Analysis of Hedging Effectiveness of Index Future against Stock Indices Movement - Term Paper Example

University A dissertation submitted by You’re Name in full In fulfillment of the requirements of Analysis of Hedging Effectiveness of Index future against Stock Indices movement Submitted: Month, Year CERTIFICATION I certify that the ideas, designs and experimental work, results, analyses and conclusions set out in this dissertation are entirely my own effort, except where otherwise indicated and acknowledged. I further certify that the work is original and has not been previously submitted for assessment in any other course or institution, except where specifically stated. Student Name Student Number: ____________________________ Signature ____________________________ Date ABSTRACT Hedging helps in increasing the value of relevant stock index. For portfolio managers, the selection of effective strategy for hedging is very important than the efficiency of the future markets. In order to make effective hedging strategy, it is important the right decisions are made concerning getting the optimal hedging ratio and the effectiveness of that hedging selected. The hedge ratio is described as that of ratio of number of units that have been traded in the future markets to that traded in the spot market. Objectives of the investors are a crucial determinant on getting the best hedging strategy. With global economy, with high level of volatility and uncertainty in the exchange rates, there is need for effective strategy to help in managing risk emanating from the fluctuation of exchange rates. Investors need to protect their investment for any future uncertainty and due to globalization of the economy, a risk in one market can be easily transferred to another market and this has the capability of affecting the overall return of a given portfolio. Therefore, this paper is trying to give an overview of different model and using this competing model to estimate the effectiveness of the hedging. TABLE OF CONTENTS ABSTRACT 3 TABLE OF CONTENTS 4 1.0 Introduction 5 2.0 Theoretical and literature review 6 3.0 Methodology 8 3.1 Regression model 8 3.2 Bivariate VAR Method 8 3.4 The Error Correction method 9 3.5 The Multivariate (GARCH Method) 10 3.6 Data 10 4.0 Empirical results 11 4.1 Regression OLS model 11 4.3 Estimation of the hedging effectiveness 18 4.4 Out of sample Analysis 19 5.0 Conclusion 19 Reference 21 1.0 Introduction For the future stock index to reduce risk of any unfavorable changes in price, hedging is very essential. Hedging helps in increasing the value of relevant stock index. For portfolio managers, the selection of effective strategy for hedging is very important than the efficiency of the future markets. In order to make effective hedging strategy, it is important the right decisions are made concerning getting the optimal hedging ratio and the effectiveness of that hedging selected. Stoll & Whaley (2015) states that for efficiency and effectiveness of the hedging, and then the future price needs to be efficient as the inefficiencies in the market would results into higher cost of hedging which may undermines the effectiveness of the future markets. Arouri, Lahiani & Nguyen (2015). Stated that the main objective of hedging is to help in minimizing the portfolio risk while on the other hand, portfolio theory assumes that hedging is a trade-off between the risk and the return. One important issue in the hedging involves determination of the hedging ratio. Normally a derivative instrument, stock index future contracts provides the traders in the stock market or investors with risk diversification and management opportunity. In order for investors manage the inherent risk in the holding stock, it is important for the investors to consider hedging as this will enables him to protect the value of his portfolio by selling the stock index in the market for future. For successful hedging to be achieved, then the price movement of the spot and the future positions should be able to offset each other (Stoll & Whaley 2015). Nevertheless, since there is basic risks which exist in the market, it is not possible to completely eliminate risk in the market. It is therefore important for the investors in the stock market to be able to understand how effective hedging can take place. 2.0 Theoretical and literature review In allowing the use of future contracts to hedge, a recognized spot position, the person investing must decide on the hedge ratio to be used. The hedge ratio is described as that of ratio of number of units that have been traded in the future markets to that traded in the spot market. Objectives of the investors are a crucial determinant on getting the best hedging strategy (Rao & Srivastava, 2014). Most research has been concentrated on three hedging methods they include the traditional hedge, minimum variance hedge and the beta hedge. The traditional approach focuses on the prospective for future contracts that are to be put in place for risk reduction purposes. The strategy involves hedger taking up positions in future or rather future positions that are the same in magnitude but different in sign to that of spot market. Which is h=-1. If prices that are directly co-related changes in the spot market the only way to eliminate them is