# Cross Currency Coefficients

When we think about correlation coefficients between two currency pairs, normally we think about correlations among the major pairs against the US dollar such as the EUR/USD, GBP/USD or their direct opposites USD/CHF and USD/JPY. One topic not mentioned in the research is the correlation among currency crosses that directly corresponds to to their USD counterparts. How these pairs move in relation to their USD counterparts will be the subject of this article as well as the Pearson Product Moment Coefficient to determine how to factor various correlation coefficients.

When we measure correlation, we are measuring strength and direction of a linear relationship between two random variables, in this instance two currency pairs. Pearson’s Product Moment Coefficient is the most popular factor because it measures an absolute value from -1 to + 1 of a pair by dividing the covariance of two variables by the product of its standard deviation. In one instance, we are measuring X and Y slopes in terms of the absolute values. Knowing absolute values of a currency pair will almost answer the question how far will a pair move in relation to its counterpart based on an X,Y slope. Specifically, to determine an exact location of the X and Y plot where prices are located at any time, use the Correlation of Determination. An absolute value of + 1 says a pair has a direct correlation and an absolute value of – 1 infers a negative correlation. But currency correlations rarely reflect a perfect relationship. Instead high 80’s or low 90’s is near perfection when the relationship is positive and 20’s to 30’s when the relationship is negatively correlated.

For example, based on September correlations we know that EUR/USD and AUD/USD has a monthly absolute value of .74, a three month absolute value of .76 and a six month absolute value of .72. This positive relationship means in terms of USD that the EURO and AUD will move together 74 percent, 76 percent and 72 percent of the time for the next six months.  What these absolute values mean in terms of currency crosses is quite different. Which way will the EUR/AUD move in terms of its EUR/USD and AUD/USD counterpart? The relationship is negative and in direct contrast to its USD counterpart. So if the EURO and AUD will move together 70 percent of the time against the USD, it has to have a negative correlation against each other and will sell off 70 percent of the time as the EURO/USD and AUD/USD moves up. So as the EURO/USD and AUD/USD move down, the EUR/AUD will move up.

The EURO/USD and GBP/USD are well known for their positive correlations. For September, the absolute values are .75 for one month, .73 for 3 months and .66 for 6 months. But these correlations are against the USD. How would  EUR/GBP correlate against this USD relationship. If both pairs rise with the USD, they must be negatively correlated against each other so the EUR/GBP will sell off  70 percent of the time as the EUR/USD and GBP/USD rise with the USD.

What if we have two pairs not so closely correlated such as the GBP/USD and AUD/USD. The absolute values are .58 for one month, .73 for three months, .70 percent for six months and .61 for a year. What does this correlation say about the GBP/AUD and how would you look at this trade knowing traditionally these two pairs normally correlate. The GBP/AUD for the month of September is going nowhere and will probably trade in a small range because the correlation is not positive or negative in terms of absolute values. In terms of correlations, this is an uncertain pair especially when its immediate counterparts signal uncertainty.  So looking at the GBP/USD and AUD/USD for GBP/AUD direction is not the place to begin. Another way may be to look at Yen crosses.

Suppose we know the GBP/USD is negatively correlated to the USD/JPY based on these September absolute values. -.05 for 1 month, -0.12 for three months, -0.07 for six months and +.16 for one year. Which way will the GBP/JPY move and how should you look at this trade in terms of correlations and absolute values. The best way is factor the cross rates to determine where the pair is presently trading. For example, GBP/JPY is derived from GBP/USD and USD/JPY. So a GBP/JPY cross rate is calculated by  taking the cross rate bid by multiplying the bid of the terms currency (top) by the bid of the base currency(bottom). For the cross rate offer, multiply the offer of the terms currency (top)by the offer of the base currency (bottom). If GBP/USD rate is 1.6000-10 and USD/JPY Yen rate is 100.00-10 then GBP/JPY cross rate is as follows. The bid would be 1.6000 X 100.00 or 160 Yen per GBP and the offer would be 1.60010 X 100.10 or 160.26 Yen per GBP. Always look at cross rate formulas as A/B X B/C = CB.

So if we correlate the GBP/JPY to the GBP/AUD based on the absolute values of the GBP/USD and AUD/USD for GBP/AUD and

GBP/USD and USD/JPY for GBP/JPY, we find those correlations to be negative. As the GBP/JPY sells off based on the one month absolute value of -.05, the GBP/AUD will rise based on the .58 absolute value of the GBP/USD and AUD/USD.

