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which is mainly driven by European countries and Canada. Beyond the 50th percentile, pooled slope coefficients gradually reverse from negative to positive.
Overall, there seems to be a difference between when uncertainty is higher than the median and lower than the median. Thus, as I argue in section 4.2, one should avoid mixing the “relatively low uncertainty” regime with the “relatively high uncertainty”
regime, which may overlook some important information, especially for Australia, European countries, and Canada.
7. Conclusion
In this paper, I revisit the Fama regression at the 1-, 3-, and 12-month horizon and find that most slope coefficients are negative and significantly different from 1 at all 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 find that, over the pre-crisis period, the UIRP violation is stronger than over the full sample period. In contrast, over the post-crisis period, slope coefficients tend to be positive and, for some countries, large and statistically significant. This finding 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
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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 indicates that, under my definition, US EPU does not classify periods well.
My first suggestion for the future research is to adjust the definition of regimes, 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 environment may be at the core of obtaining a more consistent and robust result. The second suggestion is to use other measures. For example, Berg and Mark (2018) argued that Global EPU is a measure the most significantly priced into excess returns of carry trades.31 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.
30 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).
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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
Economics, 51(1), 115-144.
Berg, K. A., & Mark, N. C. (2018). Measures of global uncertainty and carry-trade 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.
Bussiere, M., Chinn, M. D., Ferrara, L., & Heipertz, J. (2018). The new Fama puzzle.
NBER Working Paper No. 24342.
Chinn, M. D. (2006). The (partial) rehabilitation of interest rate parity in the floating rate era: Longer horizons, alternative expectations, and emerging
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 re-assessed. Mimeo.
Cho, D., Han, H., & Lee, N. K. (2019). Carry trades and endogenous regime switches
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
34
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), 1375-1389.
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.
Frankel, J., & Poonawala, J. (2010). The forward market in emerging currencies: Less biased than in major currencies. Journal of International Money and
Finance, 29(3), 585-598.
Froot, K. A., & Thaler, R. H. (1990). Anomalies: Foreign exchange. Journal of Economic Perspectives, 4(3), 179-192.
Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57, 357-384.
Hassan, T. A., & Mano, R. C. (2019). Forward and spot exchange rates in a multi-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
‧ 國
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‧
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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.
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Table I Summary Statistics of Forward Premium and Spot Exchange Rate Change
Horizon (month) 1 3 12 1 3 12
Variable forward premium 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 -1.76 -2.62 -2.84 -2.49
Japan -2.37 -2.36 -2.51 -2.44 -2.45 -2.25
Pool 1.24 1.18 1.01 -0.08 -0.24 -0.16
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.
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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**
Singapore 0.10 -0.30** -0.17***
Switzerland -0.76* -0.64 -0.54**
Japan -1.13** -1.20** -1.33***
Pool -0.61*** -0.65*** -0.61***
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 1999 whereas other countries start from January 1985. All countries end in March 2020.
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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***
Denmark -0.19 -0.50* -0.62**
the Eurozone -4.31*** -4.69*** -4.97***
Singapore -0.28 -0.73** -0.71***
Switzerland -1.06* -0.94 -0.78**
Japan -2.77*** -2.80*** -3.10***
Pool -0.59*** -0.75*** -0.82***
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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* 4.80 4.00**
Pool 0.56 1.52 1.14
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 1985 to November 2007 and the post-crisis period is from December 2007 to March 2020.
In Panel A, the Eurozone starts from January 1999.
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Table IV Slope Coefficients of the Fama Regression and US EPU Panel A: the 1-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa 2.15 1.10 -2.24* -3.04**
Panel B: the 3-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa 0.50 -0.29 -0.10 -4.14***
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Panel C: the 12-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa -0.02* -0.25 -0.34 -4.32***
New Zealand -1.77*** -0.78*** -0.35*** -0.34
Australia -1.56*** -0.59*** -0.52*** -1.14**
Norway -0.38** -1.01*** -0.68** 0.17
United Kingdom -1.18* -1.67*** -0.11 1.33
Sweden -0.91** -1.35*** -0.03 1.16
Canada -0.13 -0.96*** 0.18 0.43
Denmark -1.64*** -1.51*** -0.23* 0.54
the Eurozone -2.93* -0.88 -1.20* -1.86**
Singapore 0.26 0.25* -0.78*** -0.94***
Switzerland -3.18*** -0.44 1.20 0.13
Japan -2.46*** -1.38** -0.10 0.58
Pool -1.14*** -0.89*** -0.21*** -0.32***
N 106 105 105 95
Notes: The regime of <25th, 25th-50th, and 50th-75th are periods with US EPU which is smaller than the 25th percentile, between the 25th and 50th percentile, between the 50th and 75th percentile, and greater than the 75th percentile of all available US EPU respectively. N is the number of observations for the regime. 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 1999 whereas other countries start from January 1985. All countries end in March 2020.
