Market risk

The principal portfolio measures of market risk are VaR and stress loss. Certain risks may be controlled outside VaR in the start-up phase but the level of risk is deliberately kept small – this was, for example, the case for our commodities and base metals derivatives trading business until March 2006. There are very few market risk positions that are not included in VaR. They are not material to UBS and they are subject to other controls and reporting.

Value at Risk (VaR)

VaR is a statistically based estimate of the potential loss on the current portfolio from adverse movements in both general and idiosyncratic market risk factors. We use the same VaR model for internal risk control (including limits) and for determining market risk regulatory capital requirements.

VaR expresses the amount we might lose, but only to a certain level of confidence (99%) and there is therefore a specified statistical probability (1%) that actual loss could be greater than our VaR estimate.

Our VaR model measures risk over a certain time horizon. For internal risk measurement and control, and for determining regulatory capital, we use a 10-day horizon. We also measure and report VaR with a 1-day horizon for information and for backtesting, as explained below.

We assume that market moves occurring over these periods will follow a similar pattern to those that have occurred over 10-day and 1-day periods in the past. For general market risk, this look-back period is five years – a period which captures the cyclical nature of financial markets and is likely to include periods of both high and low volatility (see Sidebar – "VaRiations on a theme"). These historical changes are applied directly to our current positions, a method known as historical simulation.

We measure idiosyncratic risk arising not only from directly held debt and equity positions but also from derivatives (forwards, options, default swaps and other derivatives) on the same name. For equity instruments, the measure is based on the Capital Asset Pricing Model ("CAPM") supplemented by a "deal break" methodology for equity arbitrage positions, where we are typically long in the stock of one company and short in that of another. The deal break measure assesses the probability of collapse of a merger or takeover, and its impact on the two stock prices – a one-off jump move generating the same potential loss for both 10-day and 1-day VaR. For debt positions, our VaR model includes potential rating migration.

The Chairman's Office annually approves a 10-day VaR limit for UBS as a whole and allocations to the Business Groups, the largest being to the Investment Bank. Within the Business Groups, limits are allocated to lower organizational levels as necessary.

Backtesting

The distribution of potential profits and losses from our VaR model provides an indication of potential trading revenue volatility, and a change in the general level of VaR would normally be expected to lead to a corresponding change in the volatility of daily trading revenues. The 10-day VaR measure assumes that positions are not changed over this time horizon, and the absolute level of 10-day VaR should not, therefore, be interpreted as the likely range of daily trading revenues. VaR based on a 1-day horizon provides a closer estimate of the range of daily mark to market profit and loss we are likely to incur on the current portfolio under normal market conditions, but it is based on past events and is dependent upon the quality of available market data.

The predictive power of the VaR model is therefore continuously monitored by backtesting the VaR results for trading books. In backtesting we compare the 1-day VaR calculated on positions at close of business each business day with the actual revenues arising on the same positions on the next business day. These revenues ("backtesting revenues") exclude non-trading components such as commissions and fees, and estimated revenues from intraday trading. If the result is negative and exceeds the 1-day VaR, a "backtesting exception" is considered to have occurred. When VaR is measured at a 99% confidence level, a backtesting exception is expected, on average, one day in a hundred.

All backtesting exceptions and any exceptional revenues on the profit side of the VaR distribution are investigated, and all backtesting results are reported to senior business management, the Group CRO and Business Group CROs.

As required by regulations, backtesting exceptions are also notified to our internal and external auditors and relevant regulators.

Although we apply VaR measures to general market risks arising in non-trading books, we do not backtest the results because the basis of risk measurement is not consistent with the basis of revenue recognition.

Stress loss

Neither 1-day nor 10-day VaR, nor the worst case losses in the VaR distributions, reflects the worst loss that could occur as a result of extreme, unusual or unprecedented market conditions. Stress loss measures quantify our exposure to these more extreme market movements and are an essential complement to VaR. Our VaR measure is based on observed historical movements and correlations. Stress loss measures do not have to be (and should not be) constrained by historical events. Our approach is designed to ensure that a wide range of possible outcomes is explored, that we understand our vulnerabilities and that the governance and control framework is comprehensive, transparent and responsive to market conditions and developments in the world economy.

We run macro stress scenarios bringing together various combinations of potential market moves to reflect the most common types of stress event. These include an industrial country market crash with a range of yield curve and credit spread behavior, and emerging market crises, with and without currency pegs breaking. We also model a general recovery scenario. The standard scenarios are run daily, and it is against these that we track the development of our stress loss exposure and make comparisons from one period to the next. We also set limits on stress loss exposure measured against these scenarios for all Business Groups. The scenarios and their components are reviewed and re-approved by the Chairman's Office at least annually.

The macro scenarios are supplemented, as and when necessary, by specific scenarios targeting current concerns, such as sharp movements in energy prices or the impact of increased geopolitical instability in specific regions, and position-centric scenarios that attempt to capture any particular vulnerabilities or aspects of our exposure that may not be fully covered by the standard scenarios. Such scenarios, by definition, must be constantly adapted to changing circumstances and portfolios.

We analyze the VaR results beyond the 99% confidence level (the "tails" of the distribution) to better understand the potential risks of the portfolio and to help identify risk concentrations. The results of this analysis are valuable in their own right but can also be used to formulate position-centric stress tests. Although the macro scenarios incorporate generic elements of past market crises, we may continue to use the more granular detail of specific historical events which have previously generated the VaR tails when they are no longer included in the VaR historical time series, to supplement the results and benchmark the severity of our macro scenarios, or to provide a basis for ad hoc and position-centric scenarios.

Most major financial institutions employ stress tests, but their approaches differ widely and there is no benchmark or industry standard in terms of scenarios or the way they are applied to an institution's positions. Furthermore, the impact of a given stress scenario, even if measured in the same way across institutions, depends entirely on the make-up of each institution's portfolio, and a scenario highly applicable to one institution may have no relevance to another. Comparison of stress results between institutions can therefore be highly misleading, and for this reason we do not publish quantitative stress results.