Exchange Rate and Stock Price

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Journal of Business Finance & Accounting, 17(3) Summer 1990, 0306 686X $2.50

ON EXCHANGE RATE CHANGES AND STOCKPRICE REACTIONSC H R I S T O P H E R K , M A A N D G . W E N C H I K A O "

INTRODUCTIONThe volatility of exchange rate changes has increased significantly since theadoption of the floating rate regime in the early 1970s, As a result, moreuncertainty has been introduced to the linkage between international equitymarkets. Considering the associated increase in risk for international invest-ments, the choice of currency denomination adds an important dimension tothe overall portfolio decision. The required rate of return of an investmentshould reflect both the domestic required rate of return and expected changesin the value of the currency in which the investment is denominated.

The purpose of this paper is to examine stock price reactions to exchangerate changes. Under a floating rate regime, the required rate of return of stocksis shown to reflect two types of foreign exchange risks. First, the investmentis inherently affected by the transaction exposure from foreign exchange ratechanges. This is mainly due to gains or losses arising from the settlement ofinvestment transactions stated in foreign currency terms. Second, the expectedreturn is also determined by the economic exposure which is attributed tovariations in firms' discounted cash flows when exchange rates fluctuate; Thus,the equilibrium relative stock price is related to both exchange rate levels andexchange rate changes.The rest of this paper is organized as follows: the second section reviewssome related literature; the third section describes the theoretical foundation

of the paper; the fourth section presents the corresponding hypotheses, thetesting methodology and the empirical results; and the flnal section sum ma rizesthe paper,LITERATURE

Numerous efforts have been undertaken to investigate the relationship inrequired rates of return in different equity markets, Agmon (1974) and Hillard The authors are respectively, Associate Professor at Texas Tech University; and Assistant Professor


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442 MA AND KAO(1976) identify various degrees of comovements between different internationalequity indices, Koveos (1983) and Panton, Lesseg and Joy (1976) show, instead,that the different degree of comovement is attributed to the lead-lag relationshipbetween equity indices. As further demonstrated by Agmon and Lessard (1977),the same lead-lag relationship is the basis for benefits of international diversifi-cation. However, considering the treatment of the currency denominationsimply as a means of exchange, the applicability of these results seems limited.

On the other hand, examining the impact of exchange rate changes on stockmarkets, Franck and Young (1972) investigate the attribute of a multinationalfirm for which the stock return is sensitive to exchange rate changes. Crucialfactors identified include the market mix, the input mix, exchange regulationsof governments and accounting treatment of exchange gains and losses.Aggarwal (1981) explains the ex post, positive relationship between exchangerate changes and stock indices in terms of the relative competitiveness ofinternational-traded goods. However, based on their assumption that investorsonly trade in domestic financial markets, the resulting empirical evidence inboth studies understates the relationship between exchange rate changes andstock price movements. Furthermore, an exogenous foreign stock market clearlycontradicts previous findings of comovements among different stock indicesin the world exchange. The unstable relationship between exchange rate levelsand stock market indices in different periods is, therefore, attributed to thisunder-specification,

MODELIn a simple, two-market world with perfect capital mobility, investors determinethe portfolio weight as follows:

- i) (1)where luj : weight of wealth invested in thejth asset;

E{R): the expected return on the^th asset;i : investor's target return; andWg : basic weight independent to expected return.

For every one dollar of wealth, equation (1) simply specifies the portfolioweight as the present value of expected future cash flows discounted at theinvestor's risk-adjusted target return i. For simplicity, investors are assumedto aflocate their wealth between two stock markets, i,e., the domestic stockmarket and the foreign stock market. Equations (2) to (5) demonstrate theallocation of wealth between two investment outlets:


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EXCHANGE RATE CHANGES AND STOCK PRICE REACTIONS 443,,i)* - 0 (4)

i) - O (5)where * : in terms of foreigner's point of view;tu,, tuf : weights of wealth invested in the domestic stock market and

foreign stock markets;A ,, A * : numbersof shares outstanding in the domestic stock market

and in the rest of the world;W : the total wealth denominated in the foreign currency;Si : the spot exchange rate in terms of foreign currency;

