6.3 Change in implied volatility
6.3.2 VXY signal
Table 6.6 presents the performance measures of the exit- and reverse strategies based on VXY over the full sample period. The mean returns of all strategies are significant at a 5% significance level. As for VIX, the performance mea-sure of the strategies based on the change in VXY are lower compared to those based on the level of VXY. The fraction of the negative returns are similarly higher for all the strategies based on the change signal. This indicates that overall, the change signal does not time the negative returns as well as the level signal. Although the performance measures economically decreased after implementing the change signal, the mean returns are still higher compared to those of the corresponding static carry trade strategies. In Appendix B.9 the performance measures are found for the exit- and the reverse strategy over the sub-sample periods. While the strategies based on the level signal gener-ated the highest returns during the three sub-period 2006-2013, this was not the case for all strategies based on the change in VXY. For all exit strategies and Reverse1M4C and Reverse1M5C, the highest mean returns were instead observed in the sub-period 1999-2006. Yet, neither of the strategies based on the change signal, improved upon those of the static carry trade during this period, except for Exit1M1C. In the two subsequent periods, 2006-2013 and 2013-2020, the mean returns of the strategies based on the change in VXY im-proved for all the 1-month rebalance strategies. Hence, the findings somewhat support the conclusions in the results section (Section 5.3.2), with the only deviation being the first sub-period. In addition, do the findings correspond to those of Swinkels and Egbers (2015), who found that the change signal based on both VIX and VXY, improved the performance of the strategies, both in terms of mean return and Sharpe ratio.
Table (6.6) Performance measures of timing strategies based on level and change in VXY
This table reports the mean return, Sharpe ratio, nominalp-value of mean return and the fraction of negative returns of the 1-month rebalance exit- and reverse strategies. The results are based on the level and change VXYt−1 signal over the
full sample period from 30-06-1999 to 29-05-2020. The highest mean return for each of the strategies is marked by a coloured cell. The abbreviations used to
denote the strategies are described in Appendix A.1.
Exit1M Reverse1M Level Change Level Change 1C
Mean return 5.03% 3.94% 7.23% 5.03%
Sharpe Ratio 0.903 0.637 1.104 0.750 Nominal p-value 0.000 0.004 0.000 0.001 Fraction negative 31.7% 33.7% 35.3% 36.5%
2C
Mean return 4.22% 3.64% 5.84% 4.67%
Sharpe Ratio 0.924 0.762 1.168 0.917 Nominal p-value 0.000 0.001 0.000 0.000 Fraction negative 31.7% 34.1% 34.9% 36.9%
3C
Mean return 4.14% 3.58% 5.61% 4.48%
Sharpe Ratio 0.979 0.795 1.198 0.936 Nominal p-value 0.000 0.000 0.000 0.000 Fraction negative 33.3% 35.7% 36.1% 38.1%
4C
Mean return 4.11% 3.43% 5.41% 4.03%
Sharpe Ratio 0.967 0.754 1.159 0.844 Nominal p-value 0.000 0.001 0.000 0.000 Fraction negative 32.5% 34.9% 36.1% 38.1%
5C
Mean return 3.96% 3.39% 5.07% 3.93%
Sharpe Ratio 0.917 0.731 1.062 0.808 Nominal p-value 0.000 0.001 0.000 0.000 Fraction negative 33.7% 35.7% 37.3% 38.5%
Conclusion
This thesis provides evidence of the profitability of the carry trade over time and the possibility of improving upon the performance. Although the prof-itability of the carry trade is well-documented, this strategy is not without risk. The carry trade has alternated between periods of profitability as well as periods of large losses. During the financial crisis carry investors suffered losses up to 20% of the invested capital. Standing on the edge of a new crisis, caused by the global pandemic, this only stresses the importance of adjust-ing the carry trade strategy to avoid, and in particular, benefit from periods of large losses. The analysis of this thesis is based on the associated prob-lem statement, with the focal question being whether it is possible to improve upon the carry trade during volatile periods. The relevant aspects of this are covered from three research questions through a three-part analysis.
