List of Tables

IV.1.1 Active returns
IV.1.2 LPM of various orders relative to two different thresholds
IV.1.3 Normal VaR with drift adjustment
IV.1.4 The tail of the return distribution and of the active return distribution
IV.1.5 Comparison of estimates from different VaR models
IV.2.1 Normal linear VaR for different volatilities, significance levels and risk horizons
IV.2.2 Risk factor sensitivities
IV.2.3 PV01 of cash flows and volatilities of UK and US interest rates
IV.2.4 Correlations between UK and US interest rates
IV.2.5 PV01 of cash flows and volatilities of LIBOR rates
IV.2.6 Correlations between LIBOR rates
IV.2.7 Cross correlations between credit spreads and LIBOR rates
IV.2.8 Volatilities and correlations of LIBOR and credit spreads
IV.2.9 Eigenvalues of covariance matrix of UK spot rates – short end
IV.2.10 Net sensitivities on PC risk factors
IV.2.11 Stock portfolio characteristics
IV.2.12 Characteristics of 10-day returns
IV.2.13 Characteristics of an international equity portfolio
IV.2.14 Annual covariance matrix Ω of equity and forex risk factor returns
IV.2.15 VaR decomposition for diversified international stock portfolio
IV.2.16 Volatilities and correlations of risk factors
IV.2.17 VaR decomposition into equity and forex factors
IV.2.18 Volatilities and correlations of natural gas and silver futures
IV.2.19 Commodities trading desk positions on natural gas and silver
IV.2.20 1% 10-day VaR of commodity futures desks
IV.2.21 Normal and Student t linear VaR
IV.2.22 Moments of the FTSE 100 and S&P 500 indices and of the $/£ forex rate
IV.2.23 Estimated parameters of normal mixture distributions (annualized)
IV.2.24 Comparison of normal mixture and normal VaR
IV.2.25 Sample moments of daily returns on the FTSE 100 index
IV.2.26 Normal mixture parameters for FTSE 100 returns
IV.2.27 Comparison of normal and Student t linear VaR
IV.2.28 Comparison of mixture VaR estimates
IV.2.29 Effect of autocorrelation on mixture VaR
IV.2.30 Normal mixture parameters for risk factors
IV.2.31 EWMA VaR for the FTSE 100 on 18 April 2008
IV.2.32 Volatilities of and correlation between S&P 500 and NASAQ 100 indices
IV.2.33 Annual covariance matrix based on Table IV.2.32
IV.2.34 RiskMetrics VaR for US stock portfolio
IV.2.35 VaR and ETL for Student t distributions
IV.2.36 VaR and ETL for normal, Student t and mixture distributions
IV.2.37 Sample statistics for iTraxx Europe 5-year index
IV.2.38 Normal mixture parameter estimates: iTraxx Europe 5-year index
IV.2.39 VaR and ETL estimates for iTraxx Europe 5-year index
IV.3.1 Estimated values of scale exponent for S&P 500 index
IV.3.2 Estimated scale exponents for $/£ forex rate and US interest rates
IV.3.3 Recommended scale exponents for volatility indices
IV.3.4 Scaling 1-day VaR for different risk horizons and scale exponents
IV.3.5 GARCH parameters for S&P 500 index
IV.3.6 Historical VaR for S&P 500 on 31 March 2008
IV.3.7 Estimated values of scale exponent for volatility adjusted S&P 500
IV.3.8 Scaling VaR versus filtered historical simulation
IV.3.9 Historical VaR based on kernel fitting
IV.3.10 Estimates of GPD parameters (Matlab)
IV.3.11 Sample statistics used for Cornish–Fisher expansion
IV.3.12 Historical versus normal VaR for UK bond portfolio
IV.3.13 Historical VaR with different volatility adjustments
IV.3.14 Total, systematic and specific VaR, US stock portfolio
IV.3.15 Decomposition of systematic VaR into equity and forex stand-alone components
IV.3.16 Historical marginal VaR for international stock portfolio
IV.3.17 Bond position
IV.3.18 VaR decomposition for international bond position
IV.3.19 Crack spread book, 1 August 2006
IV.3.20 Total VaR and component VaRs for a crack spread trader
IV.3.21 Estimates of GPD parameters and historical VaR estimates
IV.3.22 Comparison of ETL from parametric fits to historical return distribution
IV.3.23 Stand-alone equity and forex ETL for an international stock portfolio
IV.4.1 Excel commands for simulations
IV.4.2 Simulated returns based on constant and EWMA volatilities
IV.4.3 Multi-step Monte Carlo VaR based on constant and EWMA volatilities
IV.4.4 A-GARCH model parameters
IV.4.5 Multi-step Monte Carlo A-GARCH VaR with positive and negative shocks
