經濟政策不確定性與未拋補利率平價說之關係 - 政大學術集成

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(1)國立政治大學財務管理學系研究所碩士學位論文. 政治大經濟政策不確定性與未拋補利率平價說之關係. 立. The Relationship between Economic Policy Uncertainty and. ‧ 國. 學. Uncovered Interest Rate Parity. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. 指導教授：張元晨研究生：吳彥昇. i Un. v. 博士撰. 中華民國一零九年六月. DOI:10.6814/NCCU202001120.

(2) Abstract For over forty years, many economists have found that uncovered interest rate parity (UIRP) does not hold. Most previous findings indicated that currency forward premiums negatively predict changes in spot exchange rates, however, results based on data after the global financial crisis show different patterns. In this paper, I explore the relationship between US economic policy uncertainty and UIRP and find that, when uncertainty is extremely high, forward premiums positively predict changes in. 政治大 uncertainty is moderately low, UIRP violations for currencies of European countries 立. spot exchange rates, especially for Swiss Franc and Japanese Yen. In addition, when. ‧. ‧ 國. 學. and Canada are more prevalent.. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 1. DOI:10.6814/NCCU202001120.

(3) TABLE OF CONTENTS Abstract .......................................................................................................................... 1 1. Introduction ................................................................................................................ 4 2. Uncovered Interest Rate Parity .................................................................................. 5 3. Related Literature....................................................................................................... 6 4. Data and Model ........................................................................................................ 12 4.1 Data .................................................................................................................... 12 4.2 Model ................................................................................................................. 14. 政治大 5.1 The Fama Regression ......................................................................................... 15 立. 5. Empirical Evidence .................................................................................................. 15. ‧ 國. 學. 5.2 The Fama Regression and US EPU.................................................................... 19 5.3 The Fama Regression and US EPU: the pre-crisis and post-crisis period ......... 24. ‧. 5.3.1 the pre-crisis period ..................................................................................... 25 5.3.2 the post-crisis period .................................................................................... 28. y. Nat. io. sit. 6. Robustness Check .................................................................................................... 28. n. al. er. 7. Conclusion ............................................................................................................... 31. i Un. v. References .................................................................................................................... 33. Ch. engchi. 2. DOI:10.6814/NCCU202001120.

(4) LIST OF TABLES Table I Summary Statistics of Forward Premium and Spot Exchange Rate Change .. 36 Table II Slope Coefficients of the Fama Regression.................................................... 37 Table III Slope Coefficients of the Fama Regression: the pre-crisis and post-crisis period ................................................................................................................... 38 Table IV Slope Coefficients of the Fama Regression and US EPU ............................. 40 Table V Slope Coefficients of the Fama Regression and US EPU: the pre-crisis period .............................................................................................................................. 42 Table VI Slope Coefficients of the Fama Regression and US EPU: the post-crisis period ................................................................................................................... 44. 治. LIST 政 OF FIGURES 大. 立. ‧ 國. 學. ‧. Figure I The Time Series of the US economic policy uncertainty (US EPU) index.... 46 Figure II Rolling Estimates of Slope Coefficients of the Fama Regression in Different Regimes................................................................................................................ 47. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 3. DOI:10.6814/NCCU202001120.

(5) 1. Introduction Uncovered interest rate parity (UIRP) refers to a no-arbitrage condition in which neither domestic nor foreign investors can, on average, earn excess return through borrowing money from low-interest-rate countries and lending it to high-interest-rate countries. That is, UIRP implies that the expected change in the spot exchange rate equals to the interest rate differential. However, empirical evidence in previous literature is usually against the validity of UIRP. For example, Fama (1984) documented that forward premiums negatively predict changes in spot exchange rates. This anomaly. 政治大. is known as the forward premium puzzle (FPP).. 立. There are many papers that surveyed the negative correlation between forward. ‧ 國. 學. premiums and spot exchange rates changes (e.g. Froot and Thaler, 1990; Engel, 2014). For instance, the survey by Froot and Thaler (1990) found that, if one runs a regression. ‧. of spot exchange rates changes on forward premiums (thereafter, the Fama regression),. Nat. sit. y. the slope coefficient is negative on average. This anomaly is still lacking of good. n. al. er. io. explanations. In addition, results based on data after the global financial crisis (GFC). i Un. v. indicated the FPP shows a different pattern, i.e., forward premiums positively predict changes in spot exchange rates.. Ch. engchi. Recently, some papers re-examine the Fama regression including a risk measure. Most of these papers suggested that, when risk is high, the correlation between forward premiums and spot exchange rates changes tends to switch from negative to positive. That is, the slope coefficient of the Fama regression becomes greater than zero or even greater than unity. Since these papers usually split their sample into two regimes: the high-risk (high-volatility) regime and the low-risk (low-volatility) regime, they may overlook the correlation between forward premiums and spot exchange rates changes when risk is moderately low or when risk is moderately high. 4. DOI:10.6814/NCCU202001120.

(6) In this paper, I redesign the two-regime Fama regression by adding more regimes and substituting an uncertainty measure for a risk measure to test whether the FPP gradually reverses when uncertainty increases. My result suggests that there is no universal pattern for all countries. For individual country, results may change at different horizons. However, there are three robust findings: (i) when uncertainty increases, the slope coefficient of South Africa gradually reverses from positive to negative; (ii) when uncertainty increases, the slope coefficient of Japan and Switzerland gradually reverse from negative to positive; (iii) when uncertainty is moderately low, the slope coefficient of European countries and Canada are the most negative among four regimes.. 立. 政治大. The remaining of this paper is organized as follows. Section 2 revisits UIRP. Section. ‧ 國. 學. 3 reviews related literature. Section 4 describes data and model. Section 5 reports. ‧. empirical evidence. Section 6 concludes.. io. sit. y. Nat. 2. Uncovered Interest Rate Parity. n. al. er. UIRP is a no-arbitrage condition in which there is no difference between the expected. Ch. i Un. v. return of the domestic and foreign investment. That is, if UIRP holds, investing in a. engchi. high-interest-rate or low-interest-rate country is indifferent for investors because interest rate differential is expected to be offset by the change in the spot exchange rate. (1 + i∗t,h ) =. Et (St+h ) (1 + it,h ) … (1) St. Equation (1) is the theoretical form of UIRP. St is the spot exchange rate (units of foreign currency per unit of domestic currency) at time t, and Et (St+h ) is the expected spot exchange rate for time t+h at time t. it,h and i∗t,h is the h-month domestic and foreign interest rate respectively. In this paper, I define the domestic currency as USD. st+h − st = ft,h − st + ϵt+h … (2) 5. DOI:10.6814/NCCU202001120.

