VXY signal

rebalance strategies, the more extreme interest rate differentials seem to be more profitable. The poor performance of the 3-, 6- and 12 month rebalance strategies, indicate that investors need to actively manage their position by rebalancing more frequently during volatile periods. For the 3-, 6- and 12 month rebalancing strategies, all performance measures decreased, and for the most part, this resulted in negative mean returns. As for the carry trade, the poor results seems to be related to the unrealistic assumption that the carry traders hold on to same positions until the next rebalance period. In reality, they would more likely have unwound their position or taken the reverse carry trade position in order to reduce losses.

2013-2020

Looking at the last sub-period, all performance measures are insignificant at a 5% significance level, similar to those of the static carry trade. As discussed previously, Figure 3.1 showing the evolution of interest differential over the full sample period, displayed lower interest rate differentials in the most recent years, ultimately affecting the profitability of carry trade. Several crises oc-curred during this period, including Brexit, the US-China trade war and finally COVID-19, which led to the highest historical level of VIX. Yet, neither of the identified crisis periods took place on the 6- and 12 month rebalanced day, essentially leading to the same performance measures as the static carry trade.

With the carry returns being generally small during 2013-2020, the negative and positive impact of the mean returns were also inherently small.

1-month rebalance strategies improved slightly compared to those based on VIX and the static carry trade strategies. During 2006-2013, the mean returns of the same strategies, along with the 3-month rebalance strategies, improved economically. However, the mean returns of the 3-month rebalance strategies were statistically insignificant. In the last period, 2013-2020, the 1-month re-balance strategies improved upon the static carry trade as well, but the impact was relatively small compared to the corresponding strategies in the previous sub-periods. Although VXY identified some crisis periods, the impact is in-herently small as the negative and positive returns observed over the period are small.

Full sample period

In Table 5.8 it can be seen that the mean returns of all strategies rebalanced every 1- and 3 months are significant and performed economically better com-pared to the static carry trade. In addition, the results from using VXY_t−1 instead of VIX_t−1, improved the performance of all strategies rebalanced every 1-, 3-, and 6 months. The highest mean return and Sharpe ratio of the dynamic strategies based on VIX was observed for Reverse1M1C, with a mean return of 5.46% and a Sharpe ratio of 0.817. The strategy Reverse1M1C similarly, generated the highest mean return among the strategies based on VXY, with a mean return of 7.23% and a Sharpe ratio of 1.104.

For the static carry trade, the mean returns were relatively consistent across strategies due to the persistence in the interest rate differentials. Hence, when traders only base their carry portfolio on the respective interest differentials, it is not necessary to rebalance the portfolios very often, as the currencies tend to stay in the low or high portfolio for a longer time. However, for the dynamic strategies based on VIX and VXY, the 1-month rebalance strategies generated substantially higher mean returns compared to the rest of the strategies, indi-cating short-term persistence in the signals. When there is a crisis signal, the alternative position is kept for several months until the next rebalance day for the longer rebalancing horizon strategies. If the signal changed in any of the intermediate months, this could consequently lead to positive carry returns turning negative.

Sub-sample period

As for the dynamic strategies based on VIX, each strategy is employed on three different sub-sample periods: 1999-2006, 2006-2013 and 2013-2020. Table 5.9 (a) and (b), presents the performance of the exit- and reverse strategies in each

Table (5.8) Performance metric of exit- and reverse carry trade strategies over the full sample period based on the VIX signal This table reports the mean return, Sharpe ratio and nominal p-value of the 20 exit- and revers strategies using the VXYt−1 crisis signal. The results are based on

the sample period from 30-06-1999 to 29-05-2020. The mean returns are marked by a 3-colour scale, using the 50th percentile. The abbreviations used to denote

the strategies are described in Appendix A.1.