The preliminary part of the analysis sheds light on the profitability of the carry trade through a performance analysis across time and carry trade strate-gies. The findings showed that all strategies produced positive returns over the whole sample period, whereas the return pattern varied greatly across sub-periods. The first sub-period, 1999-2006, produced substantially higher returns, compared to the subsequent periods, 2006-2013 and 2013-2020, the main reason being high volatility during the financial crisis in 2007-2009 and the low-interest rates diminishing towards zero after the crisis.
The second part consists of a performance analysis of two alternative strategies, one in which the carry traders during crisis periods should unwind positions and one in which they should take the reverse positions. The findings showed that the dynamic strategies were able to some extent, improve upon the static carry trade. The actual improvement varied greatly across the sub-periods,
with the only sub-period leading to substantial improvements, is 2006-2013, where the financial crisis took place. The 1-month rebalance improved using both signals, but the improvements were fairly greater for the strategies based on VXY. While the other rebalance strategies generally did not improve upon the static carry trade, the shorter the rebalance frequency periods were, the better the performance. Similar to the sub-periods, it was generally only the 1-month rebalance strategies that improved upon the static carry trade over the full sample period.
To elucidate the impact of the crisis periods independently, the mean return was decomposed into the respective crises period. It became clear that some of the crisis periods led to a reduction in the mean returns after applying the alternative strategies. In fact, excluding the positive impact of the VIX signal during the financial crises, would have led to a decrease in the mean return over the full sample period. Therefore, relying on the signal may lead to even worse losses to carry investors over some crisis periods.
The findings were confirmed by implementing the stationary bootstrapping method, which showed consistency between the statistical inference based on the nominalp-value from a simple individual test and the bootstrap confidence interval. This was confirmed by the distribution of z-scores of the mean return and the bootstrap z-scores, which approximately resembled the same distribu-tional shape.
The last and third part of the thesis contributes with a robustness analysis, which showed that results, for the most part, were not driven by specific model choices. The scenario analysis conducted on the thresholds generally did not change the conclusion of the results, as the mean returns remained statistically significant. Furthermore, there was no evidence that investors have to react quickly to take advantage of the market change after testing different timing lags. The performance of the dynamic strategies decreased slightly using the change in implied volatility instead of the level. Even though the magnitude of the mean return and Sharpe ratio decreased, the dynamic strategies still improve upon the static carry trade.
Further Research
This thesis explored a selected number of parameters and model choices to ex-amine the performance of the carry trade during crisis periods. With the countless possibilities when constructing the carry trade, something which could have proved relevant to this thesis, is bound to be left out. However, to ensure clarity and coherent conclusions, limitations are necessary.
This research is conducted on synthetic interest rate differentials based on the forward and spot market. While most research within this area implements models on synthetic interest rate differentials (see Swinkels and Egbers (2015) and Menkhoff et al. (2012)), this does not allow for shorter rebalance frequen-cies. Dunis and Miao (2007), among others, use the country-specific interest rate, enabling rebalancing frequencies down to 1 day. This research showed that the performance increased with decreasing rebalance frequency. In that sense, the signal might lead to higher accuracy in regards to reallocating the currencies as well as shifting to an alternative strategy. Hence, an interesting addition of this thesis could be to test whether the results would improve if these were based on inter-bank rates and lower rebalance frequencies.
Another interesting addition to the thesis, in regards to model modifications, could be to use emerging market currencies. Most emerging currencies have shown persistence in high-interest rates, even in the most recent years where most developed currencies exhibit interest rates close to zero. The low-interest rate environment of developed currencies led to economically low and statis-tically insignificant mean returns of the carry trade in the most recent sub-period. Consequently, the dynamic strategies were not able to improve upon the carry trade, and deducing the actual impact of the signal proved to be an intricate affair. Taylor and Wang (2019) found evidence of the profitability carry trades by constructing portfolios consisting of emerging and developed
currencies in periods where this study found no such proof. Adding emerging market currencies to the study might, therefore, have contributed to a deeper understanding of the overall contribution of including the crisis signals.
