Abstract
In a recent paper, Acerbi and Székely (Risk Magazine, 76–81, 2014) presented three methods to test expected shortfall, and this is the first empirical application of that paper on emerging markets. We employ daily stock index returns from the Morgan Stanley Capital International Inc. Emerging Markets Index covering the 2000–2015 period, extending Acerbi and Székely (Risk Magazine, 76–81, 2014) results to derive the significance thresholds for the Student’s skewed-t distribution using two testing methods. We find that the thresholds for the Z1 Test and Z2 Test for skewed-t distribution are similar to the values obtained by Acerbi and Székely for Student’s t distribution. Therefore, the Z1 and Z2 thresholds are invariant to the skewed-t-shaped parameter values found in the emerging market stock indices. Empirical results show outperformance of Student’s skewed-t and Student’s t distributions over Gaussian distribution.
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Notes
Acerbi and Székely employed − 0.17 when T = 250, see Table 2, Panel A1.
We are grateful to the Reviewer for pointing this out.
P is the number of the random samples.
For Colombian stock index 3101 observations, for Chinese stock index 3201 observations, for Korean stock index 3501 observations, and for Egyptian stock index 3601 observations.
References
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Acknowledgements
The authors are very grateful for the comments of the Editor and the Reviewer, which helped to improve the original version of the paper.
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Appendices
Appendix A: Dataset description
Country index | Bloomberg ticker |
---|---|
Americas | |
Brazil | IBOV |
Chile | IPSA |
Colombia | COLCAP |
Mexico | MEXBOL |
Peru | IGBVL |
Europe, Middle East & Africa | |
Czech Republic | PX |
Egypt | HERMES |
Greece | ASE |
Hungary | BUX |
Poland | WIG |
Qatar | DSM |
Russia | INDEXCF |
South Africa | TOP40 |
Turkey | XU100 |
ASIA | |
China | SHSZ300 |
India | SENSEX |
Indonesia | JCI |
Korea | KRX100 |
Malaysia | FBMKLCI |
Philippines | PCOMP |
Taiwan | TWSE |
Thailand | SET |
Appendix B: Model selection when innovations are normally, t and skewed-t distributed
Models | GARCH(1,1) | AR(1) GARCH(1,1) | ARMA(1,1) GARCH(1,1) | ||||||