to make sure that they match the prices that are on the future markets. But for practice purposes it’s not likely that a perfect correlation will be realized between the spot and the future market existence hence causing a difference in the market. Beta hedge is majorly known as portfolio beta, their objectives and that of traditional method are the same which does gives a position in the future that is the same in size but parallel in sign position spot (Gupta & Kaur, 2015)---relying on current portfolio theory to the problem of hedging. This was the first time that risks definition and return on variance and mean were used to solve this problem. Rao & Srivastava (2014) still stands with the traditional objective of maximizing risks as the main focus of hedging but gives a definition of risks as the variance on a two-asset hedged portfolio. The imperfection in the traditional hedging methods, Gupta & Kaur (2015) developed measures of hedging efficiency as a percentage reduction found in the variance linking the un-hedged and hedged returns. Chkili (2016) while investigating the dynamism and the problems with hedging resolve that moment the finest hedge ratio has been given an estimation from a mere regression among the data considered to be historical on the spot realized returns and future prices together with the R-squared of the same regression has been well thought out as the best measure of hedging. Chkili, Aloui & Nguyen (2014) has had a lot criticism on this ratio gotten from the regression analysis method arguing that sometimes it’s so biased especially when there is an existence of a co integrating relationship amongst the return in the future and the spot itself. They wished for a model known as vector error correction to approximate the hedge ratio. This empirical method has highly been criticized on the first account it has been argued that the simple hedge ratio is as a result of the unconditional second moments while the real minimum variance hedge ratio is being based on conditional second moments. On the second account critics argue that a steady hedge ratio doesn’t take into account the variance of joint distribution of spot and prices in the future over a period of time. Modern advances in the progression econometric techniques have come up with some solutions to help address the problem. 3.0 Methodology This study focuses on four different methods for estimating the hedge ratio and tests its effectiveness for both in and out the sample of the data with around 5, 10, 15 and 20 days horizon. Three methods used here is discussed below:- 3.1 Regression model A conventional method of calculation an evaluating an optimal hedge ratio is through the simple ordinary least square (OLS) estimation using the linear regression model. For this study, for us to estimate the effectiveness of the hedging ratio, the following formula will be used. rst = α + βrft +Ɛ……………………………………………………………………………….(1) In this case we have:- rst – Is the spot rate of the return rft- is the future returns t- is the time β will help us to provide an estimate of the required optimal hedge ratio. The regression model is simple and direct to use and this beta value will be important in understanding the required ratio of the hedge used in getting the required optimal and effective hedge. 3.2 Bivariate VAR Method This option is preferred due to shortcomings of the regression model like presence of autocorrelation of residual. In order to overcoming the shortcomings of the simple linear regression, the bivariate VAR method will be used. If the optimal lag length for the future and spot returns will be selected through lag integration. This is repeated up to the point in which the autocorrelation present in the residuals are fully eliminated from the data. The following formula will be used in the calculation of the VAR model. ………………….. (2) ………………….. (3) After the process of calculating and estimating the system of the equation, the series are generated to help in calculating the hedge ratio. The minimum variance hedge ratio in this case will be given by h* = σsf/σf 3.4 The Error Correction method In conditions where the level of arrangement of spot and the future list are non-stationary and to some develop coordinated of request one, then it is imperative to utilize vector mistake rectification display (VEC) to assess the support proportion. This method will use the following two formulas:- ………. (4) ……… (5) Where in this case we have Z t-1 = St-1- δFt-1 is the correction of the error term the (1-δ) as the cointegrating vector and λs and λf as the adjustment variables in the study. In order to calculate the hedge ratio, we will be able to use the above formula in equation three above. This method is more accurate in measuring the effective hedge ratio compared to the first two ratio discussed above. 3.5 The Multivariate (GARCH Method) Due to presence of the ARCH effect in series data used in calculating the hedge ratio of financial information, the VAR model, regression model and might turn out to be extraneous in nature. In order for this paper to control the effect of the ARCH presence in the error correction model in the residuals, it is important to use the VEC multivariate GARCH model proposed by Bollveslev eta l 1988 will be used. This model is useful in this it is able to simultaneously control the restricted variance and the related covariance and covariance of the two interrelated series. The MGARCH will be calculated using Eviews software using the time varying hedge ratio using the two the spot covariance and future price with the variance of the future prices. Therefore, this will be calculated as hsft / hfft.