P2.T5. Market Risk Measurement & Management. BIS # 19, Messages from the Academic Literature on Risk Measuring for the Trading Books

Transcription

1 P2.T5. Market Risk Measurement & Management BIS # 19, Messages from the Academic Literature on Risk Measuring for the Trading Books Bionic Turtle FRM Study Notes Reading 38 By David Harper, CFA FRM CIPM

2 BIS # 19, MESSAGES FROM THE ACADEMIC LITERATURE ON RISK MEASURING FOR THE TRADING BOOKS... 3 EXPLAIN THE FOLLOWING LESSONS ON VAR IMPLEMENTATION: TIME HORIZON OVER WHICH VAR IS ESTIMATED, THE RECOGNITION OF TIME VARYING VOLATILITY IN VAR RISK FACTORS, AND VAR BACKTESTING DESCRIBE EXOGENOUS AND ENDOGENOUS LIQUIDITY RISK AND EXPLAIN HOW THEY MIGHT BE INTEGRATED INTO VAR MODELS COMPARE VAR, EXPECTED SHORTFALL, AND OTHER RELEVANT RISK MEASURES

3 BIS # 19, Messages from the Academic Literature on Risk Measuring for the Trading Books Explain the following lessons on VaR implementation: time horizon over which VaR is estimated, the recognition of time varying volatility in VaR risk factors, and VaR backtesting. Describe exogenous and endogenous liquidity risk and explain how they might be integrated into VaR models. Compare VaR, expected shortfall, and other relevant risk measures. Summarize the recent state of stress testing research and practice. Compare unified and compartmentalized risk measurement. Describe the results of research on top-down and bottom-up risk aggregation methods. Explain intermediary balance sheet management and the cyclical feedback loop from VaR constraints on leveraged investors. Explain the following lessons on VaR implementation: time horizon over which VaR is estimated, the recognition of time varying volatility in VaR risk factors, and VaR backtesting. Time Horizon 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 The commonly used square-root-of-time ( square root rule ) 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. 3

4 Time-varying volatility 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 timevarying 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 realizations can be important for VaR measurement. VaR Backtesting 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 exercise. Describe exogenous and endogenous liquidity risk and explain how they might be integrated into VaR models. Exogenous liquidity refers to market-specific, average transaction costs and can be captured by a liquidity-adjusted VaR approach. A common approach treats the exogenous cost of liquidity (COL) as one-half the shocked spread: q Cost of liquidity (COL) t = Pt 2 confidence Note: this is equivalent to Kevin Dowd s exogenous spread 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, characterized 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. Endogenous liquidity effects are particularly important when: o The underlying asset is not very liquid, o The size of the position is important with respect to the market, o Large numbers of small investors follow the same hedging strategy, o The market for the underlying of the derivative is subject to asymmetric information, which magnifies the sensitivity of prices to clusters of similar trades 4

5 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. 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 Compare VaR, expected shortfall, and other relevant risk measures. Value at Risk (VaR) VaR has become a standard risk measure in finance. Notwithstanding its widespread use, it has been criticized for its lack of subadditivity, a property that implies that compartmentalized 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. Although lack of subadditivity is considered the most consequential, VaR is not a coherent risk measure because it does not meet all four (4) of the following conditions: Subadditivity (diversification): R(L1 + L2) R(L1) + R(L2) Positive homogeneity (scaling): R(λL) = λ*r(l) for positive λ Monotonicity: R(L1) < R(L2) if L1 < L2 Transition property: R(L + a) < R(L) a Why does subadditivity matter? From McNeil et al (2005): Subadditivity reflects the idea that risk can be reduced by diversification, the use of non-subadditive risk measures in a Markowitz-type portfolio optimization problem may lead to optimal portfolios that are very concentrated and that would be deemed quite risky by normal economic standards. If a regulator uses a non-subadditive risk measure in determining the regulatory capital for a financial institution, that institution has an incentive to legally break up into various subsidiaries in order to reduce its regulatory capital requirements. Subadditivity makes decentralization of risk-management systems possible. Expected Shortfall The most prominent alternative to VaR is expected shortfall; expected shortfall 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. 5