(7) Equation (2) is a common form of UIRP for empirical tests. st is the log spot exchange rate at time t, and st+h is the log realized spot exchange rate at time t+h. ft,h is the log h-month forward exchange rate. ϵt+h is the error term at time t+h (white noise). Two assumptions are required for deriving equation (2) from equation (1). The first assumption is covered interest rate parity (CIRP) has to hold. That is, (1 + i∗t,h ) =. Ft,h (1 + it,h ) … (3) St. where Ft,h is the h-month forward exchange rate. When CIRP holds, the interest rate differential equals the forward premium. Thus, if UIRP also holds, the expected change. 政治大 difference between the realized and expected spot exchange rate is white noise. That is, 立 in the spot exchange rate equals the forward premium. The second assumption is the. ‧ 國. 學. st+h − Et (st+h ) = ϵt+h … (4). where ϵt+h is the forecast error at time t+h (white noise). This assumption is known. ‧. as rational expectation.. sit. y. Nat. UIRP is commonly tested with these two assumptions using a regression-based. er. al. iv n C st+h − st = αh+eβ(f i εU… (5) t) + nt,hg−csh n. premium.. io. method, i.e., a regression of the realized change in the spot exchange rate on the forward. Equation (5) is the so-called Fama regression, though, it was first tested by Tryon (1979). The null hypothesis for coefficients in this equation is α = 0 and β = 1 respectively. The focus of this paper is the slope coefficient β.. 3. Related Literature Previous literature documented the slope coefficient in equation (5) not only deviates from the theoretical value but also points in the wrong direction. That is, β is empirically different from 1 and usually less than 0. This anomaly is the so-called 6. DOI:10.6814/NCCU202001120.

(8) forward premium puzzle (FPP). Fama (1984) tested FPP using data of 9 countries 1 and found that all slope coefficients are negative over the 1973 to 1982 period. Bansal (1997) examined the same 9 countries and reported that 7 out of 9 slope coefficients are negative2 over the 1981 to 1995 period. Results of Bansal (1997) and Fama (1984) are similar even though their sample periods are different. In addition to developed economies, Bansal and Dahlquist (2000) investigated emerging countries and found that, for developed economies, 12 out of 16 slope coefficients are negative, whereas, for emerging countries, only 3 out of 12 slope coefficients are negative.3 They concluded that the. 政治大. FPP is not a universal phenomenon, i.e., the FPP does not seem to be present in. 立. emerging countries.. ‧ 國. 學. Chinn (2006) found that the slope coefficient of developed economies at the 3-, 6-,. ‧. and 12-month horizon are all negative, except for Italy. However, at the 5- and 10-year horizon, slope coefficients are all positive, except for Norway.4 He also found that, at. y. Nat. io. sit. the 1-month horizon, only 6 out of 14 slope coefficients of emerging and newly. n. al. er. industrialized countries are negative.5 He concluded that empirical evidence against. Ch. i Un. v. UIRP is still present, i.e., the short-term interest rate differential remains a biased. engchi. predictor of the ex post change in the spot exchange rate, especially for the G7 countries. Frankel and Poonawala (2010) confirmed the result of Chinn (2006) using seemingly unrelated regressions (SUR). They found that, compared to developed countries, the forward premium is indeed a less biased predictor of the realized change in the spot. Belgium, Canada, France, Italy, Japan, the Netherlands, Switzerland, the United Kingdom, and West Germany 2 The slope coefficient of France and Italy are positive. 3 For developed economies, only the slope coefficient of France, Italy, Spain, and Sweden are positive; for emerging countries, only the slope coefficient of Greece, Mexico, and India are negative. 4 See Chinn and Meredith (2004) for similar results and a discussion. 5 The six economies are Hong Kong, India, Mexico, Saudi Arabia, South Africa, and Turkey. Note that Bansal and Dahlquist (2000) classified Hong Kong as a developed economy and did not find the slope coefficient of Turkey is negative. 7 1. DOI:10.6814/NCCU202001120.

(9) exchange rate for emerging countries. Chinn and Quayyum (2013) reviewed empirical evidence against UIRP at both short and long horizons over the period up to 2011. They found that deviations from UIRP are larger at short horizons than at long horizons. However, the difference is smaller than that documented in Chinn and Meredith (2004) and Chinn (2006). They attribute the weaker horizon effect partly to the advent of extraordinarily low interest rates. Moreover, the result of the Fama regression for individual countries at both short and long horizons differ between using USD and GBP as the base currency. Thus, they suggested that the cross-sectional variation is critical in testing UIRP.. 政治大. Chinn and Frankel (2019) used both the rational and survey-based expectation. 立. methodology to re-examine UIRP at the 3- and 12-month horizon. They found that,. ‧ 國. 學. with the rational expectation methodology, for euro legacy currencies6, 5 out of 7 slope. ‧. coefficients are either negative or close to 0. However, for Italy and Spain, whose inflation rates are among the highest in their sample over the 1986 to 1998 period (the. y. Nat. io. sit. pre-euro period), slope coefficients are significantly positive at short horizons.7 For. n. al. er. other currencies8, all slope coefficients are also either negative or close to 0. The only. Ch. i Un. v. exception is that of Sweden at the 3-month horizon. Like Italy and Spain, the inflation. engchi. rate of Sweden is relatively high over the pre-euro period. In contrast, with the surveybased expectation methodology, they reported that all slope coefficients at both 3- and 12-month horizon are either positive or close to 1. The only exception is that of Japan at the 3-month horizon. Thus, slope coefficients of UIRP estimated without the rational expectation assumption, i.e., only with the assumption that CIRP holds, point in the. Belgium, France, Germany, Ireland, Italy, the Netherlands, and Spain The finding that UIRP tends to hold better at short horizons for currencies of countries with higher inflation rates is consistent with that documented in Bansal and Dahlquist (2000), Chinn and Meredith (2004), Chinn (2006), and Frankel and Poonawala (2010). 8 the Eurozone, Denmark, Norway, Sweden, Switzerland, the United Kingdom, Japan, Australia, Canada, and New Zealand 8 6 7. DOI:10.6814/NCCU202001120.

(10) right direction. They concluded that the difference between these two methodologies is due to bias in exchange rate expectations9 and suggested that biased expectations are an important reason why forward premiums point in the wrong direction for ex post spot exchange rates changes. Bussiere et al. (2018) re-examined the FPP for exchange rates of 8 developed countries10 against the US dollar over the January 1999 to June 2019 period. They found that, only the slope coefficient of Canada is positive at the 3- and 12-month horizon. They then split their sample period into two subperiods. The first subperiod is the pre-crisis period ranging from January 1999 to August 2007 whereas the second. 政治大. subperiod is the post-crisis period ranging from September 2007 to June 2019. Over the. 立. pre-crisis period, all slope coefficients are significantly negative at both 3- and 12-. ‧ 國. 學. month horizon. In contrast, over the post-crisis period, all slope coefficients are positive. ‧. at both 3- and 12-month horizon. Moreover, over the post-crisis period, half of slope coefficients are significant at the 12-month horizon11. These findings suggested that the. y. Nat. io. sit. relationship between the interest rate differential and the ex post spot exchange rate. n. al. er. change differs between the pre- and post-crisis period. They called this new anomaly. Ch. i Un. v. as “the new Fama puzzle”. The anomaly is robust to four different base currencies12. In. engchi. addition, they tested UIRP by relaxing the rational expectation assumption and reported that all slope coefficients are positive at both 3- and 12-month, except for the United Kingdom at the 3-month horizon. Interestingly, most point estimates did not either change their values or switch their signs from pre-crisis to post-crisis period. They argued that the difference between these two periods can be attributed to a large extent to the change in the correlation of expectation errors and interest rate differentials. That. The finding argues that, in equation (2) and (4), ϵt+h are not white noise. Canada, Switzerland, Denmark, the Eurozone, Japan, Norway, Sweden, and the United Kingdom 11 Canada, Japan, Norway, and the United Kingdom 12 USD, JPY, EUR, and GBP 9 9. 10. DOI:10.6814/NCCU202001120.

