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Trade Intensity and Purchasing Power Parity

Dooyeon Cho Antonio Doblas-Madrid

Department of Economics Corresponding author

Kookmin University Department of Economics

Seoul 136-702 Michigan State University

Republic of Korea 110 Marshall-Adams Hall

Phone: +82 2 910 5617 East Lansing, MI 48824

Fax: +82 2 910 4519 United States of America

Email: [email protected] Phone: +1 517 355 8320

Fax: +1 517 432 1068

Email: [email protected]

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Abstract

In this paper, we seek to contribute to the PPP literature by presenting evidence of a link

between trade intensity and exchange rate dynamics. We first establish a negative effect of

trade intensity on exchange rate volatility using panel regressions, with distance as an instru-

ment to correct for endogeneity. We also estimate a nonlinear model of mean reversion to

compute half-lives of deviations of bilateral exchange rates from the levels dictated by rela-

tive PPP, and find these half-lives to be significantly shorter for high trade intensity currency

pairs. This result does not appear to be driven by Central Bank intervention. Finally, we show

that conditioning on PPP may help improve the performance of popular currency trading

strategies, such as the carry trade, especially for low trade intensity currency pairs.

JEL Classification: C13; C52; F31; F47

Keywords: Trade intensity; Deviations from PPP; Exchange rate volatility; Carry trades; Mean

reversion

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1 Introduction

For international economists, exchange rate determination is a topic of perennial interest and a

formidable challenge. While some models—such as Taylor et al. (2001), Molodtsova and Papell

(2009), Mark (1995) and others—have outperformed Meese and Rogoff (1983)’s famous random

walk, the fraction of movement explained, let alone predicted, remains small.

According to Rogoff (2008), the most consistent empirical regularity is purchasing power par-

ity (PPP). Despite their volatility, real exchange rates appear to revert back to long-run averages

as predicted by relative PPP. In this paper, we investigate whether the degree of trade intensity

(TI henceforth) between two countries affects mean reversion in their bilateral real exchange

rate. Our hypothesis is straightforward. PPP is based on the Law of One Price, which in turn

relies on goods arbitrage. As deviations from PPP widen, the number of goods for which price

differences exceed transaction costs should increase. As agents exploit emerging opportunities

for goods arbitrage, they increase demand for goods in cheap locations and supply in expensive

ones. This reequilibration should be stronger between close trading partners, presumably due

to lower transaction costs—which include transport and tariffs, but also fixed costs like trans-

lating, advertising, licensing, etc. Sooner or later, goods trade should translate into currency

trades and affect nominal exchange rates, which typically drive most of the variability in real ex-

change rates. Although turnover in foreign exchange (forex) markets far exceeds export values,

this stabilizing effect of exports on exchange rates need not be insignificant. In fact, forex mar-

ket participants often claim that exports matter because, while speculative traders drive most

volume, they open and close positions very frequently. By contrast, export driven transactions

generate positions that are opened but never closed, exerting pressure on exchange rates in a

much more consistent direction. Moreover, if investors take trade into account—for example

by favoring countries with trade surpluses—when deciding which currencies to buy, speculative

trades may actually complement the effect of exports.

We consider a sample of 91 currency pairs involving 14 countries over the period 1980-2005.

To define and quantify TI, we largely follow Betts and Kehoe (2008). Our measures of TI between

countries A and B are based on the magnitude of the bilateral trade between them, relative to A’s

(and/or B’s) total trade. Not surprisingly, TI and exchange rate volatility are negatively correlated

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in our sample. This correlation is likely a product of causality in both directions. As mentioned

above, TI may reduce volatility through goods arbitrage, which exerts pressure to reduce devi-

ations from PPP. In the other direction, there is the argument—often brought up in defense of

fixed exchange rates—that lower exchange rate volatility may increase trade between countries

by reducing uncertainty and hedging costs. Since we are primarily interested in the first direc-

tion of causality, we begin the analysis by implementing panel regressions with exchange rate

volatility as a dependent variable and TI as one of our independent variables, using the distance

between two countries as an instrument. This approach is similar to that of Broda and Romalis

(2009). Coefficient estimates from these regressions across various specifications show a nega-

tive effect of TI between two countries on their bilateral real exchange rate. We also find that,

consistent with the literature on carry trades (see, for instance, Bhansali (2007)) exchange rate

volatility increases with the absolute value of interest rate differentials. While most of the cur-

rencies in our sample are floating during all or most of the sample period, there are some excep-

tions. However, our results remain qualitatively unchanged when we drop or control for pegged

currency pairs. Our results are moreover robust to the use of different measures of exchange

rate volatility and TI, and to considering only major currency pairs, as opposed to minor/exotic

pairs. Finally, the results are qualitatively preserved when we restrict attention to just the first,

or second half, of the 1980-2005 period.

Motivated by Michael et al. (1997) and Taylor et al. (2001), who provide evidence of nonlinear

mean reversion in a number of major real exchange rates, we quantify the size and persistence

of PPP deviations using a nonlinear model. Specifically, we estimate an exponential smooth

transition autoregressive (ESTAR) model, which allows the speed at which exchange rates con-

verge to their long-run equilibrium values to depend on the size of the deviations. The model

allows for the possibility that real exchange rates may behave like unit root processes when close

to their long-run equilibrium levels, while becoming increasingly mean-reverting as they move

away from equilibrium. For our comparison, we restrict attention to 35 highest and 35 lowest

currency pairs, as ordered by TI. We make this choice to ensure that the difference in trade in-

tensities between the two sets of currency pairs is so large and stable that variations of TI over

time are negligible in comparison to the differences in trade intensities between the two sets of

pairs. After estimating the ESTAR models, we investigate the dynamic adjustment in response to

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shocks to real exchange rates in the estimated ESTAR model by computing the generalized im-

pulse response functions (GIs) using the Monte Carlo integration method introduced by Gallant

et al. (1993). We find that, as hypothesized, the estimates of the half-lives of deviations from PPP

for a given currency pair are higher the less intense the trade relationship between two countries.

For currency pairs in the high TI group, the average half-life of deviations from PPP is given by

20.26 months, whereas for low TI pairs, it is 26.34 months. Moreover, this finding is statistically

significant.

We also verify that our result is not driven by Central Bank intervention. That is, a possible

concern when interpreting our results is that, if Central Banks exhibit more fear of floating in

response to exchange rate fluctuations against important trading partners, the observed differ-

ences in volatility may primarily be due to official reserve transactions, rather than trade. To

address this concern, we consider various proxies for intervention—specifically the volatility of

reserves and interest rates, following Calvo and Reinhart (2002). To judge by these measures,

government intervention is unlikely to be the reason for faster convergence in high TI cases,

since the degree of currency intervention is typically lower for high TI currency pairs.

Finally, we investigate whether our findings on TI and mean reversion can be used to improve

the performance of forex trading strategies, such as the carry trade. To do this, we perform an

exercise similar to Jordà and Taylor (2012). We simulate a PPP-augmented carry trade, which

gives a buy signal only if there is a positive interest rate differential and the high interest currency

is undervalued according to relative PPP. The criterion to decide whether a currency is over- or

undervalued is simply whether the (lagged) real exchange rate is above or below its historical

average by a percentage � . (The higher � , the greater of degree of undervaluation needed to

satisfy the PPP condition.) We compare the performance of this PPP-augmented carry trade

to a plain carry trade, which chases high interest rate differentials regardless of PPP valuations.

We do this separately for a high TI and for a low TI portfolio. Across all our specifications of

the carry trade, the PPP-augmented strategy outperforms the plain carry, in the sense that it

has higher Sharpe ratios. These gains from conditioning on PPP tend to be greater in the low

TI portfolio. Moreover, the optimal � is also higher in the low TI case. While these results are

obtained in sample, we find that the same patterns do hold out-of-sample, although the gains

from conditioning on PPP become smaller, especially in the high TI group.

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The rest of the paper is organized as follows. In Section 2, we describe our data and define

variables. In Section 3, we provide evidence of a linkage between TI and exchange rate volatil-

ity using panel regressions. In Section 4, we present and discuss empirical results from ESTAR

models. We also conduct and discuss stationary tests for estimated ESTAR models. Further, we

investigate whether our half-life estimates are mainly driven by government intervention. In

Section 5, we apply our findings to currency trading strategies. In Section 6, we conclude.