--- which will be the time varying ratio. 3.6 Data The data used in analyzing this study will be derived from the New York stock exchange with stock index future and S&P index for the period of 1986 to 2015. The data will be collected from the NSE website and only relevant data will be collected and organize for the analysis. The data will be presented in form of tables and graphs where necessary. All the four test will be carried out with the researcher using the relevant data which will be used in the analysis of this case to estimate and analyze of Hedging effectiveness of index future against stock indices movement 4.0 Empirical results This section discusses the empirical results from the four models discussed in the methodology. The empirical analysis was conducted and analysis was done using Eviews. 4.1 Regression OLS model The regression model results are shown in the table below:- Table 1.0: OLS Regression results Variable Coefficient Std. Error t-Statistic Prob.   FP 0.027849 0.000659 42.26201 0.0000 C 0.022863 0.034381 0.665009 0.5115 R-squared 0.984565     Mean dependent var 1.217933 Adjusted R-squared 0.984014     S.D. dependent var 0.847121 S.E. of regression 0.107107     Akaike info criterion -1.565643 Sum squared resid 0.321211     Schwarz criterion -1.472229 Log likelihood 25.48464     Hannan-Quinn criter. -1.535759 F-statistic 1786.077     Durbin-Watson stat 1.379008 Prob(F-statistic) 0.000000 From the table above, α = 0.022863, β = 0.027849 R2 = 0.984565. Therefore, using the first model the edge ratio will be β = 0.027849. The second model is the estimation of the hedge ratio using the VAR model and the results from the Eviews is shown in Table 2 Below. Table 2: The Bivariate VAR Model Estimates Equation (2) SP Equation (3) FP SP(-1)  1.552737  37.76572  (0.58313)  (24.1148) [ 2.66276] [ 1.56608] SP(-2) -1.010655 -26.86954  (0.57143)  (23.6308) [-1.76865] [-1.13706] FP(-1) -0.011652 -0.070008  (0.01491)  (0.61678) [-0.78123] [-0.11351] FP(-2)  0.021983  0.677736  (0.01413)  (0.58441) [ 1.55556] [ 1.15968] C  0.050706  1.262276  (0.09062)  (3.74739) [ 0.55957] [ 0.33684]  R-squared  0.914831  0.886019  Adj. R-squared  0.900019  0.866196  Sum sq. resids  1.584460  2709.664  S.E. equation  0.262468  10.85410  F-statistic  61.76287  44.69680  Log likelihood  0.477176 -103.7435  Akaike AIC  0.323059  7.767395  Schwarz SC  0.560953  8.005289  Mean dependent  1.154143  40.91679  S.D. dependent  0.830076  29.67281 From this model, we recall that in order to get the optimal hedge ratio the formula is given by:- Where:-δsf covariance ƐsƐf δf = Ɛf In order to calculate the hedge ratio here Will have:- Table 3: Optimal Hedge ratio using Bivariate VAR Model Values Covariance (ƐsƐf) 0.000195 Variance (Ɛf) 0.000209 h* 0.933 The third step is to calculate the hedge ratio using the vector error model from the data of spot and future prices. The results are shown in the table below:- Table 5: The Vector Error Correction Estimates Model Error Correction: D(SP) D(FP) Coint Eq1  0.668483  56.74549  (0.65994)  (25.5853) [ 1.01294] [ 2.21790] D(SP(-1))  0.886632  28.68181  (0.52491)  (20.3501) [ 1.68912] [ 1.40942] D(SP(-2)) -1.860029 -74.80484  (0.52636)  (20.4066) [-3.53374] [-3.66573] D(FP(-1)) -0.016662 -0.652466  (0.01430)  (0.55435) [-1.16529] [-1.17699] D(FP(-2))  0.037930  1.416303  (0.01228)  (0.47623) [ 3.08778] [ 2.97399] C -0.096724 -4.010205  (0.04251)  (1.64807) [-2.27533] [-2.43328]  R-squared  0.502149  0.568357  Adj. R-squared  0.383613  0.465585  Sum sq. resids  0.938071  1409.951  S.E. equation  0.211353  8.193933  F-statistic  4.236252  5.530273  Log likelihood  7.045513 -91.71023  Akaike AIC -0.077445  7.237795  Schwarz SC  0.210518  7.525759  Mean dependent -0.089000 -3.074074  S.D. dependent  0.269204  11.20865  Determinant resid covariance (dof adj.)  0.324400  Determinant resid covariance  0.196242  Log likelihood -54.63920  Akaike information criterion  5.084385  Schwarz criterion  5.756301 From the equation of calculating the optimal hedge ratio, we recall that in order to get the optimal hedge ratio the formula is given by:- Where:-δsf covariance ƐsƐf δf = Ɛf For the calculation of the hedge ratio using the above formula will have:- Table 6. Optimal Hedge Ratio from the VEC Model Value Covariance (εs εf ) 0.000194 Variance (Ɛf) 0.000207 h* 0.937 In order for us to establish the efficiency of the model two and the model three, it is important for us to investigate or use the fourth model to examine the characteristics of the residuals. We will be able to plot the residuals of these two equations to establish the effect. The graphs are shown below:- Equation 2 Equation 3 Equation 3 From the above table, we conclude that there is no presence of the ARCH effect in the data and we can conclude with the interpretation of the results. The calculation of the hedge ratio in this case will be:- Table 7: GARCH Model of Estimation GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1) Variable Coefficient Std. Error z-Statistic Prob.   