(11) is, “the new Fama puzzle” might dissipate as the co-movement of expectation errors and interest rate differentials changes, expectations error variability shrinks, or interest rate variability rises. Chinn and Quayyum (2013) and Bussiere et al. (2018) both indicated that changes in the economic environment influence the FPP. In other words, the FPP is regimedependent. Brunnermeier et al. (2008) found that (i) currencies with similar interest rates co-move with each other, suggesting that the carry trade13 affects spot exchange rates changes; (ii) carry trades are subject to currency crashes, i.e., carry trade returns are negatively skewed; (iii) increases in risk measured by VIX and the TED spread are. 政治大. positively correlated with the sudden unwinding of carry trade positions and carry trade. 立. losses, i.e., currency crashes; (iv) a higher VIX predicts higher excess returns and the. ‧ 國. 學. excess return predictability of the interest rate differential reduces after including VIX. ‧. as a control variable, that is, currency crash risk helps resolve the FPP14. Clarida et al. (2009) showed that carry trades collect currency premiums to generate. y. Nat. io. sit. persistent excess returns, but when volatility increases, the sharp unwinding of carry. n. al. er. trade positions results in losses. They argued that the widely documented negative slope. Ch. i Un. v. coefficient in regressions of spot exchange rate changes on forward premiums is an. engchi. artifact of the volatility regime. In the high-volatility regime, the regression produces a positive slope coefficient greater than unity. Ichiue and Koyama (2011) used a regimeswitching model 15 to examine how exchange rate volatility and the depreciation of low-interest-rate currencies are related to each other at short horizons. They found that the relationship is strongly influenced by switches of the regime. Low-interest-rate. The trading strategy consists of shorting low-interest-rate currencies and longing high-interest-rate currencies. 14 See Ranaldo and Söderlind (2010), Berg and Mark (2018) and Husted et al. (2018) for similar analyses. 15 A regime-switching model is also known as a Markov-switching model, which was advanced in economics and finance by Hamilton (1989). 10 13. DOI:10.6814/NCCU202001120.

(12) currencies appreciate less frequently, but once they do, movements are faster than when they depreciate. This is because carry trade positions are forced to unwind rapidly when the regime switches from low-volatility to high-volatility. They also indicated that exchange rate volatility and the depreciation of low-interest-rate currencies are mutually dependent. That is, the depreciation of low-interest-rate currencies contributes to maintaining a low-volatility environment. Cho et al. (2019) used an endogenous regime-switching model with an autoregressive latent factor to investigate the profitability of carry trades. They reported that carry trades are profitable in a regime with low exchange rate volatility, signifying the failure of UIRP, whereas they yield. 政治大. losses in a regime with high exchange rate volatility, implying the reverse of the FPP.. 立. In contrast, Ismailov and Rossi (2018) used various economic uncertainty measures16. ‧ 國. 學. to investigate whether uncertainty can explain deviations from UIRP at the 3-month. ‧. horizon. They found that deviations from UIRP are stronger in periods of exceptionally high uncertainty and weaker in periods of low uncertainty. Thus, they argued that,. y. Nat. io. sit. relative to the high-uncertainty environment, UIRP tends to hold in the low-uncertainty. n. al. er. environment. Similarly, Ramírez-Rondán and Terrones (2019) used a panel threshold. Ch. i Un. v. regression model and survey-based exchange rate expectations to examine the extent to. engchi. which economic uncertainty affects UIRP. They showed that there is a statistically significant threshold that splits their sample into two regimes: a low-uncertainty regime and a high-uncertainty regime. UIRP holds in the former, but it does not hold in the latter. Their finding is robust to different uncertainty measures, control variables, horizons, and estimation methods.. the VIX, the macroeconomic uncertainty index, the financial uncertainty index, the economic policy uncertainty index, the global foreign exchange volatility risk, and the exchange rate uncertainty index 11 16. DOI:10.6814/NCCU202001120.

(13) 4. Data and Model 4.1 Data The main analyses in this paper are based on two kind of data. One is the exchange rate data and the other is economic uncertainty measure. The former are an extended version of data used in Hassan and Mano (2019).17 They range from October 1983 to March 2020 and contain monthly observations of US dollar-based changes in spot exchange rates and forward premiums at the 1-, 3-, and 12-month horizon across 42 currencies. 18 The latter are the US economic policy uncertainty (US EPU) index.19. 政治大. The US EPU index begins in January 1985. Thus, for a complete analysis of the. 立. relationship between US EPU and UIRP, only countries with exchange rate data starting. ‧ 國. 學. at least from January 1985 and lasting until March 2020 are included in my sample. For. ‧. example, euro legacy currencies are excluded because they have been replaced by the euro since 1999, i.e., their exchange rate data are truncated. The 13 countries which. y. Nat. io. sit. meet my requirement are Australia, Canada, Switzerland, Denmark, Hong Kong, Japan,. n. al. er. Malaysia, Norway, New Zealand, Sweden, Singapore, the United Kingdom, and South. Ch. i Un. v. Africa. Hong Kong is excluded due to currency board system and Malaysia is also. engchi. excluded because it adopted capital control from September 1998 to July 200520. In addition, although the Eurozone (treated as a country) does not meet my requirement, it is still included due to its importance in the currency market nowadays. INSERT TABLE I HERE. The extension is done by updating spot and forward exchange rates over the July 2010 to March 2020 period from Datastream. 18 It is noteworthy that updated forward premiums are not checked by the data-cleaning procedure mentioned in Hassan and Mano (2019). 19 The index is created by Baker et al. (2016). (https://www.policyuncertainty.com/us_monthly.html) See Baker et al. (2016) for how the index is constructed and see Ismailov and Rossi (2018) and Ramírez-Rondán and Terrones (2019) for how the index and UIRP are correlated. 20 Hassan and Mano (2019) mentioned, in their online appendix, that they drop the exchange rate data of Malaysia from August 1998 to June 2005 because their forward exchange rates are zero. 12 17. DOI:10.6814/NCCU202001120.

(14) Table I reports summary statistics of forward premium and spot exchange rate change for each 12 countries at the 1-, 3-, and 12-month horizon. The countries are sorted in descending order by the annualized mean forward premium (i.e., interest rate differentials). Thus, it can be seen that, the 3 countries with highest mean forward premium are South Africa, New Zealand, and Australia. Currencies of these countries are called “target currencies” due to often being target currencies of carry trades. In contrast, the 2 countries with lowest mean forward premium are Japan and Switzerland. Currencies of these countries are called “funding currencies” because they are often being funding currencies of carry trades The trading strategy of shorting funding. 政治大. currencies and longing target currencies, i.e., the carry trade, yields an excess return at. 立. all three horizons on average. For example, without transaction costs, a trading strategy. ‧ 國. 學. of shorting Japan Yen and Swiss Franc and longing South African Rand, New Zealand. ‧. dollar, and Australia dollar, yields an annualized excess return 6.17%, 6.17%, and 6.31% at the 1-, 3-, and 12-month horizon respectively. Thus, the FPP is present in my. y. Nat. io. sit. sample. In addition, summary statistics for pooling all countries’ forward premium and. n. al. er. spot exchange rate change data at the 1-, 3-, 12-month horizon are reported in the last. Ch. i Un. v. row of Table I. It is noteworthy that the pooled result does not include the Eurozone. engchi. throughout this paper because its start date is inconsistent with others’ start date. INSERT FIGURE I HERE Figure I plots the time series of US economic policy uncertainty (US EPU) and periods with “extremely high uncertainty”. Periods are defined as “extremely high uncertainty” if their US EPU are greater than the 75th percentile of all available US EPU. Under this definition, whether periods are defined as “extremely high uncertainty” is not affected by splitting the sample period into subperiods.21 Figure I shows that. See Ismailov and Rossi (2018) and Ramírez-Rondán and Terrones (2019) for alternative definitions for the “high uncertainty” period (regime). 13 21. DOI:10.6814/NCCU202001120.

