Correlation and Regression of Forex Currency Pairs

Download the PDF File: correlations-fx-and-stock-result

This is a research done by myself using SPSS and weekly historical data of Forex currency closing price and return. The research is intended to gives an insight regarding the co-movement between currency pair and the size of the movement itself based on regression model.

Correlation in FX

In order to understand the co-movement between major currency pair, I investigated the correlation of movement between EURUSD, USDJPY, GBPUSD, AUDUSD, and XAUUSD. I also include crude oil and S&P500 index in the analysis. The result is outlined below, with highlighted column representing significant relationship between the variables.

Strong relationship (>0.4) could be observed between:

  • EURUSD and GBPUSD, AUDUSD
  • GBPUSD and AUDUSD
  • AUDUSD and S&P500
  • Crude Oil and S&P500
  • S&P500 and AUDUSD, crude oil

Practically, for traders this mean that if EURUSD is increased by 1% that week, we could expect that GBPUSD will also increase. We can conclude that the movement between EURUSD and GBPUSD should be in the same direction, but we cannot know the size movement itself. If large divergence occurred, the trade could be in form of SHORT EURUSD and LONG GBPUSD, with the hope of converging gap. Stop Loss could be tailored to trader’s risk aversion profile.

1

Period of sample: January 2000 – February 2017 (weekly closing)

 

Regression for FX Pair

Apart from the correlation table above, I also regressed the return of each currency pair among other variables. The purpose is to predict the movement size of a currency pair based on the movement of other pairs. The statistically significant result is displayed below, with higher Adjusted R Square means better model predictability of the dependent variable. Here, I want to highlight the regression result of EURUSD, GBPUSD, AUDUSD, as they have Adjusted R Square greater than 40%.

EURUSD

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .707a .499 .498 .00997490
a. Predictors: (Constant), AUDUSD, USDJPY, GBPUSD
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .089 3 .030 296.584 .000b
Residual .089 892 .000    
Total .177 895      
a. Dependent Variable: EURUSD
b. Predictors: (Constant), AUDUSD, USDJPY, GBPUSD
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) .000 .000   .682 .495
USDJPY -.216 .023 -.220 -9.193 .000
GBPUSD .477 .030 .443 16.116 .000
AUDUSD .235 .021 .301 11.037 .000
a. Dependent Variable: EURUSD

About 50% of EURUSD movement could be explained by three other currency pair, namely USDJPY, GBPUSD, and AUDUSD. Note the – sign in front of the B coefficient of USDJPY, due to the reverse nature of EURUSD and USDJPY pairs.

Let’s take a look at the example of February 26th return for each pairs affecting EURUSD movement (USDJPY, GBPUSD, AUDUSD).

USDJPY return = 1.84%

GBPUSD return = -1.57%

AUDUSD return = -1.56%

According to the model displayed in SPSS, EURUSD return should be:

EURUSD = -0.216 USDJPY + 0.477 GBPUSD + 0.235 AUDUSD

EURUSD = -0.216 (1.84%) + 0.477 (-1.57%) + 0.235 (-1.56%)

EURUSD = -0.39744% -0.74889% -0.3666%

EURUSD = -1.5129%

In reality, EURUSD only decreased by -0.43% during the period, a far cry from -1.5129% predicted by the model. However, this is not always the case, on the average the error will hover around 0.76%. This error comes from the 50% other variables that is not captured by the model and explain the movement of EURUSD. We repeat the process in excel for GBPUSD and AUDUSD and conclude the result at the end.