FP 0.026674 0.001025 26.01631 0.0000 C 0.045452 0.020403 2.227714 0.0259 Variance Equation C 0.000108 0.000145 0.749360 0.4536 RESID(-1)^2 0.615843 0.413277 1.490145 0.1362 GARCH(-1) 0.388111 0.198727 1.952983 0.0508 R-squared 0.981697     Mean dependent var 1.217933 Adjusted R-squared 0.981043     S.D. dependent var 0.847121 S.E. of regression 0.116636     Akaike info criterion -2.767670 Sum squared resid 0.380909     Schwarz criterion -2.534138 Log likelihood 46.51506     Hannan-Quinn criter. -2.692961 Durbin-Watson stat 1.008923 From the table above, we can find β=0.026674. In addition, α =0.045452, p-value in both cases is < 0.05 indicating that the null hypothesis is rejected and acceptance of alternative hypothesis. 4.3 Estimation of the hedging effectiveness Accordingly, this is the same data which has been used in establishing the effective hedge ratio which is the annual returns from 1986 to 2015. Out of these sample we have picked sample of 3 months, 6 months, 9 months and 12 months to estimate the effectiveness of the hedging ratio. Using the old effectiveness ratio should be equivalent to the R-squared found in the linear regression and this should be compared with other available strategies in the market. XX notes that the effectiveness of the hedging should be realized only if the hedge ratio derived from the different strategies mean return is higher than the competing strategy. This calculation has been done in the table below:- Table 8: Mean Return for within sample Method h* 3 months 6 months 9 months 12 months OLS 0.027849 0.041% 0.040 0.037 0.031 Bivariate VAR 0.933 0.041% 0.040 0.037 0.032 Vector Error Correction 0.937 0.042% 0.041 0.038 0.032 GARCH model 0.026674 0.043% 0.041 0.038 0.033 From the table, Vector error correction has the higher hedging ratio but GARCH model has the higher overall mean return hence is the most appropriate model which gives the most effective hedging ration. Table 9: Average Variance Reduction for within sample Method h* 3 months 6 months 9 months 12 months OLS 0.027849 93.36% 93.36% 93.36% 93.36% Bivariate VAR 0.933 83.67% 83.67% 83.67% 83.67% Vector Error Correction 0.937 89.69% 89.69% 89.69% 89.69% GARCH model 0.026674 91.41% 91.41% 91.41% 91.41% In this case the reduction in variance shows that for smaller time the optimal hedge ratio which is developed from the OLS is better than other competing alternative 4.4 Out of sample Analysis The out of sample analysis is shown in the table below: Average variance reduction outside the sample Method h* 3 months 6 months 9 months 12 months OLS 0.027849 91.92% 91.92% 91.92% 91.92% Bivariate VAR 0.933 93.20% 93.20% 93.20% 93.20% Vector Error Correction 0.937 93.27% 93.27% 93.27% 93.27% GARCH model 0.026674 93.16% 93.16% 93.16% 93.16% This further shows the effectiveness of the model used in the hedging. 5.0 Conclusion The traditional method and strategy of hedging spot and future options has faced many criticism. This is due to the fact that the behaviour of spot and the future prices do not behave the same. With global economy, with high level of volatility and uncertainty in the exchange rates, there is need for effective strategy to help in managing risk emanating from the fluctuation of exchange rates. Investors need to protect their investment for any future uncertainty and due to globalization of the economy, a risk in one market can be easily transferred to another market and this has the capability of affecting the overall return of a given portfolio. Therefore, this paper is trying to give an overview of different model and using these competing model to estimate the effectiveness of the hedging. The four modern methods can be used easily in calculating the hedging ratio and then calculating the mean variation using the calculated ration to establish the effectiveness of the spot and future derivatives in the market. Using average variation reduction in outside the sample we get that the smaller the duration the better the chances of managing the hedging risk using the simple OLS method. Reference Arouri, M. E. H., Lahiani, A., & Nguyen, D. K. (2015). World gold prices and stock returns in China: insights for hedging and diversification strategies. Economic Modelling, 44, 273-282. Chkili, W. (2016). Dynamic correlations and hedging effectiveness between gold and stock markets: Evidence for BRICS countries. Research in International Business and Finance, 38, 22-34. Chkili, W., Aloui, C., & Nguyen, D. K. (2014). Instabilities in the relationships and hedging strategies between crude oil and US stock markets: do long memory and asymmetry matter?. Journal of International Financial Markets, Institutions and Money, 33, 354-366. Gupta, K., & Kaur, M. (2015). Examining the Hedging Effectiveness of Futures Contracts over Pre and Post Financial Crisis Period: Evidence from National Stock Exchange of India. International Journal of Banking, Risk and Insurance, 3(2), 10. Rao, T., & Srivastava, S. (2014). Twitter sentiment analysis: How to hedge your bets in the stock markets. In State of the Art Applications of Social Network Analysis (pp. 227-247). Springer International Publishing. Stoll, H. R., & Whaley, R. E. (2015). Commodity index investing and commodity futures prices. Read More