Fiscal Cyclicality and Currency Risk Premia Zhengyang Jiang * November 12, 2018 Government surpluses load on a common factor, but to different degrees. In the cross-section, countries whose government surpluses are more cyclical with respect to the common factor tend to have higher nominal interest rates and higher currency returns. Their currency returns are also more exposed to a common risk factor, leading to a correspondence between the factor structure in government surpluses and the factor structure in currency returns. In a frictionless model, I show these results are consistent with the idea that currencies are priced as the claims to government surpluses. * Department of Finance, Kellogg School of Management, Northwestern University. 2211 Campus Drive, Evanston, IL 60208. Email: [email protected]. This paper is a part of my PhD thesis. I acknowledge with deep gratitude the mentorship of John Cochrane and Hanno Lustig as my advisors, and the guidance of Adrien Auclert, Svetlana Bryzgalova, Sebastian Di Tella, and Darrell Duffie on my dissertation committee. For helpful comments, I thank Torben Andersen, Samuel Antill, Jonathan Berk, Shai Bernstein, YiLi Chien, Jesus Crespo Cuaresma (discussant), Peter DeMarzo, Ian Dew-Becker, Xiang Fang, Steven Grenadier, Benjamin H´ ebert, Robert Hodrick, Oleg Itskhoki, Patrick Kehoe, Peter Koudijs, Arvind Krishnamurthy, Ye Li, Edith X. Liu (discussant), Matteo Maggiori, Konstantin Milbradt, Sergio Rebelo, Rob Richmond, Dimitris Papanikolaou, Cheng Peng, Paul Pfleiderer, Jesse Schreger, Kenneth Singleton, Ilya Strebulaev, Viktor Todorov, Christopher Tonetti, Victoria Vanasco, Adrien Verdelhan, Jonathan Wallen, Yi David Wang, Rui Xu, Mindy Xiaolan Zhang, and seminar participants at Northwestern Kellogg, UW Foster, NYU Stern, Imperial College Business School, LSE, New York Fed, USC Marshall, Chicago Booth, Wharton, WFA, Vienna Symposium on Foreign Exchange Markets, and Cubist Systematic Strategies. I thank Daojing Zhai for excellent research assistance. 1
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Fiscal Cyclicality and Currency Risk Premia
Zhengyang Jiang∗
November 12, 2018
Government surpluses load on a common factor, but to different degrees. In the cross-section,
countries whose government surpluses are more cyclical with respect to the common factor
tend to have higher nominal interest rates and higher currency returns. Their currency
returns are also more exposed to a common risk factor, leading to a correspondence between
the factor structure in government surpluses and the factor structure in currency returns.
In a frictionless model, I show these results are consistent with the idea that currencies are
priced as the claims to government surpluses.
∗ Department of Finance, Kellogg School of Management, Northwestern University. 2211 Campus Drive,Evanston, IL 60208. Email: [email protected]. This paper is a part of my PhDthesis. I acknowledge with deep gratitude the mentorship of John Cochrane and Hanno Lustig as my advisors,and the guidance of Adrien Auclert, Svetlana Bryzgalova, Sebastian Di Tella, and Darrell Duffie on mydissertation committee. For helpful comments, I thank Torben Andersen, Samuel Antill, Jonathan Berk, ShaiBernstein, YiLi Chien, Jesus Crespo Cuaresma (discussant), Peter DeMarzo, Ian Dew-Becker, Xiang Fang,Steven Grenadier, Benjamin Hebert, Robert Hodrick, Oleg Itskhoki, Patrick Kehoe, Peter Koudijs, ArvindKrishnamurthy, Ye Li, Edith X. Liu (discussant), Matteo Maggiori, Konstantin Milbradt, Sergio Rebelo,Rob Richmond, Dimitris Papanikolaou, Cheng Peng, Paul Pfleiderer, Jesse Schreger, Kenneth Singleton, IlyaStrebulaev, Viktor Todorov, Christopher Tonetti, Victoria Vanasco, Adrien Verdelhan, Jonathan Wallen, YiDavid Wang, Rui Xu, Mindy Xiaolan Zhang, and seminar participants at Northwestern Kellogg, UW Foster,NYU Stern, Imperial College Business School, LSE, New York Fed, USC Marshall, Chicago Booth, Wharton,WFA, Vienna Symposium on Foreign Exchange Markets, and Cubist Systematic Strategies. I thank DaojingZhai for excellent research assistance.
1
2
I. Introduction
I find a high level of commonality in the changes in government surplus-to-debt ratios.
Across 11 developed countries, the first principal component explains 43% of their variations
from 1991 to 2017, and this fraction rises to 55% in the subsample starting from 2007. All
countries are exposed to this common factor, but to different degrees. A country has a
higher government surplus cyclicality if its government surplus-to-debt ratio is more exposed
to this factor. In this paper, I show how government surplus cyclicalities explain currency
risk premia in the cross-section.