(15) uncertainty is extremely high in periods of well-known events, such as Black Monday, the global financial crisis, the Eurozone crisis, the Brexit crisis, the China-United States trade war crisis, and, recently, the COVID-19 pandemic crisis. However, it seems that US EPU contains little information about events in Asia, that is, US EPU does not capture uncertainty in Asia, because the index does not rise a lot in periods of the Asian financial crisis.. 4.2 Model In addition to re-examining the Fama regression, i.e., the equation (5), the aim of this. 政治大 EPU into the Fama regression. The model is described below. 立. paper is exploring the relationship between US EPU and UIRP. Thus, I introduce US. ‧ 國. 學. st+h − st = (α1 + β1 (ft,h − st )) D1𝑡 + (α2 + β2 (ft,h − st )) D2𝑡. ‧. + (α3 + β3 (ft,h − st )) D3𝑡 + (α4 + β4 (ft,h − st )) D4𝑡 + ε … (6). y. Nat. Equation (6) is the Fama regression with four regimes. D1𝑡 , D2𝑡 , D3𝑡 , and D4𝑡 equals. io. sit. to 1 if US EPU at time t is smaller than the 25th percentile (<25th), between the 25th. n. al. er. and 50th percentile (25th-50th), between the 50th and 75th percentile (50th-75th), and. Ch. i Un. v. greater than the 75th percentile (>75th) of all available US EPU respectively. Thus, all. engchi. shaded areas in Figure I indicate periods in which D4𝑡 equals to 1. Recall that those periods are called “extremely high uncertainty”. Similarly, periods of <25th, 25th-50th, and 50th-75th are called “extremely low uncertainty”, “relatively low uncertainty”, “relatively high uncertainty” respectively. It is noteworthy that models used in Ismailov and Rossi (2018) and Ramírez-Rondán and Terrones (2019) are both two-regime, i.e., “low uncertainty” and “high uncertainty”. The reason for using a four-regime setting rather than a two-regime setting is that some important information may be overlooked when mixing the “relatively high uncertainty” regime with the “extremely low uncertainty” regime. An analysis with a similar setting is done by Clarida et al. (2009). 14. DOI:10.6814/NCCU202001120.

(16) They split their sample into two regimes: the low-volatility regime and the highvolatility regime. The former is defined as periods in which the implied 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. 政治大. significant threshold (i.e. the percentile) that minimizes the sum of squared errors to. 立. split their sample into two regimes, the aim of this paper is to explore whether the. ‧ 國. 學. 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.. sit. y. Nat. n. al. er. io. 5. Empirical Evidence 5.1 The Fama RegressionC h. engchi. i Un. v. 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 1month horizon and Canada at the 12-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, 15. DOI:10.6814/NCCU202001120.

(17) 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.. 政治大. Finally, slope coefficients of pooled regressions are all negative and significantly. 立. different from 1. The results are in line with empirical evidence - the FPP exists in the. ‧ 國. 學. 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. y. Nat. io. sit. and Poonawala (2010), and Ismailov and Rossi (2018). In addition, the weakness of the. n. al. er. horizon effect becomes more apparent because the value and statistical significance. Ch. i Un. v. level of the 1-month and 12-month slope coefficient of the pooled regression are the same.. engchi. 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. 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) 16 22. DOI:10.6814/NCCU202001120.

(18) 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.. 政治大. Compared to the full sample period, slope coefficients of Sweden at all three horizons. 立. are closer to 1 over the pre-crisis period. These findings are consistent with what. ‧ 國. 學. documented in Bansal and Dahlquist (2000) and Chinn and Frankel (2019), that is, over. coefficient.. ‧. the pre-euro period, the high inflation rate 23 of Sweden results in a positive slope. y. Nat. io. sit. Although the number of positive slope coefficients over the pre-crisis period is more. n. al. er. than the full sample period, 20 out of 36 slope coefficients either switch their signs from. Ch. i Un. v. positive to negative or become more negative, especially for Eurozone and Japan. The. engchi. 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 1month 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. The high inflation rate is a common characteristic among emerging countries, which are found not to deviate from UIRP. 17 23. DOI:10.6814/NCCU202001120.

(19) 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.. 政治大. Panel B of Table III reports slope coefficients of the Fama regression over the. 立. December 2007 to March 2020 period, i.e., the post-crisis period, at the 1-, 3-, and 12-. ‧ 國. 學. 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. y. Nat. io. sit. Bussiere et al. (2018), that is, the direction of the FPP reversed after the GFC. They. n. al. er. called this new anomaly as “the new Fama puzzle”. This anomaly is further supported. Ch. i Un. v. by slope coefficients of pooled regressions over the post-crisis period because all of. engchi. 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. However, Ichiue and Koyama (2011) compared their 3-month results with 6-month results and had a discussion on the horizon effect. 18 24. DOI:10.6814/NCCU202001120.

(20) conducting a pooled analysis using a sample period including more observations from the post-crisis period.. 5.2 The Fama Regression and US EPU Table III shows that there is a prominent difference, which reverses the FPP, between the pre-crisis and the post-crisis period. What is the cause of the difference? One possible answer may be seen from Figure I which illustrates that most shaded areas are plotted in periods after the GFC. Precisely, up to 66% of “extremely high uncertainty” lie in the post-crisis period which only accounts for 35% of the full sample period. That. 政治大 post-crisis period is full of uncertainty. Thus, it is reasonable to conjecture that the 立 is, when measuring the economic environment using US EPU, one can assert that the. ‧ 國. 學. difference between the pre-crisis and post-crisis period is the degree of uncertainty.. When uncertainty soars, the FPP reverses, i.e., the direction of the UIRP violation. ‧. changes. This conjecture is supported by results in Clarida et al. (2009)25, Ichiue and. sit. y. Nat. Koyama (2011)26, and Cho et al. (2019)27, however, all of them utilized exchange rate. al. er. io. volatility to measure the economic environment. Thus, it may be worthwhile to use an. v. n. uncertainty measure, rather than a risk measure, to explore what the role economic environment plays in the FPP.. Ch. engchi. i Un. INSERT TABLE IV HERE Panel A of Table IV reports slope coefficients of the Fama regression in four regimes, i.e., “extremely low uncertainty”, “relative low uncertainty”, “relative high uncertainty”,. Clarida et al. (2009) reported that the slope coefficient of Australia, Switzerland, the United Kingdom, Norway, New Zealand, and Sweden become positive when the exchange rate volatility is extremely high whereas that of Canada, the Eurozone, and Japan remains negative. 26 Ichiue and Koyama (2011) suggested that when exchange rate volatility becomes higher, slope coefficients of the Fama regression become more positive. They also indicated that the absolute value of slope coefficients in the high-volatility regime are greater than in the low-volatility regime. 27 Cho et al. (2019) reported that the slope coefficient of Australia, Switzerland, the Eurozone, and Japan in the high-volatility regime become positive whereas that of the United Kingdom remains negative. 19 25. DOI:10.6814/NCCU202001120.

