Econometric Modeling and the Effectiveness of Hedging Exposure to Forging Exchange Risk - Research Proposal Example

Econometric Modeling and the Effectiveness of Hedging Exposure to Forging Exchange Risk Name Institution Date Introduction There is a great financial risk posed in the world economy as a result of the instability of the currencies involved. In order to avert the impacts that could be associated with such financial risk, there have been efforts to seek means of reducing the risk magnitude. It is for such reason that certain instruments have been developed with the intention of reducing the risk. In this case, all the risk reduction instruments are used for optimal risk reduction effects. A hedge ratio thus will be formulated through determination of the optimal tally of the instruments of risk reduction. This process is done through analysis of the correlation existent between the tool for risk reduction and thee spot instrument. Hedging thus potentially reduces economic exposure. Hill & Schneeweis (1981) hold that although hedging might not entirely be of great concern when existing futures contract is represented by foreign currency, although determination of the kind of futures contract to be employed for the purpose of currency hedging if hedging of no futures contract that can be subjected to hedge is possible. The risks involved with the movement of prices have been reduced through the portfolio approach and the minimum risk ratio for hedging as developed by Johnson. The process of risk reduction seeks to achieve a significant shift of value of the item being hedged. This explains why hedging effectiveness is measured through determination of the extent to which the derivative of hedging offsets the true hedging. Some argument have been put forward that reliable assessment of the success of futures contracts can be undertaken through application of the hedging effectiveness determination methods. In light of Moosa (2004), Joseph (2000) and Moosa, I.A. and McDonald (2005),money market hedging is understood as a hedging technique involving the risk for foreign exchange through such means as trading of commercial papers, bankers acceptances or treasury bills, utility of the in the financial market with high liquidity levels or utility of the black market resources. Marshall (2000) argues that since foreign exchange can be hedged through various means as currency options, futures and forwards, the money market never stands as the most convenient or cost-effective method through which large scale institutions and corporations will get to hedge such a risk. However, the method is the most viable option for firms that are small scale and their financial bases are insufficient to guarantee entry into ford contract or future market. The method is effective in protection against fluctuation of currency. Cross currency hedging involves a fundamental strategy for investment in which a position is taken for a currency, which is succeeded by futures position of the same spot although opposite in nature on a different currency with the same movements of the price, as held by Moosa (2004) &,Brooks &Chong (2001). As the movement of price for the 2 currencies is expected to show close correlation, the present currency negative shift is expected to be offset by a positive spot on the futures. Cross hedging has been applied in the markets that lack futures markets that are not viable for the present currency. This project seeks to assess the impact of the process of econometric modelling in the determination of the ratios of hedges with intent to realize any form of variations on the cross currency and money market hedging exposure to the risks of foreign exchange. The project will undertake a study of 4 major approaches to the study of hedge ratio estimation. The four models are the conventional model in levels, a first difference model, a quadratic model and the error correlation model. Derivation of these models relied on the rates of exchange and the interest rates of the CHF, CAD and AUD. the conventional approach has been used in the determination of the hedge ratio through application of the spot price change regression of the change in price of futures with special analysis and application of the technique of ordinary least squares (Lien 1996; Brooks, Henry &Persand 2002). Developed by Ederington during his pioneer work, the model through OLS regression effectively presents the hedge ratio in optimal measures between the futures and spot contracts (Ederington 1979). The quadratic model has had a number of applications, and optimization has been such an application. The model has equally been relevantly applied in the determination of the hedge ratio. Markowitz’s quadratic model is such a model that has received much application. The model is effective in the process of efficient portfolio determination with intent to optimally reduce the variance (risk) with regard to a specified return. Engle and Granger (1987) are behind the development of the cointegration theory (Lien 1996). The theory seeks to develop integration of short-term dynamics and the long-term relationship of equilibrium. Such integration reveals that 2 series which are non-stationary with a stationary linear combination must be characterised by a correction representation for the error present, and the 2 series are mandatorily cointegrated. If any equation developed under the error correlation model fails to identify the term for error correction or the short term dynamics, the equation is basically a misspecification. Such formulated equations are prone to realize unreliable hedge ratio values. The model can effectively carry out tests for cointegration and realize reliable results. The paper follows a logical order. Chapter I cover the introduction of the research topic, chapter 2 tackles the paper’s literature review, chapter 3 is a discussion of the empirical testing methods, chapter 4 gives the results obtained from empirical testing and chapter 5 summarizes the paper through the conclusion. 