To see this point, consider a model in which each country’s government only issues local
currency debt, and the debt is the claim to the government’s surpluses. Then, the real value
of the government debt reflects the present value of government surpluses, which fluctuate
across business cycles. On the other hand, since the notional payment of the government
debt is fixed in the unit of the local currency, the value of the local currency must adjust in
response to changes in government surpluses.
Therefore, currencies that are associated with more cyclical government surpluses tend to
depreciate more when the common factor in government surpluses declines. To compensate
investors for bearing this risk, these currencies have to offer higher risk premia. Notice,
however, their risk premia are not compensation for government default. In this model,
governments never default because they can always inflate away their local currency debt.
Currencies with higher risk premia can compensate investors by either raising nominal
interest rates or promising future appreciation. If each country’s monetary policy is set
so that its nominal exchange rate does not permanently drift upwards or downwards with
respect to other currencies, the country’s nominal interest rate must reflect its government
surplus cyclicality. So, a country with a higher government surplus cyclicality not only has
a higher currency return but also has a higher nominal interest rate.
Finally, the common variation in government surpluses also generates a factor structure
in currency returns. Lustig, Roussanov and Verdelhan (2011) define each currency’s carry
3
beta as the exposure of its excess return with respect to the carry trade return, which is
the return differential between high interest rate currencies and low interest rate currencies.
They find currencies with higher carry betas tend to have higher returns. My model offers
an economic explanation for this factor structure: Currency returns load on a common risk
factor because their government surpluses are exposed to a common shock. The carry trade
bets on currencies whose government surpluses are more cyclical, and is therefore correlated
with the common factor in currency returns.
In summary, my model connects currency risk premia to the fiscal side of the economy. I
derive closed-form characterizations and test them in the sample of 11 developed economies.
Figure 1 summarizes the main result. A country with a higher government surplus cyclicality
tends to have a higher nominal interest rate, a higher currency expected return, and a higher
carry beta. Government surplus cyclicalities explain 62% of the cross-country variation in
average quarterly nominal interest rates, 78% of the variation in average quarterly currency
excess returns, and 52% of the variation in carry betas. This result is robust after I account
for the fact that government surplus cyclicalities are estimated.
1 2 3 4 5
−0.
6−
0.2
0.2
0.6
Government Surplus Cyclicality
Nom
inal
Inte
rest
Rat
e D
iffer
entia
l (%
)
Australia
CanadaDenmark
Germany
Japan
New ZealandNorway
Sweden
Switzerland
United Kingdom
United States
1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
Government Surplus Cyclicality
Cur
renc
y E
xces
s R
etur
n (%
)
Australia
Canada
Denmark
Germany
Japan
New Zealand
Norway
Sweden
Switzerland
United Kingdom
United States
1 2 3 4 5
−0.
6−
0.2
0.2
0.6
Government Surplus Cyclicality
Cur
renc
y R
etur
n’s
Car
ry B
eta
Australia
Canada
DenmarkGermany
Japan
New ZealandNorwaySweden
Switzerland
United Kingdom
United States
Fig. 1.—Government surplus cyclicality explains currency risk premia. I plot each country’s government
surplus cyclicality against its currency’s quarterly average nominal interest rate differential with respect to
the U.S. dollar, quarterly average excess return with respect to the U.S. dollar, and carry beta. Data are
quarterly, 1980Q2—2017Q4. I use the longest sample possible for each currency. The dashed line is the best
fitting straight line from ordinary least squares.
4
Moreover, the government surplus-to-debt ratio can be decomposed into a GDP-to-debt
component, a tax-to-GDP component, and a spending-to-tax component. It is mainly the
spending-to-tax component that drives government fiscal shocks and determines government
surplus cyclicalities. This result suggests that currency risk premia are mainly influenced by
government fiscal policies rather than underlying economic conditions.
Finally, I construct a currency portfolio sorted by conditional government surplus cycli-
calities, which are estimated from rolling window regressions. The cross-country strategy
takes a long position in currencies whose conditional government surplus cyclicalities are
higher than the cross-country median, and a short position in other currencies. The return
of this strategy is strongly correlated with the carry trade return, and offers a Sharpe ratio
similar to that of the carry trade. Because conditional government surplus cyclicalities are
estimated from data available ex-ante, this approach is an out-of-sample evaluation of the
fiscal condition’s return predictability. This result confirms that the carry trade is profitable
because it loads on currencies whose government surpluses are cyclical.
This paper proceeds as follows. Section II formulates the model and derives its predictions.
Section III describes the data. Sections IV, V, and VI report the main empirical results. Sec-
tion VII concludes. The Appendix contains proof and data sources. The Internet Appendix,
available on my personal website, contains additional empirical results.
