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An extract of parameter estimates of the 12 market returns Table 2 was assigned to a smaller |a — @|. Then, the average of all the ranks for each method were calculated and displayed as mean rank in Table 4. A smaller mean rank indicates an overall better match between a and & which is a sign of superior performance. Similarly, we studiec the cases for holding a short position in the investment. In these cases, the VaR is defined by

Table 2 An extract of parameter estimates of the 12 market returns Table 2 was assigned to a smaller |a — @|. Then, the average of all the ranks for each method were calculated and displayed as mean rank in Table 4. A smaller mean rank indicates an overall better match between a and & which is a sign of superior performance. Similarly, we studiec the cases for holding a short position in the investment. In these cases, the VaR is defined by

Related Figures (11)

Summary statistics of stock market and exchange rate returns
Summary statistics of stock market and exchange rate returns
Fig. 1. Sample mean and standard deviation of the market index returns.
Fig. 1. Sample mean and standard deviation of the market index returns.
Model selection: ranking of AIC and SBC (in parantheses) Table 3
Model selection: ranking of AIC and SBC (in parantheses) Table 3
Sample coverage for the long position of the 12 market indices Table 4
Sample coverage for the long position of the 12 market indices Table 4
Sample coverage for the short position of the 12 market indices Table 5
Sample coverage for the short position of the 12 market indices Table 5
Fig. 2. Boxplots showing the distribution of the sample coverage & in various scenarios. Dotted reference lines locate the position of a. The top, medium and bottom panels correspond to the Ist, 2.5th and 5th percentiles, respectively. The left and right columns refer to the long and short positions. M.K.P. So, P.L.H. Yu/ Int. Fin. Markets, Inst. and Money 16 (2006) 180-197
Fig. 2. Boxplots showing the distribution of the sample coverage & in various scenarios. Dotted reference lines locate the position of a. The top, medium and bottom panels correspond to the Ist, 2.5th and 5th percentiles, respectively. The left and right columns refer to the long and short positions. M.K.P. So, P.L.H. Yu/ Int. Fin. Markets, Inst. and Money 16 (2006) 180-197
Fig. 3. Boxplots showing the distribution of the sample coverage & for the 12 market indices. Dotted reference lines locate the position of a. The top, medium and bottom panels correspond to the Ist, 2.5th and 5th percentiles, respectively. ~ To check the performance of the seven models in each stock market, we present the boxplots showing the distribution of sample coverage in Fig. 3. Among the 12 indices, AOI and FTSE100 have the least variation, and JSX, NASDAQ and NIKKEI show the largest
Fig. 3. Boxplots showing the distribution of the sample coverage & for the 12 market indices. Dotted reference lines locate the position of a. The top, medium and bottom panels correspond to the Ist, 2.5th and 5th percentiles, respectively. ~ To check the performance of the seven models in each stock market, we present the boxplots showing the distribution of sample coverage in Fig. 3. Among the 12 indices, AOI and FTSE100 have the least variation, and JSX, NASDAQ and NIKKEI show the largest
Sample coverage for the long position of the four exchange rates Table 6
Sample coverage for the long position of the four exchange rates Table 6
Fig. 4. Boxplots showing the distribution of the sample coverage & for the four exchange rates. Dotted reference lines locate the position of a. The top, medium and bottom panels correspond to the Ist, 2.5th and 5th percentiles, respectively. We fitted the seven models to the exchange rate returns and computed estimates of VaR in 1995-1998. Comparing the summary results in Tables 6 and 7, we find very consistent performance results in long and short positions. For a = 1%, all the t-error models out- perform the normal-error models. GARCH(f) and IGARCH(f) are the best two models in estimating VaR for both positions. IGARCH appears to be the best choice for a = 2.5% though GARCH(f) performs equally well in terms of the mean rank in short position. In the cases of the above two a@ values, RiskMetrics performs the worst in all cases except in the short position with a = 2.5% where FIGARCH(f) shows even higher mean rank. This suggests that RiskMetrics should not be recommended to estimate small percentage VaR for exchange rates. On the other hand, for a = 5%, RiskMetrics is recorded as the best and the second best in long and short positions, respectively. Fig. 4 shows the distribution of
Fig. 4. Boxplots showing the distribution of the sample coverage & for the four exchange rates. Dotted reference lines locate the position of a. The top, medium and bottom panels correspond to the Ist, 2.5th and 5th percentiles, respectively. We fitted the seven models to the exchange rate returns and computed estimates of VaR in 1995-1998. Comparing the summary results in Tables 6 and 7, we find very consistent performance results in long and short positions. For a = 1%, all the t-error models out- perform the normal-error models. GARCH(f) and IGARCH(f) are the best two models in estimating VaR for both positions. IGARCH appears to be the best choice for a = 2.5% though GARCH(f) performs equally well in terms of the mean rank in short position. In the cases of the above two a@ values, RiskMetrics performs the worst in all cases except in the short position with a = 2.5% where FIGARCH(f) shows even higher mean rank. This suggests that RiskMetrics should not be recommended to estimate small percentage VaR for exchange rates. On the other hand, for a = 5%, RiskMetrics is recorded as the best and the second best in long and short positions, respectively. Fig. 4 shows the distribution of
Sample coverage for the short position of the four exchange rates Table 7
Sample coverage for the short position of the four exchange rates Table 7
Best two models based on mean ranks Table 8 the sample coverage for the four exchange rates. Comparing this distribution with that for the 12 market indices in Fig. 3, the sample coverage is less dispersed in the exchange rates. This indicates the VaR estimation for exchange rates is less dependent on the methods used than stock market index data. It is also noteworthy that unlike models for stock market indices, models with fat-tailed errors for exchange rates demonstrate superior performance for estimating extreme VaR, such as a = 1%, in both long and short positions.
Best two models based on mean ranks Table 8 the sample coverage for the four exchange rates. Comparing this distribution with that for the 12 market indices in Fig. 3, the sample coverage is less dispersed in the exchange rates. This indicates the VaR estimation for exchange rates is less dependent on the methods used than stock market index data. It is also noteworthy that unlike models for stock market indices, models with fat-tailed errors for exchange rates demonstrate superior performance for estimating extreme VaR, such as a = 1%, in both long and short positions.
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Applied EconomicsValue at RiskFinancial Institutions and MarketsMarket Risk
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