1. Literature review This chapter reviews the techniques of econometric modeling and sufficiently looks at the possible change these models can initiate on cross currency and money market hedging of foreign exchange risk exposure. In this order, the scrutiny of the hedge effectiveness is relevant and viable when there exists a situation expected to realize significant and considerable change to the hedged item value. The types of economic modeling discussed here entail a significant movement of prices of items hedged with rough offsetting of the hedging derivatives. It is therefore possible to draw relevant conclusions on the futures success financially though review of the futures contracts using the conventional model in levels, the first difference model, the quadratic model and the error correlation model and their potential effects on the hedge ratio. According to McDonald & Moosa (2003), a number of classification of modes of estimating the hedge ratio through empirical means have been devised. The OLS conventional model (level), the conventional model for first difference, the quadratic model and the error correlation models are the major models through which the hedge ratio can be determined. These models have been critiqued for their various attempts to accurately estimate the hedge ratio, as well as for their inherent design weaknesses. For instance, the OLS model has been criticized for its lacks consideration for time distribution variations, serial correlation, cointegration and heteroskedasticity (Gupta & Singh 2009). The failure to appropriately consider cointegration, the OLS model does not achieve effectiveness and correctness in the attempt to give the results in the underhedging context. Although other models were subsequently developed as a means of countering the weaknesses identified in the conventional model using OLS, the error correlation model has been considered as the most effective of all the models in the determination of an effective hedge ratio. The superiority assigned to the ECM model have been linked to its better and more reliable results. Such a model as the Autoregressive Conditional Heteroskedasticity gives much emphasis to the serial correlation that does not receive adequate consideration by the OLS model. The basic strength held by the ARCH based models of hedge ratio estimation lies with their ability to recognize the variant time distributions compared to the OLS model, as proposed by Kroner & Sultan, (1993). In theoretical considerations, the capabilities of the ECM and the ARCH models of hedge estimation seem more superior to the conventional models. However, the results obtained from the various models do not show significant variations, thus the superiority of the ECM model is not justifiable. Moosa (2003), in his study on the impacts of the choice of model to be used in the estimation of an effective hedge ratio and its reliability in the result obtainable with due study of the impacts on the cross currency and futures hedging, an argument propounded by Chen, Lee & Shrestha (2003). The data collected from the foreign and stock exchange markets reveals that selection of a given preferable model does not have significant result variations. The study uses the four models with little differences on the effectiveness on hedging. The study holds that the most significant factor of consideration in hedge effectiveness assessment is the correlation between the unhedged price spot and the instruments for hedging. Moosa (2003) notes that before financial hedging is executed, it is important that the decision whether to hedge or not be reached, and the process for achievement of a full spot hedging in case hedging is to be undertaken. Further flaws are detected on the conventional model in the study when specified in levels since as the short-term dynamics are not given due consideration, while the first difference is noted for ignoring the term for error correction with regard to the long-term data. Misspecification by the models of conventional design therefore raises questions on their hedge ratio effectiveness. This is linked to the results of the hedge ratio form the conventional models which as there is a likelihood of obtaining a ratio that is erroneous if the first difference does not entail the mechanism for the term for error correction. The GARCH model has been used in the hedge performance estimation. The model undertakes a comparison of the performance of the hedge ratio from the correlation of the constant of the vector generalized autoregressive conditional heteroscedasticity (VGARCH) model with the OLS. However, a study on the models of VGARCH reveals that OLS has a better realization of a more reliable performance of the hedge ratio as a result of the overly variant models of VGARCH. The study drew its data from the commodity futures, stock index futures and currency futures. With the main objectives of gaining knowledge on optimal hedge ratio in order to be skilled in the art of variance minimization in every stock and to have the knowledge relevant to optimal hedge ratio application in order to achieve risk reduction, Figlewski conducted the first ever study of the effectiveness of hedging for the 500 S&P stock index futures (Gupta & Singh 2009). The study looked at futures within 1982 June and 1983 September. He carried out an estimation of the OLS hedge ratio. The researcher came to learn that out-of sample MVHRs performance was far desirable as opposed to the beta hedge ratios. As proposed by Junkus & Lee (1985), the stock index in the US was studied with regard to the effectiveness of hedging under various strategies of hedging. In this study, Lee and Junkus however, as opposed to popular theoretical opinion, learnt that the hedge ratio obtainable through application of OLS model outperformed the ratios achievable with other models (Al-Loughani&Moosa 2000). In their study, Lee and Junkus also emphasize on the superiority of the results of the MVHR model. In another study conducted by Holmes in 1995, an examination of the hedging effectiveness of ex ante. The study considered the timeframe of 1984 to 1992. Holmes revealed