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5.3.2 the post-crisis period
INSERT TABLE VI HERE
Table VI reports post-crisis slope coefficients of the Fama regression in four regimes at the 1-, 3-, 12-month horizon across 12 countries. As mentioned above, the post-crisis period is full of uncertainty, i.e., there are few periods defined as
“extremely low uncertainty” in the post-crisis period. Thus, results of “extremely low uncertainty” are not reported.
Comparing results in Table V to those in Table VI, at all three horizons, all slope coefficients change. For “relatively low uncertainty” and “relatively high uncertainty”, most slope coefficients change from negative to positive, whereas, for “extremely high uncertainty”, most slope coefficients change from positive to negative. These findings can be confirmed by slope coefficients of pooled regressions, especially at the 3-month horizon.
In general, compared to using pre-crisis data, using the post-crisis data (with all available US EPU), slope coefficients of the four-regime Fama regression are different.
This result is similar to what documented in Bussiere et al. (2018), that is, the relationship between forward premiums and spot rate changes differs between the pre-crisis and post-pre-crisis period. Thus, under my definition, US EPU does not help classify periods with the same characteristic because slope coefficients are sensitive to different subperiods.
6. Robustness Check
Since results in section 5.3 have shown that the model in this paper is sensitive to different subperiods, one may further doubt the necessity of adding more regimes, i.e., the robustness of results in section 5.2. I deal with these concerns by reporting rolling estimates, that is, I alter the upper and lower bound of the regime simultaneously, for
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example, from <25th to 1th-26th (the size of the regime remains unchanged), and see whether slope coefficients gradually change when uncertainty increases or visibly be the lowest when uncertainty is moderately low.
INSERT FIGURE II HERE
Figure II reports results of the rolling estimation. Since, as shown in section 5.2, the correlation between US EPU and UIRP is sensitive to different horizons (because it is a variable observed at time t), I only report 1-month results. Figure II (a) illustrates that, for “target countries”, only slope coefficients of South Africa change from positive to negative with the increase in uncertainty. However, the statement “slope coefficients of South Africa gradually reverse when uncertainty increases” should be taken carefully because the slope coefficient changes from negative to positive when comparing the 31th-56th regime to the 43th-68th regime. That is, one should avoid longing South African Rand when uncertainty hits the 56th-68th percentile. For Australia, estimates remain close to zero when the regime rolls from 29th-54th to 62th-87th. Thus, the best timing for longing Australian dollar may be when uncertainty is extremely low or greater than the 87th percentile. Nonetheless, the regime effect on New Zealand is subtle because most slope coefficients of New Zealand are smaller than zero. In other words, longing New Zealand dollar in all regimes, on average, makes money. In contrast, Figure II (b) demonstrates that, for
“funding countries”, slope coefficients gradually change from negative to positive with the increase in uncertainty. The statement “the FPP of Switzerland and Japan gradually reverses when uncertainty increases” is robust. The timing for slope coefficients of “funding countries” to be greater than unity is when uncertainty hits the 80th percentile. Thus, investors should avoid shorting Switzerland Franc and Japanese Yen when uncertainty is extremely high.
Figure II (c) illustrates that, for Nordic countries, slope coefficients estimated
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around the 50th percentile are obviously at the lowest level. Thus, not only the statement “UIRP violations of European countries are more prevalent when uncertainty is moderately low” is robust but also the bound of “relatively low
uncertainty” is optimal. However, the timing for slope coefficients of Nordic countries to become positive differs. Longing Norwegian krone should be avoided when
uncertainty hits the 56th percentile, whereas, longing Swedish krona and Danish krone should be avoided when uncertainty hits the 80th percentile. It is noteworthy that rolling estimates of Sweden move closely with those of Denmark. Figure II (d) demonstrates that, rolling estimates of the United Kingdom and Canada are similar to those of Nordic countries, that is, their slope coefficients estimated around the 50th percentile are at the lowest level. In addition, the timing for slope coefficients of the United Kingdom and Canada to be greater than unity is when uncertainty hits the 75th percentile, which is close to the result of Sweden and Denmark.29 The Eurozone also behaves in a similar pattern like Nordic countries, the United Kingdom, and Canada.
The only difference is the FPP of the Eurozone becomes the strongest among all regimes (and stronger than all other countries) in the 35th-60th regime. Finally, as mentioned in section 5.2, Singapore behaves in a similar pattern like South Africa.
However, from rolling estimates, it seems that Singapore is more in line with the statement “slope coefficients gradually reverse from positive to negative”. When uncertainty is higher than the 50th percentile, the profitability of shorting Singapore dollar becomes greater and stable, especially when uncertainty is extremely high.
Figure II (e) reports rolling estimates of the pooled slope coefficient. One can see that the FPP is strongest when the uncertainty is between the 25th and 50th percentile,
29 It is noteworthy that slope coefficients of Canada greatly differ between being estimated in the 72th-97th regime and in the 75th-100th regime. This result may be driven from the exclusion of 72th-74th, the inclusion of 98th-100th, or both. No matter what, it indicated that some observations are influential in exploring the FPP.
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which is mainly driven by European countries and Canada. Beyond the 50th percentile, pooled slope coefficients gradually reverse from negative to positive.
Overall, there seems to be a difference between when uncertainty is higher than the median and lower than the median. Thus, as I argue in section 4.2, one should avoid mixing the “relatively low uncertainty” regime with the “relatively high uncertainty”
regime, which may overlook some important information, especially for Australia, European countries, and Canada.