## Abstract

We discuss currency volatility as a measure of currency instability using 15 currencies from developed and emerging economies. The IMF and others have recorded how countries manage their exchange rates to promote sustainable economic growth by designing exchange rate regimes as a pillar within economic policy. The findings herein show how to track currency instability using a given currency's volatility against the volatility of a benchmark currency of importance to the given currency. This is termed relative volatility. The study proceeds to test whether the parity factors and country risk factor are significantly correlated with exchange rate relative volatility.

## 1.  Introduction

The aim of this paper is to provide a new concept—namely, relative volatility—as a suitable measure of instability of a phenomenon and apply it as an appropriate measure to track a target currency's instability in developed and emerging economies to learn some lessons for currency management policy. Instability of currencies of a single country or a group of countries could be tracked applying this idea. Next, the study investigates whether the widely used two-key monetary factors (i.e., relative inflation and relative interest rate) as well as a country risk factor (from the international capital asset pricing model, ICAPM) are in fact the significant drivers of the relative volatility (that is, the changeability) of a given currency or a group of currencies relative to a benchmark currency.

The countries selected for study fall into seven free-floating currencies (UK, Canada, EU, Japan, Switzerland, Sweden, and Norway) and eight floating countries (Brazil, India, Indonesia, Korea, Malaysia, the Philippines, Thailand, and Turkey) using monthly as well as quarterly data of each of these currencies against the US$exchange rates over 1998 to 2017. Malaysia, which is categorized as “other managed arrangement (or residual)”, is the only exception in terms of currency regime classification by the IMF. The relative measure has never been used to study any of these currencies.1 Exchange rate volatility has been at the center of several financial crises, and continues to derail sustainable economic growth, perpetrate economic declines, and concurrently also precipitate financial instability. Thus, we are motivated to contribute this idea to better benchmark the volatility that is at the center of instability. The relative volatility is the rate of change of a currency, measured as the standard deviation of the square root of the volatility of a currency divided by the standard deviation of a relevant benchmark currency that matters for analysis (e.g., the US$). If the standard deviations of each of the two are the same, then we have a relative volatility ratio equal to 1.00—indicating a stable relationship with the target currency. If a given currency's volatility is higher than the volatility of the benchmark, the relative volatility is greater than 1.00 (indicating growing instability); the converse is a value less than 1.00, which means that the currency is becoming less volatile—as, for example, if a new monetary policy reduces the given currency's standard deviation of its currency (see Appendix for relevant definitions).

Pursuing exchange rate stability has become a major concern within economic policy circles since 1973, when the international monetary regime, the Bretton Woods system, was ended, replacing the US$-cum-gold standard with free-floating or other currency management regimes. How well currency stability is achieved by a given country could be measured using three new ideas suggested here: relative volatility, degree of cointegration, and speed of adjustment to benchmark currency of peers. We explore these ideas by applying these measures to the experiences of several major countries with a free-floating exchange rate regime over some 20 years. Currency behavior is a window to economic significance of events that shape economic development. The Brexit vote in June 2016 led the UK currency, the pound sterling, to decline by about 11 percent. That is a massive correction predicting impending exchange rate volatility for the British currency, with consequences likely to linger for decades: at press time, the British currency has lost further ground. In this paper, we apply a new measure of currency volatility relative to a chosen trading country, which enables an observer to track a given behavior of a currency relative to a target country or region, as the case may require. We use the relative volatility measure as a dependent variable to identify how this relative measure is correlated with monetary theory and country risk factors as explained in Section 3. Although the study of exchange rate dynamics has been extensive over a century of research on this subject, there is a dearth of published material on how to measure exchange rate volatility beyond using the standard deviation (SD) or the coefficient of variation (CoV) of a given currency over a given period or the value-at-risk (VaR) measure. These measures are inadequate for two reasons. First, what matters for tracking instability of a phenomenon such as exchange rate is how to relate one currency's measure relative to a class to which that currency belongs as being relevant for policy reasons. Such a measure would be more appropriate for not just tracking but also for ranking a given currency against a benchmark considered appropriate for any set of trade-linked economies such as the EU or a closely linked central currency, the U.S. dollar (US$). That is, a measure of volatility of a currency must be in relation to a country (or group) with which the currency has relevance or importance—say, through trade linkages as argued in this paper. The link could well be capital flow or other economic benefits that accrue to a country in relation to another country or group of countries. Thus the stability of UK's pound sterling should be measured relative to, say, the EU currency or US$because these two groups have intense trade relations with the UK. The second reason why SD or CoV is inappropriate is that these measures are one currency's behavior against itself, so these do not qualify as a more accurate ranking device across a meaningful group that is the benchmark based on common linkages such as trade. Besides, making a measure relative to a desirable target enables a more meaningful way of representing the relationship of a currency with the target of comparison. As is the VaR, which measures the impact on, say, an entity's core capital, from an $x$ percent depreciation. For these reasons, a measure relative to a benchmark (be it the currency of a trade-linked country or the average currency value of a group of trade-linked countries such as NAFTA) is required. This benchmark is illustrated in this paper by using a US$ proxy as the benchmark. Any other currency could be used as long as the chosen benchmark currency is relevant for the given country. More details of how this is done is found in Section 3 and in the Appendix. Using this relative measure, we can illustrate how a given currency's stability could be mapped relative to the benchmark. We further propose an alternative measure of risk, the theory-consistent (Solnik 1974; Lessard 1976) country risk measure in the international capital asset pricing model, when we searched for factors that drive the relative volatility.