that portfolio managers vitally need FTSE- 100 futures contracts if they are to potentially avoid risk (Holmes, 1995). In 1996, Chou et al. undertook a study of NSA and NSA index futures contract in Japan. They basically undertook to compare the effectiveness of hedging with the aid of variant intervals of time. A documentation was prepared which argued that the effectiveness obtained by the conventional OLS model outperformed the hedge obtained from application of the error correction technique. This argument is with regard to the in-sample time frame. However, out-of sample results reveal the exact opposite, on which the hedge by the error correction technique outperforms the results of the conventional OLS model. Switzer and park assessed 3 stock index futures on their hedging effectiveness. In S&P 500, Toronto index futures and MMI futures, it was ascertained that the performance of the bivariate GARCH realized better results as compared to the hedge performance by the OLS model. The dynamic model has been identified as a better model in the determination of hedging effectiveness (Gupta & Singh 2009). This is as proposed by Powalla and Lypny, who conducted a study in the year 1998, where they undertook an examination of the hedging effectiveness using the GARCH (bivariate 1, 1) model in the DAX futures German stock index. In 2002, Thompson and Laws also did undertake an investigation involving the ex-ante model in which the hedging effectiveness of the LIFFE stock index futures were considered. Similarly, in 2000, Holmes and Butterworth also investigated FTSEMid 250 and FTSE- 100 index futures contracts. The study results revealed that large scale enterprises could most effectively achieve reliable hedge for their portfolio through FTSE-100, while small scale firm hedge portfolio effectiveness would be mostly achieved through application of FTSE Mid 250 as argued by Butterworth, Holmes &University of Durham (1997). However, a major shift in the studies of the model effectiveness in the recent research studies have shown slightly variant results, as they have given superiority to the results obtained from the conventional models. Such is the study conducted by Moosa in 2003 and Lien et al in 2002, whose results confirmed that hedge ratio estimation by the conventional model in levels using OLS as opposed to the advanced models as the first difference, quadratic and the error correlation modelswhich were developed with the aim of correcting the flaws inherent in the OLS levels conventional model (Al-Loughani&Moosa 2000). Hedging effectiveness evaluations have as well been carried out in India, though they have been less frequent as compared to other world economies. In 2007, Kumar and Roy did undertake an assessment of hedging effectiveness on the futures of wheat. Using he conventional model with OLS in order to estimate the hedge ratio, they learnt that the contracts considered did not offer appropriate hedge for thepurpose of risk avoidance. However, Durai and Bhaduri studied the Nifty futures hedging effectiveness in which they learnt that better hedge performance could be achieved if only the OLS conventional model was applied within short time horizons (Vipul 2013). It is noteworthy that in case the first difference of Y identifies as being completely random with no autocorrelation and as being stationary, it implies that Y can be described through a model of random walk (Jesswein, Kwok & Folks 1995). This model suggests that every value is a random step away in relation to the position of the previous value. However, the first difference of Y can be stationary, although it doesn’t identify as being completely random. In this regard, the value of the first difference at the specific time period t shows positive autocorrelation with its previous values at past time periods, implying a more complex projection model such as ARIMA or exponential smoothing might yield positive desirable results. it is important to note that a random and stationary DIFF(Y) significantly characterizes a model of random walk is most effective for Y as the original series, and not the assumption that DIFF(Y) should have a model for random walk being fitted to it. There is logical equivalence in the fitting a model of random walk to Y and fitting a constant mean model to DIFF(Y). The quadratic model has had a number of applications, and optimization has been such an application (Broll, Chow & Wong 2001). The model has equally been relevantly applied in the determination of the hedge ratio. Broll, Chow & Wong (2001) undertake a study in which they present evidence empirically with regard to the non-linear exchange rates for spot futures and their links, thereby generating a model of utility to identify the economic effects involved for a firm dealing export services. The model developed indicates that the firm is able operate with more export while adopting over hedging in currency futures that lack bias in case the relationship for exchange rates for spot futures is not linear, but rather convex, and vice versa. This implies that availability of currency futures alternatives which are priced fairly resents firms with the choice to utilize them together with the currency futures if enhanced hedging is to be realized which counters the risk exposure to its nonlinear rate of exchange. Such a situation thus provides options of hedging roles rationale under nonlinear underlying uncertainty (Broll, Chow & Wong 2001). Optimization of the portfolio has continued to be a field that effectively responds to a number of statistical applications that seek to utilize the features of quadratic and linear optimization. The overall nonlinear optimization occurs in portfolio optimization because there is model acknowledgement and nonlinearity capturing, non-normality and asymmetry which have links to returns in practice. Further, it is worth noting that products with complex financial bases often times entail a number of relationships that are nonlinear and which result in nonlinear parameter estimation optimization, hedging and tracking. Instruments of credit