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Keywords: Interest rate parity, International Finance


In recent years, the world's global economic environment has provided new challenges to governments around the world. Many developed countries' economies have experienced low rates of economic growth and stagnation. Central bankers around the globe have been extremely busy trying to determine the best course of action that would allow these economies to get back to healthy rates of growth. Under monetary policy, central bankers are able to manage the money supply and influence interest rates indirectly, and make changes to the central bank's interest rates charged to banks and influence interest rates directly. With traditional monetary policy tools failing to correct the economic deflation in several countries, the central banks have taken unprecedented steps. Through the use of monetary policy tools, central banks have taken interest rates to very low levels, or zero in some instances; and in the Euro zone, Japan, and Switzerland, to negative rates. These negative rates represent the nominal interest rate prevalent in these countries' money markets. A negative interest rate means that customers would be paid to borrow money or would pay to deposit money. The decision to bring rates into negative territory is related to the desire to stimulate the economy by making it costly for banks to hold excess reserves of cash (Coppola, 2013), prompting them to invest those reserves in the form of business and consumer loans.

The lower rates (in theory) should entice businesses and consumers to borrow to finance new purchases or refinance existing, more costly, debt. However, if large companies are taking advantage of lower rates to issue bonds to purchase other companies or buy back their own stock, this type of borrowing does not necessarily promote economic growth (Anonymous, 2013). Consumers, on the other hand are reluctant to borrow money, although it has been reported that, in the U.S. the average loan amount for a car purchase has increased to $30,032 (LeBeau, 2016), and the number of cars sold in 2015 reached an all-time high. This is significant, as the delinquency rates of sub-prime auto loans continues to grow prompting some to warn of a sub-prime auto loan bubble (Gorzelani, 2016). It is widely documented that long periods of low interest rates tend to encourage speculative booms; and, excessively low rates tend to create bubbles as investors choose to forget their cost of debt in search of higher capital gains (Anonymous, 2013).

In Japan, banks have started to charge fees on some deposit and savings accounts in an attempt to pass the negative interest rate cost from excess reserves to their customers. Bank customers in Japan, who are characterized as a nation of savers, are withdrawing a portion of their savings in response to these new fees imposed on the deposit and savings accounts. Bank customers in Japan prefer to keep cash at home rather than having to pay the fee to keep their savings in the bank (Barnato, 2016). Are savings accounts becoming safe deposit boxes? If depository customers are keeping a portion of their savings at home, would this practice entail the risk that this cash is not safe? According to Pesek (2016), there are unintentional psychological consequences to negative rates. If savers are concerned about their rainy day funds, they will tend to hoard more savings and spend less, rather than borrow at low rates to boost consumption.

The Theoretical Relationship of Interest Rate, Inflation and Currency Exchange Rates

According to Interest Rate Parity, Purchase Power Parity, and the Fisher Effect, internationally countries are tied together by their currency exchange rates and interest rates. If discrepancies exist between currency exchanges and interest rates between the countries, opportunities exist for riskless profits, also known as arbitrage. Arbitrage restores equilibrium to currency and interest rates markets. The ratio of the interest rates between two countries must equal the ratio of forward currency contracts and their spot currency rates, also known as parity. This relationship between interest rates, inflation rates and currency exchange rates are directly related through the following equations:

[mathematical expression not reproducible] (1)

Where r$ is the interest rate in the domestic country and rf is the interest rate in another country, E(1+Infl$) is the expected rate of inflation in the domestic country and E(1+Inflf) is the expected rate of inflation in another country, and F$ is the forward currency rate in domestic relative to a foreign country and S$ is the spot rate in U.S (domestic) relative to a foreign currency. The question becomes, have negative rates caused rifts in interest rate parity such that arbitrage of currency is possible?

This paper looks at the actual impact of negative interest rates, describes the methodology used to test parity, provides the results of our findings, and offers some opportunity for future research.


Given that it has only been in the last few years that countries have experimented with negative interest rates as part of an economic stimulus package, very little research has been done on the impact of the negative rates on interest rate parity. The gamut of research focuses on the outcomes of the negative rates on the overall economy. Below we discuss the actual impacts as seen in current literature.

