4. MethodologyMost empirical studies employ OLS method to estimate the effect of interest rate and FX rate changes on bank stock returns. Thus, following model is estimated with OLS:rt = β0 + β1MRKt + β2INTt + β3FXt + μt ð1Þwhere rt is the return of the ith stock at time t; MRKt is the return of the market index which is considered to reflect economy-wide factorsINTt is the return of a risk-free interest rate or bond index; and, FXt is the return of the foreign exchange rate (FX). β0 is the intercept term and μt, is an error term with the assumption of an iid condition. The suitability of the OLS estimation is tested with the ARCH test. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) process, first introduced by Bollerslev (1986), is estimated next. The GARCH (1, 1) process is specified as follows:rt = γ0 + γ1MRKt + γ2INTt + γ3FXt + εtσ2t = α0 + α1ε2t−1 + βσ2t−1ð2Þwhere other parameters are defined as before, the variance equation includes the long-term average volatility α0, news about volatility from the previous period which is defined as an ARCH term and the previous period's forecast variance which is defined as the GARCH term. The GARCH specification requires that in the conditional variance equation, parameters α0, α1 and βshould be positive for a non-negativity condition and the sum of α1 and β should be less than one to secure the covariance stationarity of the conditional variance. Moreover, the sum of the coefficients α1 and β must be less than or equal to unity for stability to hold.The following GARCH (1, 1) model is used next, to analyze whether interest return and FX rate return volatility have any impact on the stock return volatility of individual banks and bank portfolio. INTt and FXt2 are used to measure the interest rate and FX rate return volatility.rt = γ0 + εtσ2t = α0 + α1ε2t−1 + βσ2t−1 + θ1INT2t + θ2FX2
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