*+ l) the expected foreign stock return for the rest of the world; andthe expected domestic return converted into the foreigncurrency.Assuming the wealth is denominated in the foreign currency, equation (2)converts investment payoffs from the domestic market into foreign currency

values. The portfolio weights in equations (4) and (5) depend on the differencebetween the expected rate of return and the target return i. In terms of theforeign currency, the expected holding period return from the domesticinvestment is:

For simplicity, we assume:

Hence,E{R,,,)* = ( , , , ) + ( ., ,, ) (6)

where e,+ i is the exchange rate appreciation.Equation (6) implies that returns of domestic investments for foreign investors

depend on expected domestic returns and expected appreciation of the domesticcurrency. Transaction exposure of an investment is thus defined as changesin returns after the conversion of investment payoffs from one currency toanother. Combining equation (2) through (6):

rt, + p, + s, = w + E{R,,t) - E{Rr.i) + (,,,) (7)where n, = ln(A /Af,*), /), = ln{P/P^), w = \n{wjw*), s, = \x\S, and in' isthe natural logarithm.

Equation (7) specifies the (wealth) stock equilibrium condition, i,e,, therelative stock supply is equal to the relative stock demand. The equilibriumcondition, in turn, depends upon the relative wealth position, the expected


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444 MA AND KAOstocks are issued in the current period if the equity price for the next periodis expected to fall, (2) more stocks are currently issued if stocks are denominatedin a strong currency expected to depreciate in the future, and (3) it is moredifficult to sell new stocks if an already large supply of stocks is outstanding.Hence, new issues in the current period are negatively related to the expecteddomestic return, expected currency appreciation and the outstanding supplyof stocks:

h, = a' - &'{E{R,,,) - E{RU,)) - e'E{e,,{) - 0'n, (8)where 0 < a ' , /3' , 6', < 1,Equation (8) may be further rearranged into the following:

h, = a - /3[(,,,) - E{R*,^)] - eE(e,^,) - 4>rt, (9)w h e r e a = a'l{\ - 0 ' ) > 0 , / 3 = ^'l{\ - < j ) ' ) > 0,6 = 0 7 ( 1 - < t > ' ) > 0;and 0 = 0' /(l - ') > 0.

Equations (10) and (11) below present the expected required rate of returnfor each stock market. It is assumed that the expected stock return reflectseconomic exposure of the domestic economy, i.e., the impact of changes incurrency values to future cash flows. The cash flow of a typical economy isaffected by exchange rate changes either through price competition in the world-wide product market, or through the cost impact of imported goods. On a microbasis, economic exposures of exchange rate changes are hypothesized as follows:

A) Export sales will be negatively affected by the expected appreciationof the domestic currency. This is due to the relatively higher price ofproducts in terms of the foreign currency in international markets.

B) The importing firm will benefit from the appreciation of the domesticcurrency, since it results in lower import costs.

Thus, the expected return on the stock market is determined in thefollowing fashion:

,) = KR, + (1 - K)^E{e,,^) + V, (10)) = KR; + (1 - K)rE{e,,^) + 6, (11)

where v,, e, are white noises and 0 < K < 1.The first term in the right-hand side of equations (10) and (11) represents

a random process generating the component of expected return which isindependent from the foreign sector. Note that the impact of the expectedexchange rate change on stock returns depends on both the importance ofinternational trades in the domestic economy, 1 K, and the degree of the


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EXCHANGE RATE CHANGES AND STOGK PRIGE REAGTIONS 445expected appreciation of the domestic currency. The net impact of the exchangerate change is determined by the relative importance of importing firms vsexporting firms within a given economy. Alternatively, the sign of f dependson the status of the trade imbalance, i.e.,

c > s: If the domestic economy is import dominant, then f < 0,c < s: If the domestic economy is export dominant, then f > 0.