A. Literature review
This paper connects the currency literature with the fiscal literature. The currency liter-
ature has documented the carry trade anomaly (Brunnermeier, Nagel and Pedersen (2008);
Lustig and Verdelhan (2007); Lustig, Roussanov and Verdelhan (2011); Burnside, Eichen-
baum and Rebelo (2011); Engel (2014)) and found a factor structure in currency returns
(Lustig, Roussanov and Verdelhan (2014); Fourel et al. (2015); Verdelhan (2018)). Hassan
and Mano (2014) shows that this factor structure is related to the cross-sectional component
of currency risk premia. I offer a fiscal explanation for these patterns.
My model is closest to Gourio, Siemer and Verdelhan (2013); Colacito et al. (Forthcoming)
5
that explore heterogeneous loadings on global shocks as the key determinant of currency risk
premia, to Engel and West (2005); Gourinchas and Rey (2007, 2014); Farhi and Gabaix
(2016) that derive exchange rates as present values, and to Maggiori and Gabaix (2015) that
model risk-averse international investors.
On the other hand, the fiscal literature studies how fiscal conditions affect domestic and in-
ternational prices. Burnside, Eichenbaum and Rebelo (2001, 2003); Corsetti and Mackowiak
(2001); Daniel (2001a) show how fiscal shocks affected exchange rates during currency crises.
The fiscal theory of the price level connects fiscal conditions to domestic price levels (Sargent
Note: I regress the common surplus factor on fundamental variables, currency factors and stock marketperformance. Because the common surplus factor is the average 4-quarter change in government surplus-to-debt ratios, all explanatory variables except VIX are growth rates or cumulative returns over the same 4-quarter periods. The constant is not reported. The standard errors are heteroskedasticity and autocorrelationconsistent. ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.
spending both contribute to the variation in the common surplus factor.
The common surplus factor also comoves with the carry trade factor. The common surplus
factor is not correlated with the dollar factor in the univariate regression, but it is positively
correlated with the dollar index once the MSCI world stock return index is controlled for.
Finally, the common surplus factor is higher when the stock market performs well. In
univariate regressions, the common surplus factor is positively correlated with the MSCI
world equity return and negatively correlated with the VIX index. The VIX index no longer
explains the common surplus factor once the MSCI world equity return is controlled for.
The last column in Table 2 regresses the common surplus factor on currency risk factors
and stock market performance. These financial variables explain 40% of the variation in the
common surplus factor.
21
V. Currency Risk Premia in the Cross-Section
A. Main results
Having established the existence of the common factor in government surplus-to-debt ra-
tios, I test my model’s key predictions. Proposition 1 and 2 predict that a currency with a
higher government surplus cyclicality has a higher average excess return and a higher average
nominal interest rate. As discussed in Section III, I use the regression coefficient bi from
Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
= ai + bi · ft+1 + εit+1
as a proxy for the government surplus cyclicality ϕi.
In Figure 1 in the introduction, I have shown that the regression coefficient bi is positively
associated with the average nominal interest rate differential and the average currency excess
return with respect to the U.S. dollar. I run 4 tests to quantify this relationship.
The first test is ordinary least squares (OLS). I regress each country’s average nominal
interest rate differential or average currency excess return with respect to the U.S. dollar on
its regression coefficient bi:
1
T
T∑t=1
(logRf,i
t − logRf,USt
)or
1
T
T∑t=1
ri,USt+1 = λ0 + λbi + ei. (11)
I regard each currency’s regression coefficient bi as a known constant, and run a linear
regression in the cross-section of countries. Table 3 reports the results. A one-standard
deviation increase in a country’s regression coefficient bi is associated with a 0.32% higher
nominal interest rate and a 0.24% higher currency excess return per quarter. The government
surplus cyclicality explains 62% of the cross-country variation in the average nominal interest
rate and 78% of the cross-country variation in the average currency excess return.
The next three tests recognize the fact that the regression coefficient bi is estimated from
a regression. The second test corrects for the estimation errors in bi using the generalized
22
Table 3
Currency Risk Premia in the Cross-Section
Dependent Variable Test #Quarters λ Std Error R2 (%) α Test p Value
Note: I report the estimates of the risk premium parameter λ from the four tests. The estimates λ are scaledto express the change in the dependent variable in basis points for a unit increase in the government surpluscyclicality. #Quarters is the number of quarters used in each test. OLS and the Fama-Macbeth test allowsome countries to have missing observations. α Test is the test statistics against the null that all pricingerrors are jointly zero. Under the null, it follows a Chi-squared distribution, and I also report its p value.The standard errors from the GMM, the Shanken test, and the Fama-Macbeth test are heteroskedasticityand autocorrelation consistent.
method of moments (GMM). The moment conditions are
(Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
)− ai − bift+1 = 0,((
Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
)− ai − bift+1
)ft+1 = 0,(
logRf,it − logRf,US
t
)− λbi − λ0 = 0 or ri,USt+1 − λbi − λ0 = 0.
The first two moment conditions estimate the proxy bi for government surplus cyclicality.