Exit Reverse

1M 3M 6M 12M 1M 3M 6M 12M

1C

Mean return 5.03% 2.83% 2.51% 1.58% 7.23% 3.09% 1.97% 0.28%

Sharpe ratio 0.903 0.535 0.425 0.232 1.104 0.486 0.292 0.040 Nominal p-value 0.000 0.015 0.053 0.289 0.000 0.027 0.182 0.855 2C

Mean return 4.22% 2.72% 2.37% 1.94% 5.84% 2.64% 1.83% 0.99%

Sharpe ratio 0.924 0.615 0.485 0.369 1.168 0.486 0.334 0.182 Nominal p-value 0.000 0.005 0.027 0.093 0.000 0.027 0.127 0.407 3C

Mean return 4.14% 2.79% 2.53% 2.19% 5.61% 2.77% 2.07% 1.41%

Sharpe ratio 0.979 0.686 0.545 0.441 1.198 0.558 0.408 0.276 Nominal p-value 0.000 0.002 0.013 0.045 0.000 0.011 0.063 0.208 4C

Mean return 4.11% 2.86% 2.48% 2.04% 5.41% 2.85% 1.98% 1.39%

Sharpe ratio 0.967 0.681 0.530 0.399 1.159 0.563 0.392 0.263 Nominal p-value 0.000 0.002 0.016 0.069 0.000 0.011 0.074 0.230 5C

Mean return 3.96% 2.61% 2.27% 1.55% 5.07% 2.54% 1.72% 0.95%

Sharpe ratio 0.917 0.607 0.467 0.291 1.062 0.490 0.332 0.174 Nominal p-value 0.000 0.006 0.034 0.185 0.000 0.026 0.130 0.427

of the three periods.

1999-2006

Evaluating Table 5.9 (a) and (b), the performances measures of all strategies performed substantially better during this period compared to the other sub-periods, due to the high-interest rate differentials. The 1-month rebalance strategies improved slightly compared to the static carry trade. The mean return of the static carry trade Carry1M5C increase from 6.19% to 6.41%

while the Sharpe ratio increased from 1.268 to 1.318, after employing the reverse strategy Reverse1M5C (see Appendix B.2). As emphasised previously, it seems that the persistence in the signal is short-lived, as the strategies with rebalancing frequency higher than one month generally generated lower mean returns compared to those of the static carry trade. Neither of the crises identified by the VXY signal during this period is associated with any of the

Table (5.9) Sub-sample test: VXY

The table reports the mean return, Sharpe ratio and nominal p-value of the 20 exit- and reverse strategies using the VXYt−1 crisis signal. The results are presented for three different sub-periods, 1999-2006, 2006-2013 and 2013-2020. The

abbreviations used to denote the strategies are described in Appendix A.1.

(a)

Exit

Sub periods 1999-2006 2006-2013 2013-2020

1M 3M 6M 12M 1M 3M 6M 12M 1M 3M 6M 12M

1C

Mean return 5.86% 5.13% 5.91% 4.93% 6.31% 1.84% -1.11% -1.20% 2.40% 1.41% 2.68% 0.96%

Sharpe ratio 1.000 0.904 0.912 0.826 1.052 0.331 -0.161 -0.141 0.499 0.319 0.736 0.181 Nominalp-value 0.009 0.018 0.017 0.031 0.006 0.381 0.669 0.708 0.191 0.404 0.056 0.635 2C

Mean return 4.79% 4.84% 5.21% 4.34% 5.52% 1.55% -0.79% 0.00% 2.07% 1.69% 2.65% 1.42%

Sharpe ratio 1.102 1.150 1.100 0.964 1.032 0.305 -0.130 0.000 0.542 0.441 0.819 0.346 Nominalp-value 0.004 0.003 0.004 0.012 0.007 0.419 0.729 1.000 0.155 0.250 0.034 0.365 3C

Mean return 5.52% 5.81% 6.06% 5.45% 4.55% 0.94% -0.65% -0.47% 2.17% 1.54% 2.10% 1.52%

Sharpe ratio 1.243 1.383 1.335 1.219 0.995 0.220 -0.116 -0.074 0.608 0.434 0.674 0.437 Nominalp-value 0.001 0.000 0.001 0.002 0.010 0.560 0.758 0.844 0.111 0.257 0.080 0.254 4C

Mean return 6.03% 6.59% 6.15% 6.08% 4.37% 0.80% -0.56% -1.60% 1.80% 1.09% 1.77% 1.59%

Sharpe ratio 1.324 1.428 1.307 1.241 0.969 0.186 -0.100 -0.252 0.510 0.322 0.584 0.461 Nominalp-value 0.001 0.000 0.001 0.001 0.012 0.622 0.791 0.504 0.181 0.399 0.129 0.229 5C

Mean return 6.30% 6.66% 6.75% 6.23% 3.79% 0.15% -1.32% -2.64% 1.71% 0.93% 1.30% 1.00%

