Crosspair allegiance and carry trades

March 26, 2016 01:00 PM

The carry trade is based on a simple premise: You buy (lend) a high interest rate currency and short (borrow) a low interest rate currency. The low interest rate currency becomes the fund currency while the high interest rate currency becomes the investment. The historical assumption is that as long as the condition of Uncovered Interest Parity fails, actual carry trades may last for years as an arbitrage until a possible shock hits the markets or until the disparity in interest rates compresses to Covered Interest Parity, whereby positions are covered.

In this first of two parts, we investigate the EUR/USD, USD/JPY and the EUR/JPY using regression analysis to determine where EUR/JPY sits in relation to both pairs in a carry trade. We found that EUR/JPY switches allegiance period to period.

Data & methodology

To understand the relative relationship and position of EUR/JPY in terms of USD/JPY and EUR/USD 5,532 exchange rates between weekly and monthly closing spot prices were documented for the pre-crisis period from Jan. 5, 2000, to July 4, 2008, and in the post-crisis period from July 4, 2008, to April 15, 2014. A total of 12 samples were observed, separated by weekly and monthly time frames for each paired relationships.

The year 2000 was chosen to yield consistency as it allowed one full year of euro market trading from its January 1999 introduction and because world central banks adopted interval meetings every six weeks. To further capture the true market price and accurate simple regression analysis, July 2008 was chosen as the start date for the post-2008 period because market prices failed to reflect the housing crisis dilemma that occurred in mid-August of that year.

For pre- and post-2008, EUR/USD and USD/JPY were employed as the dependent variable and EUR/JPY as the independent variable. To understand a true cause and effect, EUR/USD as the dependent variable was positioned against USD/JPY as the independent variable for both pre- and post-2008 periods, weekly and monthly. The research design assumption was EUR/USD or USD/JPY influences EUR/JPY but to guard against a false presupposition, EUR/USD was measured against USD/JPY to add validity and determine a possible positional balance against the sample statistics.

The U.S. dollar was chosen as it remains “on either side of every trade 87% post-2008 and 90% pre-2008,” based on the Bank of International Settlements. The euro maintains its status as the second most active currency, according to the BIS. The Japanese yen, third most traded currency, experienced a 63% increase in daily turnover activity from 2010 to 2013.


Now we’ll take a look at the correlations between each crosspair pre- and post-crisis.

For the time frame of 2000 to 2008, EUR/USD and EUR/JPY not only shared a 0.93% correlation on a weekly basis but a healthier and positive r-squared covariance of 0.87%. Based on rho population parameters (a measure of variable dependence), the correlation and r squared values are significant throughout all samples. By 2008 to 2014, the weekly relationship shifted dramatically to a correlation of 0.60% and r-squared of 0.36%. This shift is apparent in the residual plots shown in “Non-stable relationship” (below). A similar shift occurred in monthly data.

We see a dramatic shift in the USD/JPY and EUR/JPY correlation from the pre- to post-crisis period. For the weekly time frame between 2000 and 2008, the crosspair correlation was a negative 0.11% with an r-squared of 0.01%, while the weekly period between 2008 and 2014 turned positive with a 0.91% correlation and an r-squared of 0.83% (see “Shifting signs,” below). The monthly data provided confirmation of this crosspair correlation shift, as the correlation was a negative 0.15%, with an r-squared of 0.02%, while it was a positive 0.91% with an r-squared of 0.82% from 2008-2014.

With respect to the EUR/USD and the USD/JPY correlation, an interesting relationship developed between 2000 and 2008 as the weekly correlation revealed a negative 0.45% and an r-squared of 0.20%. This further demonstrated the allegiance EUR/JPY shared with the EUR/USD pre-2008. In the 2008 to 2014 period, the weekly correlation of the EUR/USD and the USD/JPY crosspair turned positive at 0.22% with an r-squared of 0.05% (see “New era,” below). This relationship, however meager, also was confirmed in the monthly data.

As a consequence of the r-squared values, a 13% unexplained variation between EUR/USD and EUR/JPY pre-2008 existed, while post-2008 experienced an 18% and 17% unexplained variation between USD/JPY and EUR/JPY. For EUR/USD and USD/JPY pre-2008, 80% of the weekly variation is unexplained while the 77% variation is unexplained in the monthly time frame. Post-2008, there is a 95% unexplained variation in the weekly time period and 97% for the monthlies.

Looking at all the residual plots, we can see that all display constant variance across values, (also known as homoscedasticity) non-linearity to response variables, and lack autocorrelation. In addition, residual means are zero, therefore slope and intercept lines are accurate.

EUR/JPY allegiance

A possible explanation why the EUR/JPY crossrate transferred its allegiance from the EUR/USD to the USD/JPY is seen in rho as a measure of the correlation significance in the pre-2008 period.

Based on rho analysis, correlations for EUR/USD and EUR/JPY were approaching the upper limits of the 95% and 99% significance percentiles for the weekly and monthly periods. As a corollary, USD/JPY and EUR/JPY approached critical 95% and 99% rho limits for both the weekly and monthly time frames. EUR/USD possibly saw its meridian against EUR/JPY and USD/JPY, a possible base, evidenced by rho.

