When the U.S. Stock Market Becomes Extreme?
Abstract
:1. Introduction
2. Methodology
2.1. Tail Distribution
2.2. Threshold Selection
2.3. Three Extreme Risk Management Measures
3. Data Analysis
3.1. Data Description
3.2. Data Filtering Process
Z | Z | ||
---|---|---|---|
Mean | −0.0032 | Q5 (residual) | 2.9403 |
(p-value) | (0.401) | ||
Median | 0.0202 | Q5 (squared residual) | 7.2983 * |
(p-value) | (0.063) | ||
Maximum | 7.0191 | Q10 (residual) | 11.504 |
(p-value) | (0.175) | ||
Minimum | −13.1417 | Q10 (squared residual) | 11.546 |
(p-value) | (0.173) | ||
Std. Dev. | 1.0001 | Q20 (residual) | 20.090 |
(p-value) | (0.328) | ||
Skewness | −0.5062 | Q20 (squared residual) | 16.385 |
(Z-statistic, p-value) | (−16.2613, 2.2×10-16) | (p-value) | (0.566) |
Kurtosis | 7.8954 | μ | 0.0002 *** |
(Z-statistic, p-value) | (36.6956, 2.2×10-16) | (Z-statistic) | (4.7722) |
Jarque–Bera | 16607.86 *** | −0.0812 | |
(p-value) | (0.0000) | (Z-statistic) | (−1.0679) |
Engle LM (1) | 6.0183 ** | 0.1853 ** | |
(p-value) | (0.0142) | (Z-statistic) | (2.4722) |
Engle LM (2) | 6.3745 ** | ω | 9.37e-07 *** |
(p-value) | (0.0413) | (Z-statistic) | (15.5038) |
Engle LM (5) | 7.2949 * | α | 0.0306 *** |
(p-value) | (0.1996) | (Z-statistic) | (13.0564) |
Engle LM (10) | 11.4924 | γ | 0.0884 *** |
(p-value) | (0.3205) | (Z-statistic) | (28.0765) |
q1% | −2.5373 | β | 0.9154 *** |
(Z-statistic) | (415.2990) | ||
q5% | −1.6240 | Log-likelihood | 54439.85 |
q95% | 1.5658 | Akaike criterion | −6.8220 |
q99% | 2.3426 | Number | 15950 |
3.3. Descriptive Statistics
3.4. Quantile Regression
4. Empirical Findings
4.1. Threshold Selection Results
Mean residual life plot | +1.20 | −1.40 |
Threshold plot | [+0.09; +1.50] | [−0.80; −1.80] |
Optimal selection | +0.9388 | −1.3735 |
4.2. Tail Characteristics
ξ | −0.0411 *** | 0.1359 *** |
(s.e) | (0.0143) | (0.0274) |
β | 0.5671 *** | 0.5168 *** |
(s.e) | (0.0140) | (0.0201) |
Threshold | +0.9388 | −1.3735 |
Nb. Exceedances | 2443 | 1278 |
Percentile | 0.8468 | 0.9198 |
Neg. Lik. | 957.047 | 608.1859 |
4.3. The Extreme Downside Risk
Probability | VaR-GPD | ES-GPD | VaR-normal | ES-normal |
---|---|---|---|---|
0.9900 | −2.6166 | −3.4104 | −2.3263 | −2.6652 |
0.9950 | −3.1151 | −3.9873 | −2.5758 | −2.8919 |
0.9990 | −4.4709 | −5.5564 | −3.0902 | −3.3670 |
0.9995 | −5.1526 | −6.3454 | −3.2905 | −3.5543 |
0.9999 | −7.0068 | −8.4912 | −3.7190 | −3.9584 |
Period | Lower bound | Upper bound | Lower bound | Upper bound | ||
---|---|---|---|---|---|---|
1 | 2.8586 | 2.7746 | 2.9425 | −3.2857 | −3.1384 | −3.4330 |
2 | 3.1921 | 3.0833 | 3.3008 | −3.8502 | −3.6283 | −4.0720 |
5 | 3.6186 | 3.4683 | 3.7689 | −4.6829 | −4.3138 | −5.0519 |
10 | 3.9307 | 3.7426 | 4.1188 | −5.3854 | −4.8609 | −5.9098 |
20 | 4.2340 | 4.0031 | 4.4649 | −6.1572 | −5.4325 | −6.8819 |
50 | 4.6219 | 4.3271 | 4.9166 | −7.2958 | −6.2255 | −8.3661 |
100 | 4.9057 | 4.5577 | 5.2537 | −8.2564 | −6.8526 | −9.6601 |
4.4. EVT with Raw Returns
4.5. Robustness Check
5. Conclusions
Conflicts of Interest
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- 3Note that for the sake of prudence, the return periods of 84 and 27 years correspond to their respective return level absolute upper bound
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Aboura, S. When the U.S. Stock Market Becomes Extreme? Risks 2014, 2, 211-225. https://doi.org/10.3390/risks2020211
Aboura S. When the U.S. Stock Market Becomes Extreme? Risks. 2014; 2(2):211-225. https://doi.org/10.3390/risks2020211
Chicago/Turabian StyleAboura, Sofiane. 2014. "When the U.S. Stock Market Becomes Extreme?" Risks 2, no. 2: 211-225. https://doi.org/10.3390/risks2020211