Visually, look at these two pairs, GBP/JPY and GBP/AUD. Subtracting the GBP aspect of this relationship leaves two base pairs that have negative correlations based on their absolute values. How do you know.

AUD/USD to USD/JPY correlations are as follows. 1 month correlations .08, 3 month .04, 6 months .18 and 1 year .48. This relationship doesn’t change if we inverse correlate USD/JPY to AUD/USD, statistical figures remain the same.

What does the GBP/JPY and GBP/AUD relationship say to the above EUR/AUD example. The GBP/AUD and the EUR/AUD should both move in tandem because they are positively correlated based on their positive absolute values. Although EUR/AUD should move faster than GBP/AUD because the EUR/AUD is more closely correlated to the EUR/USD and the AUD/USD.

So if the EUR/USD and the GBP/USD both experience a sell off and the EUR/AUD, GBP/AUD and EUR/GBP all rise, we can look at EUR/AUD, GBP/AUD and EUR/GBP as US dollar pairs. To sell the EUR/USD and GBP/USD simply means you are selling the EUR and GBP against the US dollar. This means dollar pairs such as the USD/CHF, USDJPY and USD/CAD all move up as the EUR/USD, GBP/USD sell off. Likewise, the correlations of USD/CHF, USD/JPY, USD/CAD, GBP/AUD, EUR/GBP and EUR/AUD all have absolute values closely aligned with the US Dollar and move in tandem with each other. So a long EUR/AUD or EUR/GBP is a long US Dollar position the same as USD/CHF, USD/JPY and USD/CAD.

How would we look at opposite correlation crosses like the GBP/CHF when absolute values don’t align. GBP/CHF is comprised of GBP/USD and USD/CHF so maybe we want to triangulate these pairs using the above cross rate formulas. Absolute values align like this. For GBP/USD to USD/CHF absolute values are  one month -.64, -.67 for three month, -.57 for 6 months and -.45 for one year. Looking at absolute values for negatively aligned crosses never correlate so direction must be determined using indicators, candles and charts especially if our answer can’t be found by triangulating these pairs using the cross rate formulas. Another method to determine direction for GBP/CHF may be to look at other related pairs that have negative alignments such as the EUR/CHF, AUD/CHF, AUD/CAD or even the Yen pairs since all move in tandem with GBP/CHF. Or look at pairs that have negative correlations for further confirmation such as EUR/AUD and GBP/AUD.

The false premise regarding currencies is the US dollar plays no part in various cross rates when in fact the US dollar is the beginning of all traded pairs and dictates all directions for all traded pairs in the world. As long as the US Dollar is the currency of exchange for traded goods and commodities in the world and the dominant reserve currency, it will always set direction for all currency pairs and their various crosses. So always look to dollar direction by checking the USD Index before choosing which pairs to trade.

So the question can you execute trade decisions based on correlations and absolute values. The simple answer is it depends because some correlations have tendencies to change over time. What would cause changes in absolute values could be outside influences such as economic situations within certain nation’s economies, which way interest rates are heading within nations, the question of  how much risk traders are willing to add and changing central bank policies. In uncertain economic environments, traders may be willing to stay away from cross pairs and institute safe trades such as straight USD pairs. A bombshell announcement like a collapsed housing market or a decision by a central bank to add massive liquidity to their economies would cause traders to bail out of cross and carry trade pairs quickly leaving the unsuspected holding massive losses. So the question of risk must be a factored decision before contemplating any cross pair trade.

Take the GBP/AUD example as our question of risk. Normally these pairs have strong correlations and an interest rate difference between the two pairs at 2.5 percent. Yet because of uncertain economic times in England coupled with a series of poor economic announcements over time, the correlations are uncertain in terms of absolute values. Even with carry trade potential to earn interest, traders are not willing to risk capital to these trades.

When economic growth or the potential for growth exists, absolute values will change and correlations will change with those values. Notice the one year absolute value between AUD/USD and USD/JPY. Today that value sits at .48 yet the short term gauges barely a relationship. Is this a forecast for growth between these nations later or a forecast for growth for the region. Possibility of a statistical relationship so far.

Know also while  statistical relationships may exist between currency pairs, many pairs are statistically correlated to

other factors such as stock market moves, treasury yields, risk indices such as the VIX index and option risk reversals. Interest rates are and always will be the driving force behind any currency trade whether its a cross or straight USD trade. So in uncertain economic times, traders are best advised to trade USD pairs and trade cross pairs when growth returns.

September 2009

Brian Twomey is a currency trader and adjunct Political Science Professor at Gardner-Webb University.