THE STATISTICAL RELATIONSHIP BETWEEN THE EUR/USD EXCHANGE RATE AND THE GREEK, SPANISH, AND GERMAN STOCK MARKET.

Spyros Mamalis

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The sovereign debt crisis problem of Greek state became apparent at 2009 along with that of other European countries but it is considered as the most severe in terms of debt percentage per GDP (177% of GDP, Wall Street Journal 2015). (officially the rescue mechanism was activated at April 2010).

ASE-Greek stock index which could be used as a proxy of the Greek economy has followed a downward trend since then. Greece has Euro as a currency.

Eur/Usd exchange rate has been following a similar downward trend. (both euro and usd are used as reserve currencies and have similar characteristics)

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6.5

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7.5

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8.5

log(ASE)

2000m1 2005m1 2010m1 2015m1month year

ASE-Athens Stock Index

.1

.2

.3

.4

.5

log(

Eur/U

sd)

2000m1 2005m1 2010m1 2015m1month year

Euro/USD

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EU

R/U

SD

Greek stock index

Spanish stock index

German stock index

Is there a statistical relationship between the eur/usd exchange rate and the Greek, Spanish, German stock index?What is the indices behavior towards the exchange rate and the opposite. An attempt to compare this behavior will be made but for detailed, in depth comments, future research will provide more information.

The similar trend followed by the Greek index and Euro (proxy: Eur/Usd) is more than obvious and according to that the following questions come to mind:

Research Question:

**As a measure of comparison: Spanish index (IBEX35) is used since Spain faces the sovereign debt crisis and has common characteristics with Greece. On the other

hand German stock index (DAX) is used as a proxy of the strongest economy in Europe.

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Literature Review: Stock index statistical relationship to exchange rate

Unidirectional causality running from exchange rate to stock prices:

Bokhari 2013, found causality running from exchange rate to stock price for India for the period of 1997-2010.

Unidirectional causality running from stock prices to exchange rate:

Wickremasinghe 2006, found causality running from stock prices to exchange rate for Sri Lanka for the period of 1986-2004.

Bidirectional causality, causality running both ways:

Bokhari 2013, found causality running both ways for Bangladesh and Nepal for 1997-2010 4

Neither of the above, no causality:

Ihsan, Baloch and Jan 2015, did not find any causality between exchange rate and stock price for Pakistan for 2012-2014.

Literature Review: Stock index statistical relationship to exchange rate

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Methodology:

Approach Quantitative: 1

• Information Criteria applied (AIC,HQIC, SBIC, FPE)

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• ADF(Augmented Dickey Fuller) test performed. Further visual

scatterplot inspection for trends.

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• VAR models construction. Information criteria applied once more to

choose the optimal lag length for the models

4• Granger Causality Discussion

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• Information criteria are used in order to find the optimal lag length of each individual variable and perform the ADF test. Also information criteria are employed once more to choose the optimal lag length of the model.

• ADF test is performed to test if the variables under consideration are stationary (correction of integrated variables follows non-stationary results)

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• A VAR model is formulated because the variables are treated similarly and interdynamic relationships are considered (we do not know which is the cause and which is the effect) ,and in order to test if the variables are statistically related to each other (two methods: 3 bivariate, and one four variable VAR model are formulated).

• Granger Causality Discussion is followed based on the t distribution instead of the chi square due to the relatively small sample size and due to the fact that only one lag is included, thus discussion based on t distribution could provide more accurate results regarding the causality between the variables under consideration. 8

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1 2 3 41

1 2 3 4

1 2 3 41

1 2 3 4

1

*

t e t te

e e e et g t tg

g g g g

s s s st s t ts

d d d d

t d t td

LnE LnE U

LnXG LnXG U

LnXS LnXS U

LnXD LnXD U

1 2 1

1 2 1

*t eg eg eg t teg

t ge ge ge t tge

LnE LnE U

LnXG LnXG U

1 2 1

1 2 1

*t es es es t tes

t se se se t tse

LnE LnE U

LnXS LnXS U

1 2 1

1 2 1

*t ed ed ed t ted

t de de de t tde

LnE LnE U

LnDAX LnDAX U

Data Description:

The data for the stock indices closing prices are monthly, and the time span is from December 1999 until June 2015. Those data are provided by Yahoo Finance.

The data for the EUR/USD exchange rate closing prices are monthly and the time span included is from the September 2005 until June 2015. Those data are acquired from Oanda. (https://www.oanda.com/resources/about/)

All the data used are logged as it is the case for financial data, to attribute the percentage changes more accurately, and all of them are differenced in order to induce stationarity. (notation: DLnX, x the variable under consideration)(The expense of inducing stationarity is that some information is lost in the long run after taking the first difference)

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RESULTS:

a. Information criteria dictate as the optimal lag length the 1st for the VAR models

therefore the research results will be for the short run time horizon. (remember monthly data are used, so the lagged value (t-1) is the value one month before)

b. ADF test proposes that the variables are integrated I (1), stationarity is induced

after taking the first difference.

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RESULTS (cont.):

c. VAR model results:

i. Three bivariate VAR models: The significant results propose:

• An 1% increase in Greek stock index will be followed by an 0.075 % increase in exchange rate. • An 1% increase in Spanish index will be followed by an 0.136 % increase in exchange rate.• An 1% increase in the German index will be followed by an 0.115 % increase in exchange rate.• An 1% increase in the Eur/USD exchange rate will be followed by an 0.520 decrease in Spanish stock index.

****We consider the above with the assumption that all the other variables are held constant.

i. One four-variable VAR model: The significant results propose:

• An 1% increase in the Spanish index will be followed by an 0.097% at the Eur/USD exchange rate

****We consider the above with the assumption that all the other variables are held constant. 11

d. Granger Causality Discussion Summary:

Granger Causality Indices vs EUR/USD Exchange rate

ASE, Greek stock index-Exchange rate

ΔLnXGt ΔLnEt

IBEX35, Spanish stock index-Exchange rate

ΔLnXSt ΔLnEt

DAX, German stock index-Exchange rate

ΔLnDAXt ΔLnEt

Bivariate VAR models 10 percent level of significance

Four-variable VAR model 10 percent level of significance

12The causality is tested at this table, so the only information provided is If there is feedback or not and not the magnitude or the negative or positive impact on the independent variable.

Conclusion:

Unidirectional Causality running from Greek and German index to EUR/USD exchange rate, according to three bivariate VAR models

Bidirectional causality between the Spanish index and the EUR/USD exchange rate, according to the three bivariate model.

Unidirectional Causality running from the Spanish index to EUR/USD exchange rate according to the four variable VAR model.

Although the results support mainly causality running from indices to the exchange rate, the causality from exchange rate to indices at all cases is close to significant (small p values, but not small enough to reject the Null hypothesis).

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REFERENCES:

Bokhani, H., (2013). Social Relationship between Exchange Rate and Stock Prices, a case on SAARC economies. Academy of Contemporary Research Journal, Volume II, 175-181

Nieh, C., Lee, C. (2001). Dynamic relationship between stock prices and exchange rates for G7 countries, Quarterly Review of Economics and Finance 41; 477-490

Stavarek, D., (2004): Stock Prices and Exchange rates in the EU and the USA: Evidence of their Mutual Interactions. Published in: Finance

a úvěr - Czech Journal of Economics and Finance , Vol. 55, No. 3-4 (2005): pp. 141-161

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Thank you!

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