The last moment condition estimates the relationship λ between government surplus cycli-
cality and currency risk premia. In order to estimate the covariance matrix of residuals, all
countries’ time series should have the same length. So, in this procedure I use the subsample
that contains no missing observation, which starts from 1991.
I report the first-stage GMM result in Table 3. The estimate λ is consistent with the
OLS results, suggesting a positive relationship between government surplus cyclicality and
currency risk premia.
23
The third test uses the Shanken (1992) correction. The sample is shorter because this pro-
cedure also requires that the sample contains no missing observation. When the dependent
variable is the currency excess return, the estimate λ and its standard error are similar to
those from the GMM.
The fourth test follows the Fama and MacBeth (1973) procedure. I estimate the regression
coefficient bi from the entire time series, and then estimate the coefficient λ from Eq. (11)
using the cross-section in each quarter. I only require that there are at least four countries
with non-missing observations to admit a quarter into my sample, and report the sample
average of the estimate λ in each quarter. When the dependent variable is the currency
excess return, the estimate λ is smaller than the estimates from the other tests.
B. The source of government surplus cyclicality
The government surplus-to-debt ratio can be decomposed into 3 components:
sit+1
Bit
≡GDP i
t+1
Bit
·τ it+1
GDP it+1
·τ it+1 − git+1
τ it+1
.
The GDP-to-debt ratio measures the quantity of domestic production per unit of govern-
ment debt, reflecting the country’s underlying economic condition. The tax-to-GDP ratio
measures the quantity of tax revenue per unit of domestic production, reflecting the govern-
ment’s tax policy. The surplus-to-tax ratio measures the quantity of government spending
per unit of tax revenue, reflecting the government’s spending policy.
Take the four-quarter log difference,
∆4 logsit+1
Bit
≡ ∆4 logGDP i
t+1
Bit
+ ∆4 logτ it+1
GDP it+1
+ ∆4 logτ it+1 − git+1
τ it+1
,
where ∆4 = (I − L4) takes the difference between the variable and its value 4 quarters ago.
24
On the left-hand side, I use the approximation formula Eq. (9):
∆4 logsit+1
Bit
≈Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
.
On the right-hand side, because the government surplus τ it − git can be negative, I use the
spending-to-tax ratio git/τit to represent log((τ it − git)/τ it ).
Then, I can examine which component explains the variation in the government surplus-
to-debt ratio. To do so, I regress the change in the government surplus-to-debt ratio on its
three components:
Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
= a+ c1∆4 logGDP i
t+1
Bit
+ c2∆4 logτ it+1
GDP it+1
+ c3∆4 git+1
τ it+1
+ εit+1.
Table 4 reports the regression results. All three components are correlated with the change
in the government surplus-to-debt ratio. However, the spending-to-tax ratio alone explains
69% of the variation, and drives out the explanatory power of the other two components.
This result suggests that the variation in the government surplus-to-debt ratio is mainly
driven by the government’s fiscal policy rather than the country’s economic condition.
Table 4
Decomposition of Government Fiscal Shock
(1) (2) (3) (4)
∆ log(GDP it+1/Bit) 0.034∗∗∗ −0.004
(0.010) (0.004)∆ log(τ it+1/GDP
it+1) 0.211∗∗∗ −0.0001
(0.019) (0.018)∆(git+1/τ
it+1) −0.245∗∗∗ −0.246∗∗∗
(0.009) (0.012)
Observations 1,578 1,578 1,578 1,578
R2 0.027 0.205 0.693 0.693
Note: I regress the change in government surplus-to-debt ratio on its three components. It is a panelregression across all countries and quarters. The constant is not reported. Standard errors are clustered byquarter. ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.
25
Now that the spending-to-tax ratio drives the variation in the government surplus-to-debt
ratio, can its cyclicality explain currency risk premia? To answer this question, I repeat the
same tests in Table 3, but replace the government surplus-to-debt ratio with the spending-
to-tax ratio and other components.
For example, in the OLS test, I regress each of the three components on the common
surplus factor in each country’s time series:
∆ logGDP i
t+1
Bit
= ai1 + bi1 · ft+1 + εi1,t+1,
∆ logτ it+1
GDP it+1
= ai2 + bi2 · ft+1 + εi2,t+1,
∆gitτ it
= ai3 + bi3 · ft+1 + εi3,t+1,
and then regress each country’s average currency excess return with respect to the U.S. dollar
on one of the coefficients bi1, bi2, and bi3.
I also repeat the GMM, the Shanken test and the Fama-Macbeth for each of the components
of the government surplus-to-debt ratio. Table 5 reports the test results. The association
between the spending-to-tax ratio’s cyclicality and the currency excess return is the strongest:
It has the highest R2 and the highest t statistics, and the null that all pricing errors are jointly
zero is not rejected in its GMM test.
This result suggests that the cross-country variation in currency risk premia is mostly
due to the governments’ fiscal policies. In the Internet Appendix, I also report the results
using the nominal interest rate differential as the dependent variable. The cyclicality of
the spending-to-tax ratio also explains the cross-country variation in nominal interest rate
differentials.