Figures 1 to 3 are representations of how selected exchange rates covered in this paper have evolved over 20 years covering two business cycles. Figure 1 shows the plots of the seven free-floating currencies against the US$. Figure 1. Relative volatility of floating currencies to base year Note:CAD = Canadian dollar; EURO = euro; JPY = Japanese yen; NOK = Norwegian krone; SEK = Swedish krona; CHF = Swiss franc; GBP = British pound sterling. Figure 1. Relative volatility of floating currencies to base year Note:CAD = Canadian dollar; EURO = euro; JPY = Japanese yen; NOK = Norwegian krone; SEK = Swedish krona; CHF = Swiss franc; GBP = British pound sterling. It is evident when reviewing the plots that all seven currencies have experienced change in value. All currencies were represented as starting at an index value of 100 (the straight line). The Canadian dollar, the British pound, and Swedish krona experienced greater volatility than the others (i.e., euro, yen, krone, and franc). We present the plots of floating currencies of developing countries in Figure 2. Three currencies—those of Brazil, India, and Turkey—have relatively more relative volatility than the other five currencies. The Thai bhat, Indonesian rupiah, and the Malaysian ringgit have the lowest volatility among these eight cases. Relative to free-floating country volatility, the eight plots show very high volatility values. This means that the emerging economies have about four times the volatility of free-floating currencies. This is noteworthy. One conclusion supported by these plots is that free-floating countries experience volatilities at about one-fourth that of developing countries. This comparison is only valid if we take the volatility as starting at a base year. If the base year changes, then this conclusion also changes. Figure 2. Relative volatility of floating currencies to base year Note:BRL = Brazilian real; INR = Indian rupee; IDR = Indonesian ruppiah; KES = Kenyan shilling; KWR = Korean won; MYR = Malaysian ringgit; THB = Thai baht; TRY = Turkish lira. Figure 2. Relative volatility of floating currencies to base year Note:BRL = Brazilian real; INR = Indian rupee; IDR = Indonesian ruppiah; KES = Kenyan shilling; KWR = Korean won; MYR = Malaysian ringgit; THB = Thai baht; TRY = Turkish lira. Figure 3 shows the plots of the Malaysian ringgit in relation to five currencies of closely trade-linked countries to answer a policy question. Evidence of exchange rate behavior in Malaysia can also be found in Yoshino, Kaji, and Ibuka (2003). If one assumes that these five countries are closely linked (e.g., forming a trading group with large inter-country trade arrangements) then one could ask how a given country fares within the group. In this case we express the behavior of the ringgit against the other countries because we are interested in policymaking for the ringgit. The Malaysian ringgit has the same level of relative exchange rate value as the British pound, and the Philippine peso, meaning the ringgit holds its value as do the other two. The Malaysian ringgit depreciated the most against the Singapore dollar, followed by the US$, whereas there is appreciation against the Indonesian rupiah.

Figure 3.

Note:GBP = British pound sterling; INR = Indian rupee; MYR = Malaysian ringgit; PHP = Philippine peso; SGD = Singapore dollar; USD = U.S dollar.

Figure 3.

Note:GBP = British pound sterling; INR = Indian rupee; MYR = Malaysian ringgit; PHP = Philippine peso; SGD = Singapore dollar; USD = U.S dollar.

Hence, the use of our relative volatility measure enables a policymaker to address how to evaluate the currency from the national policy point of the ringgit. This figure is an example of Malaysian ringgit behavior in relation to the currencies of five trading partners. There is sign of significant depreciation of the ringgit against the US$, and appreciation against the Indonesian rupiah over the period of about three decades. This kind of analysis can be easily done for any country, so that the relative volatility becomes a policy-relevant tool to formulate which of the currencies of closely traded countries must be managed by which means to reduce the volatility of the ringgit (in this example) to levels that would promote stable currency value, as in Sussangkarn (2017). The overall aim of this policy formulation is to identify the target currencies for managing the monetary side of the currency. If done carefully, the long-run result will be a stable value for one's currency value. The rest of the paper is divided as follows. Section 2 describes the theoretical literature, and Section 3 discusses concept development and measurement equations. Section 4 then describes how the proposed measures could be used for ranking and other analyses using the eight selected currencies for this paper. Section 5 concludes. ## 2. Theoretical literature The focus of this paper is grounded in major theories in international finance and exchange rate determination: Cassel (1918) for purchasing power parity (PPP); Fisher (1930) for the international Fisher effect (IFE); and country risk in Solnik (1974). Even though these theories have been applied in most studies as well as regularly in practical policy decisions in a variety of contexts, there is still no unanimity of findings on the theory-predicted results, especially about the parity theorems. We believe a parsimonious approach may be valid before exploring the exchange rate movements as being determined by many variables across the board. Existing studies suggest large variation in several currency exchange rates, which started in earnest in 1973. Taylor and Taylor (2004) and Burnside, Eichenbaum, and Rebelo (2011) are recent reviews that suggest a continuing interest in this topic. Researchers have begun to re-examine exchange rate behavior, especially after the global financial crisis of 2008–09, when currency trading volume jumped almost 60 percent (Hatemi-J 2008; Dimitriou and Simos 2013). There is fresh interest in both theoretical and empirical studies on exchange rate determination. Under the monetarist approach of exchange rate determination, the PPP and the IFE are assumed to fully explain how currency exchange rates are determined. “Do they” or “Don't they” are the outcomes we explore. Recent researchers have added few non-parity factors (Ariff and Zarei 2016) to the two parity factors from monetary theories. Do these matter? Scant evidence is available that the PPP holds in the short run, although, using a novel approach, one study (Manzur and Ariff 1995) provides support for a long-run equilibrium (see also Hall et al. 2013). There is ample literature supporting the IFE on the exchange rate (Edison and Melick 1999). Hence, the literature relevant to this study is from studies on inflation and interest rate differences (Ho and Ariff 2012). ### 2.1 Purchasing power parity The PPP suggests that the exchange rate is periodically affected by the relative price differences in traded goods/services across any two trading-partner countries (Cassel 1918). PPP is often said to have originated in Spanish literature on inflation during the periods of gold importation from the New World. It examines the relationship between the exchange rates across different countries. It asserts that inflation, measured as price differentials across any two trading countries, should be offset by exchange rate changes. Hence, any two identical goods produced in any two countries are said to have a similar base price, as stated by the law of one price for the same basket of goods traded across two economies with different currencies. Scholars in international finance and macroeconomics have found PPP's potential for a wide range of applications, especially in the post–Bretton Woods era. It also provides a basis for international comparison of income and expenditure under an equilibrium condition, given an efficient arbitrage in goods traded. Most importantly, it is a theory for short-run as well as long-run exchange rate determination, whereby the authorities would set or steer a nominal exchange rate that satisfies international competition, the so-called Q ratio. The relative version of PPP states that a country's currency will be adjusted based on the ratio of the rate of inflation and its trading partner's inflation rate. Subject to periodic fluctuations of real exchange rates, there is a possibility for the relative PPP to hold in the long-run but not the short run. This study uses the relative version of PPP, as in the following equation: $lnEjt=aj+bjlnPtdPtfjt+μjt,$ (1) where, $E$ is the exchange rate of country $j$ over time period $t$, $Pd$ represents domestic prices, and $Pfrepresents$ foreign prices. ### 2.2 International Fisher effect A linkage between interest rate and inflation is postulated in a so-called theory of interest (Fisher 1930), which predicts that the nominal interest rate is equal to the sum of real interest and expected inflation rates, dubbed the domestic Fisher effect. There is a further prediction that such behavior would also lead to interest rate differences between any two nations by a corresponding change in the nominal exchange rates. The relationship between interest rate and inflation is one-to-one, assuming a world of perfect capital mobility with no transaction costs involved. Furthermore, the real interest rate is assumed to be unrelated to the expected inflation with its value determined solely by real economic factors such as capital productivity and investor time preference. This hypothesis plays a crucial role, given the fact that, subject to the correlation between real interest rate and inflation, the nominal interest rate will not be fully adjusted after a change in the expected inflation. Many studies have been conducted on the IFE theory, going back to the 1980s. Generally, the law of one price for interest rates (somewhat like PPP for real goods) holds when there is equilibrium in the foreign exchange market, whereby deposits of all currencies possess an identical rate of return. Any change in a country's interest rate will create disequilibrium in its currency, requiring long-term adjustments of the other country's exchange rate to restore the new equilibrium. In other words, the ratio of changes in exchange rates is determined by the ratio of domestic to foreign (relative) interest rates, as shown in the following equation: $Et+1Et=1+itd1+itf,$ (2) where $id$ is the domestic interest rate, $if$ represents the foreign interest rate, and $E$ is defined as in equation (1). Accordingly, the IFE states that the interest rate differences across countries are unbiased predictors of any future changes in the spot nominal exchange rates. Tests on this theorem suggest that the interest rate differences are correlated significantly with exchange rate changes, although most tests show that, because of underspecification of this relationship, the explained variation is very low (as shown by low R2 values in tests). Hence, there is also a need to re-examine whether such test results are due to simpler methodology used in prior research. Much of the findings in the literature emanate from the use of the existing methodology of cross-sectional or time series regression in previous studies (Hansen and Hodrick 1980; Mishkin 1984; Mark 1985; Edison 1987; Meese and Rogoff 1988; Throop 1993; Lee and Kim 2018). Only in recent years have papers with robust regression methodologies started to appear. We believe many of the findings we have reviewed in this section are the result of not using the latest econometric refinements. Hence, we believe that this topic should be revisited to see whether the robust estimators from these refinements would yield results to support the parity theorems. A third idea applied in this paper is measuring the country risk as the international beta risk in Solnik's theory. By finding the correlation of one country's stock index returns to the world stock index, we are able to use a country risk variable at the economy-wide level. This measure has been operationalized in Ariff and Marisetty (2012) and is measured using Solnik's model: $Rj,t=αj+βjRwt+ɛt,$ (3) $βj=Covrj,rwσw2,$ (4) where $Rj,t$ is the country's equity index annualized return for country $j$ over time $t$ and $Rw$ is the world equity index annualized return. As for the country risk, the coefficient $βj$ on the global stock index is an appropriate risk measure that could be an explanatory variable for currency behavior, although this has not been applied in any study to date. We propose to use this as a country risk measure to test whether this variable is correlated with currency behavior (exchange rate and/or volatility of exchange rate). ## 3. Concept development Instability of a phenomenon is usually measured by the volatility as the rate of change of a phenomenon X across time [as ln (Xt /Xt−1)] with t indicating interval of time used for measurement – in this paper, monthly intervals. The square root of volatility is then a measure of instability of the item measured, as in equation (1): $σxtxt-1=∑lnxtxt-1-lnxtxt-1¯2n-1,$ (5) where x represents the ratio of a target currency over the US$. This measure of population standard deviation (SD) indicates how volatile a currency is at a given test period. SD has been commonly used as an indicator of instability.2 Another measure, again limiting to the same currency, is the coefficient of variation (CoV), which is the ratio from dividing the SD of a currency with its own average rate of change in the same test period. CoV is often used as a measure of risk of a currency, meaning that the higher this ratio, the higher is the risk of this currency compared with the CoV of another currency. CoV is measured as in equation (2):
$COV=σlnxtxt-1μlnxtxt-1.$
(6)

The larger the CoV ratio, the greater is the likely instability of the currency. This measure is relative to the first two statistical moments of the same phenomenon—that is, a currency has no regard on how that currency behaves in relation to another currency of importance.

The next measure is preferred when the volatility of a currency is relativized to the volatility of another currency of importance (close trade-linkage is the basis on which another currency may be important, so may be chosen). There is a slight problem here: The British pound sterling is expressed in terms of actual observed US$values. For devising a measure appropriate for a trade-linked group, there is the US$ Index (USDI) available as an alternative to the actual US$values. We thus propose to use the SD of the rate of change of the USDI.3 If both currencies have the same levels of volatility at a given period, then the relative volatility would equal unity. Otherwise, it will either be greater than unity if the given currency is more volatile or less than 1 if the given currency is less volatile than the benchmarked important currency. It is our assumption that most currencies would have slightly higher relative volatility (RV) than unity, given the lower volatility of the US$, if indeed the comparison unit is the dollar. Hence the relative volatility can be measured as the ratio of the SD of a currency $x$ with the SD of a benchmark currency:
$RV=σlnxtxt-1σlnytyt-1,$
(7)
where $y$ represents the ratio of US$in relation to a basket of currencies. This measure is a unit for comparing, say, British pound sterling SD with the US$ SD. If the RV of the pound against the dollar is the same across time, then the RV would be 1.00. Any deviation around 1.00 is an indicator of exchange rate instability of the pound sterling currency. Similarly, by measuring the RV of the euro, we would have two numbers for the pound and euro, respectively, to compare. The size of this measure would be used to measure the instability of the pound and the instability of the euro. That would show which currency is more unstable than the other, which is a practical and very useful measure for ranking a given number of countries with significant trade linkages with the United States. Please refer to the Appendix for how the variables are set up and tested.