Sharpe ratio 1.343 1.405 1.390 1.234 0.836 0.035 -0.226 -0.403 0.488 0.275 0.415 0.282 Nominalp-value 0.001 0.000 0.000 0.001 0.029 0.927 0.549 0.287 0.200 0.471 0.278 0.460

(b)

Reverse

Sub-periods 1999-2006 2006-2013 2013-2020

1M 3M 6M 12M 1M 3M 6M 12M 1M 3M 6M 12M

1C

Mean return 6.18% 4.87% 5.39% 3.96% 11.42% 3.14% -3.26% -3.42% 3.49% 1.53% 3.79% 0.30%

Sharpe ratio 1.040 0.849 0.815 0.640 1.466 0.408 -0.425 -0.386 0.628 0.284 0.702 0.055 Nominalp-value 0.007 0.026 0.033 0.092 0.000 0.281 0.261 0.307 0.100 0.457 0.068 0.886 2C

Mean return 5.33% 4.67% 4.91% 3.51% 9.45% 1.59% -2.69% -1.48% 2.42% 1.73% 3.40% 1.07%

Sharpe ratio 1.204 1.093 1.017 0.750 1.546 0.230 -0.401 -0.215 0.602 0.369 0.796 0.248 Nominalp-value 0.002 0.005 0.008 0.049 0.000 0.542 0.288 0.570 0.115 0.335 0.039 0.516 3C

Mean return 5.82% 5.70% 5.66% 4.71% 8.15% 1.47% -1.87% -1.67% 2.63% 1.12% 2.45% 1.21%

Sharpe ratio 1.282 1.343 1.216 1.012 1.467 0.238 -0.301 -0.259 0.725 0.275 0.656 0.330 Nominalp-value 0.001 0.001 0.002 0.009 0.000 0.529 0.425 0.492 0.059 0.472 0.088 0.388 4C

Mean return 6.24% 6.49% 5.60% 5.25% 7.50% 1.24% -1.40% -2.55% 2.30% 0.73% 1.70% 1.45%

Sharpe ratio 1.338 1.398 1.153 1.029 1.401 0.198 -0.228 -0.395 0.624 0.192 0.474 0.404 Nominalp-value 0.001 0.000 0.003 0.008 0.000 0.600 0.545 0.296 0.103 0.614 0.216 0.291 5C

Mean return 6.41% 6.44% 5.94% 5.45% 6.59% 0.55% -2.01% -3.54% 2.11% 0.42% 1.10% 0.84%

Sharpe ratio 1.318 1.349 1.174 1.026 1.193 0.085 -0.320 -0.529 0.583 0.114 0.307 0.230 Nominalp-value 0.001 0.001 0.002 0.008 0.002 0.821 0.396 0.163 0.127 0.766 0.422 0.548

larger economic crises labelled in Figure 5.5 Section 5.2.2.

2006-2013

In the previous analysis of VIX, the mean returns displayed a substantial im-provement of the 1-month rebalancing strategies over this sub-period. This improvement was even larger for VXY, as can be seen in Table 5.9. In fact, the mean return of Reverse1M1C increased from 8.92% to 11.42% after apply-ing the VXY signal instead of VIX to time the strategy. The correspondapply-ing static carry trade, Carry1M1C, generated a mean return 1.40%, indicating sub-stantial improvement over this sub-period. Contrary to the static carry trade, all the mean returns obtained from the 1-month rebalance strategies measures were statistically significant at a 5% significance level. While the 3-month re-balance strategies improved compared to the static carry trade as well, these were far from the levels observed for the 1-month strategies. Reverse3M1C increased from -2.65% to 3.14% after applying the VXY signal instead of VIX to time the strategy. Both signals identified a crisis period in October 2008, where the monthly return of Carry1M1C in the subsequent month was down to -10.33%. However, in January 2009, the carry1M1C generated a negative return of -7.29%, which was only identified by VXY. This might partly explain the fairly larger improvement compared to VIX.

2013-2020

As described in Section 5.3.1, this period is characterised by a low-interest rate environment leading to small interest rate differentials, which is also reflected in the mean returns using VXY. The performance measure of 1-month re-balance strategies economically improved upon the corresponding static carry trade strategies, but the levels are far from the ones observed in the previous sub-periods. The greatest improvement is observed for Reverse1M1C, which increased from 0.98% to 3.49%. Although this period include the US-China trade war and COVID-19 crises, the impact is inherently small as the negative and positive returns observed over the period is small.