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It is interesting to note that when viewed in terms of
measure 1, historical simulation does appears to be a reasonable model
which neither significantly overestimates or underestimates risk over
the full range of confidence levels.
In fact, on the basis of this measure, one could perhaps reject model 5 (tail
emphasized GARCH(1,1)) as being too conservative - in the sense of always
over-estimating risk. In general the message from figures 1u and 1m is that
models 1 and 3 have similar behaviours at low confidence level but in the
regime beyond the
level - tables are turned and - model 1 becomes far
superior than all models except model 5. We also find that there is not
much too choose between models 2 and 4.