IV.4.6 Risk factor returns, volatilities, sensitivities and correlations
IV.4.7 Volatilities and correlations of LIBOR and credit spreads
IV.4.8 Comparison of Monte Carlo VaR estimates for credit spreads
IV.4.9 PC sensitivities and the PC Cholesky matrix
IV.4.10 Parameters of normal mixture distribution for three stocks
IV.4.11 Parameters of normal distribution for three stocks
IV.4.12 Comparison of normal and normal mixture Monte Carlo scenario VaR
IV.4.13 Bivariate GARCH model parameters
IV.4.14 Comparison of normal GARCH and Student t GARCH VaR
IV.5.1 Delta and vega effects (symmetric negative price–volatility relationship)
IV.5.2 Delta and vega effects (asymmetric negative price–volatility relationship)
IV.5.3 Delta and vega effects (asymmetric positive price–volatility relationship)
IV.5.4 Characteristics of equity indices and their options
IV.5.5 1% 10-day VaR under different rebalancing assumptions
IV.5.6 Comparison of 10% and 0.1% 10-day VaR under different rebalancing assumptions
IV.5.7 Comparison of VaR and ETL for long and short calls and puts
IV.5.8 Disaggregation of option VaR into price, volatility and interest rate VaRs
IV.5.9 Characteristics of European options on S&P 500 futures
IV.5.10 Historical VaR with Greeks approximation
IV.5.11 Position Greeks of large international stock option portfolio
IV.5.12 Value Greeks of a large international stock option portfolio
IV.5.13 Historical VaR for a large international stock option portfolio
IV.5.14 Limits on value Greeks of the crude oil option portfolio
IV.5.15 Historical VaR of the crude oil option portfolio
IV.5.16 Historical volatilities and correlations for risk factors of S&P 500 option
IV.5.17 Effect of non-linearity and non-normality on 1% daily Monte Carlo VAR
IV.5.18 Student t Monte Carlo VAR with and without daily rebalancing
IV.5.19 Long-term VaR estimates for static and dynamic portfolios
IV.5.20 Bivariate GARCH model parameters
IV.5.21 Monte Carlo VaR for option based on constant volatility and GARCH
IV.5.22 Risk factor covariance matrix (×104)
IV.5.23 Risk factor volatilities and correlations
IV.5.24 Comparison of Monte Carlo and historical VaR
IV.5.25 Risk factor volatilities and correlations
IV.5.26 Monte Carlo versus historical VaR for a large international stock option portfolio
IV.5.27 Risk factor correlations
IV.5.28 Monte Carlo VaR of the crude oil option portfolio
IV.5.29 Eigenvalues of 10-day historical covariance matrix for crude oil futures
IV.5.30 Normalized eigenvectors for first two eigenvalues in Table IV.5.29
IV.5.31 Monte Carlo PC VaR for the portfolio of crude oil options
IV.5.32 Volatility beta estimates relative to 3-month volatility
IV.5.33 Influence of vega mapping on VaR for a portfolio of crude oil options
IV.6.1 Advantages and limitations of different levels of risk assessment
IV.6.2 Discount rate volatilities and correlations
IV.6.3 Computing the cash-flow map and estimating PV01
IV.6.4 OLS and EWMA beta, index volatility and VaR for HBOS stock.
IV.6.5 Normal linear VaR estimates and approximate standard errors
IV.6.6 VaR standard errors based on volatility and based on quantile
IV.6.7 Basel zones for VaR models
IV.6.8 Coverage tests on RiskMetrics™ VaR of S&P 500 index
IV.6.9 Exceedances and t ratio on standardized exceedance residuals
IV.6.10 Results of likelihood ratio test
IV.7.1 Scenario categorization, with illustration using the iTraxx index
IV.7.2 VaR estimates based on historical scenarios
IV.7.3 Prices for crude oil futures ($/barrel)
IV.7.4 Expected weekly returns, standard deviations and correlations
IV.7.5 Normal mixture VaR versus normal VaR
IV.7.6 Analyst's beliefs about credit spreads
IV.7.7 Six sigma losses
IV.7.8 Results of worst case loss optimization
IV.7.9 Sample moments of S&P 500 and FTSE 100 index returns during global crash period
IV.7.10 Adjusting VaR for uniform liquidation
IV.7.11 Stressed VaR at different confidence levels based on Monte Carlo GARCH
IV.8.1 Aggregation of economic capital
IV.8.2 Aggregate RORAC as a function of correlation
IV.8.3 Effect of cost of capital and correlation on aggregate RAROC
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3.23.101.1