The Actual Impact of Negative Interest Rates

Central banks have cautiously overseen the implementation of quantitative easing (QE), zero interest rate policies, credit easing, etc.; now these central bankers have unleashed negative nominal interest rates (Roubini, 2015). In today's environment, many European banks have deteriorated balance sheets that carry high levels of risky loans. By the same token, these risky loans are not sufficiently capitalized to be able to absorb potential losses. The result of this situation would be that banks would be hesitant to lend; thus, hoarding more cash. Additionally, the squeeze on the banks' margins would also force banks to increase rates. These two outcomes more closely resemble monetary tightening, not easing (Coppola, 2013). According to Fest (2016), the negative EuroLibor has led banks to initiate zero interest rate floors on Collateralized Debt Obligations to prevent the negative rate spilling over into the commercial lending arena.

In Japan, negative interest rates caused a spike on prices of the government's 40-year bond. These gains can only be compared to those experienced in emerging markets (Bird, 2016).

The ECB, Bank of Japan, and the central banks in Switzerland, Sweden, and Denmark have embraced negative interest rates because they are hoping that capital will flow to countries that offer better returns causing their own currencies to devalue relative to other countries. This is a new form of currency war. The problem is that in a system in which currencies are allowed to float freely relative to each other, "one currency can fall only if another one rises." (Maley, 2016, p.1). Furthermore, states Maley, in a global economic environment in which demand growth is anemic, there is no country in the world who wants a currency that is relatively stronger.

According to Peter Wilson, an analyst with Wells Fargo (2015), there is little evidence that negative rate policy has proven to boost growth or diminish deflation. Wilson's analysis shows that in the Eurozone speculation on lower rates will continue to undermine the Euro. The impact of these policies has been manifested in "reduction of bank profitability, reduction in income, damage to insurance and pension models, and distortion in equity markets" (p. 1), all of which have serious implications for consumers and investors. In Switzerland, Atkins (2016) points out that negative long-term effects have investors around the world concerned about the impact of negative interest rates on the financial industry. Hilsenrath and Torry (2016) point out that U.S. Federal Reserve Bank officials do not believe that a policy of negative rates is warranted. In fact, officials stated that they are "looking to gradually raise rates from exceptionally low levels" (p. 2), as the economy and the job market are expected to grow. Additionally, Hilsenrath and Torry point out that, in their 2016 Jackson Hole, Wyoming meeting, central bankers from different countries implied diminished enthusiasm in continuing to push the negative rate policy that they had previously embraced. U.S. officials are also hoping that a policy of negative interest rates is never needed due to the lack of certainty about whether or not such policy is effective.


This study is designed to test whether interest rate parity holds after a negative interest rate has been activated by the central bank in three currencies: Yen, Swiss Franc, and Euro.

Ho: Interest rate parity holds (there is no difference in the mean ratios of interest rates and currency exchanges).

Ha: Interest rate parity does not hold and there exists opportunities for arbitrage.


To explore the impact of negative rates on interest rate parity, countries whose central banks have introduced negative interest rates were selected. The Euro, Yen, and the Swiss Franc were chosen to test parity. As a robustness test, the Canadian Dollar and the Mexican Peso were also chosen in the test as these countries did not have negative rates.

Interest rate parity has been tested extensively in the past. According to Pipatchaipoom and Norrbin (2010), the method for calculating interest rates can have an impact on findings of parity. Certain factors, such as the way in which inflation is estimated and the assumption of rational expectations, result in differences in forecasting parity. As a result, this paper uses nominal interest rates quoted on short-term debt securities to mimic actual trading.

Chinn (2006) discusses various timeframes for estimating interest rates and forward currency contracts and finds that these timeframes can have an impact on forecasting parity. Thus, the use of short-term debt securities and specific forward contracts based on currencies examined was chosen as the best method to measure potential parity equilibrium.


Equation (2) was used to test for equality and a two sample t-test was run to determine whether or not there is a significant difference in the two sides of the equation for each country. A significant difference would indicate that the opportunity for arbitrage exists. The hypothesis is that equality holds and the alternative is that it does not hold.

1 + r$ / 1+rf = F$/S$ (2)

The left side of the equation is referred to as the "rate side" and the right side of the equation is referred to as the "currency side." A significant p-value would indicate that parity does not hold and the potential for arbitrage exists.

According to the Economic Times (2017), arbitrage is defined as "the profit making market activity of buying and selling of the same security on different exchanges or between spot prices of a security and its future contract."


The analysis was performed by collecting weekly currency and interest rate data for each of the sample countries relative to the US dollar from November 13, 2015 to August 19, 2016. The interest rates are the domestic bond rates on short-term (3 month) government issues, the spot exchange rate is the average of the bid/ask spread, and the forward rates used were the #1 contracts with roll on the first month for all countries except Mexico where #2 contract was used.