Brunnermeier et al. (2008) measured the funding constraints during the fi-nancial crisis by applying the VIX and TED spread. The TED spread is the difference between the LIBOR inter-bank market interest rate and the T-bill rate. An increase in the TED spread has a similar effect in regards to the funding constraints as the VIX. Brunnermeier et al. (2008) concluded that higher levels of the TED spread and the VIX index predicts future returns of the static carry trade. Little attention has been given to the potential of the TED spread utilisation as a trading signal to implement a dynamic strat-egy. Brunnermeier et al. (2008) specify one disadvantage of the TED spread over the VIX index, namely the lower statistical power of the TED. Dunis and Miao (2007) implemented the exit- and reverse strategy using a timing signal based on the time-varying RiskMetrics volatility model. This specific case of a GARCH model was used to measure the conditional market volatility, from with trading decisions were adopted if the given level of the conditional volatility was breached. Adding other indices like the TED spread and the conditional market volatility to the research could contribute to a broader overview of the impact when incorporating different trading signals for the carry trade.
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Abbreviations
A.1 Strategy abbreviations
Strategy:
Carry- strategies based on the carry trade strategy Exit - strategies based on the exit strategy
Reverse - strategies based on the reverse strategy Rebalancing horizon:
1M - strategies rebalanced every 1 month 3M - strategies rebalanced every 3 month 6M - strategies rebalanced every 6 month 12M - strategies rebalanced every 12 month Currencies:
5C- strategies based on 10 currencies 4C- strategies based on 8 currencies 3C- strategies based on 6 currencies 2C- strategies based on 4 currencies 1C- strategies based on 2 currencies
Tables
B.1 Descriptive statistics
Table (B.1) Descriptive statistics of spot exchange rate This table reports the mean, minimum, maximum, standard deviation as well as
the kurtosis and skewness for the end-of-month spot exchange rates available in the period from 28-05-1999 to 29-05-2020
AUD CAD CHF DKK EUR GBP JPY NOK NZD SEK
Mean 1.343 1.241 1.157 6.320 0.849 0.643 106.7 7.159 1.557 7.953 Min 0.910 0.949 0.788 4.706 0.631 0.481 76.25 5.082 1.142 5.930 Max 2.048 1.605 1.798 8.797 1.181 0.821 133.8 10.50 2.520 10.89 Std. dev 0.270 0.184 0.255 0.939 0.126 0.083 13.06 1.275 0.339 1.215 Kurtosis -0.073 -1.046 -0.133 0.092 0.086 -0.583 -0.107 -1.156 0.872 -0.723 Skewness 0.641 0.223 0.992 0.799 0.797 0.185 -0.699 0.271 1.319 0.399
Table (B.2) Descriptive statistics of forward exchange rates This table reports the mean, minimum, maximum, standard deviation as well as
the kurtosis and skewness for the end-of-month 1-, 3-, 6- and 12 month forward rates available in the period from 28-05-1999 to 29-05-2020.
1-month forward exchange rate
AUD CAD CHF DKK EUR GBP JPY NOK NZD SEK