VI. The Factor Structure of Currency Returns
Lustig, Roussanov and Verdelhan (2011) show that the carry trade factor explains the
26
Table 5
Decomposition of Government Surplus Cyclicality
Explanatory Variable Test #Qtrs λ Std Error R2 (%) α Test p Value
GDP-to-Debt Ratio OLS 152 6.59 (5.33) 14.53
GDP-to-Debt Ratio GMM 108 45.56 (47.61) 488.98 0.00GDP-to-Debt Ratio Shanken 108 7.26 (9.35) 11.04 0.27
GDP-to-Debt Ratio Fama-Macbeth 137 6.70 (9.15) 10.72 0.30
Tax-to-GDP Ratio OLS 152 8.78 (8.93) 9.71Tax-to-GDP Ratio GMM 108 48.93 (36.03) 44.11 0.00
Tax-to-GDP Ratio Shanken 108 16.56 (14.88) 4.39 0.88
Tax-to-GDP Ratio Fama-Macbeth 137 17.11 (13.88) 12.43 0.19Spending-to-Tax Ratio OLS 152 −9.98 (4.78) 32.60
Spending-to-Tax Ratio GMM 108 −26.80 (16.88) 4.32 0.93
Spending-to-Tax Ratio Shanken 108 −13.51 (9.11) 7.80 0.55Spending-to-Tax Ratio Fama-Macbeth 137 −17.48 (8.74) 14.94 0.09
Note: I report the estimates of the risk premium parameter λ from the four tests described in Table 3.The dependent variable is currency excess return. The estimates λ are scaled to express the change in thedependent variable in basis points for a unit increase in the explanatory variable. #Quarters is the numberof quarters used in each test. α Test is the test statistics against the null that all pricing errors are jointlyzero. Under the null, it follows a Chi-squared distribution, and I also report its p value. The standard errorsfrom the GMM, the Shanken test, and the Fama-Macbeth test are heteroskedasticity and autocorrelationconsistent.
cross-section of currency risk premia, and Fourel et al. (2015); Verdelhan (2018) show that it
also explains currency returns. Proposition 3 offers a fiscal explanation: Currency loadings
on the carry trade return have a factor structure because government surpluses are exposed
to the common surplus factor to different degrees. In this section, I examine the extent
to which the factor structure in currency returns corresponds to the factor structure in
government surpluses.
A. Government surplus cyclicality and currency return beta
As in Proposition 3, a currency’s carry beta βicarry is defined as the exposure of its excess
return in dollar with respect to the carry trade factor:
ri,USt+1 = αi + βicarryrcarryt+1 + εit+1. (12)
The last panel of Figure 1 in the introduction plots each country’s regression coefficient
27
bi against its carry beta. This figure confirms Proposition 3: A currency with a higher
government surplus cyclicality tends to be more exposed to the carry trade factor.
Table 6 provides a detailed analysis. Panel A reports each currency’s carry beta from
from Eq. (12). Countries with higher government surplus cyclicalities, such as Australia and
New Zealand, have positive carry betas, whereas countries with lower government surplus
cyclicalities, such as Japan and Switzerland, have negative carry betas. The R2 is higher for
countries whose carry betas are greater in absolute values. Compared with Table 1, the carry
trade factor explains a smaller fraction of variation in currency returns than the common
surplus factor does for the variation in government fiscal shocks.
By Proposition 3, since bi measures the government surplus cyclicality of country i, country
i’s carry beta has the following functional form:
βicarry = ζ0 + ζbi.
Panel B tests this relationship in two ways. The first test regards each currency’s carry beta
βicarry and government surplus cyclicality bi as known constants, and runs a linear regression
Table 6
Factor Structure in Currency Returns
Panel A: Carry Beta
Japan Switzerland Germany Denmark US UK Canada Sweden Norway New Zealand Australiaβicarry −0.65 −0.29 −0.17 −0.10 0.00 0.31 0.34 0.40 0.41 0.63 0.71
Panel B: Carry Beta vs. Government Surplus Cyclicality
Test #Quarters ζ Std Error R2 (%)
OLS 152 0.34 (0.10) 54.95GMM 108 0.49 (0.21)
Note: Panel A reports the coefficient βicarry, its standard error, and the R2 of Eq. (12) for each country.
Panel B reports the test statistics. #Quarters is the number of quarters used in each test. The standarderrors from the GMM are heteroskedasticity and autocorrelation consistent.
28
in the cross-section of countries:
βicarry = ζ0 + ζbi + ei.
The OLS results suggest that a one-standard deviation increase in government surplus
cyclicality is associated with a 0.30 increase in slope beta, and government surplus cyclicality
explains 55% of the cross-country variation in the slope beta.