Arbitrage was tested using data on forward contract volumes. The purpose is to test for arbitrage as a corrective measure to restore parity. In order to accomplish this, data was collected on future contracts during the test period to see if volumes increase because of a rift in parity.


The first country explored is Japan. On January 29th, Japan dropped rates into the negative territory. Figure 1 presents the graphical representation of each side of the equations where the left side of the equation is called the "rate side" and the right side of the equation is called the "currency side."

Table 1 shows the t-test of the mean difference between the Japanese Yen and the US dollar. Figure 2 is the volume of forward contracts. To engage in arbitrage, an arbitrageur would trade forward contracts of the foreign currency (in this case, the Japanese Yen) to create a risk-free trade. The increase in the volume of trading in those specific contracts would cause a fluctuation in the forward rates (the price) of these contracts, resulting in a return to parity. As can be seen, the interest rate ratio remained relatively stable throughout the test period while the currency slowly dropped to reach a parity level in July 8, 2016. It would appear that the negative position that Japan took may have helped but other confounding events prevent a clear-cut conclusion. After the negative rate change in January 2016, the dollar began to fall relative to the Yen. Based on this, it would appear that the significant difference that existed in the parity until the first of July would represent an opportunity for arbitrage. A p-value below the 0.01 level indicates that parity did not hold over the test period. Increases in volume of contracts matches the ratio trends on currency, which would indicate the possibility of arbitrage occurring during these times.

The next country is Switzerland, shown in Figure 3. As was the case with Japan, the rates remained relatively stable with most volatility occurring on the currency exchange side. A significant t-test (in Table 2) shows that there may have existed opportunities for arbitrage in the Swiss Franc relative to the US dollar during the test period. The first large drop occurred when the Swiss abandoned the cap on the franc. Prior to our test period, the Swiss rate was negative and remained so throughout the test period.

The value of the Swiss Franc during the research period was greatly impacted by changes in the Euro. Brexit threats in June caused up and down volatility in the currency relative to the US throughout the remainder of the test period. As with Japan, the significant difference, p-value below the 0.01 level, indicates a break in parity and the possibility for arbitrage. Based on the volume of trades (shown in Figure 4), it would appear as though the volume drops off as parity is reached at the beginning, but remains somewhat volatile during the remaining period. The two sides never reached parity again indicating that arbitrage did not correct the rift in interest rate parity.

The third and final currency evaluated with negative rates is the Euro. Figure 5 provides a pictorial of the parity and the test statistics. Unlike Japan and Switzerland, the Euro and the US show volatility in rates as well as currency. Overall, they do appear to mirror each other up until mid-May, when the currency exchange became much more volatile. This is the period of the Brexit. The test statistic (in Table 3) shows a significant difference in the means, rejects the hypothesis of parity, and could indicate an opportunity for arbitrage. The volume graphic (in Figure 6) also shows volatility in trades of forwards, but despite these trades, parity is not restored.

Based on the t-statistics on the above countries, we must reject the null hypothesis that parity exists and entertain the possibility of arbitrage opportunities in these currencies. Also, if arbitrage would result in a return to parity, the volume indicators do no support sufficient activity to return to interest rate parity. We do recognize that it is impossible to be certain as there are many confounding events that are occurring globally, for which we cannot control.

As a robustness test, the rates and currency exchanges for Mexico, which did not have negative rates during the test period, and Canada, which did not introduce negative rates until the last data point in the test period, but announced the intent in May, were tested.

Figure 7 depicts information related to Canada. Canadian rates did not turn negative until our last data point of August 19, 2016. As can be seen from the graphic, parity held until mid-May when the currency became volatile due to the announcement of the potential for negative rates. It would appear that parity may have been followed on the last data point when the rates in Canada went negative, with a sharp rise in both the rate and currency ratios. According to the test statistic shown in Table 4, the difference in the means is not significant and hence parity would hold with possible arbitrage opportunities beginning in mid-May. According to Watson (2016), Canadian rates continued in the negative range with at least one bank successfully selling negative rate bonds purchased by investors. Furthermore, Watson argues that investors bought these bonds with the hope of preserving capital, even though they knew some of it would be lost; a behavior that can be attributed to uncertainty.

Figure 8 presents graphics and the test statistic related to Mexico. Mexico has not employed a negative rate during the research period and its data was used as a robustness test. The t-test depicted in Table 5 shows that no significant difference between the rate and currency side exists over the time-period. Overall, the two sides of the equation mirror each other with a consistent gap up until July 2016, which is when the Republican Presidential nominee was announced. Because the chosen nominee had campaigned on the idea of altering NAFTA and increasing border protections at the Mexican border, this may be the cause for the significant drop in the currency at that time. This drop may have caused an opportunity for arbitrage.