and their respective modes of managing variance (risk) also adopt the concept of nonlinearities which are characteristically hard to incorporate into quadratic or linear models. The main benefit garnered from use of the quadratic model is the index tracking optimization. The problem of index tracking entails the difficulty of realizing a portfolio with the minimum assets possible with intent to minimize the index tracking error measurement selected, or to enhance the index portfolio and portfolio correlation. Such problems necessarily require few assets in order to avert a portfolio’s holding of minimal spots and limitation of costs of transaction and administration. The model suggests slight variations in effectiveness on hedging with regard to the set hedging objectives. There is significance dominance of effects of ratio duration-horizons, specifically contributed by the horizons adopted by the various financial bodies. In view of Broll, Chow & Wong (2001), the model shows a direct connection between risk reduction and high values for hedge ratios. The model further holds that high hedge ratio values are vital for undesirable negative returns. According to Chen, Lee & Shrestha (2004), there is the effect of increase of hedging effectiveness with time horizons that are long, with total disregard for the portfolio adopted. The error correlation model has been given superiority by the results obtained from a study that the NSA index along with the time interval NSA index in order to carry out reliable comparison of the models of error correction (Ghosh 1993). The Japanese Average stock (Nikkei) was the context for this study. A general assumption that the hedge ratios obtained from the execution of the error correlation model are more effective and the error performance is better with the same model when compared to results obtainable in the study from the other three kinds of hedge ratio determination. Although temporal aggregation may not have significant effects on the hedge ratio estimates, it rates highly among the vital factors to consider in any attempts of hedge ratio procurement. Comparison of the error correlation model with the conventional model reveals that the conventional model does make presumption on the term for error correction format (Al-Loughani&Moosa 2000). Such formats have been applied in the determination of equations for calculation of hedges for future index series. 2. Methodology This chapter is broken down into subsections which are an identification of the testing stages and the procedures of estimation. Such subdivision is necessitated by the nature of the selected methods seek to find out whether hedge ratio econometric modelling has subsequent impacts on the form of effusiveness of cross currency and money market hedging exposure to model testing and foreign exchange risk. The Bloomberg database is the major source of the data set subjected to manipulation to derive the variables that they are referred to in this chapter. In more specific terms, the variables identify as the interest rates of 3 countries and their corresponding exchange rates. Empirical results and data, the fourth chapter, will thus undertake an in-depth discussion, manipulation and analysis of the generated data 2.2 Hedge ratio estimation Calculation of the forward rate for interest parity is vital toward the attempts to determine the hedge ratio estimation for money market hedging. The parity is to be determined between and,,. Equation (1) captures such interest parity. [1] Where; gives the forward rate estimation as experienced in 2 currencies. represents the $AUD represents the $CAD gives the spot rate existing between the 2 types of currencies represents the rate of interest for the currencies ( is ($CAD) and is ($AUD)) For hedging in a money market, the rate of exchange could represent the hedged and the unhedged positions with the representations and respectively. On the other hand, for hedging in cross currency, the rate of exchange for the hedged and the unhedged positions is determined through the representationsand respectively, where z is a representation of CHF. 2.2.1 Conventional Model (Levels) The conventional approach has been used in the determination of the hedge ratio through application of the spot price change regression of the change in price of futures with special analysis and application of the technique of ordinary least squares using levels of significance. Developed by Ederington during his pioneer work, the model through OLS regression effectively presents the hedge ratio in optimal measures between the futures and spot contracts (Ederington 1979). The OLS regression is the main representation of the conventional model where the rate of exchange for the unhedged position forms the dependent variable while the rate of return on (the price) the instrument of hedging, which identifies as either the futures or forward contract, is the explanatory variable. Money market and cross currency under the conventional model (level) are defined by the equations 2 and 3. [2] [3] In the second equation, is realized by which gives the unhedged spot exchange rate logarithm, while is realized as which gives hedging instrument forward rate logarithm. determines the hedge ratio estimate. In this case, the regression’s R2 is vital in the measurement of the effectiveness of hedging. The third equation has representing which gives the exchange rate logarithm for the unhedged position whereas is a representation of which derives the exchange rates logarithm forthe instrument for hedging. Here, gives the hedge ratio estimate, implying that the regressions measures the effectiveness of hedging. 