(21) and “extremely high uncertainty”, over the January 1985 to March 2020 period at the 1-month horizon across 12 countries. For countries of the well-known target currency (thereafter, “target countries”), when uncertainty is extremely low, Australia and New Zealand deviate from UIRP strongly whereas the slope coefficient of South Africa is 2.15 and not significantly different from 1. In contrast, for countries of the well-known funding currency (thereafter, “funding countries”), when uncertainty is extremely low, the slope coefficient of Japan and Switzerland are both negative and smaller than -2. However, only the former is significantly different from 1. Additionally, for Nordic countries, although all slope. 政治大. coefficients are negative when uncertainty is extremely low, only the slope coefficient. 立. of Denmark is significantly different from 1. Finally, for other countries, when. ‧ 國. 學. uncertainty is extremely low, only the slope coefficient of Canada is negative and. ‧. significantly different from 1. It is noteworthy that my result of the Eurozone and the United Kingdom are very different from those documented in previous literature28.. y. Nat. io. sit. Results below are compared to “extremely low uncertainty” cases. For “target. n. al. er. countries”, when uncertainty is extremely high, the slope coefficient of New Zealand. Ch. i Un. v. and Australia become either not significantly different from 1 or closer to 1. However,. engchi. the UIRP violation of South Africa becomes statistically significant. In contrast, for “funding countries”, when uncertainty is extremely high, the UIRP violation reverses. The slope coefficient of Japan and Switzerland are both greater than 4 but not significantly different from 1. Additionally, for Nordic countries, when uncertainty is extremely high, all slope coefficients become positive and not significantly different from 1. Finally, for other countries, when uncertainty is extremely high, the slope coefficient of the United Kingdom becomes more positive whereas the slope coefficient. See Clarida et al. (2009), Ichiue and Koyama (2011), and Cho et al. (2019) for results using exchange rate volatility. 20 28. DOI:10.6814/NCCU202001120.

(22) of Canada, the Eurozone, and Singapore either become more negative or switch their signs from positive to negative. Overall, compared to “extremely low uncertainty” cases, a third of countries (South Africa, Canada, the Eurozone, and Singapore) exhibit a stronger UIRP violation when uncertainty is extremely high. However, only the result of South Africa is statistically significant and a similar result of Canada has been reported in Clarida et al. (2009). Thus, the result largely supports the conjecture: the FPP reverses when uncertainty soars. Using a pooled analysis, the result becomes much clearer. The FPP exists when uncertainty is extremely low but vanishes when uncertainty is extremely high.. 政治大. The contribution of this paper is to explore the UIRP violation when the economic. 立. environment is “relatively low uncertainty” or “relatively high uncertainty”. Results. ‧ 國. 學. below are also compared to “extremely low uncertainty” cases. For “target countries”,. ‧. when uncertainty is relative low, the slope coefficient of New Zealand and Australia become less negative whereas that of South Africa becomes less positive. In contrast,. y. Nat. io. sit. for “funding countries”, when uncertainty is relatively low, their slope coefficients both. n. al. er. become less negative. Finally, for Nordic and other countries, when uncertainty is. Ch. i Un. v. relatively low, all slope coefficients become either more negative or switch their signs. engchi. from positive to negative, except for Singapore.. Overall, compared to “extremely low uncertainty” cases, only 5 out of 12 slope coefficients become less negative or more positive when uncertainty is relatively low. In contrast, up to half of countries exhibit a stronger UIRP violation when uncertainty is relatively low. It seems that, although the UIRP violation reverses when uncertainty is extremely high, it does not reverse gradually with increases in uncertainty. A stronger UIRP violation exists when uncertainty is moderately low might be related to what argued in Ichiue and Koyama (2011). They indicated that the depreciation of the low-yield currency and the low-volatility environment are mutually dependent. That 21. DOI:10.6814/NCCU202001120.

(23) is, when the volatility is low, the carry trade, which make the low-yield currency depreciate, prevail. The prevalence further lowers the volatility until shocks, which make the carry trade be unprofitable, strike. If a similar relationship holds between the depreciation (appreciation) of the low-yield (high-yield) currency and the lowuncertainty environment, one should not be surprised about results of Nordic and other countries. This relationship is strongly supported by the pooled result. When uncertainty is relatively low, the slope coefficient of the pooled regression is the most negative among four regimes and significantly different from 1. However, one should note that this is not the case for “target countries”, “funding countries”, and Singapore.. 政治大. If the mutual dependence holds for the low-uncertainty environment, it is reasonable. 立. to assume that the depreciation (appreciation) of the high-yield (low-yield) currency. ‧ 國. 學. and the high-uncertainty environment are also mutually dependent. That is, the validity. ‧. of the mutual dependence may be further supported by the result of “relative high uncertainty”. Unfortunately, when uncertainty is relatively high, there are only 2 out of. y. Nat. io. sit. 12 slope coefficients (Norway and Canada) become more positive than “extremely high. n. al. er. uncertainty”. Thus, the mutual dependence does not hold for the high-uncertainty environment.. Ch. engchi. i Un. v. Despite the failure to find a universal pattern of how the UIRP violation alters when uncertainty increases for all countries, there are still some interesting findings after adding two additional regimes. The first is the UIRP violation of South Africa, Switzerland, and Japan gradually reverse when uncertainty increases. However, the direction of the reverse for South Africa and for Switzerland and Japan are opposite. The second is European countries and Canada tend to exhibit a stronger UIRP violation when uncertainty is moderately low. Next, although the result of the Fama regression over the full sample period does not change obviously at different horizons, this may not be the case for the result of the 22. DOI:10.6814/NCCU202001120.

(24) four-regime Fama regression because regimes are defined using US EPU at time t (i.e., horizon-neutral). Panel B of Table IV reports slope coefficients of the Fama regression in four regimes over the full sample period at the 3-month horizon across 12 countries. Results below are compared to “extremely low uncertainty” cases. For “target countries”, not only South Africa but also Australia and New Zealand deviate from UIRP more strongly when uncertainty is extremely high. In contrast, for “funding countries”, the slope coefficient of Japan and Switzerland still become more positive when uncertainty is extremely high. Additionally, when uncertainty is extremely high, the UIRP violation. 政治大. of Nordic countries and the United Kingdom become weaker whereas the UIRP. 立. violation of other countries become stronger.. ‧ 國. 學. Overall, compared to the 1-month result, two additional countries (Australia and. ‧. New Zealand) exhibit stronger UIRP violations when uncertainty is extremely high at the 3-month horizon. Thus, the result of four-regime Fama regression indeed changes. y. Nat. io. sit. if a different horizon is used. However, slope coefficients of pooled regressions still. n. al. er. indicate that the FPP becomes weaker when uncertainty soars. In addition, slope. Ch. i Un. v. coefficients of pooled regressions also indicate that the mutual dependence of the. engchi. economic environment and the UIRP violation becomes valid because the strongest and weakest UIRP violation lie in “relatively low uncertainty” and “relatively high uncertainty” respectively. That is, at the 3-month horizon, the mutual dependence holds for both low-uncertainty and high-uncertainty environments. Finally, Panel C of Table IV reports slope coefficients of the Fama regression in four regimes over the full sample period at the 12-month horizon across 12 countries. Results below are compared to “extremely low uncertainty” cases. For “target countries”, the slope coefficient of Australia and New Zealand are both less negative when uncertainty is extremely high whereas that of South Africa still becomes more 23. DOI:10.6814/NCCU202001120.

