Uncovered interest rate parity (UIRP) provides a crucial theoretical concept for many models in international finance and international monetary economics. Though theoretically sound, the problem, however, is that UIRP does not seem to hold up well empirically. Typically, econometric tests not only reject the null hypothesis, but also find significant slope coefficients with the wrong sign. In this paper, we argued the validity of UIRP violation that has been so widely documented as a coincidence or not. Variables used in this study are spot exchange rate and interest rate. Using quarterly edata span from 1998Q1 to 2010Q3, we run conventional regressions and simple GARCH analysis on UIRP for the case of Malaysia-UK, Malaysia-Japan and Malaysia-Singapore. Nevertheless, the empirical results show that these relationships do not support the UIRP in all cases. We, therefore, cannot reject the validity of UIRP violation such as in widely documented literature reviews. In addition, we also find that traditional (conventional) regressions on UIRP yield positive slope estimates for both Malaysia-UK and Malaysia-Japan cases, whereby for the case of Malaysia-Singapore, the beta slope estimates has a wrong sign (negative value). The result also shows that the UIRP deviation for the case of Malaysia-Singapore has the smallest standard deviation. Moreover, the volatility analysis on the UIRP deviation using simple GARCH analysis revealed that there are significant ARCH and GARCH effects in the case of Malaysia-Singapore, and it seem to be persistence in the long term period. In addition, the empirical investigation on the impact of the interest rate volatility shocks on UIRP deviation does not exist in any cases.

Uncovered interest rate parity (UIRP) is one of the fundamental relationships in international financial markets and constituting an essential basis of some main exchange rate determination theories (Hilde, 2009). It states that the nominal interest rate differential between two countries must be equivalent to or should be an unbiased predictor of the future change in the spot exchange rate. Therefore, the investors’ expected return on the domestic and foreign assets expressed in the same currency should be equal regardless of the national markets within which the foreign deposit is invested. The failure of the interest rate differential to be the unbiased predictor of the future exchange rate change is referred as the uncovered interest rate parity puzzle (Cook, 2009).

Thus, if UIRP holds, investors cannot gain an arbitrage opportunity due to high yield currency is expected to depreciate by an amount approximately equal to the interest rate differential between two countries. A violation of this relationship indicates that capital markets are not efficient and there is a possibility of arbitrage opportunity (see cook, 2009; Frankel, 1992). Besides, any finding reflecting reverse relationship is called forward premium puzzle (see Bansal & Dahlquist, 2000; Cook, 2009).

The basic assumption underlying UIRP is the efficient market hypothesis where the price should fully reflect all the information available to the market participants and thus no profitable opportunities will be possible in the market (Erdemlioglu & Alper, 2007). This means that exchange rates will quickly adjust to any new information, which should immediately be reflected in the exchange rate. Furthermore, it can be considered as a joint hypothesis that the market participants have rational expectations, and that they are risk neutral. If these assumptions are valid and UIRP holds then the expected return from holding one currency rather than another is cancelled out by the opportunity cost of holding funds in that currency versus another.

Even though many emerging markets have started liberalizing their financial markets in the late 1980s and the early 1990s, but their degrees of financial liberalization are still far behind from the developed markets (Alper, Ardic & Fendoglu, 2007). Alper et al. indicated that emerging markets have weaker macroeconomic fundamentals, more volatile economic conditions, shallower financial markets, and incomplete institutional reforms. Therefore, these characteristics may violate the assumptions of the efficient market hypothesis contributing to the deviations from the UIRP conditions. In other words, the UIRP condition is less likely to hold in emerging markets than in developed economies but to what extent?

Earlier empirical literature on the UIRP condition mostly focuses on developed economies rather than emerging markets because of lack of data (Pasricha, 2006). Recently, increases in the degree of financial liberalization in emerging markets enabled many researchers to analyze foreign exchange market efficiency in these economies (Alper et al., 2007). It is the lack of a comprehensive survey reviewing this recent literature in emerging market, especially Malaysia that motivates this study.

