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06 October 2015

**Out with old risk metric, in with the new. Welcome to Expected Shortfall**** **

The Basel Committee on Banking Supervision has been revising its market risk framework since 2012. The result of its ‘fundamental review of the trading book’ (FRTB , BCBS 219) is expected to be implemented by January 2018, with 2016-17 scheduled for calibration and testing. The consultation phase for the new regulatory framework is still ongoing and has featured several Quantitative Impact Studies, highlighting the framework’s complexity.

Even if the final standard is yet to be agreed, it is reasonably safe to say that the BCBS will retire the well-established VaR (value at risk) for the calculation of market risk capital requirements, bringing to an end the most important risk metric in banking after 20 years. To replace it, another risk measure has moved from the academic world to that of market risk practitioners: the expected shortfall (ES), also known as conditional VaR.

The ES is the expected value of all changes in the portfolio value in the tail of the P+L distribution that exceed the VaR. By construction, the ES will always be more conservative than the VaR. Most observers expect that the Basel Committee will take this into account by reducing the current confidence level from 99.0% to an expected 97.5%.

The VaR was devised by Dennis Weatherstone, a former JP Morgan CEO. In the aftermath of the 1987 he demanded that his market risk team produced a simple and easily comparable report of the potential losses for the next trading day – on a single page and delivered no later than 45 minutes after market close. After the famous ‘Report 4.15’ was implemented, the new risk measure quickly became industry standard and was accepted for the calculation of regulatory capital requirements for market risk when it was added to Basel I in 1996.

Keeping in mind the origins of the VaR, it is clear that this concept was never intended as a comprehensive risk metric for all applications and for longer holding periods. For example, one major criticism of the VaR is that P+L distributions that have totally different risk implications for the bank might show the same VaR because not all properties of the P+L distribution are reflected. In addition, you lose information about the individual risk drivers of your portfolio and their potential effects when you aggregate P+L impacts from a huge number of risk factors in one single number.

It is important to point out that neither VaR nor ES are able to forecast a maximum loss. Both risk measures provide instead a statistical estimation that is valid under normal market conditions – a fact that even senior management sometimes needs to be reminded of.

If a bank’s market risk model is correctly calibrated, the actual moves in the portfolio value
*must* exceed the VaR or the ES several times in a given time period, depending on the confidence level and holding period (that’s why an additional multiplicator for market risk capital requirements is applied). If the changes in portfolio value never
exceed the VaR, this would be an indication that the market risk model is too conservative, leading to unnecessarily high capital requirements.

But events that break banks don't occur under normal market conditions. Here, the switch from VaR to Expected Shortfall reflects a fundamental change in philosophy for market risk calculation and management. In the current Basel II.5 framework, a bank has to survive in normal market conditions with a given confidence level, while the goal of FRTB is to ensure survival in extreme market conditions by capturing tail risks.

A well-known drawback of VaR is that it completely relies on the probability of events and doesn’t consider their severity (the height of the incurred loss). When determining the quantile, each realisation of the change in portfolio value is weighted equally. It is simply a digital decision: either an event lies within the quantile or it doesn’t, regardless of the actual loss. Consequently, the VaR completely neglects information about the P+L distribution outside the relevant quantile. The 99% VaR doesn't care if your 0.02% probability loss is EUR 1 mln or EUR 1 bln, but these are the extreme events that may break a bank.

The ES tackles these issues by including information about all relevant extreme events of the P+L distribution. By calculating the expected value of the changes in portfolio value, each tail event is weighted by its impact and contributes to the ES. It is widely agreed by market participants, that at least from a theoretical point of view the ES is a superior concept.

In contrast to the VaR it can be shown that the ES is a coherent risk measure. The VaR does not satisfy the required mathematical property called subadditivity, which means that in some cases it doesn’t reflect the risk reduction from diversification effects. However, this might only be a theoretical benefit because even if academic examples can be created easily, according to market practioners the missing subadditivity of VaR rarely has practical consequences.

Apart from its mathematical properties, in practice the actual benefit from switching to ES for risk management and capital requirements is limited by the available data. For calculation of the ES you need to work with hard-to-estimate extreme events that
occur with very low probability but with huge impacts. The sensitivity on the tail that the BCBS considers the main advantage of the ES may also turn out to be a big downside.* *

The most widely used calculation method for the VaR is the empirical estimation based on a historical time series of the risk factors which normally consists of 250 to 1,000 trading days. Typically only very few tail events relevant for the ES calculation
might be included in the sample and calculating the expected value from only two or three data points, for example, each with a very large P+L impact, raises the risk of instabilities. Aaron Brown, a risk management expert, states: ”Expected shortfall […]
is infinitely sensitive to events with infinitesimal probability. All the evidence in the history of the universe can never tell you expected shortfall".*
*Consequently the meaningfulness of the resulting ES has to be carefully analysed to avoid generating a false sense of accuracy and safety.

It is important to point out that the replacement of VaR by ES proposed in the FRTB is only relevant for market risk and doesn’t affect the calculation of capital requirements for other risk categories such as counterparty credit risk. There is still extensive use for VaR and its importance is unlikely to diminish. However, once banks and regulators have become familiar with the properties of ES and the industry has had a chance to gain some practical experience, the new risk metric is likely to gain significance and an increasing number of applications in risk management.

*References: Risk Magazine*

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