(25) negative. That is, the 12-month result is similar to the 1-month result. In contrast, for “funding countries”, the 12-month result is similar to the result not only at the 1-month horizon but also at the 3-month horizon. That is, for all three horizons, slope coefficients of “funding countries” switch their signs from negative to positive when uncertainty soars. Additionally, results of Nordic countries and the United Kingdom are also consistent for all three horizons. Finally, at the 12-month horizon, the UIRP violation of Canada and the Eurozone become weaker when uncertainty is extremely high, whereas Singapore still shows a pattern like South Africa. Overall, there are up to 10 out of 12 countries exhibit a weaker UIRP violation when. 政治大. uncertainty soars at the 12-month horizon. This result strongly supports that there is a. 立. negative correlation between the FPP and US EPU. However, one should note that, the. ‧ 國. 學. slope coefficient of the pooled regression is still negative and significantly different. ‧. from 1 when uncertainty is extremely high. The result indicates that the FPP still exists, even though the UIRP violation of most countries become weaker when uncertainty. y. Nat. io. sit. soars. In addition, at the 12-month horizon, slope coefficients of pooled regressions. n. al. er. only indicate that the weakest UIRP violation lies in “relatively high uncertainty”. Ch. i Un. v. whereas the strongest UIRP violation does not show up in “relatively low uncertainty”.. engchi. Thus, whether the mutual dependence exists or, precisely, manifests itself in producing the strongest (weakest) UIRP violation for a certain regime remains unknown. Results at all three horizons argue that, the correlation between the UIRP violation and US EPU is sensitive to different horizons.. 5.3 The Fama Regression and US EPU: the pre-crisis and postcrisis period Following the subperiod analysis in Section 5.1, the full sample period is again divided into two subperiods: the pre-crisis period and the post-crisis period. The start 24. DOI:10.6814/NCCU202001120.

(26) date of the post-crisis period is December 2007. As mentioned in Section 4.1, whether periods are defined as “extremely high uncertainty” is not affected by how many subperiods the full sample period are divided into because all available US EPU are always used to classify periods. Thus, even though “extremely high uncertainty” refers to periods with the 25% highest US EPU, the ratio of the number of “extremely high uncertainty” in a subperiod to the length of the subperiod may be different from 25%. This is also the case for “extremely low uncertainty”, “relatively low uncertainty”, and “relatively high uncertainty”. One should note that the aim of the subperiod analysis in this section is to check, for example, whether periods defined as “extremely high. 政治大. uncertainty” show a consistent pattern between these two subperiods, rather than to. 立. explore the correlation between the UIRP violation and US EPU using only pre-crisis. ‧ 國. 學. or post-crisis US EPU.. ‧. 5.3.1 the pre-crisis period INSERT TABLE V HERE. y. Nat. io. sit. Panel A of Table V reports pre-crisis slope coefficients of the Fama regression in four. n. al. er. regimes at the 1-month horizon across 12 countries. Results below are compared to. Ch. i Un. v. Panel A of Table IV. For “target countries”, the slope coefficient of Australia in. engchi. “extremely high uncertainty” changes from -1.88 to 3.18. In contrast, for “funding countries”, results remain almost unchanged. Additionally, for Nordic and other countries, all slope coefficients in “extremely high uncertainty” either switch their signs from negative to positive or become much more positive. Among slope coefficients of Nordic countries in “extremely high uncertainty”, those of Sweden and Denmark even become significantly different from 1. That is, for Sweden and Denmark, periods defined as “extremely high uncertainty” exhibit very strong but unconventional (i.e., positive) deviations from UIRP in the pre-crisis period. Overall, at the 1-month horizon, the main difference between the pre-crisis period 25. DOI:10.6814/NCCU202001120.

(27) and the full sample period is the degree of the reverse of the UIRP violation when uncertainty is extremely high. The result is strongly supported by slope coefficients of pooled regressions. In addition, slope coefficients of pooled regressions indicate that, when uncertainty is relative low, the FPP is the strongest, whereas, when uncertainty is relative high, the FPP is not the weakest. These findings are consistent with those over the full sample period. Panel B of Table V reports pre-crisis slope coefficients of the Fama regression in four regimes at the 3-month horizon across 12 countries. Results below are compared to Panel B of Table IV. For “target countries”, no slope coefficient changes much. In. 政治大. contrast, for “funding countries”, results remain almost unchanged. Additionally, for. 立. Nordic and other countries (except for the Eurozone), all slope coefficients in. ‧ 國. 學. “extremely high uncertainty” either switch their signs from negative to positive or. ‧. become more positive (less negative). Among slope coefficients of Nordic countries in “extremely high uncertainty”, that of Denmark becomes significantly different from 1.. y. Nat. io. sit. Overall, at the 3-month horizon, the main difference between the pre-crisis period. n. al. er. and the full sample period is also the degree of the reverse of the UIRP violation when. Ch. i Un. v. uncertainty is extremely high. The result is again supported by slope coefficients of. engchi. pooled regressions. In addition, slope coefficients of pooled regressions indicate that, when uncertainty is relative low, the FPP is the strongest, however, when uncertainty is relative low, the FPP is not the weakest. The latter result is inconsistent with that over the full sample period. Panel C of Table V reports pre-crisis slope coefficients of the Fama regression in four regimes at the 12-month horizon across 12 countries. Results below are compared to Panel C of Table IV. For “target countries”, no slope coefficient changes a lot. In contrast, for “funding countries”, deviations from UIRP of Japan become much stronger in all four regimes. However, the UIRP violation of Japan still becomes weaker when 26. DOI:10.6814/NCCU202001120.

(28) uncertainty increases. Additionally, for Nordic and other countries, most slope coefficients in “relatively high uncertainty” and “extremely high uncertainty” either switch their signs from negative to positive or become more positive. The exceptions are the slope coefficient of Canada in “extremely high uncertainty” and the slope coefficient of Singapore and the Eurozone in both “relatively high uncertainty” and “extremely high uncertainty”. Overall, at the 12-month horizon, the differences between the pre-crisis period and the full sample period are (i) Japan exhibits stronger UIRP violation in all four regimes; (ii) for Nordic and other countries (except for Singapore and the Eurozone), the reverse. 政治大. of the UIRP violation becomes stronger not only when uncertainty is extremely high. 立. but also when uncertainty is relatively high. The second finding can be confirmed by. ‧ 國. 學. slope coefficients of pooled regressions. In addition, slope coefficients of pooled. ‧. regressions indicated that, when uncertainty is relative high, the FPP is the weakest, nonetheless, when uncertainty is relative low, the FPP is not the strongest. These results. y. Nat. io. sit. are consistent with those over the full sample period.. n. al. er. In general, compared to using the full sample data, using the pre-crisis data (however,. Ch. i Un. v. with all available US EPU), results of “extremely high uncertainty” at all three horizons. engchi. and results of “relatively high uncertainty” at the 12-month horizon change. In other words, results of “extremely low uncertainty” and “relatively low uncertainty” are similar. This is reasonable because, as mentioned in Section 4.1, most periods with exceptionally high uncertainty show up after the GFC, i.e., most periods with low uncertainty lie in the period before the GFC. Results over the full sample period when uncertainty is extremely low or relatively low are dominated by the pre-crisis data. Thus, there is no difference between the low-uncertainty result of the pre-crisis period and the full sample period. 27. DOI:10.6814/NCCU202001120.