As the result of that, the purpose of this paper is to examine the UIRP condition in Malaysia following the restructuring Malaysian economic after the Asian Crisis 1997 aftermath using the conventional regressions and simple GARCH analysis by looking at the Malaysia-U.K, Malaysia-Singapore and Malaysia-Japan cases. The structure of the paper is as follows: UIRP and the selected review of empirical testing of this condition are discussed in the next section. In section 3, we describe the data set and methodology. Section 4 and 5 present the empirical results and conclusion respectively.

## SELECTED LITERATURE REVIEW

UIRP has been studied for many different currencies, time-periods and interest rates maturity horizons (mainly in the developed markets) but the majority of the papers rejected the UIRP condition (α = 0, β = 1) empirically (e.g Cuiabano & Divino, 2010; Huisman, Koedijk, Koo & Nissen, 1998; King, 1998; Pasricha, 2006). Some of the reasons of this deviation are the existence of (time varying) risk premiums, peso-problems, market inefficiencies and neglected persistent autocorrelation in the forward premium., as well as small sample problems (Francis, Hassan and Hunter (2002); Huisman etal., 1998). Surprisingly, some study results indicated the forward puzzle, which is, the forward premium or forward discount (interest rate differential) predicted the expected spot exchange rate change in the wrong direction. Erdemlioglu and Alper (2007) pointed out the main factors that cause deviation of UIRP due to transaction costs, the choice in currency pairs and time horizons, and the violation of the joint hypothesis of rational expectations or risk neutrality.

Even though the consensus among the empirical researchers loosely supported for the UIRP, theorists and policy makers have often ignored the matter (Bekaert, Min & Yuhang, 2007). One of the reasons a continued use of the hypotheses due to the fact that the UIRP deviation are currency and maturity dependent (Drakos, 2003). It may be that irrational behavior or short-term market frictions causes a short-run deviation of the theory but the deviations seem to be less severe at long horizons. However, there is a mix empirical support for this argument.

Using the long term interest rate, Mehl and Cappiello (2007) had found support of UIRP for the case of dollar rates in relation to other major floating currencies (e.g ), but not in comparison to emerging market currencies. Meanwhile, at the medium-term horizon, the paper had detected the sign of nonlinearities in UIRP condition for the dollar rates in relation to some of the major floating currencies (e.g ). Meanwhile, Inci (2006) study results also reported the similar situation when using the short term and long term interest rate for comparison. The study found out that UIRP did not hold for US-United Kingdom, US-Switzerland, US-Japan, US-Germany, US-France and US-Italy cases using the short-term interest rate differential. The relationship also had a negative slope coefficient but insignificant except for US-Italy where the coefficient was positive, though, still significantly less than one. This negative relationship is consistent with the forward premium puzzle. Chinn (2006) study results also indicated the failure of interest differential as the unbiased predictor of the future change in the spot exchange rate over the short horizons with very low R square value. The value of β closed to unity over the longer horizon maturity.

On the contrary, there was evidence of UIRP condition when using long-term interest rate differential, which showed a positive and significant slope coefficient. Bekaert et.al (2007) also highlighted that the variability and persistence of risk premiums were different across countries that might influence the deviations of UIRP. However, in Chaboud and Wright (2004) study findings showed that there were supportive of the UIRP hypothesis over the short horizon of high frequency data, but it was not persistent. However, in King (1998) study, the findings showed support for the UIRP in the case of New Zealand-Australia relationship regardless of the choice of the forecast horizon.

Alper et al (2007) concluded that emerging markets deal with a different situation due to the existence of additional types of risk premia, high inflation, financial contagion and asymmetric information. However, with the financial account liberalizations in the last two decades, there is an opportunity to investigate the foreign exchange market efficiency in emerging markets via testing for the UIRP (Chinn, 2006). In other words, there is little reason to believe that the unbiasedness hypothesis and UIRP should hold in emerging markets.

Regarding the issue of UIRP deviation in emerging markets, Greger (2010) indicated this deviation as an indicator of the lack of financial market integration. Francis et al. (2002) pointed out that deviations from UIRP in the emerging markets were indeed characterized by a time-varying component that is compensation for non-systematic risks. Surprisingly, they found out that there was contrasting effects of liberalization on UIRP across some Latin American and Asian countries in general, where the results showed that the deviations from UIRP were significantly affected by the liberalization of capital markets.

