Table 3 Generalized CM VaR bounds versus FFT VaR from best fitted return distributions
From: An explicit version of the Chebyshev-Markov-Stieltjes inequalities and its applications
CM VaR bound of order m | SMI and SP500 data sets | ||||
|---|---|---|---|---|---|
SMI 3Y/1D | SP 3Y/1D | SMI 24Y/1D | SP 24Y/1D | SP 63Y/1M | |
1 | 14.10674 | 14.10674 | 14.10674 | 14.10674 | 14.10674 |
2 | 5.70929 | 5.80257 | 6.38478 | 6.57694 | 5.52054 |
3 | 4.63181 | 5.08737 | 5.85193 | 5.97425 | 5.05367 |
4 | 4.33603 | 5.08073 | 5.81340 | 5.97368 | 5.03519 |
5 | 4.24284 | 4.51830 | 5.15713 | 5.19075 | 4.07623 |
6 | 4.20294 | 4.04401 | 5.01443 | 4.88268 | 3.91300 |
7 | 4.18175 | 3.98179 | 4.91795 | 4.88033 | 3.89962 |
8 | 4.17181 | 3.97972 | 4.51596 | 4.56437 | 3.41525 |
9 | 4.16756 | 3.96797 | 4.44315 | 4.29779 | 3.31145 |
10 | 4.16568 | 3.45184 | 4.42918 | 4.28693 | 3.30855 |
maximum loss | 4.20421 | 5.93094 | 9.39704 | 8.18808 | 5.95942 |
Normal approx. | 2.57583 | 2.57583 | 2.57583 | 2.57583 | 2.57583 |
FFT VaR | SMI 3Y/1D | SP500 3Y/1D | SMI 24Y/1D | SP 24Y/1D | SP 63Y/1D |
VG | 3.18228 | 3.09191 | 3.55423 | 3.69317 | 2.65234 |
NVG | 3.15521 | 3.08703 | 3.42190 | 3.52504 | 2.49884 |
TLF-BG | 3.46466 | 3.58737 | 3.83378 | 3.92492 | 3.57468 |
TLF | 3.42602 | 3.57239 | 3.78536 | 3.71739 | 3.54963 |
NIG | 3.43097 | 3.56194 | 3.72618 | 3.78626 | 3.58135 |
NTS | 3.44828 | 3.60691 | 3.62529 | 3.72720 | 3.54761 |
best fit FFT | NVG | NVG | NTS | TLF | NTS |
max. FFT VaR | TLF-BG | NTS | TLF_BG | TLF_BG | NIG |