(29) 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”,. 政治大. most slope coefficients change from negative to positive, whereas, for “extremely high. 立. uncertainty”, most slope coefficients change from positive to negative. These findings. ‧ 國. 學. 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. y. Nat. io. sit. available US EPU), slope coefficients of the four-regime Fama regression are different.. n. al. er. This result is similar to what documented in Bussiere et al. (2018), that is, the. Ch. i Un. v. relationship between forward premiums and spot rate changes differs between the pre-. engchi. crisis and post-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 28. DOI:10.6814/NCCU202001120.

(30) 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. 政治大. coefficients of South Africa gradually reverse when uncertainty increases” should be. 立. taken carefully because the slope coefficient changes from negative to positive when. ‧ 國. 學. 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. y. Nat. io. sit. 62th-87th. Thus, the best timing for longing Australian dollar may be when. n. al. er. uncertainty is extremely low or greater than the 87th percentile. Nonetheless, the. Ch. i Un. v. regime effect on New Zealand is subtle because most slope coefficients of New. engchi. 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 29. DOI:10.6814/NCCU202001120.

(31) 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. 政治大. those of Nordic countries, that is, their slope coefficients estimated around the 50th. 立. percentile are at the lowest level. In addition, the timing for slope coefficients of the. ‧ 國. 學. 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.. y. Nat. io. sit. The only difference is the FPP of the Eurozone becomes the strongest among all. n. al. er. regimes (and stronger than all other countries) in the 35th-60th regime. Finally, as. Ch. i Un. v. mentioned in section 5.2, Singapore behaves in a similar pattern like South Africa.. engchi. 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,. It is noteworthy that slope coefficients of Canada greatly differ between being estimated in the 72th97th 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. 30 29. DOI:10.6814/NCCU202001120.

(32) 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.. 7. Conclusion. 政治大. In this paper, I revisit the Fama regression at the 1-, 3-, and 12-month horizon and. 立. find that most slope coefficients are negative and significantly different from 1 at all. ‧ 國. 學. three horizons similar to those widely documented in previous literature. In addition, I. ‧. do not find the UIRP violation tends to be weaker at a longer horizon. By splitting the sample period into two subperiods: the pre-crisis period and the post-crisis period, I. y. Nat. io. sit. find that, over the pre-crisis period, the UIRP violation is stronger than over the full. n. al. er. sample period. In contrast, over the post-crisis period, slope coefficients tend to be. Ch. i Un. v. positive and, for some countries, large and statistically significant. This finding. engchi. confirms the presence of “the new Fama puzzle” (Bussiere et al., 2018). Then, I explore the relationship between the difference between the pre-crisis and post-crisis result of the Fama regression with economic uncertainty measure. I choose US EPU, which indicates that uncertainty is pretty high after the GFC, as a proxy to split my sample into four regimes. Although the relationship between US EPU and the UIRP violation varies with horizons for most countries, there are three countries, i.e., South Africa, Japan, and Switzerland, whose deviations from UIRP always reverse gradually with increases in economic uncertainty. The UIRP violation of South Africa gradually reverses from positive to negative whereas that of Japan and Switzerland 31. DOI:10.6814/NCCU202001120.

(33) gradually reverse from negative to positive. In addition, for Nordic countries, when uncertainty is relatively low, they usually exhibit the strongest UIRP violation among four regimes. Thus, “relatively low uncertainty” seems to play a role in the FPP. This finding may be attributed to the mutual dependence of the economic environment and the UIRP violation. Using a subperiod analysis, I find that slope coefficients of four-regime Fama regression are inconsistent between the pre-crisis and post-crisis period. For example, slope coefficients in “extremely high uncertainty” tend to be positive over the pre-crisis period whereas those tend to be negative over the post-crisis period. This result. 政治大. indicates that, under my definition, US EPU does not classify periods well.. 立. My first suggestion for the future research is to adjust the definition of regimes,. ‧ 國. 學. which I assume investors can always use all available US EPU to classify periods. It is. ‧. very likely that the result in this paper is distorted due to the hindsight about US EPU30. Hence, how investors actually form their information set and perceive the economic. y. Nat. io. sit. environment may be at the core of obtaining a more consistent and robust result. The. n. al. er. second suggestion is to use other measures. For example, Berg and Mark (2018) argued. Ch. i Un. v. that Global EPU is a measure the most significantly priced into excess returns of carry trades.. 31. engchi. The last suggestion is to test different models. Although the setting in this. paper try to avoid mixing “relatively high uncertainty” with “extremely low uncertainty”, the absolute value may still substantially differ in a certain regime. To deal with this concern, one may simply introduce an interaction term, e.g., the uncertainty index multiply by the forward premium, into the Fama regression32.. Hassan and Mano (2019) even argued that the negative slope coefficient of the Fama regression is due to the hindsight about forward premiums. They reported that, without the hindsight, slope coefficients of the Fama regression become positive. 31 However, the start date of Global EPU is January 1997. It is far later than the start date of US EPU, which is January 1985. 32 See the equation (3) in Ichiue and Koyama (2011). 32 30. DOI:10.6814/NCCU202001120.

(34) References Baker, S. R., Bloom, N., & Davis, S. J. (2016). Measuring economic policy uncertainty. The Quarterly Journal of Economics, 131(4), 1593-1636. Bansal, R. (1997). An exploration of the forward premium puzzle in currency markets. The Review of Financial Studies, 10(2), 369-403. Bansal, R., & Dahlquist, M. (2000). The forward premium puzzle: Different tales from developed and emerging economies. Journal of International. 政治大 Berg, K. A., & Mark, N. C. (2018). Measures of global uncertainty and carry-trade 立 Economics, 51(1), 115-144.. ‧ 國. 學. excess returns. Journal of International Money and Finance, 88, 212-227.. Brunnermeier, M. K., Nagel, S., & Pedersen, L. H. (2008). Carry trades and currency. ‧. crashes. NBER Macroeconomics Annual, 23, 313-348.. sit. y. Nat. Bussiere, M., Chinn, M. D., Ferrara, L., & Heipertz, J. (2018). The new Fama puzzle.. er. io. NBER Working Paper No. 24342.. al. iv n C h e nexpectations, rate era: Longer horizons, alternative g c h i Uand emerging n. Chinn, M. D. (2006). The (partial) rehabilitation of interest rate parity in the floating. markets. Journal of International Money and Finance, 25(1), 7-21. Chinn, M. D., & Frankel, J. (2019). A third of a century of currency expectations data: The carry trade and the risk premium. Mimeo. Chinn, M. D., & Meredith, G. (2004). Monetary policy and long-horizon uncovered interest parity. IMF Staff Papers, 51(3), 409-430. Chinn, M. D., & Quayyum, S. (2013). Long horizon uncovered interest parity reassessed. Mimeo. Cho, D., Han, H., & Lee, N. K. (2019). Carry trades and endogenous regime switches 33. DOI:10.6814/NCCU202001120.