The second test corrects for the estimation errors using the generalized method of moments
(GMM). The moment conditions are
Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
− ai − bift+1 = 0,(Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
− ai − bift+1
)ft+1 = 0,
ri,USt+1 − (ζ0 + ζbi)rcarryt+1 − ci = 0,(ri,USt+1 − (ζ0 + ζbi)rcarryt+1 − ci
)rcarryt+1 = 0.
The first two moment conditions estimate the regression coefficient bi, which proxies for
the government surplus cyclicality. The last two moment conditions estimate the carry beta
βicarry, imposing the functional form (ζ0 + ζbi). Consistent with the OLS result, ζ is positive.
A higher government surplus cyclicality bi corresponds to a higher carry beta βicarry. A
country with a more cyclical fiscal condition also has riskier currency returns.
B. Currency portfolios sorted by conditional government surplus cyclicality
Now that a country’s government surplus cyclicality also reflects its currency’s risk expo-
sure, I can construct the carry trade from the fiscal data. First, I estimate the conditional
government surplus cyclicality of country i in quarter t by running the regression Eq. (10)
29
over a rolling window of T quarters:
Snom,ik+1
Bik
P ik−3
P ik+1
−Snom,ik−3
Bik−4
= ait + bitfk+1 + εi,tk+1, (13)
for k = {t− T, . . . , t− 1}.
In the earlier part of the sample, some countries’ government surpluses and debt quantities
are missing. I exclude a country/quarter observation (i, t) from panel the whenever there is
any missing variable in the entire rolling window from quarter t− T to quarter t− 1. I use
a look-back horizon of T = 4, 8, 20 or 40 quarters.
Then, I sort currencies into two quarterly-rebalanced portfolios based on their conditional
government surplus cyclicalities bit. Portfolio Low contains the currencies whose conditional
government surplus cyclicalities are below or equal to the cross-country median, and Portfolio
High contains those whose conditional government surplus cyclicalities are above the median.
The cross-country strategy invests a dollar in each currency in Portfolio High, and shorts a
dollar’s worth of each currency in Portfolio Low. The average log return of this strategy is
rxct+1def=
1
N
∑i∈Hxct
ri,USt+1 −∑i∈Lxct
ri,USt+1
,
where Hxct =
{i : bit > median({bjt}j)
}, Lxct =
{i : bit ≤ median({bjt}j)
}.
Table 7 reports the means, the Sharpe ratios, and the correlation matrix of the carry trade
return and the cross-country strategies’ returns. Regardless of the look-back horizon, the
Sharpe ratios of the cross-country strategies are slightly lower than that of the carry trade.
Surprisingly, a sample of four quarters is enough to estimate conditional government surplus
cyclicalities that predict currency returns in the cross-section.
Moreover, the cross-country strategies’ returns are positively correlated with the carry
trade return. I also report the alpha from regressing the carry trade return on the return
of each cross-country strategy. These strategies’ returns explain 24% to 52% of the average
30
Table 7
Portfolios Sorted By Conditional Government Surplus Cyclicality
Avg Return (%) SR Correlation Matrix Alpha of Carry Trade (%)
Note: I estimate each currency’s conditional government surplus cyclicality using a rolling window regressionEq. (13), and sort currencies based on this estimate. Avg return is the quarterly average return, and SR isthe quarterly Sharpe ratio. The standard errors are obtained from 10,000 rounds of bootstrapping. In eachround, I resample the quarters with replacement.
excess return of the carry trade.
VII. Conclusion
In this paper, I show how government surplus cyclicalities explain the cross-country vari-
ation in currency risk premia and give rise to a factor structure in currency returns. These
results are consistent with the asset pricing view that an asset’s risk premium is driven by
the systematic risk exposure of its cash flows.
This framework has broader implications. In this model, I assume constant real exchange
rates in order to focus on currency risk premia. In Jiang (2018), I show that if prices are
sticky but exchange rates are flexible, government fiscal conditions drive both nominal and
real exchange rates.
In this model, investors hold government debt for its cash flows. In Jiang, Krishnamurthy
and Lustig (2018), we assume that investors also derive convenience benefits from holding
the US government debt, and show how this extension explains the dollar’s exchange rate.
31
Appendix
Appendix A: Proof
Proof of Lemma 1: Consider any country i. Combine the government budget condition Eq. (1) with Euler equation
Eq. (3),
sit + Et[
Λt+1
ΛtBitQ
it+1
]= Bit−1Q
it. (A1)
I iterate this equation forward, and obtain
Bit−1Qit = lim
T→∞
(T∑j=0
Et[
Λt+jΛt
sit+j
]+ Et
[Λt+T+1
ΛtBit+TQ
it+T+1
]). (A2)
If Assumption 1 holds, i.e.