There are few empirical studies testing the UIRP condition in Malaysia (e.g Francis et al., 2002; Goh, Lim & Olekalns, 2002). Most of these studies used US dollar as foreign currencies for testing the UIRP conditions and showed deviation of UIRP condition. Existing of risk premia was one of the reasons.

In conclusion, even though the UIRP hypothesis was intensively tested since the creation of the theory, there were exist of mix supports in the empirical evidence. This controversy, therefore, motivates the conduct of this research on the UIRP condition in Malaysia by looking into different type of currencies relationship where the empirical evidences are still not clearly developed.

## DATA AND METHODOLOGY

The data consists of quarterly nominal interest rates for four countries (Malaysia, United Kingdom (UK), Singapore and Japan) and nominal exchange rates between the MYR and three other currencies (UK, Singapore and Japan) for the period 1998:Q1 until 2010:Q3. UK, Singapore and Japan have a significant economic relationship with Malaysia due to their trading activities. The interest rate and exchange rate data are constructed from two sources. The exchange rate and domestic interest rate data have been obtained from the Central Bank of Malaysia database. We collected the foreign interest rates from their respective central bank database. We used 3-month interbank interest rate for Malaysia, Singapore and UK, whilst, for Japane we used 3-month certificate of deposit for Japan. The data is constructed to be non-overlapping at a quarterly interval.

There are vast studies in explaining both the UIRP theory and model. However, in this study, the construction of the UIRP model follows closely to studies done by Erdemlioglu (2007), Goh, Lim and Olekalns (2006), Horobet, Dumitrescu and Dumitrescu (2009), and Adrangi, Raffiee and Shank (2007). In this study, we employed descriptive statistics analysis, conventional regression, unit root tests and GARCH in analyzing empirically UIRP theory and its related characteristic (e.g. deviation, stationarity and volatility).

According to the efficient market hypothesis, in an efficient speculative market, the price should fully reflect the information available to the market participants (Erdemlioglu & Alper, 2007). Therefore, there is no excess returns via speculation could be earned. Economists tried to find out this idea by testing the joint hypothesis that the market participants have the rational expectations, and they are risk neutral. If the theory holds, then the expected return from holding one currency must be offset by the opportunity cost of holding funds in that currency versus another. In other words, the domestic interest rate must be higher than the foreign interest rate by an amount equal to the expected depreciation of the domestic currency. In general, the uncovered interest rate parity condition is thus:

(1)

where s is the logarithm of the spot exchange rate at time t (and k is the time to maturity), and i and i* are the nominal interest rates in the domestic and foreign countries respectively. The common means of testing UIRP is via (traditional (conventional) regression analysis. Using covered interest rate parity (CIP) condition, we can derive an OLS regression which tests our hypothesis. CIP claimed that the nominal domestic interest rate must be higher than the nominal foreign interest rate by an amount equal to the forward discount on the domestic currency. The difference between CIP and UIRP is that when you take a covered position you are eliminating uncertainty by using a forward rate. Therefore CIP is:

(2)

where ft is the logarithm of the k-period ahead forward rate at time t. By substituting equation (2), CIP, into equation (1), UIRP, and adding an error term, , we get a regression of the form:

(3)

or in other form:

(4)

Empirical assessments of UIRP as a framework for predicting the future spot exchange rate have distinguished two issues: the size of the prediction errors, and the question of whether the predictions are systematically biased. On the first issue, it becomes widely known that interest differentials explain only a small proportion of subsequent changes in exchange rates. On the second issue, the hypothesis of unbiasedness can be assessed by testing whether in equation (3) or in equation (4). Notably, the test that the slope coefficient is unity receives strong support from studies based on (3) but is soundly rejected by studies based on (4), at least for prediction horizons of a year or less. However, the apparent conflict between the two sets of regression evidence has been resolved in favor of the latter finding, as it is now accepted that (3) is not a legitimate regression equation (Isard, 2006).

