32. 2011年2月04日 18:13:04: nJF6kGWndY
バーゼル銀行監督委員会 http://www.fsa.go.jp/inter/bis/bis_menu.htmlMessages from the academic literature on risk measurement for the trading book BCBS Working Papers No 19 January 2011 This report summarises the findings of an ad hoc group of the Basel Committee's Research Task Force based on its review of the academic literature relevant to the regulatory framework for the trading book. This project was carried out in the first half of 2010 acting upon a request from the Basel Committee's Trading Book Group. It builds on and extends previous work by the Research Task Force on the interaction of market and credit risk. The literature review was complemented by feedback from academic experts at a workshop hosted by the Deutsche Bundesbank in April 2010 and reflects the state of the literature at this point in time. Executive summary This report summarises the findings of an ad hoc working group that reviewed the academic literature relevant to the regulatory framework for the trading book. This project was carried out in the first half of 2010 acting upon a request from the Trading Book Group to the Research Task Force of the Basel Committee on Banking Supervision. This report reflects the views of the individual contributing authors and should not be construed as representing specific recommendations or guidance by the Basel Committee for national supervisors or financial institutions. The report builds on and extends previous work by the Research Task Force on the interaction of market and credit risk (see Basel Committee on Banking Supervision (2009a)). The literature review was complemented by feedback from academic experts at a workshop hosted by the Deutsche Bundesbank in April 2010, and reflects the state of the literature at this point in time. Please note that the term “value-at-risk” (VaR) should be interpreted henceforth in a broad sense as encompassing other common risk metrics, with the exception of Section 3 in which risk metrics are compared directly. The main findings of the group are summarised below in the order of the Sections of the report. 1. Selected lessons on VaR implementation There is no unique solution to the problem of the appropriate time horizon for risk measurement. The horizon depends on characteristics of the asset portfolio (such as, market liquidity) and the economic purpose of measuring its risk; for example, setting capital or setting loss limits for individual trading desks. Scaling of short-horizon VaR to a longer time horizon with the commonly used square-root-of-time scaling rule has been found to be an inaccurate approximation in many studies. This rule ignores future changes in portfolio composition. At present, there is no widely accepted approach for aggregating VaR measures based on different horizons. Time-varying volatility is a feature of many financial time series and can have important ramifications for VaR measurement. Time-varying volatility can give rise to issues regarding the potential pro-cyclical effects of VaR-based capital measures. The effects of time-varying volatility on the accuracy of simple VaR measures diminish as the time horizon lengthens. In contrast, volatility generated by stochastic jumps will diminish the accuracy of long-horizon VaR measures unless the VaR measures properly account for the jump features of the data. Distinguishing between time-varying volatility and volatility changes that owe to stochastic jump process realisations can be important for VaR measurement. Backtests that focus on the number of VaR violations have low power when the number of VaR exceptions is small. The power of backtests can be improved modestly through the use of conditional backtests or other techniques that consider multiple dimensions of the data like the timing of violations or the magnitude of the VaR exceptions. No consensus has yet emerged on the relative benefits of using actual or hypothetical results (ie P&L) to conduct backtesting exercises. 2. Incorporating liquidity The literature distinguishes, first, between exogenous and endogenous liquidity; and, second, between normal (or average) liquidity risk and extreme (or stress) liquidity risk.
