6 36 2 16 6 539 16 39 4 9 16 4 831 16 716 3 16 726 2

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Unformatted text preview: 6 2 16 6 5.39 16 39 .4 9 16 4 8.31 16 71.6 3 16 72.6 2 16 6 5.19 16 6 8.9 8 16 4 6 .19 16 34 .16 16 24 .51 16 39 .4 6 16 4 2.50 16 4 5.6 5 16 34 .75 16 12.31 159 5.38 16 07.9 4 16 11.15 16 10.05 16 09 .12 159 2.23 16 03.14 159 9 .29 16 00.06 16 06 .4 9 16 09 .22 16 35.14 16 38.16 16 4 7.6 5 16 4 6 .80 16 4 7.57 16 53.6 6 16 4 1.4 3 16 50.07 16 76 .4 8 16 79 .21 16 6 3.38 16 71.01 16 55.00 16 6 4 .9 2 16 6 7.23 16 6 5.02 16 6 9 .39 16 6 2.4 6 16 6 8.54 16 82.75 16 78.07 16 6 8.9 3 16 6 7.6 1 16 71.84 16 78.83 16 6 1.4 5 16 56 .25 16 4 2.76 16 4 6 .28 16 32.81 16 38.34 16 4 0.6 5 16 4 1.89 16 36 .6 2 16 29 .58 16 21.80 16 21.08 16 32.52 16 10.88 16 15.27 159 9 .6 2 159 6 .4 8 16 12.33 16 13.50 16 21.35 16 23.26 16 30.4 8 16 20.28 16 19 .00 159 2.6 4 156 8.07 156 9 .9 6 159 0.35 1586 .4 3 156 7.9 5 1570.4 4 159 1.9 4 159 5.57 16 15.72 16 09 .9 7 16 20.4 7 16 16 .6 8 16 17.4 6 16 30.4 8 16 30.6 8 16 34 .83 16 22.28 16 29 .83 16 32.82 16 51.14 16 4 4 .25 16 55.6 5 16 4 8.52 16 51.6 5 16 59 .84 16 6 3.10 16 6 6 .82 16 55.10 16 59 .78 16 6 7.25 16 57.88 16 6 8.39 16 4 5.17 16 37.82 16 4 0.4 0 16 30.6 7 16 4 0.6 2 16 4 7.79 16 4 7.4 8 16 72.4 9 16 78.10 16 77.09 16 88.83 16 72.08 16 59 .51 16 6 2.84 16 59 .07 16 4 7.13 16 31.81 16 39 .08 16 4 7.6 9 16 31.74 16 32.4 9 16 36 .76 16 20.85 16 19 .4 8 16 4 3.57 16 6 5.01 16 6 8.55 16 72.6 5 16 73.10 16 73.16 16 9 2.22 1719 .6 4 1726 .34 1724 .59 1724 .08 1722.6 7 1738.32 1754 .33 1753.9 9 174 1.72 1751.57 1753.9 7 1734 .4 5 174 4 .71 174 4 .31 1751.55 1753.09 174 7.34 174 0.33 176 6 .9 0 176 5.37 176 6 .6 3 176 5.33 174 5.83 1754 .75 176 4 .35 176 2.51 1778.54 1785.51 1789 .14 1785.51 1772.19 1772.87 1788.9 3 179 5.6 6 179 6 .4 9 1788.76 1801.58 1801.71 1801.9 8 179 9 .55 1784 .9 6 176 4 .30 1758.07 176 4 .6 3 176 2.12 176 8.17 1757.51 176 4 .72 174 9 .4 8 1759 .9 8 1777.03 176 0.28 174 6 .6 1 1735.4 2 1729 .33 Return σ Sta ndar dized 2 t R eturn R t/ σt N GAR C H (1, 1) σ Monte-Carlo Simulations Sta ndar dized 2 t R eturn R t/σ t λ RiskMetrics 0.9 4 NGARCH(1,1) Parameters α 0.054 4 581 β 0.834 74 75 ω θ 1.714 E-06 1.373876 9 La st Da y Value s of σt RiskMetrics NGARCH(1,1) 1% VaRs Risk Metrics Monte-Ca rlo FHS 1% ES Risk Metrics Monte-Ca rlo FHS Day 1 Draw Rnd Shock 1 2 3 4 5 6 7 Return Day 2 σ 2 t Rnd Shock Return Day 3 2 t Rnd Shock Return Day 4 σ 2 t Rnd Shock Return Day 5 σ 2 t Rnd Shock Return Day 6 σ 2 t Rnd Shock Return Day 7 σ 2 t Rnd Shock Return Day 8 σ 2 t Rnd Shock Return Day 9 σ 2 t Rnd Shock Return D a y 10 σ 2 t Rnd Shock Return σ 2 t 1 0-Da y R eturn ES Calculations 10 0 Larges t L oss es Rank 1 2 3 4 5 6 7 Filter ed H is tor ic al Simula tion Day 1 Draw Discrete Nums 1 2 3 4 5 6 7 Std Return Day 2 Return σ 2 t Discrete Nums Std Return Day 3 Return σ 2 t Discrete Nums Std Return Day 4 Return σ 2 t Discrete Nums Std Return Day 5 Return σ 2 t Discrete Nums Std Return Day 6 Return σ 2 t Discrete Nums Std Return Day 7 Return σ 2 t Discrete Nums Std Return Day 8 Return σ...
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