In order to test for interest rate parity, the basic equation and techniques described in the literature were used. Theoretically, interest rate parity should hold or arbitrage will return the market to parity. The problem is that theoretically all other variables can be held constant; however, this is a global equation that makes holding other confounding variables constant, in reality, impossible. As is the case discussed by Stoll (1972), market imperfections such as transaction costs can have an impact on returning to equilibrium. Such transaction costs include the spread between the bid and ask currency prices in both the forward and spot rates. Although the mid-point between the bid / ask spread was used, it does not fully eliminate transaction costs.


The current global economic environment presents tremendous challenges to central bankers around the world. The unprecedented level at which interest rates have been set have had consequences that central bankers had not anticipated, including a currency war with trading partners, the withdrawal of funds from consumer accounts, and the reluctance of financial institutions to lend money to consumers and businesses. Additionally, in countries using negative interest rates as a monetary tool to stimulate economic activity, interest rate parity does not hold, creating the opportunity for arbitrage. The rift appears to occur primarily in the ratio of currencies rather than in the interest rates. The most probable reason for why arbitrage cannot correct the disparity is that only money center banks can borrow at the parity rate, which for these countries is negative. The average trader would not be afforded the opportunity to borrow at a negative interest rate and as such, disparity would continue.


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Chinn, M. D. (2006). The (partial) rehabilitation of interest rate parity in the floating rate era: Longer horizons, alternative expectations, and emerging markets. Journal of International Money and Finance, 25, 7-21.

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Eugenie Ardoin

Arturo Rodriguez

University of Louisiana at Monroe

About the Authors:

Eugenie Ardoin is Assistant Professor of Finance at the University of Louisiana at Monroe. Dr. Ardoin earned her D.B.A. from Louisiana Tech and holds the Louisiana Real Estate Commissions Endowed Professorship of Finance. Dr. Ardoin has published articles in the areas of finance and small business management.

Arturo Rodriguez is Assistant Professor of Management at the University of Louisiana at Monroe and has a doctoral degree in Organizational Development and Change Management from Colorado Technical University. Dr. Rodriguez served as a commercial lender and AVP for a community bank in Albuquerque, NM, and has had 7 years of banking experience in Different facets of banking.
Table 1
t-Test of the Mean Difference between Japanese Yen and US Dollar

                              Rates Side  Currency Exchange Side

Mean                           1.0040101   1.24491967
Variance                       2.243E-06   0.02539437
Observations                  37          37
Hypothesized Mean Difference   0
df                            36
t Stat                        -9.195322
P(T<=t) two-tail               5.562E-11
t Critical two-tail            2.028094

Table 2
t-Test of the Mean Difference between Swiss Franc and US Dollar

                              Rates Side  Currency Exchange Side

Mean                           1.0102701   1.00293123
Variance                       2.732E-07   9.2423E-06
Observations                  37          37
Hypothesized Mean Difference   0
df                            38
t Stat                        14.471621
P(T<=t) two-tail               4.829E-17
t Critical two-tail            2.0243942

Table 3
t-Test of the Mean Difference between Euro and US Dollar

                              Rates Side  Currency Exchange Side

Mean                           1.0049172   1.00156931
Variance                       1.244E-06   1.6303E-06
Observations                  37          37
Hypothesized Mean Difference   0
df                            71
t Stat                        12.011228
P(T<=t) two-tail               9.07E-19
t Critical two-tail            1.9939434

Table 4
t-Test of the Mean Difference between Canadian Dollar and US Dollar

                              Rates Side  Currency Exchange Side

Mean                           0.9980269   0.99977117
Variance                       1.987E-06   3.8589E-05
Observations                  37          37
Hypothesized Mean Difference   0
df                            40
t Stat                        -1.6656678
P(T<=t) two-tail               0.1035937
t Critical two-tail            2.0210754

Table 5
t-Test of the Mean Difference between Mexican Peso and US Dollar

                              Rates Side   Currency Exchange Side

Mean                            0.9658275   0.98800025
Variance                        1.411E-05   7.3777E-05
Observations                   36          36
Hypothesized Mean Difference    0
df                             48
t Stat                        -14.190919
P(T<=t) two-tail                8.481E-19
t Critical two-tail             2.0106348
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Author:Ardoin, Eugenie; Rodriguez, Arturo
Publication:International Journal of Business, Accounting and Finance (IJBAF)
Article Type:Report
Date:Sep 22, 2017

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