2.2.2 Conventional Model (First Differences) The time series’ first difference identifies as the change series from a single given period to the subsequent period. In a case where the time series Y has its value denoted by Ytat a specific period t, the first difference of the time series at the particular period is thus projected to be equal to Yt-Yt-1. The form of representation of the first difference greatly differs with regard to the form of field of application (Brooks &Chong 2001). For instance, the application of fist difference in statgraphics sees the representation of first difference for Y as DIFF(Y), while a similar representation in regress reveals a representation of the first difference as Y_DIFF1. In the conventional model with levels, the short-run dynamics are ignored as opposed to their consideration in the first difference model as suggested by RFR. It however should be noted that the first difference model also ignores the long-run relationship. Equation [4] summarises the money market under the first difference model, while equation [5] represents the cross currency as specified in the first difference. [4] [5] identifies as the first difference to . This defines the unhedged position (spot) rate of exchange logarithm. has it first difference represented by , which is a representation of the forward rates logarithm to the instrument of hedging. The hedge ratio estimate is represented by, implying that measurement of the effectiveness of hedging is achieves through of the regressions, as captured in equation [4]. Equation [5], on the other hand has the first difference to given by that represents the rate of exchange logarithm to the unhedged position (spot). Here, has its first difference represented by , which gives the hedging instrument’s rate of exchange logarithm. Similar to equation [4], the hedge ratio estimate is represented by, implying that measurement of the effectiveness of hedging is achieves through of the regressions. 2.2.3 Quadratic Model Quadratic models identify as the model that assumes the most basic form in case of non-linearity of the functional component or element, and the model parameters remain unknown. The model developed byBroll, Chow & Wong (2001)indicates that the firm is able operate with more export while adopting over hedging in currency futures that lack bias in case the relationship for exchange rates for spot futures is not linear, but rather convex, and vice versa. This implies that availability of currency futures alternatives which are priced fairly resents firms with the choice to utilize them together with the currency futures if enhanced hedging is to be realized which counters the risk exposure to its nonlinear rate of exchange. Equation [6] of this chapter defines the money market quadratic model. On the other hand, equation [7] captures the cross currency quadratic model. [6] [7] In equation [6], giveswhich is the exchange rate logarithm for the unhedgedspot position while gives as the forward rate logarithm of the instrument for hedging, and is the hedge ratio estimate. gives the hedging instrument the quadratic value. gives that is the exchange rate logarithm for position that is unhedged while is represented by , which gives the exchange rate logarithm for the instrument for hedging. In the equation [7], is the estimate value for the ratio for the hedge. The hedging instrument quadratic value is represented by. 2.2.4 Error Correction Model Engle and Granger (1987) are behind the development of the cointegration theory. The theory seeks to develop integration of short-term dynamics and the long-term relationship of equilibrium (Ghosh 1993). Such integration reveals that 2 series which are non-stationary with a stationary linear combination must be characterised by a correction representation for the error present, and the 2 series are mandatorily cointegrated. If any equation developed under the error correlation model fails to identify the term for error correction or the short term dynamics, the equation is basically a misspecification. Such formulated equations are prone to realize unreliable hedge ratio values. Equation [8] defines the money market model for error correlation while cross currency model for error correlation is represented through equation [9]. [8] [9] in equation [8] gives the first difference of. This is the representation for the exchange rate logarithm for the unhedgedposition. Further, shows the first difference lagged spot rate, while is a representation of the first difference of which gives the forward rate logarithm of the instrument for hedging. Here, is the estimate value for the hedge ratio. Identifies as the lagged forward rate first difference. A description of the term for the error correction is presented in. The first difference in equation [9] to is, which the exchange rate logarithm to the unhedged spot is. The spot rates’ lagged first difference is represented by , while the first difference to is which gives the hedging instrument price logarithm, with being the hedge ratio estimate. The hedging instrument lag is given by while is a description of the term for correlation error. 2.3 Estimation of the Variance Ratio and Variance Reduction Due to the need to evaluate the effectiveness of hedging with regard to the different models identified, a hedge is regarded appropriate and viable if the risk of the return rate or price of the unhedged spot shows positive significance compared to the risk of the rate of return or price of the hedged spot. Through effective variance estimation and proper methods of reducing the variance, effective hedging is achieved, which enhances risk reduction. In such contexts, futures markets are a vital component in provision of effective hedging. This can be determined if the ratio of the risk meets the condition of, with holding as the size of the sample. The ratio for the variance for the money market is thus specified by equation [10] while equation [11] defines the risk ratio for cross currency. [10] With regard to equation [10]; [10], gives the risk of the return of the unhedged spot. gives the risk on return of the hedged spot. [11] Where; [11], is a determination of the risk on return of the unhedged spot. represents the risk on return of the hedged spot. Comparison of the effectiveness achieved by use of both hedges on the basis of reduction of the risk can be arrived at through calculation using equation [12]. References Al-Loughani, N.E. and Moosa, I.A. 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