---|---|---|---|---|---|---|---|---|---|
Stock index | Log likelihood | AIC | BIC | Log likelihood | AIC | BIC | Log likelihood | AIC | BIC |
Panel A: Normal | |||||||||
Brazil | − 9703.64 | 5.11 | 5.10 | − 9704.75 | 5.11 | 5.10 | − 9705.45 | 5.10 | 5.10 |
Chile | − 12,112.69 | 6.37 | 6.37 | − 12,132.88 | 6.38 | 6.37 | − 12,138.10 | 6.39 | 6.38 |
Colombia | − 9727.28 | 6.27 | 6.27 | − 9760.99 | 6.29 | 6.28 | − 9761.02 | 6.29 | 6.28 |
Mexico | − 9679.34 | 5.09 | 5.09 | − 9680.24 | 5.09 | 5.08 | − 9680.70 | 5.09 | 5.08 |
Peru | − 9679.34 | 5.09 | 5.09 | − 9680.24 | 5.09 | 5.08 | − 9680.70 | 5.09 | 5.08 |
Czech Rep | − 10,954.30 | 5.76 | 5.76 | − 10,954.63 | 5.76 | 5.75 | − 10,955.25 | 5.76 | 5.75 |
Egypt | − 10,128.27 | 5.62 | 5.62 | − 10,188.31 | 5.66 | 5.65 | − 10,189.32 | 5.66 | 5.65 |
Greece | − 9968.73 | 5.24 | 5.24 | − 9992.49 | 5.26 | 5.25 | − 10,109.36 | 5.32 | 5.31 |
Hungary | − 10,529.39 | 5.54 | 5.53 | − 10,531.51 | 5.54 | 5.53 | − 10,532.80 | 5.54 | 5.53 |
Poland | − 9679.34 | 5.09 | 5.09 | − 9680.24 | 5.09 | 5.08 | − 9680.70 | 5.09 | 5.08 |
Qatar | − 11,755.57 | 6.19 | 6.18 | − 11,823.58 | 6.22 | 6.21 | − 11,823.75 | 6.22 | 6.21 |
Russia | − 8954.01 | 4.71 | 4.70 | − 8954.06 | 4.71 | 4.70 | − 8954.07 | 4.71 | 4.70 |
South Africa | − 9679.34 | 5.09 | 5.09 | − 9680.24 | 5.09 | 5.08 | − 9680.70 | 5.09 | 5.08 |
Turkey | − 9679.34 | 5.09 | 5.09 | − 9680.24 | 5.09 | 5.08 | − 9680.70 | 5.09 | 5.08 |
China | − 8809.01 | 5.50 | 5.50 | − 8809.86 | 5.50 | 5.49 | − 8810.71 | 5.50 | 5.49 |
India | − 10,364.87 | 5.45 | 5.45 | − 10,367.15 | 5.45 | 5.45 | − 10,396.30 | 5.47 | 5.46 |
Indonesia | − 10,876.98 | 5.72 | 5.72 | − 10,893.35 | 5.73 | 5.72 | − 10,894.53 | 5.73 | 5.72 |
Korea | − 10,145.89 | 5.80 | 5.79 | − 10,146.14 | 5.79 | 5.79 | − 10,147.57 | 5.80 | 5.78 |
Malaysia | − 9679.34 | 5.09 | 5.09 | − 9680.24 | 5.09 | 5.08 | − 9680.70 | 5.09 | 5.08 |
Phillipines | − 10,619.01 | 5.59 | 5.58 | − 10,631.41 | 5.59 | 5.58 | − 10,637.45 | 5.60 | 5.59 |
Taiwan | − 10,328.95 | 5.43 | 5.43 | − 10,356.28 | 5.45 | 5.44 | − 10,558.47 | 5.55 | 5.54 |
Thailand | − 10,931.66 | 5.75 | 5.74 | − 10,941.49 | 5.76 | 5.75 | − 10,943.82 | 5.76 | 5.75 |
Panel B: Student’s t | |||||||||
Brazil | − 10,073.49 | 5.30 | 5.29 | − 10,074.55 | 5.30 | 5.29 | − 10,076.03 | 5.30 | 5.29 |