2 Data and variable definitions

2.1 Data sources

We collect monthly nominal exchange rates vis-à-vis the US Dollar (USD) from January 1980

through December 2008 for the following 13 currencies: Australian Dollar (AUD), Canadian Dol-

lar (CAD), Euro/Deutsche Mark (EUR/DEM), Great Britain Pound (GBP), Japanese Yen (JPY),

Korean Won (KRW), Mexican Peso (MXN), New Zealand Dollar (NZD), Norwegian Krone (NOK),

Singapore Dollar (SGD), Swedish Krona (SEK), Swiss Franc (CHF), and Turkish Lira (TRY). To

choose the currencies, we follow the BIS Triennial Central Bank Survey, and focus on the 20

most traded currencies in 2010. Six of the top twenty currencies, the Hong Kong Dollar (in 8th

place), Indian Rupee , Russian Ruble, Chinese Renminbi, Polish Zloty (in places 15-18), and the

South African Rand (in place number 20) were dropped due to data limitations, being fixed for

most of the sample period, or both. Combining each of the 14 currencies with the rest, we obtain

a total of 91 bilateral trade relationships and real exchange rates.

For all 14 currencies, we collect monthly money market interest rates, price indices, in par-

ticular the consumer price index (CPI), and foreign exchange reserves. We retrieve these data

from the IMF’s International Financial Statistics (IFS) database. Data for annual exports used to

measure trade intensity (TI) are borrowed from Betts and Kehoe (2008).1

1The data along with a data appendix for annual exports to measure TI are publicly available at Timothy Kehoe’swebpage, http://www.econ.umn.edu/~tkehoe/research.html.

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2.2 Measuring exchange rate volatility and trade intensity

The aim of this paper is to investigate the link between TI and exchange rate volatility. Our

hypothesis is that the more intense the trade relationship between two countries, the less volatile

their bilateral real exchange rate. To investigate the link between them, we start by defining our

measures of exchange rate volatility and TI.

The real exchange rateQt is defined as

Qt � StPtP �t; (1)

where St is the nominal exchange rate measured as the price of one unit of domestic currency in

terms of foreign currency, and Pt and P �t denote domestic and foreign price levels, respectively.

The log real exchange rate qt is given by

qt � st + pt � p�t ; (2)

where st, pt and p�t denote the logarithms of their respective uppercase variables. The real ex-

change rate is the price of one unit of domestic goods in terms of foreign goods.

To measure exchange rate volatility volij between countries i and j, we calculate the standard

deviation of the monthly logarithms of the bilateral real exchange rates over the one-year period

for each currency pair. (As a robustness check, we will also use different time windows such as

the three-year window and six-year window.) Specifically, volij is given by

volij =

�1

T � 1TPt=1

�qij;t � qij

�2� 12; (3)

where qij;t is the monthly logarithm of the bilateral real exchange rate between countries i and

j, and qij is the mean value of qij;t over a period of T months.

We define two alternative measures of TI, which aim to capture the relative importance of a

bilateral trade relationship as a fraction of each country’s total trade. Following Betts and Kehoe

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(2008), we define the maximum TI variable tradeintmaxX;Y;t between countriesX and Y as follows

tradeintmaxX;Y;t = max

8<: exportX;Y;t + exportY;X;tPall

exportX;i;t +Pall

exporti;X;t;

exportX;Y;t + exportY;X;tPall

exportY;i;t +Pall

exporti;Y;t

9=; ; (4)

where exportX;Y;t is measured as free on board (f.o.b.) merchandise exports from country X to

country Y at year t , measured in year t US dollars. According to this definition, TI only needs

to be high for one of the two countries in the bilateral trade relationship. To see how to ap-

ply this definition consider for example the Korea-US relationship. With Korea accounting for

just 5.3 percent of US trade, and the United States accounting for 39.6 percent of Korean trade,

tradeintmaxX;Y equals 39.6. We also define tradeintavgX;Y;t as an alternative measure to (4). Instead of

picking the highest and discarding the lowest percentage, this measure takes both percentages

into account. More precisely, average TI tradeintavgX;Y;t between countriesX and Y is defined as

tradeintavgX;Y;t = avg

8<: exportX;Y;t + exportY;X;tPall

exportX;i;t +Pall

exporti;X;t;

exportX;Y;t + exportY;X;tPall

exportY;i;t +Pall

exporti;Y;t

9=; . (5)

Thus, this measure averages the two fractions in the bilateral trade relationship. If we apply

the definition in (5) to the Korea-US example given above, we obtain 22.5 percent instead of

39.6 percent between Korea and the United States. Both TI measures—averaged over the period

1980-2005—are reported in Table 1, panels (a) and (b) for all bilateral trade relationships. For

tradeintmaxX;Y and tradeintavgX;Y;t most observations are between 0 and 0.4, and between 0 and 0.2,

respectively, with a few outliers above these levels. In the analyses that follow, we will therefore

always verify that our results are not driven by these outliers. In Figures 1 (a) and (b), we show

scatter plots of exchange rate volatility against TI (maximum) and TI (average), respectively, for

the 91 currency pairs listed in Table 1. In addition to the presence of outliers, the scatter plots

show a negative correlation between volatility and both TI measures.

3 Panel regressions with distance as an instrument

The scatter plots from Figure 1 show a negative correlation between TI and volatility, with the as-

sociated OLS regressions producing a negative slope that is significant at the 1% level for both TI

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measures.2 These regressions, however, are fraught with obvious endogeneity problems, since

causality between volatility and TI runs both ways. To address this issue, in our preliminary re-

gressions we employ an instrumental variable (IV) estimation approach. Specifically, we use the

distance between two countries as an instrument for TI. Clearly, distance between two countries

is exogenous and not determined by exchange rate volatility. Moreover, distance is also an ap-

propriate proxy variable for TI since—as predicted by gravity models—countries that are closer

to each other tend to trade more. We thus estimate the following IV panel regression equation,

volij;t = �+ � � volij;t�1 + � tradeintij;t + � � absidij;t +N�1Pi=1

di + vij;t (6)

where � is an intercept term, volij;t is exchange rate volatility, tradeintij;t is TI (maximum) or TI

(average), absidij;t is the absolute value of the interest rate differential between two countries, i

and j, di is a dummy variable for each country i (N denotes the total number of countries), and

vij;t is an error term. Table 2 presents results from IV estimation using panel data for the effects

of TI on real exchange rate volatility. Our estimates are negative and statistically significant at the

1% level for both measures of TI, maximum and average. Besides this main finding, we also find

that exchange rate volatility increases with the absolute value of interest rate differentials, which

is consistent with the view that carry trades—which are often seen as drivers of currency trends

and sharp reversals—lead to an increase in volatility of the exchange rates between investment

and funding currencies.3

In Table 3, we conduct a number of robustness checks for results from IV estimation using

panel data: (a) we drop/control for fixed exchange rates, (b) we exclude outliers for the real

exchange rate volatility variable and the TI variable, (c) we subsample by subperiods: 1980-1992

and 1993-2005, (d) we subsample by major vs. minor, or “exotic”, currency pairs, and (e) we

construct the volatility variable using different time windows, in particular 3 and 6 years.

Regarding the first robustness test (a), it is important to verify that, since exchange rate sta-

bility is believed to promote trade, our results are not primarily driven by the choice of exchange

rate regime. In this Section, we follow IMF official classifications of regimes, as compiled by

2When we drop the USD/CAD or USD/MXN pair or both, the significance remains at 1% for average TI, but be-comes 5% for the maximum TI measure.

3When we drop the interest rate differential, the negative relation between TI and exchange rate volatility remainsunchanged.