The second set ofexpectation scheme is the exchange rate movement of eachcurrency. Specifically, the expected appreciation is assumed to follow anadaptive process:

Eiet^O = s, - s,_i + III (12)where /x, is a white noise.Substituting equations (10), (11) and (12) into the stock equation (7) andthe flow equation (9), the system becomes the following two first-orderdifferential equations:

Pi = 1//C \IK

with initial conditions: p{0) = p, n(0) = h.Solving the above system for p yields equation (13) (see Appendix A for

derivation):Pi = a - 2{1 - K){UK)q \n{s/c){Si - ^,_,) -h q(i/K - 0)si (13)

where a = p exp(Xi 0

and X] is the negative eigenvalue for the system.

M E T H O D O L O G Y

HypothesesEquation (13) can be rewritten in the following fashion:

\n{P/Pt) = a + bti{\nSi - \nS,_{) + dlnS, (14)where b = -2q{\lK){\ - /c) < 0;

d = q{\lK - /3) > 0; and


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44 6 MA AND KAOwith the rest of the world, the currency appreciation would discourage exports.This, in turn, would result in a depressed stock market composed of moreexporting firms. On the other hand, for a domestic economy experiencing atrade deficit, the currency appreciation will lower import costs and impact stockm arkets favorably. As indicated from equ ation (14), the effect of exchang e ra techanges on stock market indices might be insignificant if the economy is lessdependent on foreign trades, i.e., /c = 0. The third term demonstrates theimpact of transaction exposure from exchange rate changes. It suggests thatany investment denominated in a strong currency is preferred by investors.Note that there is an unambiguous positive impact from the exchange rate levelon the stock market, regardless of the foreign dependence of the economy.Sample and Empirical AnalysisTo test equation (14), monthly stock indices of six major industrialized countriesand corresponding monthly exchange rates are gathered from the Exchange Ratesand Interest Rates Tape provided by the Federal Reserve, United Kingdom,C ana da, France, W est Ge rm any, Italy and Ja pa n are chosen because of theirless controlled foreign exchange markets and more mobile capital markets. Themonthly merchandise exports and imports of the US with respect to each ofthese countries are gathered from Business Statistics. The sample period is fromJanuary 1973 to December 1983.Since the US stock market is the perfect substitute for the rest of the world,^the foreign stock market index is a weighted average of all foreign stock indices,and the US exchange rate is the corresponding weighted average of dollar valueswith respect to foreign curren cies. C ons equ ently, all variables are first adjustedby the weight of the international trade with the US:

Ei- 1

where6= (Expo rt,, + Im po rt,()/5 ] (Export^, +

As implied from the model, the change of the currency value, e, , is furtherweighted by the dummy variable, f, which measures the degree of export/


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EXCHANGE RATE GHANGES AND STOGK PRIGE REAGTIONS 447exchange rate change:

6 6\n{s/c)i = ln(X; Export,/ ^ Import,,).

i' - 1 i ' I

Eventually, the regression is conducted on the following relationship:ln{P/P;) = 0-1- be; + ds;. (15)

In order to correct for the bias of multicollinearity between e,' and .f / , a two-step regression procedure is followed. First, s,' is regressed against e,'. Theresulting residuals, which are independent to e/ , are used to replace s,' intesting equation (15).Testing ResultsTable 1 reports the regression statistics of equation (15). The exchange ratelevel is positively related to the stock index relative at the one percent level,while the exchange rate change is negatively related at the five percent level.The entire model is significant at the one percent level.

