since January 1, 1999 we have calculated value-at-risk for both internal and external reporting using a 99% confidence level, in accordance with BIS rules. For internal reporting purposes, we use a holding period of one day. For regulatory reporting purposes, the holding period is ten days, i.e. if the portfolio is held without change for ten days there is a 1% chance that the portfolio's market value would decline by an amount greater than the value-at-risk figure.
We believe that our value-at-risk model takes into account all material risk factors assuming normal market conditions. Examples of these factors are interest rates, equity prices, foreign exchange rates and commodity prices, as well as their implied volatilities. The model incorporates both linear and nonlinear effects of the risk factors on the portfolio value. In our model, the nonlinear effects capture risks specific to derivatives . The statistical parameters required for the value-at-risk calculation are based on a 261 trading day history (corresponding to at least one calendar year of trading days) with equal weighting being given to each observation. Since 2002, we have used an aggregation approach based on full correlation among the various risk classes.
The value-at-risk for interest rate and equity price risks consists of two components each. The general risk describes value changes due to general market movements, while the specific risk has issuer-related causes. When aggregating general and specific risks, we assume that there is zero correlation between them.
We calculate value-at-risk using Monte Carlo simulations. A Monte Carlo simulation is a model that calculates profit or loss for a transaction for a large number (such as 10,000) of different market scenarios, which are generated by assuming a joint (log-) normal distribution of market prices based on the observed statistical behavior of the simulated risk factors in the last 261 trading days. However, we still use a variance-covariance approach to calculate specific interest rate risk for some portfolios, such as in our integrated credit trading and securitization businesses. In the variance-covariance method, we derive the estimate of the potential change in market prices from the variance-covariance matrix of the risk factors under consideration. Multiplying this matrix by the proper portfolio sensitivities yields the change in the portfolio value for price movements of one standard deviation which we scale with a factor of 2.33 in order to obtain a result for a 99% confidence level.
Back-Testing
We use back-testing on our trading units to verify the predictive power of the value-at-risk calculations. In back-testing, we compare actual income as well as the hypothetical daily profits and losses under the buy-and-hold assumption (in accordance with German regulatory requirements) with the estimates we had forecast using the value-at-risk model.
A back-testing committee meets on a quarterly basis to discuss back-testing results of the Group as a whole and individual businesses. The committee consists of risk managers, risk controllers and business area controllers. They analyze performance fluctuations and assess the predictive power of our value-at-risk models, which in turn allows us to improve the risk estimation process.