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Reinhart and Rogoff (2009). (In Section 4, we will revisit the issue, focusing on de facto inter-

vention rather than officially reported exchange rate regimes.) Most currencies in our sample

are classified as floating for most of the sample period, but there are a few exceptions. Most

importantly, in some years, a few countries pegged their currencies to trade-weighted indices,

creating a negatively link between trade and volatility, almost by construction. This includes

Norway and Sweden over 1980-92 and Singapore over 1980-2005. We could not find a reason-

able way to control for this, since adding a proxy measuring the degree of “fixing” proportionally

to trade intensity is akin to having trade intensity twice. We have thus excluded all pairs involv-

ing NOK, SEK, and SGD over the relevant years. In a few other cases—namely USD/KRW over

1980-96, USD/MXN over 1980-1993, USD/TRY over 1980-1999, and CHF/EUR over 1980-81—we

encounter bilateral pegs. Following Reinhart and Rogoff (2009) we include as fixed all varieties

of constant and crawling pegs with bands no wider than�2%.4 We control for these cases using

a fixed dummy variable. We report results from this robustness test in Table 3 (a). While these

changes somewhat reduce the absolute value of the negative coefficient between trade intensity

and volatility, the coefficient remains significant at the 1% level, and thus, our qualitative re-

sults continue to hold. Moreover, as expected, the coefficient associated with the fixed dummy

is negative and significant at the 1% level.5

Next, in Table 3 (b) we truncate outliers of the dependent variable, real exchange rate volatil-

ity, by excluding all observations that are more than two standard deviations from the mean in

any period t. This has little impact on the results. Next, we also truncate outliers of the TI variable

by excluding all observations that are included in the highest 2 percent (this leads to dropping 52

observations for both TI (maximum) and TI (average), respectively.). Truncating outliers of the

TI variable also leaves our results unaltered, as can be seen in Table 3 (b). Second, we divide the

entire sample period into two subperiods: 1980-1992 (first half) and 1993-2005 (second half).

As reported in Table 3 (c), the slope coefficients for TI on volatility are greater in absolute value,

i.e., more negative, in the first half of the sample period. Qualitatively, however, results are simi-

4Note that this definition excludes the well-known episode corresponding to Britain’s ERM membership over 1989-92. While the Pound was pegged to the German Mark, the width of the band was�6%, and thus the regime is classifiedas floating.

5In untabulated results, we also reran the regressions considering as fixed and all possible combinations of pairsamong KRW, MXN, and TRY, on the grounds that, if two currencies are pegged to the USD, they are pegged to eachother—although in practice the bands around the pegs significantly weaken the degree to which pegging is ‘transitive’.In any case, results were very similar to the baseline case.

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lar across both subperiods, with coefficients remaining negative and significant at the 1% level.

Third, we investigate whether our results are different for major currency crosses, which add up

to 42 out of our total of 91, and minor/exotic currency crosses, which include the remaining 49

out of 91.6 This robustness test is driven by potential concerns about volatility differences being

driven by market liquidity, which is greater for major currency pairs. As can be seen from Table

3 (d), the results in both subsamples are almost exactly equal to each other and to the overall

results reported in Table 2. Finally, we verify that our results are not sensitive to changing the

width of the time window in the definition of our volatility variable, set at 1 year in the baseline

regressions. Results with 3 and 6 year windows are reported in Table 3 (e). Clearly, the use of dif-

ferent time windows has virtually no effect on the estimated coefficients for the other variables

of interest. Overall, the negative relationship between TI and exchange rate volatility holds up

well across the different robustness tests.

4 Estimation results from ESTAR models

While the previous section presents evidence that trade intensity reduces exchange rate volatil-

ity, a related question is whether trade intensity is also associated with faster convergence of

exchange rates to the values predicted by relative PPP. To do this, we compare whether the half

lives of PPP deviations differ between the set of 35 pairs with the highest TI and the set of 35 pairs

with the lowest TI.7 Given the evidence of nonlinearity in mean reversion presented by Taylor et

al. (2001), we compute half-lives of PPP deviations using a nonlinear exponential smooth tran-

sition autoregressive (ESTAR) model.

While we provide details in the Appendix, in broad strokes the ESTAR model can be described

as follows. There is a lower regime in which PPP deviations are small. In this regime, persistence

is mainly governed by a parameter �, which can be negative if there is mean reversion, but can

also be zero or positive, since unit root or explosive dynamics are possible. As PPP deviations

grow, however, there is a gradual shift to an upper regime in which persistence is governed by

6The most traded currency pairs in the foreign exchange market are called the major currency pairs. They in-volve the currencies such as Australian Dollar (AUD), Canadian Dollar (CAD), Euro (EUR), Great Britain Pound (GBP),Japanese Yen (JPY), Swiss Franc (CHF), and US Dollar (USD). On the other hand, the minor/exotic currency pairs aredefined as those pairs that are emerging economies rather than developed countries.

7We use TI (average) to rank currency pairs. Using TI (maximum) instead of TI (average) makes little difference.

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� + ��. By assumption, the upper regime is mean reverting, and thus, it must be that �� < 0

and � + �� < 0. A transition function, parameterized by slope parameter , determines the

speed of transition from the lower to the upper regime as PPP deviations grow. Standardized

deviations are given by (qt�d � c)2=�qt�d ; where qt�d is the d-period lagged real exchange rate,

�qt�d is the standard deviation and the location parameter c is the estimated mean level that the

exchange rate should revert to. Further parameters �1; :::; �p�1 and ��1; :::; ��p�1 capture higher-

order persistence in the lower and upper regimes, respectively. Parameters are estimated via

nonlinear least squares (NLS).8

Having estimated the ESTAR model, we follow Koop et al. (1996) to generate generalized im-

pulse response functions (GIs). (See the Appendix for details.) The generated GIs are depicted

in Figures 2 (a) and (b). In the graphs, GIs for high TI currency pairs appear to decay faster. This

impression is confirmed when we calculate half-lives of PPP deviations, which are reported in

Table 4 for high and low TI pairs. Typically, our estimates of the half-lives of deviations from PPP

for a given currency pair are higher the less intense the trade relationship between two countries.

More specifically, the average half-life in the high TI group is shorter than the average half-life

in the low TI group by about 6.1 months. The t-statistic for the difference in means test is 2.13,

allowing us to reject the null hypothesis of no difference in means.9 Thus, the half-lives of de-

viations from PPP based on the estimations of the ESTAR models and the generated GIs suggest

that deviations from PPP are corrected faster for country pairs with relatively more intense trade

relationships.

It remains to verify whether the nonstationarity of the ESTAR model can be rejected. Al-

though (�+ ��) < 0 obtains for all pairs, verifying the statistical significance of the nonstation-

arity result is a bit involved. Tests to detect the presence of nonstationarity against stationary

STAR processes have been developed by Kapetanios, Shin, and Snell (2003, KSS henceforth) and

Bec, Ben Salem, and Carrasco (2010, BBC henceforth). These two tests compute Taylor series ap-

proximations to STAR models, which have been used in the linearity test proposed by Saikkonen

8The estimation results along with the estimated transition functions, plotted against time for high and low TIcurrency pairs are available from the authors upon request.

9Although trade is endogenous to the real exchange rate, the differences in TI between these two sets of countrypairs very large and stable. In spite of dramatic movement in real exchange rates throughout the sample period, TIfor all low-intensity country pairs remain far below any high-intensity pair at all times.

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et al. (1988) and get the auxiliary regressions

�yt =r2Pr=r1

�ryt�1yrt�d +

pPj=1

�j�yt�j + "t;

where "t � iid�0; �2

�. Both tests are performed by the statistical significance of the parameters

(�r1 ,...,�r2). Norman (2009) summarizes both testing procedures, and extends to allow for a delay

parameter, d, that is greater than one. He shows that the distributions of both statistics for d > 1

are the same as the case when d = 1. KSS set r1 = r2 = 2, and derive the limiting non-standard

distribution of the t-statistic to test �2 = 0 against the null hypothesis of �2 < 0

tNL =�̂2

s:e:��̂2

� :BBC set r1 = 1; r2 = 2, and derive the limiting non-standard distribution of the Wald statistic,

FNL, to test �1 = �2 = 0 against the null hypothesis of �1 6= 0 or �2 6= 0.10 Applying both tests to

our currency pairs with de-meaned data, we obtain t-values and F -values for the KSS and BBC

tests, respectively. Histograms of the obtained values are plotted in Figure 3. Out of 35 high TI

currency pairs, KSS tests reject the null in 1 case at the 1% level, 8 cases at the 5% level, and 5

cases at the 10% level. Out of 35 low TI pairs, KSS tests reject the null in 6 cases at the 1% level, 6

at the 5% level, and 1 at the 10% level. The corresponding numbers for BBC tests are 3 cases at

the 1% level, 5 at the 5% level, and 6 at the 10% level for high TI pairs, and 6 cases at the 1% level,

5 at the 5% level, and 3 at the 10% level for low TI pairs. In terms of overall rejection rates for

nonstationarity, these results are similar to those obtained by KSS and BBC in their respective

samples of real exchange rates.11

10KSS report 1%, 5%, and 10% asymptotical critical values in Table 1 on page 364. However, BBC do not provideany asymptotical critical values, and Norman (2009) reports the 5% asymptotical critical value (10.13) using MonteCarlo simulations with 50,000 replications in his paper. We thank Stephen Norman for providing us with 1% and 10%asymptotical critical values for the BBC testing procedure.