limT→∞
Et
[Λt+T+1
Λt
(∞∑k=0
Λt+T+1+k
Λt+T+1sit+T+1+k
)]= 0, (A3)
then Eq. (4), reproduced below, is a solution to Eq. (A2):
Qit =
∞∑k=0
Et[
Λt+kΛt
sit+kBit−1
]. (A4)
Other solutions to Eq. (A2) create arbitrage opportunities: If the real value of the currency is
Qi∗t =
∞∑j=0
Et[
Λt+jΛt
sit+jBit−1
]+M i∗
t (A5)
for some positive M i∗t , then the international investor can short-sell one unit of this currency and trade Arrow-
Debreu securities to replicate the government’s budget from time t. This portfolio of Arrow-Debreu securities
requires the international investor to provide a stream of cash flows {sit+j}. This stream of cash flows costs∑∞j=0 Et[(Λt+js
it+j)/(ΛtB
it−1)] at time t. Therefore, the international investor makes a net profit of M i∗
t at time
t, which is an arbitrage opportunity. A similar argument also rules out the case of a negative M i∗t .
Proof of Lemma 2: Define
V T,itdef= Et
[ΛT s
iT
Λtsit
]
32
which implies a boundary condition V T,iT = 1 and an intertemporal relationship:
V T,it = Et[
Λt+1
Λt
sit+1
sitV T,it+1
]. (A6)
Conjecture
V T,it = exp(fT−t(ϕi)),
with the boundary condition f0(ϕi) = 0.
Then f can be solved by iterating Eq. (A6):
efT−t(ϕi) = eµ−δ+12γ2σ2−γϕiσ2+fT−t−1(ϕi),
which confirms the functional form of f . Then, the currency value can be expressed as
Qit =
∞∑τ=0
Et[
Λt+τΛt
sit+τBit−1
]=
sitBit−1
∞∑τ=0
exp(fτ (ϕi)),
where the function F is defined as
F (ϕi)def=
∞∑τ=0
exp(fτ ((νit)2, ϕi)).
Proof of Proposition 1 and 2: From the Euler equation
Et[
Λt+1
Λt
Qit+1
Qit(1 +Rf,it )
]= 1,
the nominal interest rate satisfies
1
1 +Rf,it= Et
[Λt+1
Λt
Qit+1
Qit
]=
Bit−1
Biteµ−δ+
12γ2σ2−γϕiσ2
,
which simplifies to the formula in the proposition.
33
Plug in the nominal interest rate rule,
logEt[Qit+1
Qit
]= logEt
[sit+1/s
it
Bit/Bit−1
]= −∆ logBit + µ
= γϕiσ2 +
(δ − 1
2γ2σ2
)− rf,i − ηεf,it .
The log currency excess return is
ri,jt+1def= log
(Qit+1
Qit(1 +Rf,it )
)− log
(Qjt+1
Qjt(1 +Rf,jt )
)
=
(γϕiσ2 − 1
2(ϕi)2σ2 + ϕiσεct+1 + ωεs,it+1
)−(γϕjσ2 − 1
2(ϕj)2σ2 + ϕjσεct+1 + ωεs,jt+1
).
So the expected log currency excess return is
Et[ri,jt+1] = (γϕiσ2 − γϕjσ2)−(
1
2(ϕi)2σ2 − 1
2(ϕj)2σ2
).
Proof of Proposition 3:
Plugging in the interest rate target rf,i = γϕiσ2, the log nominal interest rate is
log(1 +Rf,it ) = γσ2ϕi + ηεf,it .
Let φ denote the density function of the standard normal distribution. Then the distribution the log nominal
interest rate at time t is N (γσ2ϕ, (γσ2ρ)2 + η2). The median of this distribution is γσ2ϕ. By the Glivenko–Cantelli
theorem, the sample median converges to the population median almost surely. So, the carry trade return is
rcarryt+1 =
∫r≥γσ2ϕ
ri,jt+1 −∫r<γσ2ϕ
ri,jt+1
=
∫ϕi
∫εf,it
(2 · 1{γσ2ϕi+ηε
f,it ≥γσ2ϕ} − 1
)(γϕiσ2 − 1
2(ϕi)2σ2 + ϕiσεct+1 + ωεs,it+1
)φ
(ϕi − ϕρ
)φ(εct+1)dϕidεct+1
= C1 +
∫ϕi
∫εf,it
(2 · 1{γσ2ϕi+ηε
f,it ≥γσ2ϕ} − 1
)(ϕiσεct+1
)φ
(ϕi − ϕρ
)φ(εct+1)dϕidεct+1.
34
Then
rcarryt+1 = C1 + σεct+1
∫ϕi
(2Φ
(γσ2(ϕi − ϕ)
η
)− 1
)ϕiφ
(ϕi − ϕρ
)dϕi
= C1 + C2σεct+1,
where
C2 =
∫ϕi
(2Φ
(γσ2(ϕi − ϕ)
η
)− 1
)ϕiφ
(ϕi − ϕρ
)dϕi
=2√2π
ρ2√1 +
(η
γσ2ρ
)2> 0.
It then follows that currency i’s carry beta is
βicarry =cov(rcarryt+1 , ri,jt+1)
var(rcarryt+1 )
=ϕi − ϕj
C2.