Chile | − 12,539.57 | 6.60 | 6.59 | − 12,591.60 | 6.62 | 6.61 | − 12,592.91 | 6.62 | 6.61 |
Colombia | − 9791.16 | 6.31 | 6.30 | − 9822.43 | 6.33 | 6.32 | − 9822.48 | 6.33 | 6.32 |
Mexico | − 11,369.76 | 5.98 | 5.97 | − 11,379.70 | 5.99 | 5.98 | − 11,381.80 | 5.99 | 5.98 |
Peru | − 11,516.77 | 6.06 | 6.05 | − 11,578.67 | 6.09 | 6.08 | − 11,578.72 | 6.09 | 6.08 |
Czech Rep | − 11,384.93 | 5.99 | 5.98 | − 11,387.01 | 5.99 | 5.98 | − 11,387.14 | 5.99 | 5.98 |
Egypt | − 10,246.76 | 5.69 | 5.68 | − 10,299.70 | 5.72 | 5.71 | − 10,300.79 | 5.72 | 5.71 |
Greece | − 10,676.43 | 5.62 | 5.61 | − 10,690.51 | 5.62 | 5.61 | − 10,691.40 | 5.62 | 5.61 |
Hungary | − 10,762.09 | 5.66 | 5.65 | − 10,763.42 | 5.66 | 5.65 | − 10,764.55 | 5.66 | 5.65 |
Poland | − 11,348.47 | 5.97 | 5.96 | − 11,354.27 | 5.97 | 5.96 | − 11,355.22 | 5.97 | 5.96 |
Qatar | − 12,427.34 | 6.54 | 6.53 | − 12,554.03 | 6.60 | 6.59 | − 12,556.00 | 6.60 | 6.59 |
Russia | − 9784.28 | 5.15 | 5.14 | − 9784.40 | 5.15 | 5.14 | − 9784.41 | 5.15 | 5.13 |
South Africa | − 10,073.49 | 5.30 | 5.29 | − 10,074.55 | 5.30 | 5.29 | − 10,076.03 | 5.30 | 5.29 |
Turkey | − 12,539.57 | 6.60 | 6.59 | − 12,591.60 | 6.62 | 6.61 | − 12,592.91 | 6.62 | 6.61 |
China | − 11,369.76 | 5.98 | 5.97 | − 11,379.70 | 5.99 | 5.98 | − 11,381.80 | 5.99 | 5.98 |
India | − 11,516.77 | 6.06 | 6.05 | − 11,578.67 | 6.09 | 6.08 | − 11,578.72 | 6.09 | 6.08 |
Indonesia | − 11,384.93 | 5.99 | 5.98 | − 11,387.01 | 5.99 | 5.98 | − 11,387.14 | 5.99 | 5.98 |
Korea | − 10,198.86 | 5.83 | 5.82 | − 10,198.88 | 5.82 | 5.81 | − 10,200.89 | 5.83 | 5.81 |
Malaysia | − 10,676.43 | 5.62 | 5.61 | − 10,690.51 | 5.62 | 5.61 | − 10,691.40 | 5.62 | 5.61 |
Philippines | − 10,762.09 | 5.66 | 5.65 | − 10,763.42 | 5.66 | 5.65 | − 10,764.55 | 5.66 | 5.65 |
Taiwan | − 11,348.47 | 5.97 | 5.96 | − 11,354.27 | 5.97 | 5.96 | − 11,355.22 | 5.97 | 5.96 |
Thailand | − 12,427.34 | 6.54 | 6.53 | − 12,554.03 | 6.60 | 6.59 | − 12,556.00 | 6.60 | 6.59 |
Panel C: Skewed-t | |||||||||
Brazil | − 10,084.16 | 5.30 | 5.29 | − 10,085.46 | 5.30 | 5.29 | − 10,089.21 | 5.31 | 5.29 |
Chile | − 12,552.49 | 6.60 | 6.59 | − 12,597.93 | 6.63 | 6.62 | − 12,599.91 | 6.63 | 6.61 |
Colombia | − 9797.18 | 6.32 | 6.31 | − 9826.46 | 6.34 | 6.32 | − 9826.58 | 6.33 | 6.32 |