11KSS find evidence that the tNL test rejects the null in 5 cases at the 5% significance level and another at the 10%significance level out of 10 real exchange rates against the US Dollar. BBC conclude that the FNL test rejects the nullin 11 cases out of 28 real exchange rates.

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4.1 Half-lives and government intervention

We investigate whether the observed differences in volatility may be due to Central Bank in-

tervention in currency markets, or fear of floating, instead of trade. To inquire into this issue,

we follow in the footsteps of Calvo and Reinhart (2002), using volatility of reserves and interest

rates as proxies for intervention.12 We then examine whether there is an association between

half-lives of deviations from PPP and our measures of government intervention.

We denote the absolute value of the percent change in foreign exchange reserves by j�F j =F

and the absolute value of the change in interest rate by jit � it�1j. Our first intervention proxy

is the frequency with which j�F j =F falls within a critical bound of 2.5 percent. The greater

this frequency, the less a country intervenes. This interpretation is straightforward, since pur-

chases or sales of reserves are the most direct form of intervention. For our second proxy, we

interpret volatile interest rates as evidence of attempts to stabilize the exchange rate. Thus, our

second variable is the percent of the time that interest rates change by 400 basis points (4 per-

cent) or more vis-à-vis the previous month. The more often this occurs, the greater the degree

of intervention. In Table 5, we report the observed frequencies over the period January 1980 -

December 2008. By these two measures, Japan, Singapore and the United States are examples of

countries that tend to intervene least, whereas Mexico and Turkey are among those that inter-

vene most. To quantify the overall degree of intervention, we simply rank the currencies, with 1

denoting the least intervened currency and 14 the most intervened. Averaging a currency’s two

rank orders (one for reserves, one for interest rates), we obtain a currency’s overall intervention

level. To evaluate the amount of intervention for a currency pair, we again average the overall

intervention levels of the two currencies in the pair.

Comparing intervention rankings for high versus low TI currency crosses, we obtain an aver-

age of 5.32 for high TI currency pairs, and 8.19 for low TI pairs.13 This suggests that our half-life

estimates are not mainly driven by government intervention. If anything, intervention may re-

duce the observed differences, if it successfully mitigates fluctuations in the low TI group.

12These measures are admittedly very imperfect, as they fail to capture statements about future policy, asset pur-chases (such as quantitative easing), and other tools used by policymakers influence currency markets. See Edison(1993) and Sarno and Taylor (2001) for in depth discussions about proxies for intervention operations.

13When we use percents instead of rank orders, there is little difference between high and low TI currency pairs.The use of percents does not change our main results on government intervention.

14

5 Application to currency trading

We investigate whether our results can help predict exchange rates and formulate profitable cur-

rency trading strategies. To do this, we must keep in mind that the returns of a strategy depend

not only on exchange rate movements, but also on interest rates. This is partly due to the direct

effect of interest differentials (minus bid-ask spreads) being credited/debited daily to traders’

accounts. But there is also an indirect effect. As is well-known, contrary to what uncovered in-

terest parity (UIP) would predict, in the data high-interest currencies tend to appreciate. A vast

literature documents the positive average returns of the carry trade, a strategy that profits from

this anomaly by borrowing low-interest currencies to invest in high-interest ones.14 We thus

adopt the carry trade as a benchmark, and ask whether our findings on mean reversion can help

us improve on this well-known strategy. Our exercise resembles that of Jordà and Taylor (2012),

who also include PPP as a predictor in a sophisticated version of the carry trade.15 The novelty

in our paper is that we also explore whether gains from conditioning on PPP depend on TI.

For the currencies in our sample over the period January 1986 - December 2012, we compare

a plain carry trade strategy with an augmented one. The plain strategy enters a trade (long cur-

rency A, short currency B) if the interest rate differential iAt � iBt exceeds a threshold spread�it,

i.e., if

iAt � iBt � �it: (7)

We experiment with four specifications of the threshold �it. In the first three, it is constant

at 1, 2, or 3%. In the fourth, we consider an interest differential to be high only if it is higher

than others available at the time. Thus, we set �it equal to imedt � imint , the difference between

the median and minimum interest rates in our sample. For a currency pair, if the difference

between the higher and the lower interest rates is less than �it, the strategy is inactive and no

trade is entered.

The augmented carry strategy buys currency A against B if, in addition to the interest con-

14The profitability of carry trades has been documented by Brunnermeier et al. (2008) and Burnside et al. (2006)among many others. While the failure of UIP has long been referred to as the forward premium puzzle, recent workby Lustig et al. (2011) and Menkhoff et al. (2012) has gone a long way towards reconciling the profitability of carrytrades with standard asset pricing theory by identifying risk factors that explain excess returns.

15In addition to Jordà and Taylor (2012), there have been other approaches seeking to improve the performance ofcarry trade, mostly by reducing risk. For instance, some authors have proposed diversification (Burnside et al., 2006),the use of options (Burnside et al., 2011).

15

dition (7) being satisfied, currency A is undervalued vis-à-vis currency B in the following sense.

The 12-month lagged real exchange rateQAB;t�12 (i.e., the price of A’s goods relative to B’s goods)

times a factor � must be below the long-run averageQAB;t. That is,

QAB;t�12 � � � QAB;t: (8)

The use of a lagged real exchange rate captures the idea behind the J-curve, i.e., that it takes

some time for exchange rate misalignments to influence trade.16 As a measure of the long-run

average, we compute real exchange rate’s 15-year moving average.17

QAB;t =

180Xs=1

QAB;t�s

180:

The factor � captures the degree to which currency A must be undervalued to enter a trade. If

� = 0, the PPP condition (8) always holds, and the augmented carry strategy is just the plain

carry. As � increases, (8) becomes more stringent, allowing fewer trades. If � < 1, (8) allows

currency A to be bought as long as it is “not too overvalued”. For instance, if � = 2=3, currency

A can be bought against B even if it is a bit expensive; specifically, as long as it is less than 50%

overvalued. If � = 1, condition (8) holds only if A is undervalued relative to B. Finally, if � > 1,

A can only be bought if undervalued by a given margin. For example, if � = 3=2, (8) holds only

if A is so undervalued that the (lagged) real exchange rate is below 2=3 of its long-term average.

As � continues to increase, the PPP becomes more stringent, and in the limit it is never satisfied,

meaning that the augmented PPP strategy is always idle.18

16We have chosen a 12 month lag after experimenting with multiple specifications. While the best lags seem torange between 9 and 15 months, results are still qualitatively similar for lags between 6 and 24 months, and worsensubstantially outside this range.

17We use data on real exchange rates from January 1971 to December 1985 to compute the initial average realexchange rate. Experimenting with the number of lags in the moving average, we find that, as the number of lagsrises, the moving average becomes more stable and useful as a predictor. These gains, however, peter out as thenumber of lags grows. On the other hand, more lags mean losing more observations at the start of the sample period,because they are needed to compute the first moving average. Our choice of 15 years balances these two effects. Aslong as the moving average contains at least 10 years, results remain fairly similar.

18It is important to note that, although it involves a moving average, the augmented PPP carry is not a momen-tum strategy. Momentum strategies buy currencies when the exchange rate is greater than its moving average. Thesimplest example is “Buy if St > MA(1)”, which is equivalent to “Buy if St > St�1”. Our PPP condition—especiallyfor high values of �—does the opposite, buying currencies that have substantially depreciated, i.e., buying when theexchange rate is below the moving average.

16

The augmented carry (� > 0) is more selective than the plain carry (� = 0), since it requires

more conditions and enters fewer trades. The key trade-off when choosing � is as follows. A

higher � tends to raise the average profitability of the trades entered, but it also means that,

by entering fewer trades, investors forego opportunities to profit from interest differentials and

diversify their portfolio. To find the optimal levels of � , we evaluate the performance of the plain

and augmented strategies separately for the set of 35 high and 35 low TI currency pairs from

Table 4. To compute the returns of the plain carry, for every currency pair, we check whether the

interest rate condition (7) is satisfied. If yes, the pair is active. If not, it is inactive. The return of

an active pair is given by

Rt+1 =SAB;t+1SAB;t

�"1 +

iAt+1 � iBt+1 � tc12

#; (9)

where SAB;t is the nominal exchange rate measured as the price of one unit of currency A in

terms of currency B, and tc is a transaction cost, set at 1% per annum.19 The return of an inactive

pair is zero. The portfolio return RPFt+1 (for high and low TI), is the equally weighted average of

the returns of active pairs. If no pairs are active, the portfolio returnRPFt+1 is zero. To simulate the

augmented carry we follow the same steps, with the only difference being that—as explained

above—a pair must satisfy both the interest rate condition (7) and the PPP condition (8) to be

active.