(35) in exchange rate volatility. Journal of International Financial Markets, Institutions and Money, 58, 255-268. Clarida, R., Davis, J., & Pedersen, N. (2009). Currency carry trade regimes: Beyond the Fama regression. Journal of International Money and Finance, 28(8), 13751389. Engel, C. (2014). Exchange rates and interest parity. Handbook of International Economics, 4, 453-522. Fama, E. F. (1984). Forward and spot exchange rates. Journal of Monetary Economics, 14(3), 319-338.. 政治大. Frankel, J., & Poonawala, J. (2010). The forward market in emerging currencies: Less. 立. biased than in major currencies. Journal of International Money and. ‧ 國. 學. Finance, 29(3), 585-598.. ‧. Froot, K. A., & Thaler, R. H. (1990). Anomalies: Foreign exchange. Journal of Economic Perspectives, 4(3), 179-192.. y. Nat. io. sit. Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary. n. al. er. time series and the business cycle. Econometrica, 57, 357-384.. Ch. i Un. v. Hassan, T. A., & Mano, R. C. (2019). Forward and spot exchange rates in a multi-. engchi. currency world. The Quarterly Journal of Economics, 134(1), 397-450. Husted, L., Rogers, J., & Sun, B. (2018). Uncertainty, currency excess returns, and risk reversals. Journal of International Money and Finance, 88, 228-241. Ichiue, H., & Koyama, K. (2011). Regime switches in exchange rate volatility and uncovered interest parity. Journal of International Money and Finance, 30(7), 1436-1450. Ismailov, A., & Rossi, B. (2018). Uncertainty and deviations from uncovered interest rate parity. Journal of International Money and Finance, 88, 242-259. Ramírez-Rondán, N. R., & Terrones, M. E. (2019). Uncertainty and the uncovered 34. DOI:10.6814/NCCU202001120.

(36) interest parity condition: How are they related? MPRA Paper No. 97524. Ranaldo, A., & Söderlind, P. (2010). Safe haven currencies. Review of Finance, 14(3), 385-407. Tryon, R. W. (1979). Testing for rational expectations in foreign exchange markets.. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 35. DOI:10.6814/NCCU202001120.

(37) Table I Summary Statistics of Forward Premium and Spot Exchange Rate Change Horizon (month). 1. 3. Variable. 12. forward premium. 1. 3. 12. spot exchange rate change. South Africa. 6.85. 6.63. 6.16. 5.86. 5.71. 5.55. New Zealand. 3.75. 3.62. 3.28. -0.66. -0.85. -0.73. Australia. 2.73. 2.69. 2.55. 0.80. 0.41. 0.10. Norway. 1.85. 1.76. 1.54. 0.62. 0.24. 0.30. United Kingdom. 1.49. 1.44. 1.26. -0.25. -0.25. 0.15. Sweden. 1.06. 0.99. 0.86. 0.27. 0.19. 0.38. Canada. 0.62. 0.61. 0.59. 0.21. 0.01. -0.07. Denmark. 0.43. 0.35. 0.21. -1.43. -1.48. -1.26. the Eurozone. -0.69. -0.67. -0.66. 0.32. 0.15. -0.17. Singapore. -1.07. -1.10. -1.06. -1.25. -1.34. -1.35. Switzerland. -1.71. -1.67. -2.84. -2.49. Japan. -2.37. -2.45. -2.25. Pool. 1.24. -0.24. -0.16. 立. -1.76 治 -2.62 政大 -2.36 -2.51 -2.44. ‧ 國. 1.01. -0.08. 學. 1.18. Notes: Values are annualized mean (%). Pool does not include the Eurozone. The base. ‧. currency is USD. The Eurozone starts from January 1999 whereas other countries start from January 1985. All countries end in March 2020.. n. er. io. sit. y. Nat. al. Ch. engchi. i Un. v. 36. DOI:10.6814/NCCU202001120.

(38) Table II Slope Coefficients of the Fama Regression Horizon (month). 1. 3. 12. South Africa. -0.14. -0.92**. -1.23***. New Zealand. -1.13***. -0.86***. -0.70***. Australia. -1.06***. -0.79***. -0.80***. Norway. -0.13. -0.34*. -0.41***. United Kingdom. -1.06*. -0.66. -0.19. Sweden. 0.03. -0.12. -0.09. Canada. -0.80***. -0.44***. 0.06*. Denmark. -0.45**. -0.53**. -0.58***. the Eurozone. -2.14**. -1.30. -1.28**. 0.10. -0.30**. -0.17***. Switzerland. -0.76*. -0.64. -0.54**. Japan. -1.13**. Pool. -0.61***. Singapore. 立. -1.20** 政治大. -1.33***. -0.65***. -0.61***. ‧ 國. 學. Notes: Heteroscedasticity and autocorrelation consistent (HAC) standard errors (not shown) are Newey-West with 6 lags. Asterisks denote statistical significance at the 10%(*), 5%(**), and 1%(***) level for the null hypothesis of the slope coefficient equal to one. Pool does. ‧. not include the Eurozone. The base currency is USD. The Eurozone starts from January. n. al. er. io. sit. y. Nat. 1999 whereas other countries start from January 1985. All countries end in March 2020.. Ch. engchi. i Un. v. 37. DOI:10.6814/NCCU202001120.

(39) Table III Slope Coefficients of the Fama Regression: the pre-crisis and post-crisis period Panel A: the pre-crisis period Horizon (month). 1. 3. 12. South Africa. 0.27. -0.73**. -1.04***. New Zealand. -1.38***. -1.08***. -0.97***. Australia. -0.94***. -0.83***. -1.00***. Norway. 0.02. -0.30*. -0.47***. United Kingdom. -0.54. -0.38. 0.19. Sweden. 0.32. 0.07. -0.01. Canada. -0.52***. -0.43***. -0.40***. -0.19. -0.50*. -0.62**. -4.31***. -4.69***. -4.97***. Denmark the Eurozone Singapore. -0.28. Switzerland. -1.06*. 立 -2.77***. -0.71*** -0.78**. -2.80***. -0.59***. -3.10***. 學. -0.75***. -0.82***. ‧. io. sit. y. Nat. n. al. er. Pool. ‧ 國. Japan. -0.73** 政治 -0.94 大. Ch. engchi. i Un. v. 38. DOI:10.6814/NCCU202001120.

(40) Panel B: the post-crisis period Horizon (month). 1. 3. 12. South Africa. -4.22. -2.87. -3.51**. New Zealand. 3.77. 3.57. 2.56. Australia. -1.29. -0.12. 0.02. Norway. 1.86. 2.86. 1.73. United Kingdom. 0.92. 4.16. 4.52**. Sweden. 0.33. 0.94. 0.96. Canada. -1.07. 3.89. 6.51***. Denmark. -0.28. 1.98. 1.55. the Eurozone. 0.21. 2.30. 1.82. Singapore. 0.49. -1.45. -1.64***. Switzerland. 1.08. 0.95. -0.20. Japan. 6.04*. Pool. 0.56. 立. 政治4.80 大. 4.00**. 1.52. 1.14. ‧ 國. 學. Notes: Heteroscedasticity and autocorrelation consistent (HAC) standard errors (not shown) are Newey-West with 5 lags. Asterisks denote statistical significance at the 10%(*), 5%(**),. ‧. and 1%(***) level for the null hypothesis of the slope coefficient equal to one. Pool does not include the Eurozone. The base currency is USD. The pre-crisis period is from January. y. Nat. 1985 to November 2007 and the post-crisis period is from December 2007 to March 2020.. n. er. io. al. sit. In Panel A, the Eurozone starts from January 1999.. Ch. engchi. i Un. v. 39. DOI:10.6814/NCCU202001120.