Mexico | − 11,386.78 | 5.99 | 5.98 | − 11,393.55 | 5.99 | 5.98 | − 11,397.00 | 5.99 | 5.98 |
Peru | − 11,519.84 | 6.06 | 6.05 | − 11,580.20 | 6.09 | 6.08 | − 11,580.27 | 6.09 | 6.08 |
Czech Rep | − 11,398.14 | 6.00 | 5.99 | − 11,399.26 | 6.00 | 5.98 | − 11,399.41 | 6.00 | 5.98 |
Egypt | − 10,264.72 | 5.70 | 5.69 | − 10,309.90 | 5.72 | 5.71 | − 10,312.17 | 5.72 | 5.71 |
Greece | − 10,682.95 | 5.62 | 5.61 | − 10,694.87 | 5.63 | 5.61 | − 10,696.05 | 5.63 | 5.61 |
Hungary | − 10,762.41 | 5.66 | 5.65 | − 10,763.64 | 5.66 | 5.65 | − 10,764.77 | 5.66 | 5.65 |
Poland | − 11,351.24 | 5.97 | 5.96 | − 11,356.31 | 5.97 | 5.96 | − 11,357.36 | 5.97 | 5.96 |
Qatar | − 12,427.63 | 6.54 | 6.53 | − 12,554.05 | 6.60 | 6.59 | − 12,556.04 | 6.60 | 6.59 |
Russia | − 9798.18 | 5.15 | 5.14 | − 9798.40 | 5.15 | 5.14 | − 9799.31 | 5.15 | 5.14 |
South Africa | − 11,264.57 | 5.93 | 5.92 | − 11,264.80 | 5.93 | 5.91 | − 11,264.83 | 5.92 | 5.91 |
Turkey | − 9767.90 | 5.14 | 5.13 | − 9768.24 | 5.14 | 5.13 | − 9770.02 | 5.14 | 5.12 |
China | − 8892.87 | 5.55 | 5.54 | − 8893.46 | 5.55 | 5.54 | − 8894.54 | 5.55 | 5.54 |
India | − 10,925.33 | 5.75 | 5.74 | − 10,933.50 | 5.75 | 5.74 | − 10,935.47 | 5.75 | 5.74 |
Indonesia | − 11,151.90 | 5.87 | 5.86 | − 11,157.38 | 5.87 | 5.86 | − 11,159.18 | 5.87 | 5.86 |
Korea | − 10,209.91 | 5.83 | 5.82 | − 10,210.22 | 5.83 | 5.82 | − 10,211.99 | 5.83 | 5.82 |
Malaysia | − 13,305.95 | 7.00 | 6.99 | − 13,338.38 | 7.02 | 7.01 | − 13,338.68 | 7.02 | 7.00 |
Philippines | − 11,347.10 | 5.97 | 5.96 | − 11,365.51 | 5.98 | 5.97 | − 11,365.70 | 5.98 | 5.96 |
Taiwan | − 11,149.59 | 5.87 | 5.86 | − 11,152.82 | 5.87 | 5.85 | − 11,153.16 | 5.87 | 5.85 |
Thailand | − 11,288.38 | 5.94 | 5.93 | − 11,293.07 | 5.94 | 5.93 | − 11,294.90 | 5.94 | 5.93 |
Appendix C. 99%-VaR Backtesting for different periods
Appendix D: 97.5%-VaR backtesting for different periods
Appendix E: Range of the parameters estimated for Student’s t and skewed-t distributions
Distribution | Student’s t (degrees of freedom) | Skewed-t (degrees of freedom; shape parameters) | ||||
---|---|---|---|---|---|---|
Period | Total period | Pre-crisis | Crisis | Total period | Pre-crisis | Crisis |
Brazil | 3.43–10 | 7.28–10 | 4.93–10 | 3.56–10; 0.8–1.04 | 7.93–10; 0.81–1.04 | 4.95–10; 0.79–1.03 |