For each strategy, we compute 27 years of monthly returns from January 1986 to December

2012. To evaluate performance, we focus on the annualized Sharpe ratio defined as

Sharpe =Mean(RPF )

SD(RPF )�p12; (10)

where multiplying byp12 converts a monthly ratio into an annual one.

The evolution of Sharpe ratios as a function of � is plotted in Figure 4 for all specifications

of �it. The case with � = 0 corresponds to the plain carry. For � < 0:5, PPP deviations in the

sample are too small to violate the PPP condition, and the augmented carry remains the same

19In spot foreign exchange markets, transaction costs include a bid-ask spread applied at the level of the exchangerate, and another bid-ask spread applied to the interest rates. These spreads are different across time periods, cur-rency paris, and brokers. We have chosen 1% per annum as a rough average based on spreads charged by forexbrokers such as OANDA, FXCM, and others.

17

as the plain one. Starting at around � = 0:5 for low TI 0:6 for high TI, we start finding cases

where the high-interest currency is overvalued enough to violate the PPP condition. The PPP

condition deactivates these trades, which tends to raise Sharpe ratios, especially in the low TI

group. Sharpe ratios increase for � between approximately 0.6 and 0.95 in the high TI group and

0.5 and 1 in the low TI group. Beyond 0.95, or 1, increases in � tend to lower Sharpe ratios, as the

opportunity cost from foregoing a growing number of trades outweighs the gains from increased

average quality of trades. This decline is more pronounced in the high TI group. In sum, gains

from augmenting the carry strategy are typically greater in the low TI portfolio, because there

is a wider range of values of � for which the augmented carry outperforms the plain carry, and

because there is typically a higher maximum gain in Sharpe ratio relative to the plain carry. The

optimal level of � is also higher in the low TI group. Specifically, Sharpe ratios peak for � = 0.95,

0.95, 0.97, 0.95 in the high TI group and 1, 1, 1, 1.14 in the low TI group, for �it respectively

equal to 1%, 2%, 3%, and imedt � imint . These optimal values of � , along with peak Sharpe ratios,

are reported in Table 6, panel (a). For both high and low TI, in all four specifications of �it, the

Sharpe ratio for the augmented carry is higher than for the plain carry. Gains from conditioning

on PPP are also displayed in Figure 5, where we plot the evolution of 1 Dollar over time under

both strategies. In the high TI case, the augmented carry earns higher average returns than

the plain carry. Moreover, the augmented strategy is less risky, largely avoiding the 2008 crash

suffered by the plain carry. In the low TI case, the augmented carry’s mean return surpasses the

plain carry’s by an even wider margin than in the high TI case, while volatility is similar for both

strategies.20

This in-sample comparison, however, may exaggerate the benefits of conditioning on PPP,

because � is chosen with the benefit of hindsight. A ‘fairer’ test is to compare both strategies out-

of-sample. To simulate the out-of-sample augmented carry, we consider a hypothetical investor

who—for each year t 2 f1994; : : : ; 2012g—chooses � at the start of the year using only the data

available up to that point. That is, the investor sets � at the level that maximizes the augmented

carry’s Sharpe ratio over the period January 1986 - December t�1, and updates � yearly. For both

20Due to the composition of the two groups, the 2008 carry crash is less pronounced for low TI. The high TI groupincludes many major/minor pairs, such as USD/MXN, or USD/TRY. The low TI group, on the other hand, containsmany minor/minor pairs, such as MXN/TRY. In the crash, there was a sharp unwinding of carry trades in the high TIgroup, as investors rushed to the safety of the USD. On the other hand, in the low TI group, all minor currencies werefalling and therefore the overall effect was much more muted.

18

high and low TI, and for all four specifications of the interest rate condition, the out-of-sample

values of � fluctuate within a relatively narrow range of the in-sample values reported above,

with the maximizing value of � being higher in the low TI group most years. Using these values

of � , we simulate the augmented carry over the period January 1994 - December 2012, and report

performance statistics in Table 6 (B). As expected, the gains from conditioning on PPP weaken to

some extent, especially in the high TI case. For�it = 3%; and�it = imedt � imint , out-of-sample

results are similar to in-sample results. The augmented carry is clearly superior to the plain carry,

both due to higher returns and lower risk, most notably at the time of the 2008 crash. However,

for�it = 1% and�it = 2%, the augmented carry has similar volatility and slightly lower returns

than the plain carry, resulting in a mildly lower Sharpe ratios. Inspecting all cases together in

Figure 6 (A), the augmented carry comes out slightly behind in the first two graphs, but clearly

ahead in the third and fourth. In the low TI case, results remain favorable to the augmented carry.

As reported in Table 6 (B), the augmented carry has higher Sharpe ratios than the plain carry for

three out of four specifications of the interest rate condition, and higher mean returns for all four

specifications. This is clearly visible in Figure 6 (B), where the augmented carry finishes ahead

of the plain carry in all four plots.

Overall, we find conditioning on PPP to be more useful in the low TI portfolio, where ex-

change rates tend to deviate further from long-run values. This raises potential losses from

wrong predictions and gains from correct ones, as compared with the high TI case. Since in-

terest differentials are similar in both groups, staying out of trades has a similar opportunity

cost, while predicting larger swings in the low TI case provides a greater benefit.

6 Conclusion

This paper explores the interaction between exchange rate volatility and fundamentals by exam-

ining the role of TI in the reversion of exchange rates to long-run equilibrium values, as given by

purchasing power parity (PPP). Following the recent literature on nonlinearity, we estimate an

ESTAR model, which allows the speed at which exchange rates converge to their long-run equi-

librium to depend on the size of the deviations. We find estimates of the half-lives of deviations

from PPP to be higher the less intense the trade relationship between two countries. These re-

19

sults continue to hold as we perform a series of robustness tests, such as including/excluding in-

terest rates as explanatory variables, focusing on different subsamples, and experimenting with

different window widths to compute volatility. When including interest rates, we find that ex-

change rate volatility increases with the absolute value of interest rate differentials, which is con-

sistent with the notion that carry trades tend to exacerbate fluctuations in currency markets. We

also verify that the faster convergence to equilibrium values observed for high TI pairs does not

appear to be driven by Central Bank intervention. Finally, we investigate whether our findings

can be useful to improve the performance of a well-known currency trading strategy, the carry

trade. We consider strategies that combine a carry-trade component—investing in high-interest

rate currencies—with a fundamental component—purchasing currencies only if undervalued

according to relative PPP. Our findings suggest that an augmented carry trade strategy that con-

ditions on PPP fundamentals tends to perform better—in terms of higher Sharpe ratios—than a

plain carry strategy which blindly chases interest rate differentials. These findings hold in- and

out-of-sample, although they are a bit weaker in the latter case. Gains from conditioning on PPP

are generally greater for low TI currency pairs.

7 Acknowledgements

This paper has benefited from discussion with or comments by Richard Baillie, Kirt Butler, Jinill

Kim, Seunghwa Rho as well as by the Editor, Eric van Wincoop, and two anonymous refer-

ees. We would also like to thank participants at Yonsei University, Korea University, the 2010

Midwest Macroeconomics Meetings, 2010 Midwest Econometrics Group Annual Meetings, and

2011 Eastern Finance Association Annual Meetings, 2012 Econometric Society’s North American

Summer Meetings, and 2012 Australasian Meeting of Econometric Society for helpful comments.

Any remaining errors are solely the authors’ responsibility.

8 Appendix

In the appendix, we briefly introduce the ESTAR model, and describe how to estimate half-lives

of deviations from PPP.

