Do coherent risk measures identify assets risk profiles similarly? Evidence from international futures markets

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The authors consider Lévy processes with conditional distributions belonging to a generalized hyperbolic family and compare and contrast full density-based Lévy-expected shortfall (ES) risk measures and Lévy-spectral risk measures (SRM) with those of a traditional tail-based unconditional extreme value (EV) approach. Using the futures data of leading markets the authors find that ES and SRM often differ in recognizing the risk profiles of different assets. While EV (extreme value) is often found to be more consistent than Lévy models, Lévy measures often perform better than EV measures when compared with empirical values. This becomes increasingly apparent as investors become more risk averse.

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    • Figure 1. Conditional and unconditional quantiles in excess of threshold (2): long position in S&P 500
    • Figure 2. Conditional and unconditional quantiles in excess of threshold (1.5): long position in FTSE100
    • Figure 3. Conditional and unconditional quantiles in excess of threshold (2): long position in DAX
    • Figure 4. Conditional and unconditional quantiles in excess of threshold (2): long position in Hang Seng
    • Figure 5. Conditional and unconditional quantiles in excess of threshold (2): long position in Nikkei 225
    • Table 1. Generalized Pareto distribution (GDP) parameter estimates for futures indexes
    • Table 2. Conditional maximum likelihood estimates for futures indexes
    • Table 3. Anderson-Darling and left-truncated Anderson-Darling goodness-of-fit tests
    • Table 4. Estimates of ES and Lévy spectral risk measures for futures position
    • Table 5. Frequency distribution of significant estimates of ES and Lévy spectral risk measures