Chile | 4.65–10 | 8.66–10 | 4.92–10 | 5–10; 0.78–1.07 | 8.66–10; 0.81–1.08 | 4.99–10; 0.77–1 |
Colombia | 3.59–10 | 4.24–10 | 3.59–8.73 | 3.72–10; 0.77–1.06 | 4.27–10; 0.77–1.06 | 3.72–8.78; 0.87–1.05 |
Mexico | 3.22–10 | 4.54–10 | 4.04–9.71 | 3.15–10; 0.8–1.16 | 4.52–10; 0.8–1.15 | 4.08–10; 0.82–0.94 |
Peru | 3.53–10 | 4.78–10 | 3.95–10 | 3.56–10; 0.75–1.14 | 4.77–10; 0.92–1.13 | 3.94–10; 0.75–1.14 |
Czech Republic | 4.1–10 | 4.22–10 | 6.62–10 | 4.26–10;0.7–1.1 | 4.26–10; 0.7–1.1 | 6.6–10; 0.72–1.08 |
Egypt | 4.06–10 | 4.35–10 | 4.04–9.43 | 4.07–10; 0.72–1.13 | 4.37–10; 0.9–1.13 | 4.17–10; 0.74–0.9 |
Greece | 3.77–10 | 4–10 | 5.27–10 | 4.01–10; 0.71–1.21 | 4.01–10; 0.75–1.15 | 5.45–10; 0.71–1.21 |
Hungary | 5.21–10 | 6.06–10 | 5.22–10 | 5.23–10; 0.92–1.09 | 6.96–10; 0.92–1.09 | 5.23–10; 0.95–10 |
Poland | 3.62–10 | 6.05–10 | 6.41–10 | 3.76–10; 0.86–1.2 | 6.56–10; 0.86–1.2 | 6.47–10; 0.87–1.06 |
Qatar | 2.32–10 | 2.33–10 | 2.49–8.65 | 2.29–10; 0.86–1.17 | 2.28–10; 0.91–1.16 | 2.49–8.74; 0.85–1.06 |
Russia | 3.32–10 | 3.94–10 | 4.75–10 | 3.48–10; 0.77–1.03 | 4.01–10; 0.77–0.98 | 4.97–10; 0.8–1.03 |
South Africa | 3.56–10 | 6.62–10 | 7.23–10 | 3.68–10; 0.71–1.14 | 6.5–10; 0.7–1.14 | 7.19–10; 0.73–1 |
Turkey | 4.57–10 | 5.13–10 | 5.1–10 | 4.8–10; 0.8–1.14 | 5.14–10; 0.81–1.15 | 5.07–10; 0.8–1.1 |
China | 3.45–10 | 3.9–8.33 | 3.45–10 | 3.63–10; 0.72–1.3 | 4.11–10; 0.8–1.3 | 3.97–10; 0.72–0.9 |
India | 3.14–10 | 5.65–10 | 4.17–10 | 3.31–10; 0.7–1.12 | 6.28–10; 0.7–1.02 | 4.58–10; 0.84–1.12 |
Indonesia | 3.16–10 | 4.71–10 | 4.21–10 | 3.6–10; 0.76–1.12 | 4.9–10; 0.85–1.12 | 4.54–10; 0.77–1 |
Korea | 5.47–10 | 6.35–10 | 5.46–10 | 5.79–10; 0.79–1.04 | 6.21–10; 0.83–0.98 | 5.8–10; 0.8–1 |
Malaysia | 4.37–10 | 5.12–8.8 | 4.38–10 | 4.4–10; 0.77–1.14 | 5–8.95; 0.94–1.13 | 4.4–10; 0.77–1.13 |
Philippines | 3.13–10 | 3.17–10 | 4.68–10 | 3.16–10 | 3.17–10; 0.96–1.14 | 5.12–10; 0.79–1 |
Taiwan | 3.06–10 | 4.5–10 | 4.46–10 | 3.02–10; 0.77–1.19 | 4.5–10; 0.85–1.19 | 4.48–10; 0.76–0.95 |
Thailand | 4.47–10 | 4.58–10 | 4.52–10 | 3.5–10; 0.83–1.12 | 4.57–10; 0.92–1.12 | 4.47–10; 0.83–1.06 |
Appendix F: Results for Z1 and Z2 tests
Innovations | Normal | Student’s t | Skewed-t | |||
---|---|---|---|---|---|---|
Country index | Z1 | Z2 | Z1 | Z2 | Z1 | Z2 |
Panel A: Total period (January, 2000–February, 2015) | ||||||