This then predicts that the log forward rate is an unbiased predictor of the log future spot rate. In running the OLS regression in (3) we test UIRP via the joint hypothesis that and . The existing literature has approached this puzzle from a number of different ways. Empirically, the finding of a negative estimate of in equation (3) is robust.

In the first step, this study conducts unit root tests to check the order of the variables used by using the Dickey-Fuller (DF) or Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP). The DF and ADF (Dickey and Fuller, 1979) test are based on the following regressions,

(5)

where is the first difference operation, is the stationary random error and is variable series. The null hypothesis for this test was . If the null hypothesis cannot be rejected, then the data set contain unit root (non-stationary).

(6)

where is the maximum autoregressive levels, is constant, is a linear time trend, and are slope coefficients, is the error term. The null hypothesis of non-stationary series could be written as

(7)

The one-sided alternative hypothesis of stationary series could be expressed by

(8)

The length, for the ADF test was chosen by minimizing the Schwarz information criterion. The SIC criterion is defined as

(9)

where is the value of the log of the likelihood function with the parameters estimated using observations. The various information criteria are all based on -2 times the average log likelihood function, adjusted by a penalty function.

Another alternative approach is Phillips-Perron (PP) test that suggested by Phillips (1987) and extended by Perron (1988) and Phillips and Perron (1988). Rather than taking account of the extra terms in the data-generating process (d.g.p) by adding them to the regression model (as in ADF test), a non-parametric correction to the t-test statistic is under-taken to account for autocorrelation that will be present when the underlying d.g.p. is not autoregressive at first level, AR(1). Phillips and Perron (1988) propose an alternative (non-parametric) method of controlling for serial correlation when testing for a unit root. The PP method estimates the non-augmented Dickey-Fuller (DF) test equation (1), and modified the t-ratio of the coefficient so that serial correlation does not affect the asymptotic distribution of the test statistic. The PP test is based on the statistic:

(10)

where is the estimate, and the t-ratio of , is coefficient standard error, and is the standard error of the test regression. In addition, is a consistent estimate of the error variance in equation (1) calculated as , where is the number of regressors. The remaining term, , is an estimator of the residual spectrum at frequency zero.

For the purpose of volatility analysis, the basis to the formation of the ARCH (p) model introduced by Engle (1982) is as follows:

(Mean Equation) (11)

where t = 1,…, T

(Variance Equation) (12)

where is a dependent variable and is a conditional variance () and is a variable set or information which can be acquired at t time period where whereas is kx1 external variable vector which can also take the lag value of the dependent variable itself which is and is kx1 parameter vector for the external variable used. The coefficients,, and have to be positive to ensure a positive variance. The coefficient must less than 1 otherwise will continue to increase over time, eventually exploding.

The GARCH model was introduced by Bollerslev (1986) for the purpose of representing the ARCH process which has stage (q), the higher level. The GARCH model is more appropriate and parsimony when compared with the higher class ARCH model. The conditional variance equation specified in (5) is a function of three terms namely a constant term, news about volatility from the previous period, measured as the lag of the squared residual from the mean equation, and the last period’s forecast variance. All coefficients and must be positive and the coefficients and must less than 1 that is for stationary; if, we have a so-called “integrated GARCH” process or IGARCH (Hill, Griffiths & Lim, 2008). In addition, if the sum of the coefficients is very close to one, indicating that volatility shocks are quite persistent. The model for GARCH (p,q) created is presented as follows:

(13)

where t = 1,…, T

(14)

Meanwhile, the forming of the effects of volatility model based on the GARCH (1, 1) on the UIRP deviation is presented as follows (Kogid, Sook-Ching & Jusoh, 2009):

(15)

(16)

where:

y = UIRP deviation

yq = interest rates

q = Japan (JP), United Kingdom (UK) and Singapore (SG).

V2q = variance on shock in nation q after allowing changes effect in three other countries.

