### Table 1 Results of experiments with the value-at-risk model.

2006

"... In PAGE 15: ...999. The results are presented in Table1 ; the reader should be aware that we work with a maximization problem, so that the larger the value of the objective yielded by a method, the better. Therefore, what was before a lower bound on the optimal value in the chance constrained problem becomes an upper bound, etc.... In PAGE 15: ... Therefore, what was before a lower bound on the optimal value in the chance constrained problem becomes an upper bound, etc. Explanations to Table1 . aEmpirical risk makes sense only with respect to the optimal values yielded by various methods and is the empirical frequency estimate, taken over 10,000 simulations, of the probability p of violating the randomly per- turbed constraint in (P0.... ..."

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### Table 8: Value-at-Risk and Expected Shortfall at the 95th Percentile. Normal vs. Student-t copula with DoF=12, 100K-path Monte Carlo simulation.

"... In PAGE 27: ... Let us now assume that each of the 100 reference names has an objective default intensity equal to 50 basis points, the remaining parameters unchanged. Table8 compares the two dependence assumptions in terms of the 95% Value-at-Risk and Expected Shortfall that they produce for a number of loss tranches. Where we de ne the Value-at-Risk, VaR := DL 1( ) and the conditional-VaR, CVaR := 1 1 R 1 DL 1(t)dt, where DL is the discounted loss.... ..."

### Table B4 Calculation of the undiversified overnight Value-at-Risk values.

### Table 1: Quantile estimates for Mexico index. Negative quantiles are the unconditional Value-at-Risk.

"... In PAGE 10: ... We experimented with its arguments and found a good fit by setting the cosine window and the number of points used in the computations, n , equal to 100. Table1 shows the quantiles obtained from the DDP fit and the empirical ones for the Mexico index. The minimum and maximum of this data set (before standard- ization) are respectively -21.... In PAGE 11: ...31.24. It would be interesting to contrast the DDP and empirical quantile estimates to classical procedures and EVT estimates. Table1 also gives the normal and the t4 basedquantileswithlocationandscaleestimated using the classical sample mean and sample standard deviation. More robust quantiles estimates based on the t4 withthemedianandmad(constant=1.... In PAGE 11: ... These estimates are very sensitive to the choice of number of observations in the tails. Estimates given in Table1 are based on 14 and 21 observations on the left and right tail, respectively. This choice makes the thresholds equal to -5.... In PAGE 11: ...o 1.07% and 1.61%, similar to those used by the DDP estimates. Of course, it is possible to EVT estimate only quantiles associated to probabilities smaller than the chosen proportions in the tail. In order to compare the estimates givenin Table1 weobservethattheempir- ical and the EVT estimates are unable to estimate certain quantiles. The normal assumption with maximum likelihood estimates underestimate quantiles on the ex- treme tails.... ..."

### Table 5 Backtesting results for a random walk model for the levels p = 1% and p = 5%, using real stock indices and simulated random walk data, respectively. Measures for one- year value-at-risk and expected shortfall are evaluated.

2005

"... In PAGE 14: ...acktesting in done as explained in Section 7.1. Since the results vary from simulation to simulation, we repeat the whole procedure several times. The results are displayed in Table5 , together with a recapitulation of the corresponding results for stock index data (see Table 2). Note that now for these simulated processes ((7.... In PAGE 14: ... With normal innovations, for most of the 20 cases (four data sets, h = 1; 5; 22; 65; 261), VaR5% is clearly underesti- mated (V freq;5% gt; 5%), while VaR1% is overestimated for three of the four types of data, see Tables 1{4. This over- and underestimation is approximately of the same order as for the simulated time series in Table5 . Replacing normal log-returns by heavier tailed ones would even worsen the slight overestimation for the 1% level.... ..."

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### Table 9 Sensitivity Analysis of Value-at -Risk:

1998

"... In PAGE 11: ... For example, there is at least a 99% chance of the swap being of greater value than 134,678,753 Yen. Table9 here In Table 9, we show the effect of increasing the number of binomial stages. The confidence level values are quite sensitive to the binomial-density chosen.... In PAGE 11: ... For example, there is at least a 99% chance of the swap being of greater value than 134,678,753 Yen. Table 9 here In Table9 , we show the effect of increasing the number of binomial stages. The confidence level values are quite sensitive to the binomial-density chosen.... In PAGE 11: ... An increase in the binomial density, J, has the effect of including a wider range of possible exchange rates. This effect can be seen in Figure 3, where the range has been considerably extended compared with the range for J = 1 shown in Table9 . This also has a radical effect on the percentile VAR estimate.... ..."

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### Table 7: Value-at-Risk violations and HIT regression results for DJIA stocks for an equally weighted and a minimum variance portfolio

### Table 6.20 Value-at-Risk estimates (USD) one-day forecast horizon: total portfolio value is 103.719

1996

### Table 7: SensitivityofVaR with respect to market volatility

1997

"... In PAGE 16: ... Sensitivity of the value-at-risk with respect to market volatility #1B: Figures 7 and 8 illustrate the value-at-risk curve for #1B = 1 and #1B =1:3 as a function of level #0B. Table7 summarizes the associated numbers for the concave, linear and convex risk pro#0Cle. In case the volatility increases by 30#25, the value-at-risk changes by 69#25 for the concave risk pro#0Cle g , ;obviously, the value-at-risk changes by 30#25 for the linear risk pro#0Cle, and it changes by 14#25, 18#25 and respectively 20#25 for the convex risk pro#0Cle g + .... ..."

### Table 1 Backtesting results for the levels p = 1% and p = 5%, using foreign exchange rate data. Measures for one-year value-at-risk and expected shortfall are evaluated.

2005

"... In PAGE 12: ... Results for the 5% level will be used to con rm the reliability and the exibility of each approach. For foreign exchange rates ( Table1 ) all four models seem to perform rather well for appropriate choices of the calibration horizon h. The best results are obtained when the models are calibrated with monthly (h = 22) or quarterly (h = 65) data.... ..."

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