Brazil | − 0.17 | − 0.68 | − 0.08 | − 0.40 | − 0.17 | 0.23 |
Chile | − 0.25 | − 0.60 | − 0.16 | − 0.47 | − 0.22 | 0.03 |
Colombia | − 0.13 | − 0.90 | 0.00 | − 0.61 | 0.04 | − 0.22 |
Mexico | − 0.42 | − 0.88 | − 0.26 | − 0.74 | − 0.28 | − 0.17 |
Peru | − 0.49 | − 0.77 | − 0.36 | − 0.55 | − 0.35 | − 0.43 |
Czech Rep | − 0.34 | − 0.55 | − 0.19 | − 0.43 | − 0.17 | 0.00 |
Egypt | − 0.22 | − 0.78 | − 0.09 | − 0.62 | − 0.09 | − 0.17 |
Greece | − 0.32 | − 0.39 | − 0.21 | − 0.40 | − 0.19 | 0.02 |
Hungary | − 0.23 | − 0.21 | − 0.16 | − 0.06 | − 0.15 | − 0.09 |
Poland | − 0.40 | − 0.49 | − 0.25 | − 0.47 | − 0.27 | − 0.29 |
Qatar | − 0.30 | − 0.67 | − 0.09 | − 0.46 | − 0.11 | − 0.53 |
Russia | − 0.34 | − 0.72 | − 0.17 | − 0.59 | − 0.16 | − 0.09 |
South Africa | − 0.35 | − 0.43 | − 0.23 | − 0.40 | − 0.21 | 0.15 |
Turkey | − 0.12 | − 0.38 | − 0.07 | − 0.08 | − 0.03 | 0.04 |
China | − 0.14 | − 0.38 | − 0.00 | − 0.10 | − 0.02 | − 0.01 |
India | − 0.26 | − 0.62 | − 0.12 | − 0.45 | − 0.12 | 0.03 |
Indonesia | − 0.21 | − 0.78 | − 0.08 | − 0.55 | − 0.13 | 0.01 |
Korea | 0.04 | − 0.65 | 0.05 | − 0.40 | 0.07 | 0.33 |
Malaysia | − 0.42 | − 0.73 | − 0.25 | − 0.58 | − 0.25 | − 0.24 |
Philippines | − 0.29 | − 0.53 | − 0.15 | − 0.39 | − 0.16 | − 0.22 |
Taiwan | − 0.32 | − 0.78 | − 0.19 | − 0.66 | − 0.19 | − 0.20 |
Thailand | − 0.29 | − 0.61 | − 0.11 | − 0.40 | − 0.14 | − 0.18 |
Panel B: Pre-crisis period (January, 2000–July, 2007) | ||||||
Brazil | − 0.05 | − 0.56 | 0.02 | − 0.37 | 0.01 | 0.26 |
Chile | − 0.11 | − 0.36 | − 0.04 | − 0.13 | − 0.03 | − 0.00 |
Colombia | − 0.15 | − 1.18 | − 0.04 | − 0.93 | − 0.00 | − 0.17 |
Mexico | − 0.08 | − 0.74 | − 0.00 | − 0.48 | 0.00 | 0.00 |
Peru | − 0.12 | − 0.47 | − 0.02 | − 0.11 | − 0.03 | − 0.27 |
Czech Rep | − 0.29 | − 0.44 | − 0.14 | − 0.24 | − 0.12 | 0.00 |
Egypt | − 0.17 | − 0.33 | − 0.04 | − 0.15 | − 0.07 | − 0.32 |
Greece | − 0.13 | − 0.17 | − 0.03 | − 0.03 | 0.02 | 0.19 |
Hungary | − 0.13 | 0.07 | − 0.06 | 0.18 | − 0.06 | 0.15 |
Poland | − 0.19 | − 0.19 | − 0.08 | − 0.11 | − 0.05 | − 0.23 |
Qatar | − 0.45 | − 1.24 | − 0.21 | − 0.73 | − 0.18 | − 1.20 |
Russia | − 0.16 | − 0.66 | 0.00 | − 0.45 | 0.04 | 0.15 |
South Africa | − 0.11 | − 0.33 | − 0.03 | − 0.17 | 0.00 | 0.09 |
Turkey | − 0.14 | − 0.14 | − 0.13 | − 0.30 | − 0.11 | − 0.34 |
