5. Empirical Evidence
5.1 The Fama Regression
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They split their sample into two regimes: the low-volatility regime and the high-volatility regime. The former is defined as periods in which the implied high-volatility is lower than the 25th percentile, and the latter is defined as periods in which the implied volatility is greater than the 75th percentile. However, their measure is different from the measure used in this paper. To my knowledge, a setting that treats not only
“extremely high uncertainty” but also “extremely low uncertainty”, “relatively low uncertainty”, and “relatively high uncertainty” as regimes has not yet been applied to the study of how uncertainty indexes and UIRP are correlated. One should note that, in contrast to Ramírez-Rondán and Terrones (2019) in which they use a statistically significant threshold (i.e. the percentile) that minimizes the sum of squared errors to split their sample into two regimes, the aim of this paper is to explore whether the relationship between spot exchange rate changes and forward premiums alters when economic uncertainty increases. Thus, whether thresholds are optimized and whether threshold effects are statistically significant are not the focus in this paper.
5. Empirical Evidence
5.1 The Fama Regression
INSERT TABLE II HERE
Table II reports slope coefficients of the Fama regression, i.e., β in the equation (5), over the January 1985 to March 2020 period at the 1-, 3-, and 12-month horizon across 12 countries. Among 36 slope coefficients (12 countries at three horizons), only 3 out of them are positive. They are the slope coefficient of Sweden and Singapore at the 1-month horizon and Canada at the 12-1-month horizon. The results are consistent with the stylized fact that forward premiums tend to negatively predict spot exchange rates changes. Although the slope coefficient of Canada at the 12-month horizon is positive,
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it is still significantly different from 1, that is, it deviates from UIRP.
Table II also shows that deviations from UIRP at a longer horizon are not different from those at a shorter horizon, i.e., the horizon effect is not apparent, because half of countries in my sample deviate from UIRP more strongly at the 12-month horizon than at the 1-month horizon. The result seems to contradict that reported in Chinn and Meredith (2004) and Chinn (2006), but it may be attributed to what documented in Chinn and Quayyum (2013), that is, the advent of the zero interest rate bound has weaken the horizon effect. Since more recent data are used in this paper, one should not be surprised to see much weaker horizon effect.
Finally, slope coefficients of pooled regressions are all negative and significantly different from 1. The results are in line with empirical evidence - the FPP exists in the developed economy - which is widely documented in previous literature. Note that pooled results exclude the Eurozone and include only one emerging country, that is., South Africa, which is found to deviate from UIRP strongly in Chinn (2006), Frankel and Poonawala (2010), and Ismailov and Rossi (2018). In addition, the weakness of the horizon effect becomes more apparent because the value and statistical significance level of the 1-month and 12-month slope coefficient of the pooled regression are the same.
Following Bussiere et al. (2018), I split the sample period into two subperiods: one is the pre-crisis period and the other is the post-crisis period. Bussiere et al. (2018) pointed out that, according to a Chow test, all currencies involved in their analysis exhibit a significant break over the 2007 to 2008 period and they used August 2007 to split their sample.22 However, in this paper, December 2007 is used to split my sample
22 On August 9, 2007, BNP Paribas announced that it was closing three hedge funds that specialized in U.S. mortgage debt. This event is often considered as one of the first tangible signals of the financial crisis as it was followed by a freeze on the interbank lending market. (Bussiere et al., 2018)
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because the NBER's Business Cycle Dating Committee officially defines it as the date on which the recession started in the United States.
INSERT TABLE III HERE
Panel A of Table III reports slope coefficients of the Fama regression over the January 1985 to November 2007 period, i.e., the pre-crisis period, at the 1-, 3-, and 12-month horizon across 12 countries. Among 36 slope coefficients, 5 out of them are positive.
They are the slope coefficient of South Africa, Norway, and Sweden at the 1-month horizon, Sweden at the 3-month horizon, and the United Kingdom at the 12-month horizon.
Compared to the full sample period, slope coefficients of Sweden at all three horizons are closer to 1 over the pre-crisis period. These findings are consistent with what documented in Bansal and Dahlquist (2000) and Chinn and Frankel (2019), that is, over the pre-euro period, the high inflation rate23 of Sweden results in a positive slope coefficient.
Although the number of positive slope coefficients over the pre-crisis period is more than the full sample period, 20 out of 36 slope coefficients either switch their signs from positive to negative or become more negative, especially for Eurozone and Japan. The finding is in line with what documented in Bussiere et al. (2018), that is, the UIRP violation is stronger over the pre-crisis period. The result is further supported by the pooled result because, compared to the full sample period, 2 out of 3 slope coefficients become more negative over the pre-crisis period.
Since 3 out of 5 positive slope coefficients over the pre-crisis period are at the 1-month horizon, one might be interested in testing the horizon effect. From Panel A of Table III, the horizon effect still seems not to be present over the pre-crisis period
23 The high inflation rate is a common characteristic among emerging countries, which are found not to deviate from UIRP.
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because only one third of countries deviate from UIRP more weakly at the 12-month horizon than at the 1-month horizon. That is, the horizon effect becomes more obscure over the pre-crisis period. Thus, the reason why the horizon effect has been weaker suggested by Chinn and Quayyum (2013) is doubtful. The failure to find weaker UIRP violation at longer horizons reported by Chinn and Meredith (2004) and Chinn (2006) may be due to other reasons. However, one should note that the 1-, 3-, or 12-month horizon is often considered short horizons. In contrast, long horizons often refer to the 5- and 10-year horizon. Thus, comparing the 1-month result to the 12-month result may not identify the horizon effect24.
Panel B of Table III reports slope coefficients of the Fama regression over the December 2007 to March 2020 period, i.e., the post-crisis period, at the 1-, 3-, and 12-month horizon across 12 countries. Among 36 slope coefficients, up to 26 are positive and 18 are greater than 1. Only slope coefficients of South Africa are all negative over the post-crisis period. The finding is surprising but in line with what documented in Bussiere et al. (2018), that is, the direction of the FPP reversed after the GFC. They called this new anomaly as “the new Fama puzzle”. This anomaly is further supported by slope coefficients of pooled regressions over the post-crisis period because all of them are positive. Moreover, all of them are close to 1, i.e., the theoretical value, and not significantly different from 1. For example, the slope coefficient of the pooled regression over the post-crisis period at the 12-month horizon is 1.14 and not significantly different from 1. One might conclude that the FPP no longer exists in the post-crisis period by only conducting a pooled analysis. However, the conclusion cannot be applied to individual countries, especially for South Africa, the United Kingdom, Canada, Singapore, and Japan. This is what one should be aware of when
24 However, Ichiue and Koyama (2011) compared their 3-month results with 6-month results and had a discussion on the horizon effect.
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conducting a pooled analysis using a sample period including more observations from the post-crisis period.