USDJPY

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .518a .268 .261 .01231417
a. Predictors: (Constant), S&P500, XAUUSD, EURUSD, AUDUSD
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .022 4 .006 36.654 .000b
Residual .061 400 .000    
Total .083 404      
a. Dependent Variable: USDJPY
b. Predictors: (Constant), S&P500, XAUUSD, EURUSD, AUDUSD
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) .000 .001   -.769 .443
EURUSD -.284 .052 -.265 -5.486 .000
AUDUSD -.193 .051 -.219 -3.814 .000
XAUUSD -.105 .031 -.149 -3.399 .001
S&P500 .322 .037 .453 8.614 .000
a. Dependent Variable: USDJPY

GBPUSD

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .651a .424 .423 .00993143
a. Predictors: (Constant), AUDUSD, EURUSD
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .065 2 .032 328.769 .000b
Residual .088 893 .000    
Total .153 895      
a. Dependent Variable: GBPUSD
b. Predictors: (Constant), AUDUSD, EURUSD
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) .000 .000   -1.039 .299
EURUSD .463 .028 .499 16.649 .000
AUDUSD .167 .022 .230 7.689 .000
a. Dependent Variable: GBPUSD

AUDUSD

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .695a .483 .477 .01173217
a. Predictors: (Constant), S&P500, EURUSD, Crude Oil Futures, USDJPY, GBPUSD
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .051 5 .010 74.549 .000b
Residual .055 399 .000    
Total .106 404      
a. Dependent Variable: AUDUSD
b. Predictors: (Constant), S&P500, EURUSD, Crude Oil Futures, USDJPY, GBPUSD
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) -.001 .001   -1.158 .248
EURUSD .237 .057 .195 4.187 .000
USDJPY -.197 .046 -.174 -4.279 .000
GBPUSD .202 .061 .147 3.292 .001
Crude Oil Futures .035 .016 .091 2.233 .026
S&P500 .407 .034 .506 11.851 .000
a. Dependent Variable: AUDUSD

XAUUSD

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .106a .011 .009 .02338438
a. Predictors: (Constant), AUDUSD, USDJPY
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .006 2 .003 5.033 .007b
Residual .488 893 .001    
Total .494 895      
a. Dependent Variable: XAUUSD
b. Predictors: (Constant), AUDUSD, USDJPY
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) .002 .001   2.404 .016
USDJPY -.112 .055 -.068 -2.044 .041
AUDUSD .101 .043 .078 2.327 .020
a. Dependent Variable: XAUUSD

Crude Oil

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .472a .223 .215 .03756564
a. Predictors: (Constant), S&P500, EURUSD, USDJPY, AUDUSD
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .162 4 .040 28.658 .000b
Residual .564 400 .001    
Total .726 404      
a. Dependent Variable: Crude Oil Futures
b. Predictors: (Constant), S&P500, EURUSD, USDJPY, AUDUSD
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) -.001 .002   -.661 .509
EURUSD .339 .163 .107 2.080 .038
USDJPY .305 .150 .103 2.030 .043
AUDUSD .381 .157 .146 2.425 .016
S&P500 .643 .124 .306 5.196 .000
a. Dependent Variable: Crude Oil Futures

JKSE

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .170a .029 .027 .02392706
a. Predictors: (Constant), S&P500
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .007 1 .007 12.026 .001b
Residual .231 403 .001    
Total .238 404      
a. Dependent Variable: JKSE
b. Predictors: (Constant), S&P500
Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) .004 .001   3.026 .003
S&P500 -.205 .059 -.170 -3.468 .001
a. Dependent Variable: JKSE

Regression Result:

Below are the real return on currency pair (weekly closing) and the expected return for EURUSD, GBPUSD, and AUDUSD based on the regression result above. Notice that the error of the expected result and real result could be considerably huge (-1.51% for EURUSD in February 26th). However, on the average the error from the model will be 0.76% for EURUSD, 0.73% for GBPUSD, and 1.03% for AUDUSD. The model is far from perfect, but I believe it gives insight regarding the probable movement of FX pair based on other currency.

screen-shot-2017-03-04-at-11-15-49-pmscreen-shot-2017-03-04-at-11-16-25-pm

Published by Journeyman

A global macro analyst with over four years experience in the financial market, the author began his career as an equity analyst before transitioning to macro research focusing on Emerging Markets at a well-known independent research firm. He read voraciously, spending most of his free time following The Economist magazine and reading topics on finance and self-improvement. When off duty, he works part-time for Getty Images, taking pictures from all over the globe. To date, he has over 1200 pictures over 35 countries being sold through the company.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: