# Interest Rate Differential and Long-Term Currency Trends

The following materials demonstrate high correlation between the long-term currency trends and interest rate differential cycles. As the first step we measure the cyclic component of the long-term currency trends. In the second step we measure the correlation between the cyclic component of the long-term currency trends and the interest rate differential cycles.

## 15.1. Measuring the Cyclic Component of the Long-Term Currency Trends.

To measure the cyclic component of the long-term currency trends we use the **Detrended Price Oscillator** (with a time period of 12) on the monthly charts for the following currency pairs - GBP/USD, EUR/USD, AUD/USD and NZD/USD. The 12 time period is used because the long-term trend duration for these currency pairs has been found to be on average equal to 24 months (during the last 7 years). In order to identify majority of cycles in these pairs a half period DPO should be employed (24/2). The DPO indicator was chosen because it shows the **highest correlation to the interest rate differential cycles** for all of the pairs - out of all the commonly used technical indicators. This can be explained by the fact that the interest rate differentials moved in clearly visible cycles for the 4 currency pairs in question (see below) and Detrended Price Oscillator is used primarily to identify cycles in the price data. The following images demonstrate how this indicator tracks the long-tern trends - notice how in most cases the breaking of the major trendline **perfectly coincides** with the crossing of the zero line by the Detrended Price Oscillator. The fact that this oscillator so closely tracks the progression of the major trends was another reason why it was chosen for the comparison with the interest rate differentials.

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It pays to visually demonstrate the cyclic nature of the interest rate differential movement. The pictures below show how the interest rate differential cycles are **"born" out of the individual interest rate cycles **of the currencies which form the above currency pairs. The poly (from "polynomial regression") lines are the smoothed versions of the interest rate and differential curves. The function that is shown on each chart is of the smoothed interest rate differential curve (yellow); the R squared shows the closeness of fit of the smoothed curve to the original curve. Each point on the X axis correspond to one whole month, where the first and the last month are specified below each chart.

From 01.1985 to 09.2006

From 01.1994 to 09.2006

From 01.1999 to 10.2006

Two of the smoothed interest rate differential curves shown above (on the USA vs. EUR and the USA vs. NZD charts) are almost perfect **sine waves** (the function which is used to encode data cycles). This led us further to model the original interest rate differential data with the use of the following waveform equations that describe the underlying cyclic behaviour (these charts are plotted over the same time period as the corresponding charts above):

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Quote: "The sine wave is the mathematically smoothest waveform describing a cycle and harmonic motion." by John F. Ehlers in his book "MESA and Trading Market Cycles".

## 15.2. Correlation between the Long-Term Currency Trends and the Interest Rate Differential Cycles.

Given the cyclic behaviour of the interest rate differential movements we decided to compare them not to the raw currency price but to the Detrended Price Oscillator which was used to extract the cyclic component of the long-term currency trends. The following table shows the monthly values of the interest rate differential for each of the pairs along with the corresponding values of the Detrended Price Oscillator. At the bottom of the table you will find **correlation coefficients between the DPO and the Interest Rate Differential for each currency pair.**

The above correlation coefficients can be further transformed into the **coefficients of determination to measure the amount of shared variance between the interest differential and the DPO. **The amount of the shared variance tells us how much of the variance in interest rate differential can explain the variance in the DPO and vice versa. Generally, the stronger the correlation, the greater the amount of the shared variance and the more variance you can **explain** in one variable by knowing the values of the second variable. To calculate the coefficient of determination we need to multiply the correlation coefficient by itself. If the **average correlation coefficient of the above currency pairs is equal to 0,75**, then the average coefficient of determination will be equal to 0,75*0,75 = 0,57 or %57. This means that on average %57 of all long-term movements (cycles and trends) for these currency pairs can be directly explained by the changes in the interest rate differentials. To demonstrate this relationship we made the overlay plot of the Detrended Price Oscillator and the Interest Rate Differentials as is shown below:

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## 15.3. Conclusion

The above materials clearly demonstrate the existence of a strong relationship between the movement of the interest rate differentials and the long-term currency trends for the four currency pairs that were analyzed. A more extensive research is required to establish the validity of these observations across all the commonly traded currency pairs. However, given the **high level of consistency in the correlation coefficients** that were identified, we can conclude that there is a high probability that the interest rate differentials will continue to exert a powerful influence on the long-term currency trends of these and other currency pairs in the future.

## 15.4. Data Sourcses

http://www.federalreserve.gov/releases/h15/data.htm

http://www.bankofengland.co.uk/statistics/about/faq_all.htm

http://www.bundesbank.de/statistik/statistik_zeitreihen.en.php?func=row&tr=su0202

http://www.rba.gov.au/Statistics/Bulletin/F13hist.xls

http://www.rbnz.govt.nz/statistics/exandint/b2/data.html