20

8.1 The ESTAR model

The regime-switching model known as Smooth Transition Autoregressive (STAR), was developed

by Granger and Teräsvirta (1993), and Teräsvirta (1994). In this model, adjustment takes place

every period but the speed of adjustment varies with the extent of the deviation from equilib-

rium. When reparameterized in first difference form, the STAR model for the real exchange rate

qt can be written as

�qt = �+ �qt�1 +p�1Pj=1

�j�qt�j +

"�� + ��qt�1 +

p�1Pj=1

��j�qt�j

#� (qt�d; ; c) + "t (11)

where�qt�j = qt�j � qt�j�1, fqtg is a stationary and ergodic process, "t � iid�0; �2

�, and � (�) is

the transition function that determines the degree of mean reversion and itself governed by the

parameter , which determines the speed of mean reversion to PPP. The delay parameter d (> 0)

is an integer. The ESTAR model is the variant of the STAR model where transition is governed by

the exponential function

� (qt�d; ; c) = 1� exph� (qt�d � c)2 =�qt�d

iwith > 0 (12)

where qt�d is a transition variable, �qt�d is the standard deviation of qt�d, is a slope parameter,

and c is a location parameter. The restriction on the parameter ( > 0) is an identifying restric-

tion. The exponential function in Equation (12) is bounded between 0 and 1, and depends on

the transition variable qt�d. The values taken by the transition variable qt�d and the transition

parameter together will determine the speed of mean reversion to PPP.21 ESTAR models are

estimated by nonlinear least squares (NLS), with the starting values obtained from a grid search

over and c. The estimations are also implemented with the selected lag order p and delay pa-

rameter d which are suggested by the partial autocorrelation function (PACF) and the linearity

tests results, respectively, for both high and low TI currency pairs.

21For any given value of qt�d, the transition parameter determines the slope of the transition function, and thusthe speed of transition between two regimes, with low values of implying slower transitions.

21

8.2 Estimation of half-lives of deviations from PPP

We investigate the dynamic adjustment in response to the shock of the estimated ESTAR model

by computing generalized impulse response functions. The generalized impulse response func-

tion (GI), proposed by Koop et al. (1996) avoids the problem of using future information by

taking expectations conditioning only on the history and on the shock. GI may be considered as

the realization of a random variable defined as

GIq (h; "t;t�1) = E [qt+h j "t;t�1]� E [qt+h j t�1] (13)

for h = 0; 1; 2; :::. In Equation (13), the expectation of qt+h given that the shock occurs at time t

is conditional only on the history and on the shock. We generate GI functions using the Monte

Carlo integration method developed by Gallant et al. (1993). For the history and the initial shock,

we compute GI�q (h; �; !t�1) for horizons h = 0; 1; 2; :::; 100. The conditional expectations in

Equation (13) are estimated as the means over 2000 realizations of�qt+h, accomplished by iter-

ating on the ESTAR model, with and without using the selected initial shock to obtain �qt and

using randomly sampled residuals of the estimated ESTAR model elsewhere. Impulse responses

for the level of the real exchange rate, qt are obtained by accumulating the impulse responses for

the first differences. The initial shock is normalized to 1, and the half-lives of real exchange rates

to the shock are calculated by measuring the discrete number of months taken until the shock

to the level of the real exchange rate has fallen below a half.

22

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088

0.19

629

0.13

207

0.03

167

0.01

043

0.00

494

0.00

526

0.19

729

0.00

888

Swit

zerl

and

0.01

226

0.01

013

0.33

322

0.08

290

0.04

181

0.01

195

0.00

672

0.00

463

0.01

181

0.01

409

0.03

347

Turk

ey0.

0060

30.

0077

60.

2354

70.

0764

20.

0302

00.

0152

50.

0009

90.

0019

50.

0058

50.

0055

70.

0175

70.

0352

5U

nite

dSt

ates

0.12

948

0.59

842

0.16

175

0.18

303

0.36

772

0.22

461

0.49

911

0.10

091

0.05

076

0.20

369

0.08

643

0.09

857

0.11

025

No

te.V

alu

esfo

rtr

ade

inte

nsi

ty(m

axim

um

)an

dtr

ade

inte

nsi

ty(a

vera

ge)

aver

aged

over

the

sam

ple

per

iod

1980

-200

5ar

ere

po

rted

.

26

TABLE 2. EFFECTS OF TI ON REAL EXCHANGE RATE VOLATILITY

: IV ESTIMATION USING PANEL DATA

[1] [2] [3] [4]

Real exchange rate volatility at time t-1 0.121�� 0.122��

(0.021) (0.021)

TI (maximum) -0.037�� -0.033��

(0.007) (0.008)

TI (average) -0.056�� -0.050��

(0.011) (0.012)

Interest rate differential in absolute value 0.034�� 0.033�� 0.034�� 0.034��

(0.004) (0.004) (0.004) (0.004)

Intercept 0.045�� 0.045�� 0.039�� 0.039��

(0.003) (0.003) (0.003) (0.003)

No. of observations 2366 2366 2275 2275

Note. Results from IV estimation using panel data with country fixed effects are reported. The dis-

tance between two countries is used as an instrument to estimate the relationship between trade

intensity and real exchange rate volatility. The sample period is from January 1980 to December 2005,

and 91 currency pairs involving 14 countries are included. The dependent variable is real exchange

rate volatility. Standard errors are reported in parentheses below the corresponding coefficients. As-

terisks *, **, and *** indicate 10%, 5%, and 1% statistical significance, respectively.

27

TABLE 3. (A) EFFECTS OF TI ON REAL EXCHANGE RATE VOLATILITY

: CONTROLLING FOR THE EXCHANGE RATE REGIME

Robustness checks

Controlling for the exchange rate regime

[1] [2] [3] [4]

Real exchange rate volatility at time t-1 0.138�� 0.137��

(0.025) (0.025)

TI (maximum) -0.031�� -0.029��

(0.008) (0.008)

TI (average) -0.049�� -0.045��

(0.012) (0.012)

Interest rate differential in absolute value 0.035�� 0.035�� 0.035�� 0.035��

(0.005) (0.005) (0.005) (0.005)

Fixed exchange rate regime dummy -0.017�� -0.018�� -0.015�� -0.017��

(0.005) (0.005) (0.005) (0.005)

Intercept 0.035�� 0.035�� 0.029�� 0.029��

(0.005) (0.005) (0.005) (0.005)

No. of observations 1653 1653 1575 1575

Note. Results from IV estimation using panel data with country fixed effects are reported. We drop

all pairs involving currencies linked to trade-weighted exchange rate indices. These include AUD

and NZD over 1980-83, SEK and NOK over 1980-92, and SGD over 1980-2005. We also include a

“fixed” dummy variable which takes on a value of one for currency pairs, KRW/USD over 1980-96,

MXN/USD over 1980-93, TRY/USD over 1980-99, and CHF/EUR over 1980-81 under the fixed ex-

change rate regimes, and a value of zero, otherwise.

28

TA

BL

E3

.(B

)E

FF

EC

TS

OF

TI

ON

RE

AL

EX

CH

AN

GE

RA

TE

VO

LA

TIL

ITY

:T

RU

NC

AT

ING

OU

TL

IER

S

Robu

stne

ssch

ecks

Trun

cati

ngou

tlier

sfo

rrea

lexc

hang

era

tevo

lati

lity

Trun

cati

ngou

tlier

sfo

rTI

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

Real

exch

ange

rate

vola

tilit

yat

tim

et-

10.

139�

��0.

140�

��0.

127�

��0.

124�

��

(0.0

16)

(0.0

16)

(0.0

21)

(0.0

21)

TI(m

axim

um)

-0.0

45��

-0.0

40��

-0.0

40��

-0.0

36��

(0.0

06)

(0.0

06)

(0.0

11)

(0.0

11)

TI(a

vera

ge)

-0.0

68��

-0.0

61��

-0.0

55��

-0.0

49��

(0.0

09)

(0.0

09)

(0.0

17)

(0.0

17)

Inte

rest

rate

diff

eren

tial

inab

solu

teva

lue

0.01

7��

0.01

7��

0.01

6��

0.01

6��

0.03

3��

0.03

3��

0.03

4��

0.03

4��

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

04)

(0.0

04)

(0.0

05)

(0.0

05)

Inte

rcep

t0.

037�

��0.

037�

��0.

052�

��0.

051�

��0.

045�

��0.

061�

��0.

039�

��0.

052�

��

(0.0

02)

(0.0

02)

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

04)

(0.0

03)

(0.0

05)

No.

ofob

serv

atio

ns22

3522

3521

4721

4723

1423

1422

2522

25

No

te.R

esu

lts

fro

mIV

esti

mat

ion

usi

ng

pan

eld

ata

wit

hco

un

try

fixe

def

fect

sar

ere

po

rted

.We

tru

nca

teo

utl

iers

for

real

exch

ange

rate

vola

tili

ty,

and

ou

tlie

rsfo

rT

I,re

spec

tive

ly.