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Table V Slope Coefficients of the Fama Regression and US EPU: the pre-crisis period Panel A: the 1-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa 2.00 1.51 -2.39* -1.83
Panel B: the 3-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa 0.22 0.00 -0.53 -3.58***
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Panel C: the 12-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa -0.06** 0.03 -0.31 -4.21***
New Zealand -1.86*** -0.85*** -0.38** 0.63
Australia -1.76*** -0.68*** -0.29** -1.19
Norway -0.72*** -0.83*** 0.10 1.54
United Kingdom -1.18* -0.88* 0.91 3.42**
Sweden -1.25*** -1.07** 1.00 3.04
Canada -0.74*** -0.63*** 0.50 -0.05
Denmark -1.83*** -1.27*** 1.05 2.28
the Eurozone -4.05*** -5.67*** -7.17*** -7.78***
Singapore -0.23* -0.63*** -1.08*** -1.19**
Switzerland -3.36*** -1.27** 1.95 0.38
Japan -3.26*** -3.47*** -1.44** -1.47*
Pool -1.38*** -0.98*** 0.15** -0.10*
N 95 74 58 36
Notes: The regime of <25th, 25th-50th, and 50th-75th are periods with US EPU which is smaller than the 25th percentile, between the 25th and 50th percentile, between the 50th and 75th percentile, and greater than the 75th percentile of all available US EPU respectively. N is the number of observations for the regime. Asterisks denote statistical significance at the 10%(*), 5%(**), and 1%(***) level for the null hypothesis of the slope coefficient equal to one. Heteroscedasticity and autocorrelation consistent (HAC) standard errors (not shown) are Newey-West with 5 lags. Pool does not include the Eurozone. The base currency is USD. All countries start from January 1985 and end in November 2007.
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Table VI Slope Coefficients of the Fama Regression and US EPU: the post-crisis period
Panel A: the 1-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa -7.39 -3.86 -5.55
Panel B: the 3-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa -4.06* 5.09 -9.57**
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Panel C: the 12-month horizon
Regime <25th 25th-50th 50th-75th >75th
South Africa -4.56** 0.30 -8.68***
New Zealand 8.33*** 2.81 -1.30
Australia 2.03 -0.54 -0.56
Norway 5.56*** 1.12 -0.39
United Kingdom 5.52*** 5.17* 1.83
Sweden 5.60** 0.87 -0.57
Canada 9.57*** 4.91* 5.11*
Denmark 4.65** 1.34 0.02
the Eurozone 5.26** 1.42 0.32
Singapore -2.82*** -3.55*** -1.52**
Switzerland 2.21 -1.27* -0.82
Japan 8.51** 2.07 4.24
Pool 3.50*** 1.13 -0.68***
N 3 29 46 59
Notes: The regime of <25th, 25th-50th, and 50th-75th are periods with US EPU which is smaller than the 25th percentile, between the 25th and 50th percentile, between the 50th and 75th percentile, and greater than the 75th percentile of all available US EPU respectively. N is the number of observations for the regime. Asterisks denote statistical significance at the 10%(*), 5%(**), and 1%(***) level for the null hypothesis of the slope coefficient equal to one. Heteroscedasticity and autocorrelation consistent (HAC) standard errors (not shown) are Newey-West with 5 lags. Pool does not include the Eurozone. The base currency is USD. All countries start from December 2007 and end in March 2020.
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Figure I The Time Series of the US economic policy uncertainty (US EPU) index.
The black line is the US EPU index and the shaded area indicates 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.
0 50 100 150 200 250 300 350 400 450
1985/1 1990/1 1995/1 2000/1 2005/1 2010/1 2015/1 2020/1
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(a) Target Countries
(b) Funding Countries
Figure II Rolling Estimates of Slope Coefficients of the Fama Regression in Different Regimes. The y-axis is the value of the slope coefficient. The x-axis is the upper bound of the regime. For example,”30” means that the slope coefficient is estimated using observations whose US EPU are between the 5th and 30th percentile of all available US EPU.
-4 -3 -2 -1 0 1 2 3
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 South Africa New Zealand Australia
-6 -4 -2 0 2 4 6 8
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Switzerland Japan