5.3 Crisis Robust Carry Trade
5.3.4 Bootstrap hypothesis testing
Table (5.11) Impact of the VXY signal
This table reports the mean return of Carry1M1C along with the impact of using the VIX signal in the dynamic strategies, Exit1M1C and Reverse1M1C over different crisis periods defined by VXYt−1. Other crisis periods, represents periods which occurred on months outside the range of dates of the labelled crisis periods
Crisis period Start date End date Carry1M1C Exit1M1C Reverse1M1C Financial crisis 31/07/2008 30/01/2009 -1.599% 1.599% 3.198%
Greek crisis 30/09/2011 31/12/2014 -0.128% 0.128% 0.256%
Brexit 31/03/2015 29/02/2016 0.032% -0.032% -0.064%
US-China trade war 31/12/2018 31/12/2018 -0.048% 0.048% 0.095%
COVID-19 crisis 31/03/2020 31/03/2020 0.009% -0.009% -0.017%
Other crisis periods -0.459% 0.459% 0.918%
-2.193% 2.193% 4.386%
Figure (5.6) Probability density function
This figure shows the distribution of Z-scores of the mean returns for the 1static carry trade, in the color grey. The distribution of the bootstrappedZ-scores are shown with the blue lines. The red lines indicate where the x-axes are equal to 1.96 and -1.96. The abbreviations used to denote the strategies are described in
Appendix A.1.
In addition, it can be seen that, for all five distributions, for a larger fraction of the bootstrapped resamples, the two-sided null hypothesis, would have been rejected at 5% significance level, such that Z > |1.96|. In particular, the probability that the resample would produce a significant result is above 50%
for all five distributions. For Carry1M5C and Carry1M4C, the probability is 76.2% and 77.2% respectively.
Statistical significance of the performance measures
In the previous sections, the nominal p-value from a simple individual test is used to determine the statistical significance of the performance measures for the static carry trade. The bootstrap technique enables statistical inference without distributional assumption as for the nominal p-value. In Table 5.12 the mean return and the confidence interval is shown for all 20 carry trade strategies. The confidence intervals are based on a 5% significance level.
Table (5.12) Confidence intervals using bootstrapping: static carry trade
This table reports the 95% confidence interval (CI) of the bootstrapped mean return for each of the 20 static carry trade strategies. The statistical inference is aligned with those of thep-value from a two-sided test. The abbreviations used to
denote the strategies are described in Appendix A.1.
Mean return CI lower CI upper Carry1M
1C 2.84% -0.00% 6.15%
2C 2.60% 0.69% 4.60%
3C 2.67% 0.64% 4.83%
4C 2.82% 0.77% 4.95%
5C 2.84% 0.76% 5.02%
Carry3M
1C 2.49% -0.33% 5.64%
2C 2.71% 0.62% 4.95%
3C 2.70% 0.45% 5.29%
4C 2.70% 0.34% 5.36%
5C 2.51% 0.07% 5.29%
Carry6M
1C 2.98% 0.06% 6.18%
2C 2.82% 0.53% 5.29%
3C 2.86% 0.52% 5.53%
4C 2.81% 0.53% 5.41%
5C 2.63% 0.04% 5.44%
Carry12M
1C 2.79% -0.22% 6.03%
2C 2.80% 0.59% 5.08%
3C 2.84% 0.37% 5.48%
4C 2.54% 0.08% 5.23%
5C 1.96% -1.18% 5.22%
Looking at Table 5.12 the null value is included in the confidence interval for the four strategies Carry1M1C, Carry3M1C, Carry12M1C and Carry12M5C.
Thus, the mean return of these strategies is statistically insignificant at a 5%
significance level. As can be seen in Table 5.4 the nominal p-value is larger than the 5% significance level for these four strategies, and the findings after applying bootstrapping do not deviate from the findings obtained from a nor-mal distribution.
In order to examine the statistical significance of the dynamic strategies, the
bootstrap technique is applied as well. In Table 5.13 the mean returns and the confidence intervals are shown for two dynamic strategies based on VIX.
All of the mean returns are statistically significant, which corresponds to the findings in Table 5.6 using the normalp-value. In Appendix B.5 the confidence interval of the mean return for each of the three sub-periods is found. The statistical inferences are the same compared those when using the p-value, ex-cepted for strategy, Reverse1M1C, in the sub-period going from 1999 to 2006.
The nominalp-value of the strategy is equal to 14.4%, which is well above the 5% significant level (see Table 5.7). In Appendix B.5, Table B.13 the lower and upper confidence interval bounds of Reverse1M1C are found to 0.07% and 7.02%, meaning the mean return of 3.39% is statistically significant when using the bootstrap technique.
