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.

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 |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .707^{a} |
.499 | .498 | .00997490 |

a. Predictors: (Constant), AUDUSD, USDJPY, GBPUSD |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | .089 | 3 | .030 | 296.584 | .000^{b} |

Residual | .089 | 892 | .000 | |||

Total | .177 | 895 | ||||

a. Dependent Variable: EURUSD | ||||||

b. Predictors: (Constant), AUDUSD, USDJPY, GBPUSD |

Coefficients^{a} |
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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 26 ^{th} 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 |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .518^{a} |
.268 | .261 | .01231417 |

a. Predictors: (Constant), S&P500, XAUUSD, EURUSD, AUDUSD |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | .022 | 4 | .006 | 36.654 | .000^{b} |

Residual | .061 | 400 | .000 | |||

Total | .083 | 404 | ||||

a. Dependent Variable: USDJPY | ||||||

b. Predictors: (Constant), S&P500, XAUUSD, EURUSD, AUDUSD |

Coefficients^{a} |
||||||

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 |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .651^{a} |
.424 | .423 | .00993143 |

a. Predictors: (Constant), AUDUSD, EURUSD |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | .065 | 2 | .032 | 328.769 | .000^{b} |

Residual | .088 | 893 | .000 | |||

Total | .153 | 895 | ||||

a. Dependent Variable: GBPUSD | ||||||

b. Predictors: (Constant), AUDUSD, EURUSD |

Coefficients^{a} |
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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 |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .695^{a} |
.483 | .477 | .01173217 |

a. Predictors: (Constant), S&P500, EURUSD, Crude Oil Futures, USDJPY, GBPUSD |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | .051 | 5 | .010 | 74.549 | .000^{b} |

Residual | .055 | 399 | .000 | |||

Total | .106 | 404 | ||||

a. Dependent Variable: AUDUSD | ||||||

b. Predictors: (Constant), S&P500, EURUSD, Crude Oil Futures, USDJPY, GBPUSD |

Coefficients^{a} |
||||||

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 |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .106^{a} |
.011 | .009 | .02338438 |

a. Predictors: (Constant), AUDUSD, USDJPY |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | .006 | 2 | .003 | 5.033 | .007^{b} |

Residual | .488 | 893 | .001 | |||

Total | .494 | 895 | ||||

a. Dependent Variable: XAUUSD | ||||||

b. Predictors: (Constant), AUDUSD, USDJPY |

Coefficients^{a} |
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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 |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .472^{a} |
.223 | .215 | .03756564 |

a. Predictors: (Constant), S&P500, EURUSD, USDJPY, AUDUSD |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | .162 | 4 | .040 | 28.658 | .000^{b} |

Residual | .564 | 400 | .001 | |||

Total | .726 | 404 | ||||

a. Dependent Variable: Crude Oil Futures | ||||||

b. Predictors: (Constant), S&P500, EURUSD, USDJPY, AUDUSD |

Coefficients^{a} |
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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 |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |

1 | .170^{a} |
.029 | .027 | .02392706 |

a. Predictors: (Constant), S&P500 |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | .007 | 1 | .007 | 12.026 | .001^{b} |

Residual | .231 | 403 | .001 | |||

Total | .238 | 404 | ||||

a. Dependent Variable: JKSE | ||||||

b. Predictors: (Constant), S&P500 |

Coefficients^{a} |
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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 26^{th}). 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.