The resulting ranking could be done periodically, say every 3 months, to create a time series to provide a benchmark-relevant measure for policymaking. In this paper, we apply this simply to show how this measure looks for a sample of eight countries over some 20 years. Banks apply the VaR measure to see how the core capital of a bank may be affected by a given $x$ percent depreciation or appreciation of a currency.

Country beta (or country risk) is another appropriate measure of the riskiness of a given currency relative to benchmark. The strand of literature on international finance suggests evidence of a limited number of studies on the determination of a country's equity market returns. The seminal studies of Solnik (1974) and Lessard (1976) extended the mean–variance framework (Markowitz 1952) and the covariance risk of the capital asset pricing model (CAPM) to the international setting, thus establishing the relevance of country-specific systematic risk of equity returns. We believe that country risk could also be treated as an additional factor alongside the other proposed factors, explaining the movements of the exchange rates within a multifactor setup. Our proposed model is therefore based on a single equation that includes two so-called parity factors and country risk. The following equation is used to test the basic relationship among the variables.
$RVjt=θj+γ11+itd1+itfjt+γ2CPItdCPItfjt+γ3BETAjt+μjt,$
(8)
where $RV$ represents the relative standard deviation, $id$ denotes the real4 domestic interest rate, $if$ is the real foreign interest rate, the ratio represents the relative interest rate parity among the two trading partners, $CPI$ stands for the consumer price index, and the relative CPI represents the relative PPP among the two trading partners. The BETA is the representative of country risk. This test model is based on monetary theories of exchange rate determination. One could also link these measures to the theory of exchange rate dynamics. Ariff and Zarei (2016) have shown the reliability of this model.
To track the adjustment towards equilibrium in the exchange rate under study, we run an auto-regressive distributed lag (ARDL) regression. The process is normally used in econometrics to estimate the adjustment process in a series. This would also yield an error correction term (ECT) if there is a significant adjustment towards equilibrium. We further perform a panel test using an error-correction specification to determine the short- and long-run behavior of the variables, as in equation (8). The econometric techniques of Pesaran and Smith (1995) and Pesaran, Shin, and Smith (1999) for estimating nonstationary in dynamic panels and their mean group (MG) and pooled mean group (PMG) are appropriate procedures for obtaining an error-correction estimate. The MG estimator helps to obtain an overall average of coefficients after estimating N time-series regressions, and the PMG estimator relies on a combination of pooling and then averaging the coefficients. After a verification of a long-run relationship between variables, the responsiveness of any sort of deviation from the long-run equilibrium and the speed of such an adjustment are of primary interest to us. Using the ARDL (1, 1, 1) re-parameterization, the following equation is obtained and tested:
$RVit=ϕ0+δ10iPPPit+δ11iPPPi,t-1+δ20iIFEit+δ21iIFEi,t-1+δ30iBETAit+δ31iBETAi,t-1+λiRVi,t-1ui+εit.$
(9)
Accordingly, an error correction model measures the relationship between the short-run dynamics of variables and the deviation from equilibrium, as in equation (10):
$ΔRVit=ϕ0+⌀iRVi,t-1-θ0i-θ1iPPPit-θ2iIFEit-θ3iBETAit+δ11iΔPPPit+δ21iΔIFEit+δ31iΔBETAit+εit,$
(10)
where $ϕ0$ is the intercept, $⌀i=-1-λi,θ0i=ui1-λi,θit=δ10i+δ11i1-λi,θ2i=δ20i+δ21i1-λi,θ3i.$

The error correction coefficient, $⌀i$, which is a measure of the speed of adjustment, is expected to be negative and significant to verify that a long-run equilibrium exists.

Whereas the MG estimates are unweighted means of N individual regression coefficients, the PMG estimator allows for heterogeneous short-run dynamics and common long-run parity and non-parity relationships among the respective variables. Similarly, The dynamic fixed effect estimation procedure restricts the equality of coefficients of the cointegrating vector, the speed of the adjustment coefficient, and the short-run coefficients across all panels. The Hausman test statistic is used to examine the differences in the models.

The data series are monthly exchange rates, so the coefficient would indicate the number of months the exchange rate takes to adjust to its long-run path for a given currency (if measured per country without pooling the series or if a panel regression is not done). We intend to document the adjustment process for the sample of major free-floating currencies. The longer the time to adjustment, meaning that the ECT shows longer time to the long-run path, then that currency would have more instability.

## 4.  Findings and discussion

The three measures developed for understanding currency instability as well as tracking it over time are the RV, the rank order using RV, and the cointegration tests on time to equilibrium (ECT). These results are presented in that order in this section. The a priori value for the RV should be equal to 1.00 for a currency with similar relative volatility as that of the benchmark (in this paper, the US$). The graphs, one for each country, are drawn in relation to the unity value of 1.00 if two currencies behave the same way, for each of the eight currencies tested. Figure 4 refers to the behavior of the volatility of the euro against US$ volatility.

Figure 4.

Relative volatility of euro against US$, 1999–2017 Figure 4. Relative volatility of euro against US$, 1999–2017

The plot for the euro is above the line 1.00, which is the benchmark. The euro's volatility appears to move in several cycles. The currency is more volatile than the US$so the relative volatility plots above the benchmark. The euro's volatility increased during the period 2010–13 when the debt crises of Portugal, Ireland, Greece, and Spain introduced sustained uncertainty about the survival of the euro as a central currency. The plots for 14 other currencies are in the Appendix to this paper. Examining those plots shows how a given currency behaves against US$ volatility as a benchmark. That means all the sampled currencies have depreciated against the US$throughout the test period. Thus, it appears that the world's preferred trade-linked benchmark currency is the US$ and it could be used to relativize the movements (appreciation and depreciation) of individual currency. In Table 1, we provide the mean values of the RV scores for ranking the volatility of sampled countries against that of the US$. Table 1. Ranks (by mean) of the sampled currencies by relative volatility, 1998–2017  Mean Median Panel (A) Sample of free-floating currencies GBP 1.2041 (1) 1.1513 (1) CAD 1.2702 (2) 1.1826 (2) EURO 1.3713 (3) 1.3924 (4) JPY 1.3996 (4) 1.3092 (3) CHF 1.4422 (5) 1.4005 (5) SEK 1.5327 (6) 1.5681 (6) NOK 1.6003 (7) 1.5683 (7) Average 1.4029 1.3675 Panel (B) Sample of floating currencies BRL 0.9418 (1) 0.8351 (2) INR 0.9750 (2) 0.6450 (1) IDR 1.0271 (3) 0.8817 (4) KES 1.2441 (4) 0.8511 (3) KRW 1.7463 (5) 1.2895 (5) MYR 2.0346 (6) 1.7504 (7) THB 2.5618 (7) 2.2086 (8) TRY 2.7723 (8) 1.4595 (6) Average 1.6629 1.2401  Mean Median Panel (A) Sample of free-floating currencies GBP 1.2041 (1) 1.1513 (1) CAD 1.2702 (2) 1.1826 (2) EURO 1.3713 (3) 1.3924 (4) JPY 1.3996 (4) 1.3092 (3) CHF 1.4422 (5) 1.4005 (5) SEK 1.5327 (6) 1.5681 (6) NOK 1.6003 (7) 1.5683 (7) Average 1.4029 1.3675 Panel (B) Sample of floating currencies BRL 0.9418 (1) 0.8351 (2) INR 0.9750 (2) 0.6450 (1) IDR 1.0271 (3) 0.8817 (4) KES 1.2441 (4) 0.8511 (3) KRW 1.7463 (5) 1.2895 (5) MYR 2.0346 (6) 1.7504 (7) THB 2.5618 (7) 2.2086 (8) TRY 2.7723 (8) 1.4595 (6) Average 1.6629 1.2401 Note: CAD = Canadian dollar; EURO = euro; JPY = Japanese yen; NOK = Norwegian krone; SEK = Swedish krona; CHF = Swiss franc; GBP = British pound sterling; BRL = Brazilian real; INR = Indian rupee; IDR = Indonesian ruppiah; KES = Kenyan shilling; KWR = Korean won; MYR = Malaysian ringgit; THB = Thai baht; TRY = Turkish lira. This table provides a summary of ranking statistics of paired currency samples in terms of relative volatility. The British pound and Norwegian krone have the lowest and highest relative volatilities among the free-floating currencies and the Brazilian real and Turkish lira are examples of lowest and highest volatilities, respectively, in the sample of floating currencies. First, we show the rank order of the two groups of (free-floating and floating) currencies using the size of the volatility (RV) in Table 1. The ranking could be used to test whether these measures are alternatives for the instability measurement. The results affirm evidence of lower relative volatility against the US$ for the pound sterling followed by the Canadian dollar, as compared with currencies of Sweden and Norway.

In panel (B), there are eight emerging currencies. The mean and median values of the free-floating currencies are 1.4029 and 1.3675; floating currencies are 1.66 and 1.24. The relative volatility of emerging countries is higher than that of the developed free-floating countries.

### 4.1  Cointegration and equilibrium

The results of the ARDL bound tests (Pesaran, Shin, and Smith 2001; Narayan 2005) are shown in Table 2. We tested for validity of long-run relationship and speed of adjustment between the volatility of the paired currencies. The results are indicative of strong long-run association among the free-floating currencies, given the significant bound-test F-statistic, and mean reversion of the volatilities of the paired samples reported in Table 2 with the British pound indicating the fastest (i.e., 5.5 months) and the Canadian dollar having the slowest (9.61 months) adjustment to equilibrium between any two pairs. In panel (B), the results for the floating currencies, likewise, confirm the evidence of a long-run relationship, exceptions being India and Malaysia. The speed of adjustment to the long-run equilibrium is rather slower (on average 10.60 months) for the entire sample of floating currencies compared with that of free-floating currencies.

Table 2.
Long-run relationship between volatility of currency pairs
 Model specification ARDL R2 Bound-test F-statistic Long-run ECT Panel (A) Sample of free-floating currencies $σ$CAD = f(⁠$σ$US$) (1,4) 0.889 6.967** 0.436 −0.104*** (1.37) (−3.57) $σ$EURO = f(⁠$σ$US$) (3,1) 0.921 6.753** 0.828*** −0.121*** (3.68) (−3.59) $σ$JPY = f(⁠$σ$US$) (1,1) 0.723 9.497*** 0.543** −0.178*** (2.51) (−4.33) $σ$NOK = f(⁠$σ$US$) (3,1) 0.851 13.104*** 0.421** −0.178*** (2.28) (−4.88) $σ$SEK = f(⁠$σ$US$) (2,1) 0.901 11.464*** 1.015*** −0.173*** (6.16) (−4.78) $σ$CHF = f(⁠$σ$US$) (2,1) 0.893 7.912*** 0.626** −0.128*** (2.56) (−3.75) $σ$GBP = f(⁠$σ$US$) (1,4) 0.851 10.002*** 0.801*** −0.181*** (4.21) (−4.46) Average −0.151 Panel (B) Sample of floating currencies $σ$BRL = f(⁠$σ$US$) (2,2) 0.873 7.232** −1.124 −0.102 (−2.42)** (−3.69)*** $σ$INR = f(⁠$σ$US$) (1,2) 0.921 2.571 −0.317 −0.044 (−0.27) (−2.26)** $σ$IDR = f(⁠$σ$US$) (3,3) 0.891 6.326** −0.599 −0.087 (−0.91) (−3.55)*** $σ$KES = f(⁠$σ$US$) (3,3) 0.892 5.801** −1.683 −0.076 (−1.87)* (−3.06)*** $σ$KRW = f(⁠$σ$US$) (1,2) 0.736 6.911** −0.192 −0.125 (−0.56) (−3.27)*** $σ$MYR = f(⁠$σ$US$) (1,1) 0.936 2.294 −0.166 −0.037 (−0.16) (−2.14)** $σ$THB = f(⁠$σ$US$) (2,2) 0.867 9.123*** −0.615 −0.127 (−2.03)** (−4.23)*** $σ$TRY = f(⁠$σ$US$) (4,3) 0.807 10.745*** −0.792 −0.157 (−2.04)** (−4.51)*** Average −0.0943 Pesaran, Shin, and Smith (2001)critical value Lower bound Upper bound $k=1$ I(0) I(1) 99% level 6.84 7.84 95% level 4.94 5.73 90% level 4.04 4.78  Model specification ARDL R2 Bound-test F-statistic Long-run ECT Panel (A) Sample of free-floating currencies $σ$CAD = f(⁠$σ$US$) (1,4) 0.889 6.967** 0.436 −0.104*** (1.37) (−3.57) $σ$EURO = f(⁠$σ$US$) (3,1) 0.921 6.753** 0.828*** −0.121*** (3.68) (−3.59) $σ$JPY = f(⁠$σ$US$) (1,1) 0.723 9.497*** 0.543** −0.178*** (2.51) (−4.33) $σ$NOK = f(⁠$σ$US$) (3,1) 0.851 13.104*** 0.421** −0.178*** (2.28) (−4.88) $σ$SEK = f(⁠$σ$US$) (2,1) 0.901 11.464*** 1.015*** −0.173*** (6.16) (−4.78) $σ$CHF = f(⁠$σ$US$) (2,1) 0.893 7.912*** 0.626** −0.128*** (2.56) (−3.75) $σ$GBP = f(⁠$σ$US$) (1,4) 0.851 10.002*** 0.801*** −0.181*** (4.21) (−4.46) Average −0.151 Panel (B) Sample of floating currencies $σ$BRL = f(⁠$σ$US$) (2,2) 0.873 7.232** −1.124 −0.102 (−2.42)** (−3.69)*** $σ$INR = f(⁠$σ$US$) (1,2) 0.921 2.571 −0.317 −0.044 (−0.27) (−2.26)** $σ$IDR = f(⁠$σ$US$) (3,3) 0.891 6.326** −0.599 −0.087 (−0.91) (−3.55)*** $σ$KES = f(⁠$σ$US$) (3,3) 0.892 5.801** −1.683 −0.076 (−1.87)* (−3.06)*** $σ$KRW = f(⁠$σ$US$) (1,2) 0.736 6.911** −0.192 −0.125 (−0.56) (−3.27)*** $σ$MYR = f(⁠$σ$US$) (1,1) 0.936 2.294 −0.166 −0.037 (−0.16) (−2.14)** $σ$THB = f(⁠$σ$US$) (2,2) 0.867 9.123*** −0.615 −0.127 (−2.03)** (−4.23)*** $σ$TRY = f(⁠$σ$US$) (4,3) 0.807 10.745*** −0.792 −0.157 (−2.04)** (−4.51)*** Average −0.0943 Pesaran, Shin, and Smith (2001)critical value Lower bound Upper bound $k=1$ I(0) I(1) 99% level 6.84 7.84 95% level 4.94 5.73 90% level 4.04 4.78

Note: ARDL = auto-regressive distributed lag; ECT = error correction term; CAD = Canadian dollar; EURO = euro; JPY = Japanese yen; NOK = Norwegian krone; SEK = Swedish krona; CHF = Swiss franc; GBP = British pound sterling; BRL = Brazilian real; INR = Indian rupee; IDR = Indonesian ruppiah; KES = Kenyan shilling; KWR = Korean won; MYR = Malaysian ringgit; THB = Thai baht; TRY = Turkish lira.