Table (5.13) Confidence intervals using bootstrapping: dynamic strategies based on VIX
This table shows the 95% confidence interval (CI) of the bootstrapped mean return for each of the 1-month rebalance exit- and reverse strategies based on VIXt−1. The mean return is based on the full sample period 1999-2020. All ten dynamic strategies are statistically significant at a 5% significance level in line with the
conclusion using the nominal p-value. The abbreviations used to denote the strategies are described in Appendix A.1.
Mean return CI lower CI upper Exit1M
1C 4.15% 1.88% 6.46%
2C 3.87% 2.11% 5.63%
3C 3.83% 2.24% 5.44%
4C 3.98% 2.14% 5.75%
5C 3.92% 2.02% 5.76%
Reverse1M
1C 5.46% 2.10% 8.49%
2C 5.13% 2.59% 7.39%
3C 4.99% 2.93% 7.01%
4C 5.14% 3.28% 7.03%
5C 5.01% 3.14% 6.86%
Table 5.14 shows the confidence interval of the mean return based on the bootstrap resample. The table shows the mean return of the dynamic strategies based on VXY. As can be seen in the table, all of the strategies are statically significant at a 5% significance level, which was also observed using the nominal p-value (see Table 5.8). The confidence interval of the mean return for each of
significant at a 5% significance level in two sub-periods 1999-2006 and 2006-2013 and insignificant in the last period 2006-2013-2020. The statistical inference of the bootstrap confidence interval is thus aligned with statistical inference using the nominalp-value in Table 5.9.
Table (5.14) Confidence intervals using bootstrapping: dynamic strategies based on VXY
This table shows the 95% confidence interval (CI) of the bootstrapped mean return for each of the 1-month rebalance exit- and reverse strategies based on VXYt−1. The mean return is based on the full sample period 1999-2020. All ten dynamic strategies are statistically significant at a 5% significance level in accordance with
the conclusion using the nominalp-value. The abbreviations used to denote the strategies are described in Appendix A.1.
Mean return CI lower CI upper Exit1M
1C 5.03% 2.79% 7.27%
2C 4.22% 2.37% 6.02%
3C 4.14% 2.56% 5.72%
4C 4.11% 2.43% 5.76%
5C 3.96% 2.08% 5.78%
Reverse1M
1C 7.23% 3.28% 10.41%
2C 5.84% 2.79% 8.36%
3C 5.61% 3.34% 7.63%
4C 5.41% 3.42% 7.29%
5C 5.07% 3.10% 6.99%
Robustness test
The aim of this section is to show that the results presented in the previous sections are not driven by specific model choices. The analysis is based solely on the 1-month rebalancing strategies, as the remaining strategies did not display any clear improvements. The robustness analysis is organised as follow: first, the two dynamic strategies are reproduced using different model choices for the signals. Secondly, the performance of the dynamic strategies is analysed for a different definition of the index by using change instead of level. The findings are summarised at the beginning of the sections where it is found to be relevant (see Section 6.1, 6.2 and 6.3). Throughout this chapter, the strategies may be referred to using abbreviations. E.g. a revere strategy rebalanced monthly, with the use of up to 5 currencies in the short and long position, is referred to as Reverse1M5C. The full list of abbreviations used to denote the strategies is listed in Appendix A.1.
6.1 Threshold analysis
In order to obtain a deeper insight into the sensitivity of the findings in Section 5.3, a range of parameter choices related to the threshold parameter are tested.
The analysis from Section 5.3 is repeated, but instead of the threshold based on 1.5-year moving average and a standard deviation of 1.5, the mean return and the nominal p-value are shown for 1 and 2 years moving average and 1 and 2 standard deviations. The motivation for changing the two parameters is to make sure that the results are not depended on the parameter settings cho-sen in the methodology (Section 4). The two poles of standard deviations are commonly used in related literature as described in Section 4.3.1. A threshold based on a standard deviation of 2, represent the extremely volatile periods vast beyond its normal, which may lead to the exclusion of relevant periods,
included in the threshold based on 1 standard deviation. In regards to win-dow size determination, there does not seem to be consistency in the selected window size across related literature, nor any plausible arguments for the size.
However, it is essentially important to be aware that the spikes in the implied volatility may be perceived differently depending on the context, and therefore it is not the intention it is too long. Nevertheless, in order to ensure the results are robust to alternative specifications, the size is reduced and extended with 0.5 years.
Summarising the findings in this section, the mean return of dynamic strate-gies based on VIXt−1 and VXYt−1 appear relatively unaffected by choice of parameters across and within the different strategies. All the mean returns are highly significant, and economically higher compared to those of the cor-responding static carry trade strategies. Hence, the conclusion of the results in Section 5 remains the same.