Mean 1.345 1.241 1.155 6.317 0.848 0.643 106.5 7.164 1.560 7.950 Min 0.914 0.950 0.788 4.711 0.632 0.482 76.23 5.095 1.146 5.939 Max 2.048 1.605 1.797 8.804 1.182 0.820 133.6 10.50 2.519 10.89 Std. dev 0.270 0.184 0.254 0.939 0.126 0.083 12.97 1.275 0.340 1.211 Kurtosis -0.063 -1.043 -0.128 0.120 0.109 -0.585 -0.096 -1.157 0.872 -0.698 Skewness 0.649 0.227 0.994 0.815 0.810 0.178 -0.693 0.273 1.320 0.412
3-month forward exchange rate
Mean 1.349 1.241 1.152 6.310 0.847 0.643 106.1 7.174 1.566 7.943 Min 0.921 0.949 0.787 4.727 0.634 0.483 76.17 5.124 1.152 5.960 Max 2.048 1.606 1.795 8.820 1.183 0.818 133.2 10.50 2.518 10.90 Std. dev 0.269 0.184 0.253 0.938 0.126 0.082 12.81 1.275 0.340 1.206 Kurtosis -0.040 -1.036 -0.116 0.176 0.157 -0.587 -0.079 -1.158 0.874 -0.643 Skewness 0.665 0.237 1.000 0.848 0.838 0.165 -0.679 0.280 1.322 0.441
6-month forward exchange rate
Mean 1.355 1.242 1.147 6.300 0.846 0.643 105.5 7.187 1.575 7.933 Min 0.931 0.950 0.786 4.753 0.637 0.484 76.06 5.172 1.161 5.994 Max 2.049 1.606 1.791 8.837 1.184 0.816 132.5 10.49 2.519 10.92 Std. dev 0.268 0.184 0.251 0.937 0.126 0.081 12.58 1.275 0.340 1.198 Kurtosis -0.003 -1.025 -0.100 0.259 0.230 -0.590 -0.061 -1.153 0.881 -0.556 Skewness 0.689 0.253 1.007 0.899 0.881 0.148 -0.655 0.295 1.328 0.489
12-month forward exchange rate
Mean 1.367 1.242 1.136 6.277 0.842 0.644 104.3 7.210 1.592 7.916 Min 0.952 0.950 0.784 4.796 0.643 0.488 75.77 5.262 1.179 6.057 Max 2.059 1.608 1.779 8.849 1.183 0.813 130.7 10.50 2.530 10.94 Std. dev 0.266 0.183 0.248 0.934 0.125 0.079 12.15 1.274 0.342 1.185 Kurtosis 0.070 -0.999 -0.077 0.422 0.376 -0.590 -0.057 -1.122 0.894 -0.373 Skewness 0.739 0.288 1.016 0.996 0.965 0.115 -0.605 0.333 1.340 0.585
Table (B.3) Descriptive statistics of forward discount This table reports the mean, minimum, maximum, standard deviation as well as
the kurtosis and skewness for the end-of-month 3-, 6- and 12 month forward discounts based on available spot- and forward exchange rates available in the
period from 28-05-1999 to 29-05-2020
3-month forward discount
AUD CAD CHF DKK EUR GBP JPY NOK NZD SEK
Mean 0.005 0.000 -0.004 -0.002 -0.002 0.001 -0.01 0.002 0.006 -0.001 Min 0.004 0.002 0.003 0.004 0.003 0.003 0.00 0.005 0.004 0.004 Max -0.003 -0.003 -0.011 -0.009 -0.008 -0.005 0.0 -0.01 -0.002 -0.01 Std. dev 0.012 0.005 0.000 0.005 0.005 0.008 0.00 0.014 0.015 0.007 Kurtosis -1.117 -0.776 -1.263 -0.975 -1.014 -0.303 -0.322 0.040 -0.440 -1.344 Skewness -0.057 0.249 -0.420 0.028 -0.061 0.527 -0.872 0.534 -0.236 0.097
6-month forward discount
Mean 0.009 0.000 -0.009 -0.003 -0.004 0.002 0.0 0.004 0.011 -0.002 Min 0.009 0.004 0.006 0.007 0.007 0.006 0.01 0.009 0.008 0.009 Max -0.005 -0.005 -0.021 -0.017 -0.016 -0.009 0.0 -0.01 -0.004 -0.02 Std. dev 0.025 0.010 0.000 0.010 0.009 0.016 0.00 0.027 0.030 0.013 Kurtosis -1.048 -0.703 -1.253 -0.831 -0.925 -0.129 -0.072 0.303 -0.544 -1.254 Skewness -0.016 0.360 -0.373 0.030 -0.048 0.584 -0.929 0.652 -0.243 0.107
12-month forward discount
Mean 0.018 0.001 -0.018 -0.007 -0.007 0.003 0.0 0.008 0.021 -0.005 Min 0.017 0.008 0.012 0.014 0.014 0.013 0.02 0.017 0.016 0.017 Max -0.009 -0.010 -0.042 -0.032 -0.030 -0.018 -0.1 -0.02 -0.007 -0.03 Std. dev 0.048 0.020 -0.002 0.018 0.018 0.030 0.00 0.047 0.055 0.023 Kurtosis -0.948 -0.192 -1.063 -0.831 -0.915 -0.017 0.400 -0.246 -0.541 -1.228 Skewness 0.140 0.475 -0.526 0.096 -0.012 0.561 -1.003 0.558 -0.147 0.147