# Foreign Exchange

### Measuring the foreign exchange exposure

In order to establish the relationship between the stock price and exchange rate we will fallow Adler and Simon(1986) model and apply another model as Jorion(1990) approach with the aim to extend this model. This methodology will help us in measuring the sensitivity of individual company's stock price towards the exchange rate and market returns, it will measure the economic exposure as the slope coefficient from a regression of stock returns on the exchange rate. For estimating the exposure of exchange rate changes on the stock prices, we employee the two-factor "Ordinary Least Square"-OLS market model, this method is also been used by Bartov and Bodnar, Pritamani et al, 2003 and .The coefficient could be either positive or negative. The positive coefficient means when INR depreciate, the stock returns increases. Positive value of fi means that a depreciation of INR corresponds to an increase in the value of firm. the reason for nor considering the multi-currency approach to express the exposure coefficients to exchange rate risk in as many independent variables as the number of foreign currencies that appear in a firm's transactions is due to the problem of multi linearity problem copied. Schnabel (1989) supports to the above point by stating that in a multi currency approach there is a high correlation between the different exchange rates. Individual companies stock returns is the dependent variable in our regression equation and exchange rate and market returns are the independent variables. In the model, the exchange rate quotation is a direct quotation for India, which means it is shown as Indian rupee per one unit of US dollar. The exchange rate which we are considering for the methodology is the monthly bilateral exchange rate. While measuring the exposure test, some studies have considered the trade weighted exchange basket of currencies. Kathryn et al (2001) has argued that, using the trade weighted exchange basket of currencies might result in lack of power, if the nature of firm's exposure does not correspond to the exchange rate and the relative weights included in the basket. In the study, we have applied another macroeconomic variable called as the market returns which was introduced by Jorion to control for market movement. Most of the empirical studies have used the return on market portfolio as an variable along with the exchange rate as a variable to control for the common macroeconomic influences on total exposure elasticises,

### Measuring the Casualty relationship between the exchange rate and stock price

The second methodology involves the use of some of the modern statistics for investigating the interaction between the exchange rate and stock price. Here we will be applying some of the popular and commonly accepted test like unit root test, co integration test and Granger casualty test which helps in identifying the casualty relation between our variables, unlike the regression which reflect "mere" correlation between the variables. Thus this methodology well be able to explain whether the exchange rate cause a change in stock price and visa versa.According to Granger (1969), the causality test involves the test of whether lagged information on a variable Y, provides any significant information which is statistical about a variable X, by using F-test in the presence of lagged X. If not then Y does not granger cause X. In other words, by considering the past value of Xt Yt, if the series Yt can be prediected better than considering only the historic value of Yt, then we can say that the time series Xt granger-casues the time series Yt. If for all m > 0, then Xt fails to granger-cause Yt, given the conditional proboblity distribution of Yt+m ( Yt, Yt-1,...) is the same as the conditional proboblity distribution of Yt+m given both (Yt, Yt-1,....) and (Xt, Xt-1,....) we can say that Xt does not granger-cause Yt if Where, the conditional probability is denoted by Pr (), the information set at time t on the past values of Yt is denoted by ? t, and the information set containing values of Xt and Yt up to time t is denoted by Ot. The following bivariate autoregression can be used for testing the causal relationship between the two variables Xt and Yt which are stationary Where; the chosen suitable positive integer is p; and u_tand v_t are the usual disturbance terms with finite variances and zero means In the equation (4), using a statdard joint test (e.g., an F test), if k's, k>0 are jointly significantly different from zero, than the null hypothesis that Xt does not Granger-cause Yt is rejected. Similarly in equation (5), if the ? k's, k>0 coefficients are jointly different from zero, than Yt Granger-causes Xt Performing the Granger causality test requires that data should be stationary that is by differencing the variables until stationarity is achieved, the Granger causality test does not require that its variables to be co integrated and have a long run equilibrium relation. The test can be performed on any pair of variables with or without co integration From the above discussion it's clear that we need to perform two different kind of test in order to measure the casualty relation. First is the stationerty of time series and co integration test

### Stationarity: concept, test and implications

In a random variables like X1, X2.... each variable has its own probability distribution like Xt (t= 1,2,....). a time series is said to be stationary if its mean, variance and covariances remain constant over time. The stationay test could be performed by using OLS regression and by t-test. For example, let us take in to consideration of a model with the economic time series with the first order autoregressive process which would be as follows In the above model, we assume if the parameter ? equals or exceeds units, than Xt will be non-stationary, but in a time series data, if the parameter 1 then the series said to be stationary. An obvious way of proceeding with this model is by applying OLS to the model and look at ?, and secondly we can t-test by farming null hypothesis that is Ho: ?=1 against the alternative Hypothesis that HA: ?<1 and rejection of Ho means we have a stationary series.But unfortunately, following these two procedures has a number of problems. Firstly, the OLS estimator ? will be biased due to the presence of the lagged dependent variable in means and we may end up with the conclusion of rejecting the Ho: ?=1 and that Xt is stationary when it is not, so in this case test statistic cannot be trusted. Secondly, when we have a large sample we cannot rely on the test statistic being normally distributed, because of its symmetrical and non-standard distribution. D.A. Dickey and W.F. Fuller faced this problem first, so they come up with the Dickey-Fuller (DF) and the Augmented Dicky-Fuller (ADF) test. Which are the most commonly used for investigating the existence of unit root (non-stationary) in a time series.A non-stationary time series could be represented as I(1) which indicates it's a integration of first order.Jorion (1990) in his study measures the firm's exposure to exchange rate by considering the foreign sale to total sales ratio and come up with the conclusion that, over the period from 1971 to 1987, 5.5% of firms have a significant exposure at the 0.05 level. After analysing the present empirical results with that of some of the previews studies. We can come to the conclusion that their exist a relationship between the fluctuating exchange rate and stock returns