Therefore, EUR/JPY was in a crucial position, particularly when EUR/USD and USD/JPY shared essentially no relationship by unexplained variations in both pre- and post-2008, based on the correlation coefficients reported above.

What is fascinating is that EUR/JPY not only chose to strengthen its relationship to USD/JPY post-2008, but the alliance came full circle, as the dependence pre-2008 was negative and the correlation not only became positive following the crisis, but approached rho’s upper 95% confidence interval.


Covariance further reveals a strong positive relationship between EUR/USD and EUR/JPY pre-2008 on the weekly and monthly time periods. Conversely, USD/JPY and EUR/JPY pre-2008 show a strong negative association.

By the post-2008 period, covariance values had reversed on the weekly and monthly time frames to reveal that USD/JPY and EUR/JPY shared a vigorously positive alliance and EUR/USD and EUR/JPY had a barely positive relationship. As the relationship between EUR/USD and USD/JPY was barely negative pre-2008, the post-2008 period shows a slight positive relationship based on variance.

Covariance addresses first the question of joint distributions. The magnitude of covariance is defined as how far X and Y vary symmetrically from their means as a dependent rather than independent relationship. If X and Y were independent, both variables would assume zero correlation.

Covariance values are linear associations and intended to measure strength of associations. Correlation is an inequality and unit less due to its +1, -1 measure but represents a measure of a sample to address questions of cause and effect, coincidences and sample co-variation.

Covariance defines correlational strength. By measuring X and Y minus means and obtaining positive deviate values, X and Y means are positive and co vary, as was the case for EUR/USD and EUR/JPY pre-2008. Covariance is found between the bounds of correlational +1 and -1. Essentially, covariation removes part of the variability of Y that co-varies with X and focuses on the remainder sections: The residual variance.

What allowed EUR/JPY to assume a strong positive relationship with EUR/USD pre-2008 was that USD/JPY had a negative covariance with EUR/USD; USD/JPY means were negative while both EUR/USD and EUR/JPY means were positive. When the August 2008 housing crisis emerged, means for EUR/USD, USD/JPY and EUR/JPY all dropped considerably, but USD/JPY and EUR/JPY prices fell below respective means. Therefore, a new covariance relationship formed as USD/JPY and EUR/JPY.

EUR/USD maintained a weak association with EUR/JPY because EUR/USD prices remained slightly above their mean and the aftermath was lower correlation and r-squared values. Had EUR/USD prices fallen below their respective mean, EUR/USD and EUR/JPY as a covariance and correlation relationship would have completely severed and melded into a shift among the three pairs because USD/JPY was below its complementary mean. EUR/JPY choices at this juncture were either to break above the mean and reattach to EUR/USD or assume a new relationship with USD/JPY. EUR/JPY shifted allegiance from EUR/USD to USD/JPY.

Carry trade crash risks

Many studied the concept of carry trade crash risk. Brunnermeier, Nagel and Petersen (2008) reveal that investment currencies are subject to crash risk because of funding constraints relative to the implied volatility of the S&P 500. Burnside (2011) failed to classify the housing polemic as a crisis because his portfolio consisted of carry and momentum. If carry lost, then momentum profited. Hutchison and Sushko (2013) look at carry trades and macroeconomic surprises as they relate to global risk.

If the carry trade in interest rate terms and EUR/JPY’s positional change is an assessment, Europe, Japan and the United States experienced reduced interest rates since 2000. The U.S. fed funds target rate in March 2000 was 6.50%, and the Euro refinance rate was 5.75%.

The USD/EUR carry trade was the opportune position until September 2007 when the fed funds rate fell to 4.75% and the refinance rate was 5%. The EUR/USD became the new carry trade until post-2008 when both rates equalized to 0.25%.

Both the USD/JPY and EUR/JPY worked as a carry trade pre- and post-2008 because Japan’s base rate, the overnight call rate, was 0.25% in August 2000, 0% in March 2001 and 0.50% in February 2007. The overnight call rate today is 0.1%.

Gyntelberg and Remolona (2007) and many others identified the failure of the Uncovered Interest Parity condition in five-year time horizons. August 2014 was be the sixth approximate year for the USD/JPY and EUR/JPY relationship.

A speculative assumption, and a topic specific to carry trade crash risk, is that EUR/USD and EUR/JPY began their association at the time of the 1997-98 Asian financial crisis. The relationship was found in 2000 as research began. How long the relationship existed is unknown. What is known post-2008, is that the EUR/JPY and USD/JPY relationship mirrors the EUR/JPY and EUR/USD before the crisis. The question of whether a market crash will occur to force a breakdown of the allegiance to cause the EUR/JPY to switch loyalties again to EUR/USD is unknown, nor is it known if a market implosion is the essential element to experience a change.

In this first of two-parts, we examined the statistical relationship between the EUR/JPY, EUR/USD and USD/JPY and how that relationship shifted between the pre- and post-crisis periods. We also looked at the carry trade and crash risks and examined both weekly and monthly values. Next month, we will take a closer look at the evolution of the carry trade definition, explore the carry trade balance and discuss how economic change and money supply have impacted that balance.

About the Author

Brian Twomey is an independent trader and author of “Inside the Currency Market: Mechanics, Valuation and Strategies.”