29

TA

BL

E3

.(C

)E

FF

EC

TS

OF

TI

ON

RE

AL

EX

CH

AN

GE

RA

TE

VO

LA

TIL

ITY

:S

UB

SA

MP

LIN

G-

FIR

ST

VE

RS

US

SE

CO

ND

HA

LF

OF

SA

MP

LE

PE

RIO

D

Rob

ustn

ess

chec

ksSu

bper

iod

for1

980-

1992

Subp

erio

dfo

r199

3-20

05[1

][2

][3

][4

][1

][2

][3

][4

]R

eale

xcha

nge

rate

vola

tilit

yat

tim

et-

10.

108�

��0.

110�

��0.

103�

��0.

103�

��

(0.0

32)

(0.0

32)

(0.0

30)

(0.0

30)

TI(m

axim

um)

-0.0

41��

-0.0

38��

-0.0

32��

-0.0

28��

(0.0

12)

(0.0

12)

(0.0

09)

(0.0

10)

TI(a

vera

ge)

-0.0

63��

-0.0

59��

-0.0

48��

-0.0

43��

(0.0

18)

(0.0

19)

(0.0

14)

(0.0

15)

Inte

rest

rate

diff

eren

tial

inab

solu

teva

lue

0.01

7��

0.01

6��

0.01

20.

011

0.04

4��

0.04

4��

0.04

4��

0.04

4��

(0.0

07)

(0.0

07)

(0.0

08)

(0.0

08)

(0.0

06)

(0.0

06)

(0.0

06)

(0.0

06)

Inte

rcep

t0.

039�

��0.

040�

��0.

053�

��0.

053�

��0.

042�

��0.

042�

��0.

037�

��0.

037�

��

(0.0

05)

(0.0

05)

(0.0

05)

(0.0

05)

(0.0

04)

(0.0

04)

(0.0

05)

(0.0

05)

No.

ofob

serv

atio

ns11

8311

8310

9210

9211

8311

8310

9210

92

No

te.

Res

ult

sfr

om

IVes

tim

atio

nu

sin

gp

anel

dat

aw

ith

cou

ntr

yfi

xed

effe

cts

are

rep

ort

ed.

Th

een

tire

sam

ple

per

iod

isd

ivid

edin

totw

o

sub

per

iod

s:19

80-1

992

(afi

rsth

alf)

and

1993

-200

5(a

seco

nd

hal

f).

30

TA

BL

E3

.(D

)E

FF

EC

TS

OF

TI

ON

RE

AL

EX

CH

AN

GE

RA

TE

VO

LA

TIL

ITY

:S

UB

SA

MP

LIN

GM

AJO

RV

S.

MIN

OR

CU

RR

EN

CY

PA

IRS

Rob

ustn

ess

chec

ks42

maj

orcu

rren

cypa

irs

49m

inor

/exo

tic

curr

ency

pair

s[1

][2

][3

][4

][1

][2

][3

][4

]R

eale

xcha

nge

rate

vola

tilit

yat

tim

et-

10.

104�

��0.

104�

��0.

090�

��0.

091�

��

(0.0

32)

(0.0

32)

(0.0

29)

(0.0

29)

TI(m

axim

um)

-0.0

35��

-0.0

31��

-0.0

39��

-0.0

39��

(0.0

06)

(0.0

07)

(0.0

14)

(0.0

14)

TI(a

vera

ge)

-0.0

53��

-0.0

47��

-0.0

63��

-0.0

62��

(0.0

10)

(0.0

10)

(0.0

22)

(0.0

23)

Inte

rest

rate

diff

eren

tial

inab

solu

teva

lue

0.20

1��

0.19

9��

0.18

4��

0.18

2��

0.03

0��

0.03

0��

0.03

2��

0.03

1��

(0.0

21)

(0.0

21)

(0.0

22)

(0.0

22)

(0.0

05)

(0.0

05)

(0.0

05)

(0.0

05)

Inte

rcep

t0.

040�

��0.

041�

��0.

035�

��0.

037�

��0.

051�

��0.

051�

��0.

061�

��0.

061�

��

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

04)

(0.0

07)

(0.0

07)

(0.0

09)

(0.0

09)

No.

ofob

serv

atio

ns10

9210

9210

5010

5012

7412

7412

2512

25

No

te.

Res

ult

sfr

om

IVes

tim

atio

nu

sin

gp

anel

dat

aw

ith

cou

ntr

yfi

xed

effe

cts

are

rep

ort

ed.

91cu

rren

cyp

airs

are

div

ided

into

42m

ajo

ran

d49

min

or/

exo

tic

curr

ency

pai

rs.

31

TA

BL

E3

.(E

)E

FF

EC

TS

OF

TI

ON

RE

AL

EX

CH

AN

GE

RA

TE

VO

LA

TIL

ITY

:D

EF

ININ

GV

OL

AT

ILIT

YU

SIN

GD

IFF

ER

EN

TT

IME

WIN

DO

WS

Rob

ustn

ess

chec

ks 3-ye

arw

indo

w6-

year

win

dow

[1]

[2]

[3]

[4]

[1]

[2]

[3]

[4]

Rea

lexc

hang

era

tevo

lati

lity

atti

me

t-1

0.03

80.

040

0.06

20.

062

(0.0

39)

(0.0

39)

(0.0

62)

(0.0

62)

TI(m

axim

um)

-0.0

69��

-0.0

58��

-0.0

65��

-0.0

48��

(0.0

16)

(0.0

17)

(0.0

22)

(0.0

24)

TI(a

vera

ge)

-0.1

05��

-0.0

88��

-0.0

98��

-0.0

73��

(0.0

24)

(0.0

26)

(0.0

33)

(0.0

36)

Inte

rest

rate

diff

eren

tial

inab

solu

teva

lue

0.06

4��

0.06

3��

0.07

5��

0.07

4��

0.11

0��

0.10

9��

0.11

5��

0.11

4��

(0.0

10)

(0.0

10)

(0.0

11)

(0.0

11)

(0.0

16)

(0.0

16)

(0.0

16)

(0.0

16)

Inte

rcep

t0.

070�

��0.

070�

��0.

054�

��0.

055�

��0.

096�

��0.

095�

��0.

051�

��0.

051�

��

(0.0

07)

(0.0

07)

(0.0

07)

(0.0

08)

(0.0

09)

(0.0

09)

(0.0

10)

(0.0

10)

No.

ofob

serv

atio

ns81

981

972

872

845

545

536

436

4

No

te.

Res

ult

sfr

om

IVes

tim

atio

nu

sin

gp

anel

dat

aw

ith

cou

ntr

yfi

xed

effe

cts

are

rep

ort

ed.

Vola

tilit

yis

com

pu

ted

over

3-ye

aran

d6-

year

per

iod

s.

32

TABLE 4. HALF-LIFE ESTIMATES FOR REAL EXCHANGE RATES

High TI currency pairs Low TI currency pairs

Half-life Half-life

USD/CAD 32 TRY/SEK 23

USD/MXN 16 CAD/AUD 11

USD/JPY 31 TRY/KRW 43

CHF/EUR 5 SEK/AUD 12

GBP/EUR 26 CHF/SGD 29

TRY/EUR 24 MXN/CAD 28

USD/KRW 7 NZD/CAD 35

KRW/JPY 13 CHF/AUD 36

NZD/AUD 35 CHF/KRW 17

USD/SGD 56 CHF/NOK 23

SEK/NOK 36 SEK/CAD 21

SEK/EUR 15 NOK/KRW 7

JPY/AUD 22 SEK/KRW 12

GBP/NOK 3 GBP/MXN 17

USD/GBP 14 CHF/CAD 41

SGD/JPY 25 MXN/KRW 22

USD/EUR 15 SEK/SGD 19

NOK/EUR 6 TRY/CAD 33

GBP/SEK 12 SGD/NOK 28

USD/AUD 17 SGD/CAD 53

USD/TRY 39 CHF/MXN 21

NZD/JPY 24 TRY/AUD 39

USD/NZD 19 TRY/NOK 41

USD/CHF 18 TRY/SGD 32

JPY/EUR 27 SEK/NZD 23

USD/SEK 18 SEK/MXN 49

GBP/CHF 27 CHF/NZD 6

GBP/TRY 17 NZD/MXN 24

GBP/JPY 31 SGD/MXN 26

SGD/AUD 16 NOK/AUD 16

SGD/KRW 1 MXN/AUD 27

KRW/AUD 4 TRY/NZD 27

GBP/AUD 21 NOK/NZD 6

GBP/NZD 12 TRY/MXN 27

USD/NOK 23 NOK/MXN 48

Average 20.20 26.34

Note. The half-life is measured as the discrete number of months taken until

the shock to the level of the real exchange rate has fallen below a half.