Exogenous liquidity refers to market-specific, average transaction costs and can be captured by a “liquidity-adjusted VaR” approach. Endogenous liquidity refers to the price impact of the liquidation of specific positions. Endogenous liquidity depends on trade size and is relevant for orders that are large enough to move market prices; that is, it is the elasticity of prices to volumes. Endogenous liquidity may be easily observed in situations of extreme liquidity risk, characterised by the collective liquidation of positions or, more generally, when all market participants react in the same way. Portfolios, however, may be subject to significant endogenous liquidity costs under all market conditions, depending on their size or on the positions of other market participants. According to actual accounting standards, endogenous liquidity costs are not taken into account in the valuation of the trading books. A first step to incorporate this risk in a VaR measure would be to take it into account in the valuation method. Although this last topic has attained considerable popularity in the recent literature, the practical implications for risk management have yet to be developed. In practice, the time it takes to liquidate a position varies, depending on its transaction costs, the size of the position in the market, the trade execution strategy, and market conditions. Some studies suggest that, for some portfolios, this aspect of liquidity risk could also be addressed by extending the VaR risk measurement horizon. 3. Risk measures VaR has become a standard risk measure in finance. Notwithstanding its widespread use, it has been criticised in the literature for lacking subadditivity, a property that implies that compartmentalised (say, desk-wise) risk measurement based on VaR is not necessarily conservative. The problem is relevant in practice and not only relevant for very high confidence levels of VaR. The most prominent alternative to VaR is expected shortfall, which is subadditive. It is slowly gaining popularity among financial risk managers. Despite criticism focused on the complexity, computational burden, and backtesting issues associated with expected shortfall, the recent literature suggests that many issues have been resolved or have been identified as less severe than originally expected, including improvements in backtesting methodologies. At present, some financial institutions have come to more fully rely on expected shortfall metrics. Spectral risk measures are a promising generalisation of expected shortfall. They have certain advantages over expected shortfall, including favourable smoothness properties and the possibility of adapting the risk measure directly to the risk aversion of investors. From a technical perspective, spectral risk measures require little additional effort if the underlying risk model is simulations-based. 4. Stress testing practices for market risk Stress testing is often implemented as an ad hoc exercise without any estimate of the probability associated with the stress scenarios and often using modelling approaches that differ from an institution’s VaR risk measurement framework. More recent research advocates the integration of stress testing into the risk modelling framework. This would overcome drawbacks of reconciling stand-alone stress test results with standard VaR model output. Progress has also been achieved in theoretical research on the selection of stress scenarios. In one approach, for example, the “optimal” scenario is defined by the maximum loss event in a certain region of plausibility of the risk factor distribution. The regulatory “stressed VaR” approach has not been analyzed in the academic literature. From a theoretical perspective it is an imperfect solution and its purpose is to reflect that current market conditions may not lead to an accurate assessment of the risk in a more stressful environment. Certain methods that could be meaningful in this context can be identified in the earlier literature on stress testing. Employing fat-tailed distributions for the risk factors and replacing the standard correlation matrix with a stressed one are two examples. 5. Unified versus compartmentalised risk measurement Much of the risk measurement literature has focused on compartmentalised measures of risk such as interest rate, market, credit, or operational risks. In recent years, attention has shifted towards integrated or unified approaches for risk measurement that consider all risk categories jointly. From a theoretical perspective, an integrated approach is needed to capture potential compounding effects that are ignored in compartmentalised risk measurement approaches. Those approaches can underestimate risk if an asset portfolio cannot be cleanly divided into sub-portfolios along risk categories. Empirical studies suggest that the magnitude of diversification benefits – that is, the amount by which aggregate risk is below the sum of individual risks – depends upon the level at which risks are measured. At higher levels of aggregation (eg at the holding company level), the benefits are more often detected; however, at a lower (eg the portfolio) level, risk compounding can become predominant. The artificial distinction between a “trading book” and a “banking book” refers to positions, but these positions need not be exposed to different sets of risk. If the risks associated with these books are distinct, even if they are not independent, then adding the VaR measures of these books will be conservative. If the risks associated with the two books are not distinct, (eg if the separation is due only to accounting rules), then adding compartmentalised VaR risk measures is guaranteed to be conservative only if all risks relevant to each book are accounted for. If not, the sum of compartmentalised risk measures may understate the risk of the combined portfolio risk. Irrespective of the separation of assets into “books”, it is always questionable to calculate different risks for the same portfolio in a compartmentalised fashion and to hope that adding up the compartmentalised measures will be a conservative estimate of the true risk. In general, it will not be. This insight is particularly important for “backfitting packages”, such as the incremental risk charge. 6. Risk management and value-at-risk in a systemic context A number of studies are critical of VaR-based capital requirements because of their pro-cyclical nature. VaR-based capital rules require lower (higher) capital in the upswing (downturn) of the economy because volatilities of market prices of assets tend to vary over the business cycle. The procyclical nature of VaR-based capital requirements may induce cyclical lending behaviour by banks and exacerbate the business cycle. Another criticism of VaR-based capital rules is that, under these rules, banks may face incentives to bias their models towards minimising regulatory capital charges and VaR models do not take endogeneity into account. When all banks follow a VaR-based capital rule, financial institutions may be incentivised to act uniformly in booms and busts. This tendency may create endogenous instabilities in asset markets that are typically not included when individual banks measure the risks of their trading books. While procyclicality is often mentioned as a policy concern in the academic literature, the literature generally does not offer convincing solutions to how these concerns could be addressed in the regulatory framework, given that regulation should keep minimum capital requirements risk-sensitive in the cross-section.
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