China | − 0.16 | − 0.35 | − 0.07 | 0.04 | − 0.02 | − 0.54 |
India | − 0.18 | − 0.68 | − 0.09 | − 0.47 | − 0.04 | 0.25 |
Indonesia | − 0.16 | − 0.82 | − 0.06 | − 0.54 | − 0.07 | − 0.38 |
Korea | − 0.04 | − 0.54 | 0.03 | − 0.31 | 0.08 | 0.43 |
Malaysia | − 0.17 | − 0.24 | − 0.03 | − 0.09 | − 0.06 | − 0.06 |
Philippines | − 0.10 | − 0.32 | − 0.03 | − 0.58 | − 0.04 | − 0.31 |
Taiwan | − 0.18 | − 0.52 | − 0.09 | − 0.22 | − 0.07 | − 0.40 |
Thailand | − 0.23 | − 0.51 | − 0.13 | − 0.29 | − 0.11 | − 0.34 |
Panel C: Crisis period (July, 2007–February, 2015) | ||||||
Brazil | − 0.08 | − 0.54 | − 0.00 | − 0.26 | − 0.01 | 0.33 |
Chile | − 0.11 | − 0.74 | − 0.01 | − 0.53 | − 0.02 | 0.09 |
Colombia | − 0.10 | − 0.60 | 0.06 | − 0.34 | 0.07 | − 0.24 |
Mexico | − 0.17 | − 0.71 | − 0.02 | − 0.49 | 0.05 | 0.03 |
Peru | − 0.19 | − 0.70 | − 0.09 | − 0.43 | − 0.06 | − 0.28 |
Czech Rep | − 0.12 | − 0.47 | − 0.02 | − 0.37 | 0.00 | 0.00 |
Egypt | − 0.19 | − 0.75 | − 0.07 | − 0.50 | − 0.05 | 0.23 |
Greece | − 0.05 | − 0.48 | 0.02 | − 0.26 | − 0.02 | 0.00 |
Hungary | − 0.14 | − 0.40 | − 0.07 | − 0.16 | − 0.07 | − 0.22 |
Poland | − 0.07 | − 0.59 | − 0.01 | − 0.35 | − 0.01 | − 0.04 |
Qatar | − 0.15 | − 0.61 | 0.07 | − 0.25 | 0.07 | 0.07 |
Russia | − 0.16 | − 0.72 | − 0.06 | − 0.42 | − 0.02 | − 0.11 |
South Africa | − 0.09 | − 0.31 | − 0.02 | − 0.13 | 0.04 | 0.37 |
Turkey | − 0.07 | − 0.47 | − 0.04 | − 0.13 | − 0.00 | − 0.03 |
China | − 0.12 | − 0.74 | 0.02 | − 0.48 | − 0.03 | 0.44 |
India | − 0.06 | − 0.51 | 0.05 | − 0.16 | 0.05 | − 0.12 |
Indonesia | − 0.18 | − 0.79 | − 0.04 | − 0.51 | − 0.07 | 0.27 |
Korea | − 0.06 | − 0.82 | 0.03 | − 0.57 | 0.05 | 0.30 |
Malaysia | − 0.15 | − 1.01 | − 0.07 | − 0.66 | − 0.03 | − 0.21 |
Philippines | − 0.14 | − 0.69 | − 0.04 | − 0.43 | − 0.04 | − 0.42 |
Taiwan | − 0.10 | − 0.98 | 0.01 | − 0.69 | 0.01 | 0.24 |
Thailand | − 0.13 | − 0.58 | 0.02 | − 0.46 | 0.00 | − 0.02 |
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Cardona, E., Mora-Valencia, A. & Velásquez-Gaviria, D. Testing expected shortfall: an application to emerging market stock indices. Risk Manag 21, 153–182 (2019). https://doi.org/10.1057/s41283-018-0046-z
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DOI: https://doi.org/10.1057/s41283-018-0046-z