*** indicates acceptance level set at 0.01; and ** at 0.05.

This result further suggests evidence of higher persistency in the relationship between the volatility measures between the free-floating currency pairs, as can be verified from the long-run coefficients reported in column (5) of the Table 2. This table provides a report of statistics of long-run cointegration between the volatilities of the sampled countries against the US$. The results are indicative of a significant presence of mean reversion behavior of the volatilities to the long-run equilibrium, with the volatility of free-floating currencies having a faster adjustment than the floating currencies. The long-run coefficients for the floating currencies are negative, however, indicating the evidence of divergence in the long-run among the volatilities of floating currencies against the benchmark currency. The descriptive statistics of the pooled variables for the panel data analysis are shown in the Table 3. This table reports the descriptive statistics of the pooled variables across the two samples of selected countries. There is evidence of normal distribution of the data in most cases, with exceptions solely being the result of pooling of data across the sampled countries. Table 3. Descriptive statistics of the sampled currencies, 1998–2017  Mean Median Std. dev. Skewness Kurtosis Observations Panel (A) Sample of free-floating currencies RV 1.378 1.340 0.400 0.938 5.198 1,728 IFE 1.000 1.000 0.001 −0.363 4.496 1,728 PPP 0.832 0.501 0.680 1.589 3.989 1,728 BETA 0.928 0.910 0.158 0.559 3.006 1,728 Panel (B) Sample of floating currencies RV 0.073 0.072 0.368 −0.144 5.140 1,842 IFE 0.079 0.047 0.113 2.897 12.010 1,842 PPP 0.426 0.446 0.116 −0.410 3.804 1,842 BETA 0.827 0.806 0.422 0.218 3.798 1,842  Mean Median Std. dev. Skewness Kurtosis Observations Panel (A) Sample of free-floating currencies RV 1.378 1.340 0.400 0.938 5.198 1,728 IFE 1.000 1.000 0.001 −0.363 4.496 1,728 PPP 0.832 0.501 0.680 1.589 3.989 1,728 BETA 0.928 0.910 0.158 0.559 3.006 1,728 Panel (B) Sample of floating currencies RV 0.073 0.072 0.368 −0.144 5.140 1,842 IFE 0.079 0.047 0.113 2.897 12.010 1,842 PPP 0.426 0.446 0.116 −0.410 3.804 1,842 BETA 0.827 0.806 0.422 0.218 3.798 1,842 Note: RV = relative volatility; IFE = international Fisher effect; PPP = purchasing power parity; BETA = country risk. The statistics reported therein reveal that the transformed variables are normally distributed. The mean value of relative volatility of the free-floating currency sample is slightly higher than unity (1.378), indicating presence of higher volatility of the sampled currencies against the US$, as is also verified from the graphical illustration in Figure A.1 in the appendix. In panel (A), the IFE over the period shows evidence of interest rate parity between the countries, and the mean value of PPP, being the relativity between consumer prices of paired currency samples, indicates an overall lower inflation rate against that of the US$. The average country risk as shown in the fourth row of the table (0.928) is further indicative of lower average country risk in relation to the world stock index. We also notice evidence of lower mean currency volatility, interest rate, and inflation of floating countries against those of the benchmark economy. The country risk variable is also smaller in relation to the world stock index. We also use two panel-type unit-root tests of Maddala and Wu (1999), known as the Fisher test, and the cross-sectionally augmented IPS (CIPS) test, proposed by Pesaran (2007), which are robust against cross-sectional correlation of the sampled countries. The statistics suggest that the order of integration is a mix of level- and first-orders of integration. The RV, for instance, is I(0) and IFE, PPP, and BETA are I(1). These statistics in the table affirm that the variables meet the basic requirement of our proposed panel estimators. This table provides a report of three comparable panel estimators with assumptions on long-run homogeneity and heterogeneity of the variables. The PMG results are found to be a more appropriate estimator, with results indicating evidence of significant long-run equilibrium between RV and the covariates. We present the results as in tables 4 and 5, which are from an error-correction-model as developed in equation (8). Table 4 provides a summary of obtained statistics for our analysis of panel data for the sample of free-floating economies. Results are from three comparable models with different underlying assumptions. The choice of the right model is confirmed by the Hausman test verifying the validity of the long-run homogeneity versus heterogeneity of the covariates. The calculated Hausman statistics in the cases of both free-floating and floating country samples are 0.83 and 5.00, respectively, indicating that the PMG estimator is efficient and preferred. We therefore rely on the PMG results. There is evidence of significant long-run mean reversion of the RV (5.8 months) following the temporary shocks in the behavior of relative inflation and interest rates as well as the country risk factor. Table 4. Results from the sample of free-floating currencies  $Relativevolatility=fPPP,IFE,BETA$ Variables MG (t-stat) PMG (t-stat) DFE (t-stat) Convergence coefficient −0.191 (−31.20)*** −0.172 (−21.43)*** −0.171 (−13.35)*** Long-run coefficients IFE 0.393 (0.70) 0.035 (0.05) −0.178 (−0.27) PPP −0.967 (−1.69)* 0.463 (2.46)** 0.502 (2.54)** BETA −0.227 (−1.66)* −0.141 (−1.96)** −0.137 (−1.92)* Short-run coefficients $Δ$IFE 0.781 (0.76) 0.861 (0.97) 0.691 (0.93) $Δ$PPP −1.642 (−1.83)* −1.608 (−1.87)* −0.312 (−0.95) $Δ$BETA −0.081 (−0.96) −0.085 (−1.05) −0.158 (−2.74)*** Constant −0.052 (−1.14) −0.027 (−1.16) −0.029 (−1.08) No. of countries 8 8 8 No. of observations 1,891 1,891 1,891  $Relativevolatility=fPPP,IFE,BETA$ Variables MG (t-stat) PMG (t-stat) DFE (t-stat) Convergence coefficient −0.191 (−31.20)*** −0.172 (−21.43)*** −0.171 (−13.35)*** Long-run coefficients IFE 0.393 (0.70) 0.035 (0.05) −0.178 (−0.27) PPP −0.967 (−1.69)* 0.463 (2.46)** 0.502 (2.54)** BETA −0.227 (−1.66)* −0.141 (−1.96)** −0.137 (−1.92)* Short-run coefficients $Δ$IFE 0.781 (0.76) 0.861 (0.97) 0.691 (0.93) $Δ$PPP −1.642 (−1.83)* −1.608 (−1.87)* −0.312 (−0.95) $Δ$BETA −0.081 (−0.96) −0.085 (−1.05) −0.158 (−2.74)*** Constant −0.052 (−1.14) −0.027 (−1.16) −0.029 (−1.08) No. of countries 8 8 8 No. of observations 1,891 1,891 1,891 Note: The Hausman test fails to reject null hypothesis with the probability value of 0.8415, indicating that PMG results are the appropriate test results. RV = relative volatility; IFE = international Fisher effect; PPP = purchasing power parity; BETA = country risk. ***signify acceptance level set at 0.01; **at 0.05; and *at 0.10. The numbers in parentheses are t-values. Table 5. Results from the sample of floating currencies  $Relativevolatility=fPPP,IFE,BETA$ Variables MG (t-stat) PMG (t-stat) DFE (t-stat) Convergence coefficient −0.111 (−7.73)*** −0.085 (−6.62)*** −0.085 (−9.47)*** Long-run coefficients IFE 12.491 (1.31) 1.012 (4.10)*** 1.311 (3.63)*** PPP −6.954 (−1.20) 0.921 (3.21)*** 0.185 (0.55) BETA −0.912 (−0.87) 0.224 (2.63)*** 0.201 (1.75)* Short-run coefficients $Δ$IFE −1.694 (−0.91) −1.191 (−0.83) −0.156 (−5.33)*** $Δ$PPP 3.794 (2.35)** 4.521 (2.77)*** 3.337 (3.59)*** $Δ$BETA 0.065 (0.89) 0.048 (0.61) 0.028 (0.63) Constant 0.201 (1.32) −0.056 (−8.61)*** −0.029 (−1.71)* No. of countries 8 8 8 No. of observations 1,833 1,833 1,833  $Relativevolatility=fPPP,IFE,BETA$ Variables MG (t-stat) PMG (t-stat) DFE (t-stat) Convergence coefficient −0.111 (−7.73)*** −0.085 (−6.62)*** −0.085 (−9.47)*** Long-run coefficients IFE 12.491 (1.31) 1.012 (4.10)*** 1.311 (3.63)*** PPP −6.954 (−1.20) 0.921 (3.21)*** 0.185 (0.55) BETA −0.912 (−0.87) 0.224 (2.63)*** 0.201 (1.75)* Short-run coefficients $Δ$IFE −1.694 (−0.91) −1.191 (−0.83) −0.156 (−5.33)*** $Δ$PPP 3.794 (2.35)** 4.521 (2.77)*** 3.337 (3.59)*** $Δ$BETA 0.065 (0.89) 0.048 (0.61) 0.028 (0.63) Constant 0.201 (1.32) −0.056 (−8.61)*** −0.029 (−1.71)* No. of countries 8 8 8 No. of observations 1,833 1,833 1,833 Note: The Hausman test fails to reject null hypothesis with the probability value of 0.1719, indicating that PMG results are the appropriate test results. RV = relative volatility; IFE = international Fisher effect; PPP = purchasing power parity; BETA = country risk. ***signify acceptance level set at 0.01; **at 0.05; and *at 0.10. The numbers in parentheses are t-values. Interpreting the factor effects, we observe that the PPP is associated with the RV both in the short run and the long run. BETA holds in the long-run with an estimated value of −0.141, indicating a significant effect of country risk on relative volatility of the free-floating currencies, which is valid in view of significant financial integration and globalization across developed nations. We believe the insignificant IFE is the result of implementation of low and even negative interest rate policies in the selected economies. Table 5 is a summary of test statistics on the sample of eight countries practicing a floating exchange rate regime. The results are evidence of a significant long-run relationship, as verified from the obtained ECT (or the convergence coefficient) of −0.085, indicating that the speed of adjustment of the volatility to the long-run equilibrium is nearly 11.76 months. The parity factors of inflation and interest rate are found to be statistically significant in the long run, with coefficient values that are close to unity. In other words, per unit increase/decrease in relative inflation and interest rate against the benchmark currency leads to 1.012 and 0.921 units of increase/decrease in the relative volatility of the selected currencies against the benchmark currency. This table provides a report of three comparable panel estimators with assumptions on long-run homogeneity and heterogeneity of the variables. The PMG, being the most appropriate estimator, reports evidence of significant long-run relationship between the variables. The convergence coefficient suggests speed of adjustment (recovery) of the RV in the long-run to the equilibrium parity relationship being slower than is the case for free-floating currencies. ## 5. Conclusion: Instability revealed by relative measures Volatility measures as an indicator of instability have a long history in all sciences. In the period since the demise of the orderliness in currency markets from the Bretton Woods agreement, currency volatility has been at the center of several episodes of systemic instability spilling over to economic and fiscal derailments of countries. To the best of our knowledge, however, there are no significant reports on how to track the instability emanating from currency using relative measures. In mainstream economics, there are models of capacity slack that are a boon to measuring economic instability. What do we have in currency management? In this paper, we developed measures of currency instability and tested these measures using data over 20 years for 15 currencies using actual changes in currency values (and US$ values). What we have done in this paper is show the internal cohesiveness of our models. We also attempted to link these stability measures to verify whether these measures are correlated with riskiness of currency as well as monetary and trade theories.