33

TABLE 5. PROXIES FOR OFFICIAL INTERVENTION

Probability that the monthly change is

Greater than�4 percent

Within a�2:5 percent band: (400 basis points):

Country Reserves Nominal interest rate

Australia 39.37 0.00

Canada 43.97 1.72

Euro Area 66.09 0.00

Great Britain 60.63 0.00

Japan 81.03 0.00

Korea 49.14 0.57

Mexico 41.38 14.66

New Zealand 23.85 2.01

Norway 38.22 0.29

Singapore 78.74 0.00

Sweden 38.79 1.44

Switzerland 45.40 0.29

Turkey 30.46 29.89

United States 68.39 0.29

Note. Indicators of foreign exchange reserves volatility and interest rate volatility

over the period January 1980 - December 2008.

34

TABLE 6. SUMMARY STATISTICS FOR CARRY TRADE PORTFOLIOS

(A) IN-SAMPLE: JAN. 1986 - DEC. 2012

High TI currency pairs

�it = 1% �it = 2% �it = 3% �it = imedt � imint

Plain Augmented Plain Augmented Plain Augmented Plain Augmented

� = 0 � = 0:95 � = 0 � = 0:95 � = 0 � = 0:97 � = 0 � = 0:95

Average 1 month return 0.377% 0.450% 0.465% 0.562% 0.518% 0.622% 0.633% 0.724%

Standard deviation 0.016 0.017 0.019 0.018 0.021 0.020 0.024 0.021

Annualized Sharpe ratio 0.811 0.930 0.860 1.058 0.858 1.086 0.918 1.197

Low TI currency pairs



� = 0 � = 1 � = 0 � = 1 � = 0 � = 1 � = 0 � = 1:14




35

(B) OUT–OF-SAMPLE: JAN. 1994 - DEC. 2012

High TI currency pairs



� = 0 Varying � � = 0 Varying � � = 0 Varying � � = 0 Varying �




Low TI currency pairs



� = 0 Varying � � = 0 Varying � � = 0 Varying � � = 0 Varying �




36

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

Trade intensity (maximum)

Rea

l exc

hang

e ra

te v

olat

ility

VOL = 0.051 0.031 TI_max (0.002) (0.008)

(A) SCATTER PLOT OF REAL EXCHANGE RATE VOLATILITY AGAINST TRADE INTENSITY (MAXIMUM)

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

Trade intensity (average)

Rea

l exc

hang

e ra

te v

olat

ility

VOL = 0.051 0.051 TI_avg (0.002) (0.012)

(B) SCATTER PLOT OF REAL EXCHANGE RATE VOLATILITY AGAINST TRADE INTENSITY (AVERAGE)

FIGURE 1. SCATTER PLOTS OF REAL EXCHANGE RATE VOLATILITY AGAINST TRADE INTENSITY FOR 91

CURRENCY PAIRS INVOLVING 14 COUNTRIES OVER THE PERIOD 1980-2005. THE STRAIGHT LINE IS

DEPICTED BY RUNNING THE ORDINARY LEAST SQUARES (OLS) REGRESSION. THE OLS ESTIMATES

ARE REPORTED ABOVE, AND THE CORRESPONDING STANDARD ERRORS ARE IN PARENTHESES.

37

FIGURE 2. (A) GIS FOR 35 HIGHEST TI CURRENCY PAIRS

38

FIGURE 2. (B) GIS FOR 35 LOWEST TI CURRENCY PAIRS

39

t<3

.48

(1%

)3

.48<

t<

2.93

(5%

)

2.9

3<t

<2.

66 (1

0%)

2.6

6<t<

22

<t<

10<

t<1

024681012

USD

/KR

WJP

Y/AU

DU

SD/G

BPC

HF/

EUR

USD

/NZD

SGD

/AU

DG

BP/A

UD

GBP

/NZD

TRY/

EUR

KRW

/JPY

SEK/

EUR

JPY/

EUR

USD

/SEK

NZD

/AU

D

USD

/MXN

USD

/JPY

GBP

/EU

RU

SD/S

GD

SGD

/JPY

USD

/TR

YG

BP/T

RY

KRW

/AU

DU

SD/N

OK

1<t

<01<

t<2

2<t<

33<

t<4

USD

/CAD

SEK/

NO

KG

BP/N

OK

USD

/EU

RN

OK/

EUR

GBP

/SEK

USD

/AU

DN

ZD/J

PYU

SD/C

HF

GBP

/CH

FG

BP/J

PYSG

D/K

RW

t<3

.48

(1%

)3

.48<

t<

2.93

(5%

)

2.9

3<t

<2.

66 (1

0%)

2.6

6<t<

22

<t<

10<

t<1

024681012

1<t

<02<

t<3

1<t<

2

TRY/

SEK

TRY/

KRW

CH

F/SG

DM

XN/C

ADC

HF/

CAD

SGD

/CAD

TRY/

NO

KTR

Y/SG

DM

XN/A

UD

CH

F/KR

WN

OK/

KRW

SEK/

KRW

GBP

/MXN

CH

F/M

XNN

OK/

NZD

SEK/

CAD

NZD

/CAD

CH

F/AU

DC

HF/

NO

KM

XN/K

RW

SEK/

SGD

SGD

/NO

KTR

Y/AU

DSE

K/M

XNSG

D/M

XNTR

Y/N

ZDTR

Y/M

XNN

OK/

MXN

3<t<

4

CAD

/AU

DSE

K/AU

DSE

K/N

ZDC

HF/

NZD

NZD

/MXN

NO

K/AU

D

TRY/

CAD

(A)

KS

ST

ES

TR

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40

(A) �it = 1%

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 220.40.2

00.20.40.60.8

11.21.4

Threshold ( τ)A

unnu

aliz

ed S

harp

e ra

tio

High TILow TI

(B) �it = 2%

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 220.40.2

00.20.40.60.8

11.21.4

Threshold ( τ)

Aun

nual

ized

Sha

rpe

ratio

(C) �it = 3%

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 220.40.2

00.20.40.60.8

11.21.4

Threshold ( τ)

Aun

nual

ized

Sha

rpe

ratio

(D) �it = imedt � imint

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 220.40.2

00.20.40.60.8

11.21.4

Threshold ( τ)

Aun

nual

ized

Sha

rpe

ratio

FIGURE 4. ANNUALIZED SHARPE RATIOS AS A FUNCTION OF THE PPP THRESHOLD (� )

41

(A) HIGH TI CURRENCY PAIRS (B) LOW TI CURRENCY PAIRS

�it = 1% �it = 1%

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9Plain CarryAugmented Carry

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

�it = 2% �it = 2%

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

�it = 3% �it = 3%

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

�it = imedt � imint �it = i

medt � imint

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

86 88 90 92 94 96 98 00 02 04 06 08 10 12

1

3

5

7

9

11

13

FIGURE 5. IN-SAMPLE PERFORMANCE OF CARRY TRADE PORTFOLIOS ( JAN. 1986 -

DEC. 2012): EVOLUTION OF ONE DOLLAR OVER TIME

42

(A) HIGH TI CURRENCY PAIRS (B) LOW TI CURRENCY PAIRS

�it = 1% �it = 1%

94 96 98 00 02 04 06 08 10 12

1

2

3

4Plain CarryAugmented Carry

94 96 98 00 02 04 06 08 10 12

1

2

3

4

�it = 2% �it = 2%

94 96 98 00 02 04 06 08 10 12

1

2

3

4

94 96 98 00 02 04 06 08 10 12

1

2

3

4

�it = 3% �it = 3%

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

�it = imedt � imint �it = i

medt � imint

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

94 96 98 00 02 04 06 08 10 12

1

2

3

4

5

6

FIGURE 6. OUT-OF-SAMPLE PERFORMANCE OF CARRY TRADE PORTFOLIOS ( JAN.

1994 - DEC. 2012): EVOLUTION OF ONE DOLLAR OVER TIME

43

TradeIntensityandPurchasingPowerParitydoblasma/Trade_PPP_Carry.pdf · By contrast, export driven transactions ... volatility increases with the absolute value of interest rate ...

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