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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 + it,h∗ ) = Ft,h
St (1 + it,h) … (3)
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 in the spot exchange rate equals the forward premium. The second assumption is the difference between the realized and expected spot exchange rate is white noise. That is,
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.
UIRP is commonly tested with these two assumptions using a regression-based method, i.e., a regression of the realized change in the spot exchange rate on the forward premium.
st+h− st= α + β(ft,h− st) + ε … (5)
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
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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 FPP is not a universal phenomenon, i.e., the FPP does not seem to be present in emerging countries.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 the 1-month horizon, only 6 out of 14 slope coefficients of emerging and newly industrialized countries are negative.5 He concluded that empirical evidence against UIRP is still present, i.e., the short-term interest rate differential remains a biased 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
1 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.
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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.
Chinn and Frankel (2019) used both the rational and survey-based expectation methodology to re-examine UIRP at the 3- and 12-month horizon. They found that, 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 pre-euro period), slope coefficients are significantly positive at short horizons.7 For other currencies8, all slope coefficients are also either negative or close to 0. The only exception is that of Sweden at the 3-month horizon. Like Italy and Spain, the inflation rate of Sweden is relatively high over the pre-euro period. In contrast, with the survey-based 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
6 Belgium, France, Germany, Ireland, Italy, the Netherlands, and Spain
7 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
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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 subperiod is the post-crisis period ranging from September 2007 to June 2019. Over the pre-crisis period, all slope coefficients are significantly negative at both 3- and 12-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 relationship between the interest rate differential and the ex post spot exchange rate change differs between the pre- and post-crisis period. They called this new anomaly as “the new Fama puzzle”. The anomaly is robust to four different base currencies12. In 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
9 The finding argues that, in equation (2) and (4), ϵt+h are not white noise.
10 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
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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 regime-dependent. 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 positively correlated with the sudden unwinding of carry trade positions and carry trade losses, i.e., currency crashes; (iv) a higher VIX predicts higher excess returns and the 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 persistent excess returns, but when volatility increases, the sharp unwinding of carry trade positions results in losses. They argued that the widely documented negative slope coefficient in regressions of spot exchange rate changes on forward premiums is an 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 regime-switching model15 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
13 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).
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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 losses in a regime with high exchange rate volatility, implying the reverse of the FPP.
In contrast, Ismailov and Rossi (2018) used various economic uncertainty measures16 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, relative to the high-uncertainty environment, UIRP tends to hold in the low-uncertainty environment. Similarly, Ramírez-Rondán and Terrones (2019) used a panel threshold regression model and survey-based exchange rate expectations to examine the extent to 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.
16 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
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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 The US EPU index begins in January 1985. Thus, for a complete analysis of the relationship between US EPU and UIRP, only countries with exchange rate data starting 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 meet my requirement are Australia, Canada, Switzerland, Denmark, Hong Kong, Japan, Malaysia, Norway, New Zealand, Sweden, Singapore, the United Kingdom, and South Africa. Hong Kong is excluded due to currency board system and Malaysia is also 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
17 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.