Linear Approximation of the Change in Government Surplus-to-Debt Ratio:
The first step is to find a stationary time series. Let Snom,it denote the nominal government surplus, and let P it
denote the price level. Then, the government surplus-to-debt ratio can be written as
sit+1
Bit
def=
Snom,it+1 /Bit
P it+1
.
The numerator and the denominator of this fraction are not co-integrated: In the past 37 years, the numerator
Snom,it+1 /Bit fluctuates within a band, while the GDP deflator P it+1 has a strong trend. Figure A1 reports the time
series of their cross-country averages. The cross-country average of nominal surplus-to-debt ratios was −2.10% in
1980 and 0.00% in 2017; both values fall into the normal range of variation. In contrast, the cross-sectional average
of GDP deflators has increased from 0.51 in 1980 to 1.40 in 2017.
As a result, the government surplus-to-debt ratio sit+1/Bit has been declining. Economically, this pattern means
that the real government surplus backing each local currency unit of government debt has been decreasing, across all
countries.
On the other hand, the numerator Snom,it+1 /Bit is stationary. An augmented Dickey–Fuller test with 4 lags to
account for seasonal effects rejects the null hypothesis of a unit root at 5% level. Let si denote the average nominal
35
1980 1990 2000 2010 2020
−0.
020.
000.
02
date
Ave
rage
Nom
inal
Sur
plus
−to
−D
ebt R
atio
0.0
0.4
0.8
1.2
Ave
rage
GD
P D
efla
tor
Nominal Surplus−to−Debt RatioGDP Deflator
Fig. A1.—The nominal government surplus-to-debt ratio Snom,it /Bi
t−1 and the GDP deflator, averaged
across countries. The GDP deflator in each country is normalized so that its value in 2000Q1 is 1.
surplus-to-debt ratio in country i:
sidef= Snom,it+1 /Bit.
Assuming the average nominal surplus-to-debt ratio si is positive, I can linearize the change in government surplus-
to-debt ratio around si/P it−3:
logsit+1
Bit− log
sit−3
Bit−4
def= log
Snom,it+1 /Bit
P it+1
− logSnom,it−3 /Bit−4
P it−3
≈ 1
si/P it−3
(Snom,it+1 /Bit
P it+1
− si
P it−3
)− 1
si/P it−3
(Snom,it−3 /Bit−4
P it−3
− si
P it−3
)
=1
si
(Snom,it+1
Bit
P it−3
P it+1
−Snom,it−3
Bit−4
). (A7)
Intuitively, Eq. (A7) takes the nominal surplus-to-debt ratio at quarter t+ 1, adjusts it for the price level change
in the previous 4 quarters, and then compares it to the nominal surplus-to-debt ratio 4 quarters before. It accounts
for both the change in the nominal government surplus and the change in the price level.
Lastly, the average nominal surplus-to-debt ratio si may vary across countries, which affects the magnitude of Eq.
(A7). However, as the government surplus-to-debt ratio is highly persistent, its long-run average is very difficult to
estimate. For parsimony, I assume si is the same across all countries.
36
Appendix B: Data Source
Spot exchange rates and 3-month forward rates are closing rates at the end of each quarter, and they come from
three sources: WM/Reuters, Barclays Bank International and Thomson Reuters, all downloaded from Datastream.
For each currency and each quarter, I make sure the spot exchange rate and the 3-month forward rate come from
the same data source. Data from WM/Reuters take priority over data from Barclays Bank International, which take
priority over data from Thomson Reuters.
Following Du and Schreger (2016), I construct nominal interest rate differentials and currency returns based on
currency forward premia, which do not contain sovereign default risk. For robustness, I repeat my empirical analysis
in the Internet Appendix, using currency returns based on treasury yields.
The nominal government surplus, the nominal quantity of government debt, and the nominal GDP are downloaded
from Oxford Economics via Datastream. These nominal quantities are denominated in the unit of the local currency.
The GDP deflator is also downloaded from Oxford Economics via Datastream. Each country’s GDP deflator is
normalized so that its value in 2000Q1 is 1. Oxford Economics seasonally adjusts some, but not all, of these variables.
*
REFERENCES
Aguiar, Mark, Manuel Amador, and Gita Gopinath. 2005. “Efficient fiscal policy
and amplification.” National Bureau of Economic Research.
Aguiar, Mark, Manuel Amador, Emmanuel Farhi, and Gita Gopinath. 2013. “Cri-
sis and commitment: Inflation credibility and the vulnerability to sovereign debt crises.”
National Bureau of Economic Research.
Aguiar, Mark, Manuel Amador, Emmanuel Farhi, and Gita Gopinath. 2015.
“Coordination and crisis in monetary unions.” The Quarterly Journal of Economics,
130(4): 1727–1779.
Arellano, Cristina. 2008. “Default risk and income fluctuations in emerging economies.”