Table 1

The Regression Statistics for Equation (15):= a + be, -i- ds,\n{P/P;) = -0.0933 - 0.7270?, + 1.1903.r,(-0.847a) (-0.379)" (0.276)*

F = 11.13* fl-Square = 0.148a: The value in parenthesis is the standard error of the estimate.*: Significant at the 1 percent level.**: Significant at the 5 percent level.The evidence suggests that if the investment is denominated in a strong

currency, foreign investors expect to receive an ultimately higher rate of returnafter the payoff is converted into their own currency. Consequently, a highcurrency value generates a favourable transaction exposure and creates excessdemands for domestic stocks. On the other hand, consistent with the classicaltheory of balance of payment, the expected change in a country's currencyvalue tends to reverse the current status of the trade imbalance. The domesticstock market reacts favourably to the expected currency appreciation if theeconomy is import dominant. Conversely, an export dominant economy will


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448 MA AND KAOare more sensitive to transaction exposure than to economic exposure. Onepossible explanation for the difference is that the US economy is not fullydependent on foreign trades. The domestic stock market is determined by theforeign sector to a lesser extent. In addition, there is some contract rigidityin international trades in terms of responding to exchange rate changes. Thecost and sales adjustment are delayed by the contract period, and the changein relevant cash fiows is discounted in a future distant period. On the otherhand, the greater importance of the transaction exposure is attributed to therelatively more open a nd m obile U S capital ma rket. As long as the investmentis denominated in a foreign currency, all investors are invariably confrontedwith the transaction exposure.

GONGLUSIONTh is paper dem onstrates two possible impacts of changes in a coun try's cu rrencyvalues on stock price movements. Primarily, the financial effect of exchangerate changes is the transaction exposure investors face if the underlying currencyvalue is volatile. Since an investment becomes more attractive when it isdeno m inated in a strong cu rrency, high exchange rate levels are associated w ithfavourable stock price movements. On the other hand, the economic effect fromexchange rate changes suggests that, for an export-dominant country, thecurrency appreciation reduces the competitiveness of export markets and hasa negative effect on the domestic stock market. Conversely, for an import-dominated country, the currency appreciation will lower import costs andgenerate a positive impact on the stock market.

APPENDIX AUK UK e,,,) - W)IK'\

Solving for the eigenvalues of the system:[ 1//C-X, UK-0 - / 3 - 0then: X, = (-( /3 + - 1/K) - J(0 + - XUf + 4


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E X G H A N G E R A T E G H A N G E S A N D S T O G K P R I G E R E A G T I O N S 4 4 9where B, + B2 = 0/ " (2(1 " ) ln{s/c) + l)(,.^l) - W)/K = Kg

X|.B, + X2B2 = 0s, + 0U 1 + a + |8(,.^l + M) = ^ h and

For the general solution of/ '(():f ( 0 = (/I , + [X^Kg - /:,y[(>^2 - \)^imi - e x p ( - X , O ] e x p ( X , 0

with P{0) = P, and solving for A^, therefore,A, = P.

The final solution becomes:P(t) = exp( X| (X ^ + A/ + A') - (A/ + W),

where M = (X^Ko - /r,)/[X,(X2 - X,)]A^ = [-h(2{c - s) + 1)M]/[X,(X2 - X,)] + M(3/[X,(X2 - X,)].

N O T E S1 The positive root of eigenvalues is dropped from the general solution for its destabilizing prope rty.2 In a two-m arket world with a budget cons traint, inve stmen ts in the US mark et world haveto be a perfect substitute of investments to the rest of the world.

REFERENGESAggarwal, R. (1981), 'Exchange Rates and Stock Prices: A Study of the US Gapital Markets underFloating Exchange Rates' , Akron Business an d Economic Review (Fall 1981), pp. 712.Agm on, T. (1974), 'The Relations Among Equity Markets in the United States, United Kingdom ,Germany and Japan' , bourne/ of Finance (September 1974), pp. 83955.and D .R . Lessard (1977), 'Investor R ecognition of Gorp orate International Diversification',Journal of Finance (Septemher 1977), pp. 104955.Ayarslan, S. (1982), 'Foreign Exchange Rates and the Stock Prices of US MultinationalGorporations', M!rf-.


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Exchange Rate and Stock Price

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