For example, the variance shock on the Japan interest rate, V2J where a square error is attained from the following regressed equation:

(17)

## EMPIRICAL RESULTS

The UIRP deviation in Malaysia for all cases from the first quarter in 1998 to the third quarter in 2010 is shown in Figure 1 (see also Figure 6 to Figure 8). The UIRP deviation for all cases is a bit fluctuated except for Malaysia – Japan which deviates and goes up from in the mid 1998 to mid 1999 and later the trend shows a bit stable around -0.8 to -0.4. However the depreciation on the other hand shows that for the case of Malaysia – Japan, the depreciation rates is highly volatile compared to Malaysia – UK and Malaysia – Singapore (see Figure 2). Moreover, the interest rate differential for the case of Malaysia – Japan is quite stable after 1998. Malaysia – UK and Malaysia – Singapore on the other hand, the interest rate differential is rather fluctuated. The spot exchange rates for all cases indeed show highly volatile during the time periods.

Table 1 shows the descriptive statistics summary for UIRP deviation in all cases. The Malaysia – Singapore has the smallest standard deviation which is 0.3064 compared to Malaysia – UK and Malaysia – Japan which are 0.3953 and 0.4543 respectively. The empirical result also shows that the UIRP in all cases are not supported using the conventional regression analysis (see Table 2). The joint null hypothesis (H0: β0 = 0, β1 = 1) is rejected using Wald test at 1 percent significance level. We also find that the regressions on UIRP yield positive slope estimates for both Malaysia-UK and Malaysia-Japan cases, whereby for the case of Malaysia-Singapore, the beta slope estimates has a wrong sign (negative value). The estimated regression coefficients for Malaysia – UK, Malaysia – Japan and Malaysia – Singapore are 0.0149, 0.0041 and -0.0003 respectively. The R-squared (R2) is low for all cases especially for Malaysia – Singapore.

The results of the unit root tests using the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) approach is presented in Table 3. It shows that all variable series which are the spot exchange rate and the interest rate differential (for all cases) are not stationary at levels (tests including intercept and trend in the equation). All variable series are stationary and can be integrated at the first difference regardless the assumption of intercept, and intercept and trend included in the test equation. Except for Malaysia/Japan spot exchange rate which is stationary at level using ADF test when only intercept included in the test equation. Besides, the interest rate differential for Malaysia – Japan is also stationary at level (intercept included in the test equation) for both ADF and PP tests.

Table 4 reflects the volatility analysis on the UIRP deviation for each case in this study. Only Malaysia – Singapore indicate that volatility did exist (ARCH’s impact) in UIRP deviation as shown by the coefficients, which is significant, except in the case of Malaysia – UK and Malaysia – Japan. Indeed, the Malaysia – Singapore also have experienced with GARCH’s impact as shown by the coefficient, . Generally, the volatility analysis on the UIRP deviation using simple GARCH analysis revealed that there are significant ARCH and GARCH effects in the case of Malaysia – Singapore, and it seem to be persistence in the long term period.

The impact of the interest rate volatility shocks on the UIRP deviation is shown by the value of γ (see Table 5). The empirical investigation on the impact of the interest rate volatility shocks on UIRP deviation using the GARCH (1,1) model which has been modified in order to take into account the external shock impact, does not exist in any cases.

## CONCLUSION

Our primary finding is that UIRP does not hold which is consistent with the study by Goh et al (2002). We find that this is true for Malaysia – UK, Malaysia – Japan and Malaysia – Singapore cases. This indicates that there is a possibility of arbitrage opportunity between Malaysia and the studied markets due to the inefficient market as stated in Frankel (1992) study. We also find out that there is exist of forward puzzle for the case of Malaysia-Singapore indicated with the negative estimated slope coefficient. This implies that high interest rate currencies continue to appreciate. This is indeed opposite direction that UIRP dictates. The result also shows that the UIRP deviation for the case of Malaysia-Singapore has the smallest standard deviation. Moreover, the volatility analysis on the UIRP deviation using simple GARCH analysis revealed that there are significant ARCH and GARCH effects in the case of Malaysia-Singapore, and it seems to be persistence in the long term period. In addition, the empirical investigation on the impact of the interest rate volatility shocks on UIRP deviation does not exist in any cases. Given both the findings presented here as well as those in the existing literature, there is much work to be done on this puzzle, with many possible directions for future research.

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