We further extended our estimation to include theory-consistent variables as proposed in the international finance literature (Cassel 1918; Fisher 1930; Solnik 1974). We found that the relative measures co-move in the long run with the exchange rate variables and the country risk, which is indeed good news. Our findings are indicative of significant correlations between the volatility measures for paired sample countries. There is evidence of significant long-run adjustment to equilibrium following temporary shocks in the behavior of the explanatory variables. The short-run and long-run effects on volatility are also significant for the PPP, and the country risk is also significantly associated with relative volatilities across the eight free-floating currencies.

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## Notes

*

We record our appreciation for acceptance of the paper to be presented at the AEP meeting held at the Korea Institute for International Economic Policy (KIEP) in 2018. We also thank Wing Thye Woo as the organizer of this event for his invitation to this event. We express our gratitude for the comments, all of which have been addressed in this version of the paper. For the remaining errors, the authors take full responsibility.

1

There is scant literature on relative measures. The two we found are: Ariff and Lau (1996) and Ariff and Can (2009).

2

There are several versions of this measure: semi-variance, Parkinson's measure, Kunitomo measure, and so on, all of which are some innovations to make the SD appropriate for different purposes. These are found in advanced statistics books. Extreme values at the tails of the frequency distributions could also be used: fractiles, cupola, and so forth. The property of these measures as indicators of instability by comparing the same measures of another currency to make judgments about the other currency is more or less volatile as measured for a given period.

3

Currency indices are available for most major and some minor currencies. For these currencies, it is therefore possible to relativize the measure by using the SD of the rate of change in the currency index. In this study, we only use the USDI as an example. Other indices could well be used as appropriate to different purposes.

4

The model has included a variable for inflation as the ln on CPI. Hence, using nominal relative interest rate in the test for IFE would mean that the inflation factor is again included in the second variable. To rectify this, we subtracted the expected inflation from the domestic and the foreign nominal interest rates so that we test the IFE on the real interest rates.

## Appendix A

### Technical notes, variable transformation

1. Relative Volatility (RV) = $∑i=18lnxtxt-1-lnxtxt-1¯2∑i=18lnytyt-1-lnytyt-1¯2$ where x denotes domestic currency and y is the benchmark currency.

2. Purchasing Power Parity (PPP) = $CPIdCPIb$

3. International Fisher Effect (IFE) = $1+1+rd1/12-11+1+rb1/12-1$

4. Country Systematic Risk (Beta) $=Cov(rd,rw)σw2$, [The denominator is from world index.] where d and b subscripts denote domestic and benchmark countries, respectively, and w subscript represents world stock index.

Figure A.1

Relative volatility of selected currencies against the US$, 1998–2017 Figure A.1 Relative volatility of selected currencies against the US$, 1998–2017