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EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION RESEARCH PROJECT On “EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION” Submitted in partial fulfillment of the requirement for MBA Degree of Bangalore University BY Shivaraj.G Registration Number 04XQCM6086 Under the guidance of Prof.B.V.Rudramurthy M.P.Birla Institute of Management Associate Bharatiya Vidya Bhavan Bangalore-560001 2004-2006 M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION DECLARATION I hereby declare that the research project titled “EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION” is prepared under the guidance of Prof.B.V.Rudramurthy in partial fulfillment of MBA degree of Bangalore University, and is my original work. This project does not form a part of any report submitted for degree or diploma under Bangalore University or any other university. Place: Bangalore Shivaraj.G M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION PRINCIPAL’S CERTIFICATE This is to certify that Mr. Shivaraj.G, bearing Registration No: 04XQCM6086 has done a research project on “EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION” under the guidance of Prof.B.V.Rudramurthy M.P. Birla Institute of Management, Bangalore. This has not formed a basis for the award of any degree/diploma for any other university. Place: Bangalore Date: Dr.N.S.MALLAVALLI PRINCIPAL MPBIM, Bangalore M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION GUIDE’S CERTIFICATE I hereby declare that the research work embodied in this dissertation entitled “EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION” has been undertaken and completed by Mr.Shivaraj.G under my guidance and supervision. I also certify that he has fulfilled all the requirements under the covenant governing the submission of dissertation to the Bangalore University for the award of MBA Degree. Place: Bangalore Date: Prof.B.V.Rudramurthy Research Guide MPBIM, Bangalore M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION ACKNOWLEDGEMENT The successful accomplishment of any task is incomplete without acknowledging the contributing personalities who both assisted and inspired and lead us to visualize the things that turn them into successful stories for our successors. First of all I thank the Almighty God for his grace bestowed on us throughout this project. My special thanks to my project Guide Prof.B.V.Rudramurthy, who guided me with the timely advice and expertise and has helped remarkably to complete the project. Last, but not the least, I would like to thank my Parents and all my Friends for their wholehearted direct and indirect support and encouragement. SHIVARAJ.G M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION CHAPTER ABSTRACT INTRODUCTION: CONTENTS PAGE NO. 1. THOEORETICAL CONSIDERATIONS 2. LITERATURE REVIEW: 3. RESEARCH METHODOLOGY: PROBLEM STATEMENT OBJECTIVES SCOPE OF THE STUDY LIMITATIONS DATA AND SAMPLE OF DATA METHODOLOGY 4. DATA ANALYSIS: TEST FOR UNIT ROOT AND COINTEGRATION. RESULTS FROM OLS. RESULTS FROM ECM. TABLES. GRAPHS. 5. CONCLUSION: REFERENCES: M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Abstract: This research project investigates the hedging effectiveness of the NIFYT AND CNXIT stock index futures contract using weekly settlement prices for the period April 2001 to March 2006 and August 2003 to March 2006 respectively. Particularly, it focuses on three areas of interest: the determination of the appropriate model for estimating a hedge ratio that minimizes the variance of returns; the hedging effectiveness and the stability of optimal hedge ratios through time; an in-sample forecasting analysis in order to examine the hedging performance of different econometric methods. The hedging performance of this contract is examined considering alternative methods, i.e. Ordinary Least Square method and Error Correction Model, for computing more effective hedge ratios. The results suggest the optimal hedge ratio that incorporates nonstationarity, long run equilibrium relationship and short run dynamics is reliable and useful for hedgers. Comparisons of the hedging effectiveness and hedging performance of each model imply that the error correction model (ECM) is superior to the other models employed in terms of risk reduction. In this study we have estimated the hedge ratios using both the methods and compared both the methods, the hedge ratio obtained from the ECM is better compared to the OLS method. And the Adjusted R-sqr measures the effectiveness of hedge ratios determined through the OLS AND ECM methods. Finally, the results showed that CNXIT index futures contracts are better instrument for hedging and also on minimizing the market risk over the time. And also CNXIT index futures contracts reveals the better adjusted R-sqr results in both the methods compared to the NIFYT index futures contract. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Introduction. The basic motivation for hedging is to reduce or eliminate the variability of profits and firm value that arises from market changes. The effectiveness of a hedge becomes relevant only in the event of significant change in the value of the hedged item. A hedge is effective if the price movements of the hedged item and the hedging derivative roughly offset each other. Hedging through trading futures is a process used to control or reduce the risk of adverse price movements. The introduction of stock index futures contracts offer the market participants the opportunity to manage the market risk of their portfolios without changing the portfolios composition. Ederington (1979) defines hedging effectiveness as “the reduction in variance and states that the objective of a hedge is to minimize the risk”. Howard and D’Antonio (1984) define hedging effectiveness as the ratio of the excess return per unit of risk of the optimal portfolio of the spot commodity and the futures instrument to the excess return per unit of risk of the portfolio containing the spot position alone (see also, Pennings and Meulenberg, 1997). Hsin et al. (1994) measure hedging effectiveness by considering both risk and returns in hedging. However the statement “futures contracts do not introduce risk” is not correct. Numerous studies, which investigate measures of effectiveness, try to determine to what extent hedgers are able to reduce cash price risk by using futures contracts. First, Markowitz (1959) measures the hedge effectiveness as the reduction in standard deviation of portfolio returns associated with a hedge. Then, Ederington1 (1979), following the work of Working (1953), Johnson (1960) and Stein (1961), measures hedging effectiveness as the percentage reduction in variability. “He explains that a hedge is effective if the R-squared of the Ordinary Least Square regression explaining the M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION data is high, say 90%. But a high R-squared by itself is not always a reliable indicator of hedging effectiveness. However a R-sqr of > 50% shall be eligible for testing. All previous studies, which investigate measures of hedging effectiveness, use the simple Ordinary Least Squares Regression (OLS) for estimating hedge ratios. However, there is wide evidence that the simple regression model is inappropriate to estimate hedge ratios since it suffers from the problem of serial correlation in the OLS residuals and the heteroskedasticity often encountered in cash and futures price series. So, to counter the problem of inconstant variances of index futures and stock index prices, a number of papers measure optimal hedge ratios via autoregressive conditional heteroskedastic processes which allow for the conditional variances of spot and futures prices to vary over time. A second problem encountered when estimating hedge ratios arises from the cointegrative nature between spot and futures markets. If no account is made for the presence of cointegration it can lead to an under-hedged position due to the misspecification of the pricing behavior between these markets. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Theoretical considerations: S&P CNX Nifty Futures: A futures contract is a standardized forward contract, which is traded on an Exchange. NSE commenced trading in index futures on June 12, 2000. The index futures contracts are based on the popular market benchmark S&P CNX NIFTY index. NSE defines the characteristics of the futures contract such as the underlying index, market lot, and the maturity date of the contract. The futures contracts are available for trading from introduction to the expiry date. S&P CNX Nifty: S&P CNX Nifty is a well diversified 50 stock index accounting for 25 sectors of the economy. It is used for a variety of purposes such as benchmarking fund portfolios, Index based Derivatives etc. S&P CNX Nifty is owned and managed by Indian Index Services and Products Ltd (IISL), which is a joint venture between NSE and CRISIL. IISL is India's first specialized company focused upon the index as a core product. IISL have a consulting and licensing agreement with Standard & Poor's (S&P), who are world leaders in index services. The average total traded value for the last six months [from Nov 2005 to May 2006] of all Nifty stocks is approximately 49.8% of the traded value of all stocks on the NSE Nifty stocks represent about 56.5% of the total market capitalization as on March 31, 2006. Impact cost of the S&P CNX Nifty for a portfolio size of Rs.5 million is 0.07% S&P CNX Nifty is professionally maintained and is ideal for derivatives trading. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Hedging: Hedging operations exist to reduce or eliminate risk arising from the fluctuation in the price of the underlying asset. To hedge something is to construct a protective fence around it. Applied to financial markets, hedging means eliminating the risk in an asset or a liability. Applied to stock market, hedging means eliminating the risk in a investment portfolio. Since hedging is explained in terms of risk, let us explain what risk is. RISK IS NOT LOSS: It is the uncertainty of an expected future event. The uncertainty may turn out to be favourable or unfavorable. Risk is thus a neutral concept: profit and loss are merely two sides of the same coin called risk. Since hedging eliminates risk, it follows that hedging shuts the door closed to profit as well as loss: the investment is locked at a particular value, and it neither gains nor looses in value from subsequent price changes. HEDGERS SPECULATORS Hedgers are parties who are exposed to risk Speculators do not have a prior because they have a prior position in the position that they want to hedge commodity or the financial instrument against price fluctuations. They buy specified in the futures contract. By taking an or sell futures contracts in an attempt opposite position in the futures market, to earn a profit. Rather they willing parties who are at risk with an asset can to shield themselves against the risk assume the risk of price hedge their position. By doing so, they can fluctuation in the hope of profiting of from them. unexpected price changes. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Cross hedging: A cross hedge is one in which the cash asset and the asset underlying the futures contract are not identical. This situation arises when the hedger uses a futures contract with an underlying asset different from the one he is currently long or short. For example, consider a hedger who uses S&P 500 futures contracts to hedge against a decline in the value of his portfolio, which is different from the 500 component stocks in the S&P 500. Sometimes there are no available futures or market for currencies. In these cases, the risk managers might wish to use a substitute or proxy for underlying currency that is available. Use of proxy instrument for hedging underlying assets is known as cross hedging Cross hedger would like go through a simple 2 steps process to determine the optimal cross hedge: first, find the currency futures most highly correlated with the actual currency of exposure. Second, find the optimal hedge ratio using the covariance between proxy futures and actual currency. Hedging is one of the three principal ways to manage risk, the others being diversification and insurance. Let us bring out the distinction between the three. Diversification minimizes risk for a given amount of return. Hedging eliminates both sides of risk: the potential profit and the potential loss: Insurance resolves risk into profit and loss, and eliminates the loss while retaining the profit. Diversification is affected by choosing a group of assets instead of a single asset. Hedging is implemented by adding a negatively and perfectly correlated asset to an existing asset. Insurance for investment is achieved by buying a put option on the M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION investment. Diversification and hedging do not have cost in cash but may have opportunity cost. Insurance, on the other hand has explicit cost incurred in cash. Index Futures in Hedging: Index futures is the most popular and useful medium for hedging in stock market. This is in contrast to commodity and currency markets where it is not useful. The reason is that commodity and currencies are primarily consumed and are not substitutable with each other. In contrast, stocks are held for investment and can be substitutable with each other. Since the stock index comprises many stocks, it acts as a good substitute or proxy for many investment portfolios. With one index representing the stock market as a whole, the transaction costs will be minimal and the administrative work is lesser. This is the reason why stocks are physical securities but do not have futures contract; and index is a derivative and index futures is derivative on derivative. To sum up, we can use the same index futures for hedging any investment portfolio. As a general rule, a buy position or "long" in the underlying asset is covered by a sell position or "short" position in futures. Conversely, a "short" position in the underlying asset is covered by a buy position or "long" in futures. The greater the correlation between the changes in prices of the underlying asset and the futures contract the more effective is the hedge. As such, the loss in one market is partially or totally compensated by the profit in the other market, given that the traded positions are equal and opposite. It is very important to note that hedging does not necessarily improve the financial outcome, it just reduces the uncertainty. In practice, hedging is not perfect; because of the basis risk which arises due to the following reasons: i. The asset being hedged might be different than the one underlying the futures contract, i.e. using a 30y T-bill to hedge a 10y T-note; M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION ii. The hedger might be uncertain about the exact time that the delivery has to take place, i.e. a new oil ring that is expected to start extracting next summer, without knowing exactly when; and iii. The futures contract matures after the delivery date that the hedger has in mind, i.e. the hedger needs to buy steel in January but steel futures expire on March. The basis is defined as Where S(t) is the spot price of the underlying asset and F(t,T) is the price of the futures contract that has been utilized. If the asset to be hedged is the same as the one underlying the futures, then the basis on expiration is equal to zero. If the delivery date is not the same as the one that the futures matures, then the basis will signify the ``losses'' or ``gains'' of the hedge than are not known when the hedge is constructed. Example. (Basis risk: different maturities) Today, the gold price isS(t). Say that one has to deliver gold at time basis today is : . The basis on the delivery date will be , and in order to hedge takes a short position on a futures contract that matures at time T>t. The price of this contract is equal to F(t,T) , and the , Will indicate the gains [or losses] due to the hedge. See Figure.1 for a visual representation of the basis risk. Figure.1 M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Basis risk Generally speaking, the basis risk arises from uncertainty about the future interest rates and uncertainty about the future yields of the underlying asset. For investments that are difficult or costly to store, the basis risk might increase substantially. The delivery month that is as close as possible -but not earlier than, the date when the hedge matures. In considering the use of futures contracts to hedge an established spot position the investor must decide on the hedge ratio, h , to be employed. The hedge ratio is the ratio of the number of units traded in the futures market to the number of units traded in the spot market. The particular hedging strategy adopted depends crucially on the investor’s objectives. Research has concentrated on three hedging strategies: the traditional one-to one; the beta hedge; and the minimum variance hedge proposed by Johnson (1960) and also associated with Ederington (1979). The traditional strategy emphasizes the potential for futures contracts to be used to reduce risk. It is a very simple strategy, involving the hedger in taking up a futures position that is equal in magnitude, but opposite in sign to the spot market position, i.e. h = -1. If proportionate price changes in the spot market matches exactly those in the futures market, the price risk will be eliminated. However, in practice, it is unlikely for a perfect correlation between spot and future returns to exist, and hence the hedge ratio that minimizes the variance of returns will definitely differ from –1. Beta hedge ratio simply refers to the portfolio’s beta. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION The beta hedge has the same objective as the traditional 1:1 hedge that establishes a futures position that is equal in size but opposite in sign to the spot position. Yet, when the cash position is a stock portfolio, the number of futures contracts needed for full hedge coverage needs to be adjusted by the portfolio’s beta. In many cases the portfolio to be hedged will be a subset of the portfolio underlying the futures contract, and hence the beta hedge ratio will deviate from –1. However, it may be the case that the futures contract may mirror the portfolio to be hedged, and thus the beta hedge ratio will be the same as the traditional hedge ratio. According to Lypny and Powalla ‘the appropriateness of this criterion depends on whether mean futures returns are zero; if they are not, hedging may be too expensive’. Johnson (1960) proposed the minimum variance hedge ratio (MVHR) as an alternative to the classic hedge. He applied modern portfolio theory to the hedging problem. It was the first time that definitions of risk and return in terms of mean and variance of return were employed to this problem. Johnson maintained the traditional objective of risk minimization as the main goal of hedging but defined risk as the variance of return on a two-asset hedged portfolio. The MVHR (h*) is measured as follows: cov(ΔS,ΔF) h* = var(ΔF) Where, F and S represent the relative amount invested in futures and spot respectively, cov(ΔS,ΔF) is the covariance of spot and futures prices changes, and var(ΔF) is the variance of futures price changes. It should be mentioned that the minimum variance hedge is the coefficient of the regression of spot price changes on futures price changes. The negative sign reflects the fact that in order to hedge a long stock position it is necessary to go short (i.e. sell) on futures contracts. Using the MVHR assumes that investors are infinitely risk averse. While such an assumption about risk-return trade-off M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION is unrealistic, the MVHR provides an unambiguous benchmark against which to assess hedging performance. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION LITERATURE REVIEW: 1. DIMITRI KENOURGIO: “HEDGE RATIO ESTIMATION AND HEDGING EFFECTIVENESS: THE CASE OF THE S&P 500 STOCK” market index futures contract: [Department of Economics, University of Athens, 5 Stadiou Street, Office 115, 10562 Athens, Greece] This paper investigates the hedging effectiveness of the Standard & Poor’s (S&P) 500 stock index futures contract using weekly settlement prices for the period July 3rd, 1992 to June 30th, 2002. Particularly, it focuses on three areas of interest: the determination of the appropriate model for estimating a hedge ratio that minimizes the variance of returns; the hedging effectiveness and the stability of optimal hedge ratios through time; an in-sample forecasting analysis in order to examine the hedging performance of different econometric methods. The hedging performance of this contract is examined considering alternative methods, both constant and time-varying, for computing more effective hedge ratios. The results suggest that the optimal hedge ratio incorporates nonstationary, long run equilibrium relationship and short run dynamics is reliable and useful for hedgers. Comparisons of the hedging effectiveness and in-sample M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION hedging performance of each model imply that the error correction model (ECM) is superior to the other models employed in terms of risk reduction. Methodology: This paper aims to determine the appropriate model when estimating optimal hedge Ratios. The alternative models employed are the following: Model 1: The Conventional Regression Model: This model is a linear regression of change in spot prices on changes in futures Prices. Let St and Ft be logged spot and futures prices respectively, the one period MVHR can be estimated as follows: ΔSt = a + β · ΔFt + u(t) Where u(t) is the error from the OLS estimation, ΔSt and ΔFt represent spot and futures Price changes and the slope coefficient β is the optimal hedge ratio (h*). Model 2: The Error Correction Model: Engle and Granger (1987) stated that if sets of series are cointegrated, then there exists a valid Error Correction Representation of the data. Thus, if St represents the index spot price series and Ft the index of futures price series and if both series are I (1), there exists an error correction representation of the following form: ΔSt = aut + · ΔFt + Σ · ΔFt k + Σ · ΔS + e where ut-1 = St-1 – [a0 + a1Ft-1] is the error correction term and has no moving average part; the systematic dynamics are kept as simple as possible and enough lagged variables are included in order to ensure that et is a white noise process; and the coefficient β is the optimal hedge ratio. Model 3: The GARCH Mode:l M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION A useful generalization of ARCH models introduced by Bollerslev (1986) is the GARCH model, that parameterizes volatility as a function of unexpected information shocks to the market. The equation for GARCH is the following: …………(1) The equation specified above is a function of three terms: the mean α0, news about volatility from the previous period, measured as the lag of the squared residual from the mean equation e^2t-1 (the ARCH term), and last period's forecast variance σ^2t-1 (the GARCH term). The more general GARCH (p, q) calculates σ^2t from the most recent p observations on e^2 and the most recent q estimates of the variance rate. Estimation sometimes results in: a1 + β ≈ 1, or even α1 + β > 1. Value of α1 + β close to unity implies that the persistence in volatility is high. In other words, in order to intercept expression (1), suppose that there is a large positive shock et-1, and hence e^2t-1 is large, then thee conditional variance σ^2t increases. Model 4: The EGARCH Model Where ϖ, α, β, ϒ are constant parameters. The left- hand side is that of the conditional variance. This implies that the leverage effect is exponential, rather than quadratic, and that forecasts for the conditional variance are guaranteed to be nonnegative. Since , the is included, the model will be asymmetric if ϒ ≠ 0. the presence of leverage effects can be tested be the hypothesis that ϒ > 0. if the leverage effect term ϒ, after M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION running the appropriate regression, is negative and statistically different from zero, this will imply that positive shocks generate less volatility than shocks(bad news). Comparisons are then made of the hedging effectiveness associated with each hedging strategy based on the minimum variance hedge ratio estimations, using the simple OLS, the ECM, the ECM with GARCH errors and the GARCH and EGARCH models. The question of the appropriate model to use when estimating the optimal hedge ratio of the S&P 500 index futures contracts traded in the US is of considerable interest to investors wishing to use this contract for hedging In addition, comparisons of in-sample hedging performance between the four models are given. Investors are usually concerned with how well they have done in the past. Therefore, the in-sample hedging performance is a sufficient way to evaluate the hedging performance of alternative models employed to obtain the optimal hedge ratio. The measures that are most used to identify how well individual variables track their corresponding series are the Root Mean Square Errors (RMSEs), Mean Absolute Errors (MAEs) and Mean Absolute Percent Errors (MAPEs). Finally, the issue of the stability of the estimated hedge ratio is also examined in this study using the Chow’s breakpoint test for the superior model. They apply the Chow’s breakpoint test by examining parameter consistency from 19/3/1999 onwards. Conclusions: This paper estimated optimal hedge ratios and examined the hedging effectiveness of the S&P 500 index using alternative models, both constant and time-varying, over the period from July 1992 to June 2000. The findings of this study suggest that in terms of risk reduction the error correction model is the appropriate method for estimating optimal hedge ratios since it provides better results on both slope as well as adjusted R-sqr in comparison with the conventional OLS method, the ECM with GARCH errors, the GARCH model, and the EGARCH model. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION The evidence presented in this paper strongly suggests that the S&P 500 stock index futures contract is an effective tool for hedging risk. This is consistent to earlier studies on S&P 500 index covering the 1980s and early 1990s. Hence, the introduction of this contract has given portfolio managers and investors a valuable financial instrument by which they can avoid risk at times they wish to do this without liquidating their spot position or changing their portfolios composition. 2. CHRISTOS FLOROS+ and DIMITRIOS V. VOUGAS: HEDGING EFFECTIVENESS IN GREEK STOCK INDEX FUTURES MARKET: [Department of Economics, University of Portsmouth, Locksway Road, Portsmouth, PO4 8JF, UK.] This paper examines hedging effectiveness in Greek stock index futures market. It focus on various techniques to estimate variance reduction from constant and timevarying hedge ratios. For both available stock index futures contracts of the Athens Derivatives Exchange (ADEX), they employ a variety of models to derive and estimate the effectiveness of hedging. It measure hedging effectiveness using three different methods: (i) the OLS method, (ii) the method of minimum variance hedge ratio, Ederington (1979), and (iii) the method suggested by Park and Switzer (1995) where , σ^2(Unhedged) – σ^2(hedged) HE = ______________________________ σ^2(Unhedged) M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION . In both cases for Greek stock index futures, the hedge ratio from M-GARCH model provides greater variance reduction, in line with similar findings in the literature. These findings are helpful to risk managers dealing with Greek stock index futures. Methodology: Different measures of hedging effectiveness include the early measure of Markowitz (1959), the method of Ederington (1979), the measures of Howard and D’Antonio (1984, 1987), and the Lindahl’s (1991) measure. An early measure of hedge effectiveness comes from Markowitz (1959). He measures hedging effectiveness in accordance with the reduction in standard deviation of portfolio returns associated with a hedge. In this case, the greater reduction in risk, the greater is the hedging effectiveness. ΔS = c + bΔF + u He shows that a hedge is effective if the R-squared of the regression line explaining the data is high. In other words, the higher the R-squared, the greater the effectiveness of the minimum variance hedge. However, the effectiveness of the minimum-variance hedge can be determined by examining the percentage of risk reduced by the hedge (Ederington, 1979; Yang, 2001). Hence, the measure of hedging effectiveness is also defined as the ratio of the variance of the unhedged position minus the variance of the hedged position, over the variance of the unhedged position. σ^2(Unhedged) – σ^2(hedged) HE = ______________________________ σ^2(Unhedged) It compares the measures of hedging effectiveness using several types of Hedging models. Since the selection of the measure of hedge effectiveness has a considerable impact on the assessment of hedged portfolios, they measure hedging effectiveness of M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Greek stock index futures markets using Model (1), Model (2) and Model (3). To do so, the hedge ratios obtained from the methods of OLS, ECM, and BGARCH are considered. Conclusion: In this paper they investigate the hedging effectiveness of Greek stock index futures contracts. (FTSE/ASE-20 and FTSE/ASE Mid 40). To do so, they compare several techniques of measuring hedging effectiveness. In particular, they measure hedging effectiveness of Greek stock index futures markets using three different methods: (i) the OLS model, (ii) the measure of hedging effectiveness which is defined as the ratio of the variance of the unhedged position minus the variance of the hedged position, over the variance of the unhedged position, and(iii) the method suggested, and applied, by Park and Switzer (1995) and Kavussanos and Nomikos (2000). The primary objective of this paper is to examine whether the hedge ratios calculated from several methods generate better results in terms of hedging effectiveness To do so, the hedge ratios obtained from these methods of OLS, ECM, and BGARCH are considered. First, the results from the OLS model show that the R-sq. value of FTSE/ASE-20 is much higher than that of FTSE/ASE Mid 40. Therefore, the FTSE/ASE-20 index provides larger risk reduction. Furthermore, the second method indicates that the FTSE/ASE-20 contract produces the most effective hedges. In this case, for both contracts the OLS hedge ratio provides greater variance reduction. Then, following the papers of Park and Switzer (1995) and Kavussanos and Nomikos (2000), we show that the BGARCH hedge ratio provides greater variance reduction than the other models. So, the hedge ratio obtained from the Bivariate cointegration GARCH model generates better results in terms of hedging effectiveness. This is in accordance with Park and Switzer (1995), Kavussanos and Nomikos (2000) and Yang (2001). Finally, they measure the hedging effectiveness by considering the hedging performance for the post-sample periods. Using forecasting statistics for OLS model and ECM, they find that the root mean squared error of ECM is lower than that of OLS for both indices. Hence, the ECM M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION outperforms the OLS (conventional) model, and therefore, the error correction model (ECM) is superior to the conventional model. This is consistent with Chou et al. (1996). 3. STEPHEN FIGLEWSKI : HEDGING PERFORMANCE AND BASIS RISK IN STOCK INDEX FUTURES: (1984) Journal of Finance . Vol. 39. (657-669). According to STEPHEN FIGLEWSKI the return and risk for an index futures hedge will depend upon the behavior of the “ basis” i.e. , the difference between the futures price and the cash price. In general basis risk arises simply because the connection between the futures market and the cash market is imperfect, except at maturity of the futures contract. Basis risk can arise from a number of different sources and is a more significant problem for stock index co tracts than for other financial futures, like treasury bills and bonds. The most apparent cause of basis risk is the nonmarket component of return on the cash stock position. In this paper they examine the basis and the different sources of basis risk on the Standard and Poor’s 500 index contracts. Methodology: In this paper they have used constant hedge ratio and variable hedge ratio. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION h* = σpf/σ^2f To examine how effective stock index futures hedges would have been in reality, they have calculated the risk and return combinations which could have been achieved by selling standard and Poor’s 500 futures against the underlying portfolio of five major stock indexes over one week holding periods. To examine the dynamic of the basis, they ran regression of the change in the basis on the deviation from the theoretical value and the change in the spot index. Conclusion: Finally, they have observed that, a more effective hedge may be achievable with a more specialized instrument, such as industry group index futures. Another observation was that the risk minimizing hedge ratio was in all cases smaller then the beta of the portfolio being hedged, contrary to what has been suggested elsewhere. In considering the sources of basis risk in a hedge of the S&P portfolio itself, they found that dividend risk was not an important factor, while hedge duration and time to expiration of the futures contract were, to some extent. One day hedges were subject to substantially more basis risk than one week hedges, but there did not seem to be any further improvement for extending the holding period to four week. They found other evidence indicating that the character of the futures market has changes over time in the fact that the speed of adjustment of the actual futures price toward the theoretical level has increased. At present about 70 percent of a discrepancy is eliminated in one day. Overall evidence points to the conclusion that the stock index futures market is now fairly efficient and becoming more so with time. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION 4. HOLBROOK: NEW CONCEPTS CONCERNING FUTURES MARKETS AND PRICES: Working paper by. American Economic Review , Vol 52, (431-459) According to Holbrook research on futures markets during last 40 years has produced results that have required drastic revision or replacement of a great part of the previously accepted theory of futures markets and of the behavior, not only for futures prices, but of the general class of prices behavior of businessmen including speculators, and on the functioning of the price system. Empirical research has played a leading role in the advancement of economic knowledge and understanding that is described here, but the role has been a different one than economist have ordinarily thought that such research would play in advancing their science. The hedging market concept: Futures markets have usually been regarded, in the past, as essentially speculative markets. Although they rather early won recognition as useful for hedging, their hedging use was treated as a fortunate by-product, neither necessary to the existence of such a market, nor very closely related quantitatively to the amount of speculation on the market. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Irwin undertook a study of the origins of futures markets in butter and eggs. Taking advantage of the fact that there were then people still alive who had witnessed the early stages of emergence of futures markets came from hedgers rather than from speculators. The multipurpose concepts of hedging: According to the traditional concepts, hedging consists in matching one risk with an opposing risk , and hedging in futures is effective because changes in spot prices of a commodity tend to be accompanied by like changes in the futures price. The fact that hedging usually involves more than risk avoidance has been known to hedgers themselves and to some economists. Quantitative studies, perhaps surprisingly, have contributed more to understanding of hedging than have verbal inquires concerning business motivation. Particularly noteworthy among these were studies of the quantitative relation between hedged stockholding and market “carrying charges “, which brought recognition that much hedging was done to assure profits, not merely to avoid risk The traditional hedging concept represents the hedger as thinking in terms of possible loss from his stockholding being offset by gain on the futures contracts held as a hedge , the carrying-charge hedger thinks rather in terms of change in “basis” , that is, change in the spot futures price relation. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION 5. JERPME L. STEIN: THE SIMULTANEOUS DETERMINATION OF SPOT AND FUTURES PRICES: Working paper: American Economic Review, Vol. 51 (1012-1025) This paper develops a simple geometric technique for the simultaneous determination of spot and futures prices in commodity markets: The decision to hold hedged and unhedged stocks under pure competition: Unhedged holding of stocks: The expected gain from holding unhedged stocks is equal to the spot price expected to prevail at a later date (p*) minus the current spot price (p) minus the marginal net carrying costs (m). There are two components of the marginal net carrying costs: the marginal costs of storage and the marginal convenience yield, the later have a negative element in carrying cost. The concept of the marginal convenience yield has been developed by Brennan and Telser. The variable p* is a stochastic variable. There is a probability that a capital loss will be made on the holding of unhedged stocks. Expected capital loss will be p*-p-m M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION The holding of hedged stocks: When stocks are hedged, the owner incurs a liability of offset his holding of assets (stocks). His liability is the sale of a futures contract, for the delivery of one of several grades of a commodity sometime within the period of the futures contract. The owner of hedged stocks does not intend to deliver a physical commodity in fulfillment of his futures contract, but intends to repurchase a futures contract at the time that he sells his inventory of stocks/ the expected gain from holding hedged stock is equal to the expected gain from holding unhedged stocks minus the expected loss involved in the sale and purchase of a futures contract. The expected gain from holding hedged stocks is h, h = (p*-p) - (q*-q) – m. where , q is current price of futures contract q* is price of the futures contract expected at a later date. The optimum combination of hedged and unhedged stocks: An owner of stock, for sale at an uncertain price, is assumed to allocate his holding between hedged and unhedged stocks so as to maximize his expected utility. The method of optimizing developed here is based upon James Tobin’s theory of liquidity preference. As the portion of unhedged stock varies between zero and 100 percent, the expected return per unit of stock varies from h to u. Risk is inherent in each form of stockholding, where risk is defined as the situation whereby the owner may fail to receive his expected return. Tobin used the standard deviation of the expected returns as his measure of risk. Since he assumed that the probability density functions are symmetrical, a high standard deviation or variance means a high probability of both negative and positive deviations from the mean. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION 1. STATEMENT OF RESEARCH PROBLEM: Market risk i.e. systematic risk of the portfolio can be reduced through hedging. Hedging activity involves finding out of optimum hedge ratio and testing hedge ratios. Hedging through trading futures is a process by which adverse price movements can be controlled and reduced. 2. OBJECTIVES OF STUDY: Minimization of Market Risk through hedging. To test the Effectiveness of Hedging by different models. To find optimum hedge ratios. The above objectives are explained in brief as follows: M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION A portfolio is exposed to two kind of risks i.e. market risk and non market risk. One can eliminate non market risk by creating an optimal portfolio. The problem is reduction of market risk. Hence in this study we try to minimize the market risk by entering into futures market with an appropriate hedge ratio. Our objective is to minimize the market risk which is inevitable. Hedging provides risk reduction facility and by choosing appropriate hedge ratio one can protect their portfolio from the market risk. In our study we are testing the effectiveness of the hedge ratios generated by different models and see whether the hedge ratios generated by different models give optimal position. SCOPE OF THE STUDY: A hedge using index futures removes the risk arising from market moves and leaves the hedger exposed only to the performance of the portfolio relative to the market. Futures contracts enable market participants to alter risks, which they face caused by adverse and unexpected price changes. Hedging through future market is advantageous because of its low cost. This study is useful for those who are risk avers and those who wants to protect themselves from the risk arising from the unexpected market movements. The study also focuses on the effectiveness of the hedged portfolio and tests its effectiveness. The return from the unhedged portfolio is exposed to unlimited market risk. However by hedging the portfolio with appropriate hedge ratios one can minimize the unexpected market moves. DATA AND SAMPLE OF DATA: M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION The data employed in this study comprises of 260 weekly observations on the NIFTY stock index and stock index Futures contracts( 2001-2006) and 260 observations on the CNXIT and stock index futures contracts(2003 Aug-2006 Mar). Closing prices of spot indices are obtained from the www.yahoofinance.com website and prowess Database, closing prices of futures contracts are obtained from (www.nseindia.com). The NIFTY index comprises of 50 Indian companies, quoted on the NATIONAL STOCK EXCHANGE (NSE), selected from various sectors, while the CNXIT comprises of 20 Companies, that have more than 50% of their turnover from IT related activities like software development, hardware manufacture, vending, support and maintenance. Futures contracts are quoted on the NATIONAL COMMODITY AND DERIVATIVE EXCHANGE. NIFTY futures and CNX IT futures contracts have a maximum of 3-month trading cycle - the near month (one), the next month (two) and the far month (three). With effect from 28th May 2004 the Base value of CNXIT has changed from 100 to 100, to account for the above change in Base value, slicing technique has been adapted. We have confined the analysis to the near month contract because preliminary research showed that there was no much difference between the hedging properties of the nearest and second contract. Also nearly all trading volume is in the near month so that liquidity is much greater in that contract. Weekly data are preferred in this study for several reasons. First, the choice of weekly hedges is realistic and implies that hedgers in the market rebalance their futures positions on a weekly basis. Second, the one week hedge can be used to reduce risk without incurring excessive transactions costs. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Finally, the weekly hedging horizon is the most common choice of the prior empirical studies in several derivatives markets. In all estimations the futures contract nearest to expiration is used. In line with previous studies changes in logarithms of both spot and futures price are analyzed, and no adjustment is made for dividends. SAMPLE: From the past 5 years data we have taken only weekly observation on the NIFTY and NIFTY futures, 3 years CNXIT and CNXIT futures contracts. NIFTY contains 50 India companies with large market capitalization and CNXIT contains 20 companies which are into IT related activities. In this study we have taken last 5 years closing prices of NIFTY and NIFTY INDEX FUTURES CONTRACT and also CNXIT and CNXIT futures contracts. PERIOD OF STUDY AND SOURCE: In this study we have adopted 5 years weekly closing prices of NIFTY and NIFTY futures contract, and 3 years for CNXIT and CNXIT index futures contract. SOURCES: secondary data 1. www.nseindia.com 2. www.yahoofinance.com 3. Prowess Database. 4. Capital Line Plus. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION METHODOLOGY: Test of Stationary: Ho: Series of Data are non stationary or series has unit root (ρ = 0) H1: Series of Data are stationary or series does not have unit root (ρ < 1.) Test of unit root: The existence of unit roots is firstly tested using the Augmented Dickey-Fuller test (ADF) (Dickey and Fuller, 1981) through the following relationship: Δ St = α + βT + ρSt-1 + ΣγΔSt-1 + Ựt Where ΔSt = St –St-1 , St is the index of the spot market, and k is chosen so that the deviations ut to be white noise. The same relationship is used to determine the order of the futures price index ( Ft ). M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION α = constant, β = slope, T= trend, ρ = rho, γ = gamma, Ựt-1 = error term. Cointegration: Evidence of price changes in one market generating price changes in the other market so as to bring about a long-run equilibrium relationship is given below: Ft – δ0 – δ1St = εt Where Ft and St are contemporaneous futures and cash prices at time t; δ1 and δ0are parameters; and εt is the deviation from parity. If Ft and/or St are nonstationary then the Ordinary Least Square (OLS) method is inappropriate because the standard errors are not consistent. This inconsistency does not allow hypothesis testing of the cointegrating parameter δ1. If t F and t S are nonstationary but the deviations, εt , are stationary, Ft and St are cointegrated and an equilibrium relationship exists between them (Engle and Granger, 1987). For Ft and St to be cointegrated, they must be integrated of the same order. Performing unit root tests on each price series determines the order of integration. If each series is nonstationary in the levels, but the first differences and the deviations εt are stationary, then the prices are cointegrated of order (1,1), denoted CI (1,1), with the M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION cointegrating coefficient δ1 . In order to test for cointegration, two econometric procedures are implemented: the Engle-Granger two-step methodology (Engle and Granger, 1987) and the Johansen’s Maximum Likelihood approach (Johansen, 1988 and 1991). According to Engle and Granger, two basic steps are followed: 1. Testing the existence of unit roots (integration order) in each index, following Augmented Dickey-Fuller (ADF) test through equation. 2. Cointegration testing between stock index spot and futures market. Consider prices (in log) in spot market i and futures market j ( Sti and Ftj), and Pt is the vector that consist of Sti and Fti. According to Engle and Granger (1987), Sti, is said to be integrated of order d, denoted Sti – 1 (d), if the dth difference of Sti, is stationery. The vector pt is said to be cointegrated of order d, and there exists a non-zero vector δ such that δ Pt is integrated of order d-b, for b>0. If both Sti and Fti are I(1) and Pt-(CI(1,1), [ i.e. δ, Pt-I(0)] , then there are error-correction equations in the following form: ΔSti = α1 [St-1i-δ1 Ft-1j] + lagged (ΔSti and ΔFtj) + ε ti ΔFtj = α2 [Ft-1j-δ2 St-1i] + lagged (ΔSti and ΔFtj) + ε tj M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Where α1 and α2 are non-zero coefficients and εti and εtj are stationery, possibly autocorrelated error terms. Engle and Granger proposed several cointegrateion tests: however, the most preferable is the ADF statistic test. R^2 measures the proportion of the total variation in y explained by the linear combination of the regressors. The coefficients of determination express the proportion of the total variation that has been explained or the relative reduction in variance when measured about the regression equation rather than about the mean of the dependent variable. if the value of r = 0.9 , R^2 will be 0.81 and this would mean that 81% of the variation in the dependent variable has been explained by the independent variable It is usually advisable to underhedge as your confidence in the future correlation between ΔSt and ΔFt declines: that is , as the value of R^2 declines, trade fewer contracts than the number called for by h*. If R^2 is below some arbitrary value, perhaps 0.5 , then it is probably not wise to use that particular futures contract to hedge at all. 1 . ORDINARY LEAST SQUARE METHOD: The method of ordinary least square is attributed to Carl Friedrich Gauss, a German mathematician. This method is the cornerstone of most econometric theory. It makes 10 assumptions for two-variable regression. 1. Linear Regression model: The regression model should be linear in the parameters, as shown: Yi = β1 + β2Xi + Ụi Conditional expectation of Y , E(Y/Xi), is a linear function of the parameters, the β’s . Hence linear regression will always mean a regression that is linear in the parameters: the β’s . it may or may not be linear in the explanatory variables, the X’s. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION 2. X values are fixed in repeated sampling: values taken by the regressor X are considered fixed in repeated samples. More technically, X is assumed to be nonstochastic. The regression analysis is conditional regression analysis that is conditional on the given values of the regressor X. 3. Zero mean value of disturbance Ụi : given the value of X, the mean, or expected, value of the random disturbance term Ụi is zero. Technically, the conditional mean value of Ụi is zero. Symbolically, E(Ụi/Xi) = 0 This assumption states that the mean value of Ụi, conditional upon the given Xi, is zero. The assumption E(Ụi/Xi) = 0 implies that E(Yi/Xi) = β1 + β2Xi. Therefore two assumptions are equivalent. 4. Homoscedasticity or equal variance of Ụi: given the value of Xi, the variance of Ụi is the same for all observations. That is, the conditional variances of Ụi are identical. symbolically, we have var (Ụi/Xi) = E[Ụi - E(Ụi/Xi)]^2 = E[Ụi^2/Xi] = σ^2 5. No autocorrelation between the disturbances. given any two X values, Xi, and Xj, the correlation between any two Ụi and Ụj is zero. symbolically we have M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Cov (Ụi, Ụj/Xi,Xj) = E{[Ụi - E(Ụi)]/Xi}{[Ụj - E(Ụj)]/Xj} = E(Ụi/Xi)(Ụj/Xj) = 0 6. zero correlation between Ụi and Xi, or E(Ụi Xi) = 0 Cov (Ụi, Xi) = E[Ụi - E(Ụi)][Xi - E(Xi)] = E[Ụi(Xi - E(Xi))] = E(ỤiXi) - E(xi)E(Ụi) = E(ỤiXi) = 0 7. The number of observations n must be greater than the number of parameters to be estimated. Alternatively, the number of observations n must be greater than the number of explanatory variables. since E(Ụi) = 0 8. Variability in X values: the X values in a given sample must not all be the same. Technically, var(X) must be a finite positive number. 9. The regression model is correctly specified. Alternatively, there is no specification bias or error in the model used in empirical analysis. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION 10. There is no perfect multicollinearity. relationships among the explanatory variables. That is there are no perfect linear This model is just a linear regression of change in spot prices on changes in futures prices. Let St and Ft be logged spot and futures prices respectively, the one period MVHR can be estimated as follow; ΔSt = a0 + β.ΔFt + ưt Where ưt is the error from the OLS estimation, ΔSt and ΔFt represent spot and futures price changes and the slope coefficient β is the hedge ratio (h*). ERROR CORRECTION MECHANISM: (ECM) The error correction mechanism first used by Sargan and later popularized by Engle and Granger corrects for disequilibrium. An important theorem, known as the Granger representation theorem, states that if two variables Y and X are cointegrated, then the relationship between the two can be expressed as ECM. ΔSt = α0 + α1ΔFt + α2ụt-1 + εt (2) Where ụt-1= St-1[a0 + a1Ft-1] is the error correction term and has no moving average part; the systematic dynamics are kept as simple as possible and enough lagged variables M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION are included in order to ensure that εt is a white noise process: and the coefficient α1 is the optimal hedge ratio. The above equation states that ΔSt depends on ΔFt and also on the equilibrium error term. LIMITATIONS: 1. Only NIFTY and CNXIT have been selected for hedging. 2. The above study is limited to 5 years data for NIFTY and 3 years data for CNXIT. 3. The above study considers the effectiveness of hedging only through two models i.e. OLS Models and ECM model. 4. Selected scrip’s are included in both indices. 5. the above study is focused only on two indices i.e. NIFTY and CNXIT. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION DATA ANALYSIS: Test of Unit root and cointegration: Tests for the presence of a unit root are performed by conducting the Augmented DickeyFuller unit root rest under the assumption that there is no linear trend in the data generated process The series are tested at the 0 level and found stationery at 1% level, suggesting that the series are stationery. The results for NIFTY, NIFTY INDEX FUTURES AND CNXIT, M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION and CNXIT INDEX FUTURES are reported in Table 1,2,3,4 respectively. Diagrammatical representation of Stationarity is reported in Graphs1 and Graph 2. Since we have identified that both our series, the spot prices (St) and future price (Ft) of both the indices are I (0), then the presence or absence of cointegration can be investigated by simply regressing the values of the spot asset (St) on the value of the futures contracts (Ft). In particular a test for a unit root in the estimated residuals will determine the presence or absence of cointegration. Table 5 and Table 6 Shows ADF test results on residuals for both the indices. Since it shows that error term is I (0) in long run. The results suggest that the spot NIFTY Index is cointegrated with the NIFTY Index Futures and spot CNXIT Index is cointegrated with the CNXIT Index Futures contract. We can easily see the cointegration of both indices with their respective index futures contract in a graph Graph.3 and Graph 4. Evidence in favour of a cointegrated system between weekly closing prices on the stock index and weekly settlement prices on the stock index futures implies that both the cash and the futures markets have a tendency to move together in the long run deviations from equilibrium may be observed due to temporary disequilibrium forces. RESULTS OF OLS MODEL: FOR SPOT NIFTY AND NIFTY INDEX FUTURES: The optimal hedge ratio from the regression equation ΔSt = a0 + β.ΔFt + ưt Using conventional approach is presented as follows: ΔSt = 0.001834 + .521ΔFt + ưt M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION The slope coefficient β is the optimal hedge ratio. In our study it is more than 0.5 but not close to unity hence results shows it is not highly significant. Prior research studies have shown that, if the slope is close to unity then it is highly significant. The Adjusted R-sqr is measure of good fit, but in out study R-sqr is 0.255 it is very less [Table. 7]. FOR SPOT CNXIT AND CNXIT INDEX FUTURES: The regression equation as follows: ΔSt = 0.001388 + 0.833ΔFt + ưt The slope coefficient β is the optimal hedge ratio for CNXIT INDEX. In this study it is near to unity hence it is significant. And adjusted R-sqr is 0.684 indicates good fit [Table 8]. Comparison of hedge ratios and adjusted R-sqr for both NIFTY AND CNXIT are found in [Table 11]. Both, the hedge ratio and adjusted R-sqr for CNXIT are greater then NIFTY, which indicates better to go for CNXIT rather than NIFTY in case of hedging. And R-sqr suggests effectiveness of hedge. But if we compare our study with prior studies both the hedge ratios are not that much effective since both R-sqr’s are below 0.8. Prior studies suggest that R-sqr should be between 0.8 to 0.99 for effectiveness of hedge. RESULTS OF ECM: Since the spot NIFTY Index, spot CNXIT Index are cointegrated with NIFTY Index futures, CNXIT Index futures respectively, then according to Engle & Granger, an ECM must exists as presented in equation (2). Error correction equation for NIFTY and NIFTY Index futures as follows: ΔSt = 0.001838 + 0.492ΔFt + (-0.0004827ụt-1) + εt Error correction equation for CNXIT and CNXIT Index futures as follows: M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION ΔSt = -0.000162 + 0.988ΔFt + (-0.0003307ụt-1) + εt Table 9. And Table 10. Represents the summary of the error correction for both NIFTY and CNXIT respectively. By examine Table 11, we can report that the optimal hedge ratio for NIFTY is 0.492 & for CNXIT 0.988 and the error correction model for CNXIT including no lags has good fit compared to NIFTY [i.e. CNXIT, R-sqr is 0.79 and NIFTY R-sqr is 0.674]. The error correction coefficient ụt-1 is statistically significant at an ECM coefficient ụt-1 is significant at 5% level for CNXIT. The comparison of hedge ratio’s determined by the two models for both indices are presented in Table 11. Results reveal that the data chosen for the test is significant. If we look at the t-test values, they are highly significant at 5% level. Comparison of t-test for both the models reveals that ECM model has highly significant values. And the white noise i.e. short term error term is also zero in both the indices. But compared to NIFTY Index the CNXIT Index futures contract has greater significance is error reduction. This we can observe in Table 11. level for NIFTY; M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Conclusion: In this report we have estimated optimal hedge ratio and examined the hedging effectiveness of NIFTY and CNXIT Indices using OLS & ECM Models. And also we have compared, which index gives maximum risk reduction, or effective hedge ratios. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION The study has carried on NIFTY Index and CNXIT Index with their respective Futures contracts by taking the sample data over the period of 5 years for NIFTY and 3 years for CNXIT [April 2001 to March 2006 and 28th August 2003 to March 2006 respectively]. The finding of the study suggests that in terms of risk reduction the error correction model is the appropriate method for estimating optimal hedge ratios compared to the conventional OLS model. Howard & D’Antonio define hedging effectiveness as the ratio of the excess return per unit of risk of the optimal portfolio of the spot and the futures instrument to the excess return per unit of risk of the portfolio containing the spot asset alone. Here, in this study we have investigated the hedging effectiveness of NIFTY & CNXIT by looking at adjusted R-sqr, which measures the effectiveness of the hedge. Adjusted R-sqr for CNXIT is higher compared to NIFTY in both the models. And the error correction model results reveals higher R-sqr value for CNXIT Index compared to the conventional model OLS. As per the objective of the study , to examine whether the hedge ratios calculated from two methods generate better results in terms of hedging effectiveness or not. CNXIT Index provides larger risk reduction compared to the NIFTY in both the methods, and as most effective hedging tool. And also hedge ratio for CNXIT Index generated with the help of ECM is better compared to OLS. The results show that, the CNXIT Index futures contract is an effective tool for hedging the risk. [I.e. hedge ratio from OLS is 0.833 and from ECM is 0.988]. To minimize or to avoid the market risk, CNXIT Index futures contracts are better instruments as compared to the NIFTY Index futures contracts. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Table: 1 ADF Test Statistic -15.17069 1% Critical Value* 5% Critical Value 10% Critical Value -2.5735 -1.9408 -1.6163 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(SPOT) Method: Least Squares Date: 06/10/06 Time: 19:26 Sample(adjusted): 1/08/2001 12/12/2005 Included observations: 258 after adjusting endpoints M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Variable SPOT(-1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -0.920747 0.472371 0.472371 0.029425 0.222511 544.1039 Std. Error 0.060693 t-Statistic -15.17069 Prob. 0.0000 0.000466 0.040508 -4.210108 -4.196337 1.838292 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat Table:2 ADF Test Statistic -15.17069 1% Critical Value* 5% Critical Value 10% Critical Value -2.5735 -1.9408 -1.6163 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(SPOT) Method: Least Squares Date: 06/10/06 Time: 19:26 Sample(adjusted): 1/08/2001 12/12/2005 Included observations: 258 after adjusting endpoints Variable SPOT(-1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -0.920747 0.472371 0.472371 0.029425 0.222511 544.1039 Std. Error 0.060693 t-Statistic -15.17069 Prob. 0.0000 0.000466 0.040508 -4.210108 -4.196337 1.838292 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat Table: 3 ADF Test Statistic -11.94102 1% Critical Value* 5% Critical Value 10% Critical Value -2.5811 -1.9423 -1.6170 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(SPOT) Method: Least Squares Date: 06/10/06 Time: 19:25 Sample(adjusted): 1/08/2003 7/20/2005 M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Included observations: 133 after adjusting endpoints Variable SPOT(-1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -1.001180 0.519210 0.519210 0.030871 0.125799 274.3487 Std. Error 0.083844 t-Statistic -11.94102 Prob. 0.0000 -0.000533 0.044522 -4.110507 -4.088775 1.940398 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat Table: 4 ADF Test Statistic -11.73263 1% Critical Value* 5% Critical Value 10% Critical Value -2.5811 -1.9423 -1.6170 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(FUTURES) Method: Least Squares Date: 06/10/06 Time: 19:24 Sample(adjusted): 1/08/2003 7/20/2005 Included observations: 133 after adjusting endpoints Variable FUTURES(-1) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -0.978766 0.510382 0.510382 0.030576 0.123408 275.6245 Std. Error 0.083423 t-Statistic -11.73263 Prob. 0.0000 -0.000632 0.043697 -4.129692 -4.107960 1.952549 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat Table: 5 ADF Test Statistic -14.39225 1% Critical Value* 5% Critical Value 10% Critical Value -2.5735 -1.9408 -1.6163 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESIDUALS) Method: Least Squares Date: 06/10/06 Time: 19:37 Sample(adjusted): 1/08/2001 12/19/2005 Included observations: 259 after adjusting endpoints Variable RESIDUALS(-1) Coefficient -0.902002 Std. Error 0.062673 t-Statistic -14.39225 Prob. 0.0000 M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood 0.445282 0.445282 40.40181 421134.9 -1325.013 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat -0.473135 54.24563 10.23948 10.25321 1.971213 Table: 6 ADF Test Statistic -9.583220 1% Critical Value* 5% Critical Value 10% Critical Value -3.4800 -2.8830 -2.5781 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESIDUALS) Method: Least Squares Date: 06/10/06 Time: 19:42 Sample(adjusted): 1/08/2003 7/27/2005 Included observations: 134 after adjusting endpoints Variable RESIDUALS(-1) C R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Coefficient -0.827192 -0.352822 0.410288 0.405821 34.09559 153451.2 -662.0387 2.055444 Std. Error 0.086317 2.946443 t-Statistic -9.583220 -0.119745 Prob. 0.0000 0.9049 0.394552 44.23229 9.911026 9.954277 91.83810 0.000000 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) Table: 7 RESULTS FROM ORDINARY LEAST SQUARE: (NIFTY and NIFTY INDEX FUTURES) ----------------------------------------------------------------------------------------------------------Coefficients Standard Error t-Test ---------------------------------------------------------------------------------------------------------------------------------------------------------------- M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION ---------------------------------------------------------------------------------------------------------------------------------------------------------------- C ΔFt 0.001834 0.521 0.002 0.055 1.131 9.447 ---------------------------------------------------------------------------------------------------------------------------------------------------------------- Table: 8 RESULTS FROM ORDINARY LEAST SQUARE: (CNXIT and CNXIT INDEX FUTURES) ----------------------------------------------------------------------------------------------------------Coefficients Standard Error t-Test ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- C ΔFt 0.001388 0.833 0.002 0.049 0.889 16.914 ---------------------------------------------------------------------------------------------------------------------------------------------------------------- Table: 9 RESULTS FROM ERROR CORRECTION MODEL: (NIFTY and NIFTY INDEX FUTURES) --------------------------------------------------------------------------------------------------------Coefficients Standard Error t-Test ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- C 0.001838 0.001 1.712 M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION ΔFt 0.492 0.036 13.478 υt-1 -0.000483 0.000 -18.192 ---------------------------------------------------------------------------------------------------------------------------------------------------------------- Table: 10 RESULTS FROM ERROR CORRECTION MODEL: (CNXIT and CNXIT INDEX FUTURES) ---------------------------------------------------------------------------------------------------------Coefficients Standard Error t-Test ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- C ΔFt -0.000116 0.988 0.001 0.044 -0.091 22.378 υt-1 -0.000331 0.000 -8.307 ---------------------------------------------------------------------------------------------------------------------------------------------------------------- Table: 11 COMPARISON BETWEEN HEDGING MODELS: -----------------------------------------------------------------------------------------------------------NIFTY CNXIT ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- OLS Hedge Ratio 0.521 ECM 0.492 OLS 0.833 ECM 0.988 M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION Adj. R-sqr 0.255 0.674 0.682 0.790 ------------------------------------------------------------------------------------------------------------ SCOPE FOR FURTHER RESEARCH: This study is focused only on two indices i.e. NIFYT and CNXIT. We have tested hedge ratios by using 2 models i.e. OLS and ECM, however, further study can be possible for testing the hedge ratios and it effectiveness with different models like BGARCH, GARCH, VECM etc. Glossary: 1. Basis Risk: The risk to a future investor of the basis widening or narrowing. Relationship between the cash price of a good and the future prices of that good. 2. Cointegration: refers to co-movements in asset prices, not co-movements in returns. 3. Hedge Ratio: The minimum number of units of a hedging instrument needed to be held in order to minimize the overall portfolio, which is a combination of a cash position and an hedge position. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION 4. Heteroscedasticity: Difference in the variance of the return over the period. or unequal variance in returns . 5. Minimum Variance Hedge Ratio: refers as the proportion of the futures to the cash position that minimizes the net price change risk. It indicates the number of futures or options need to be bought or sold in order to reduce the variability of the total hedged position to the maximum possible extent. 6. Near month contract: it is a type of futures contract likely to be matured within a month, which is nearby in time. 7. Optimum Hedge: the hedge at which the utility of the hedger is maximized. REFERENCES: 1. Working, H (1953), Futures trading and hedging: American Economic Review, Vol. 43 , pg. 314-343. 2. Morkowitz, H.M. (1959), Portfolio selection: efficient diversification of investments, JOHN Wiley and Sons, Inc., New York. 3. Stein, J.L. (1961), The simultaneous determination of spot and futures prices: American Economic Review, Vol. 51, pg. 1012-1025. 4. Working H. (1962), New concepts concerning futures markets and prices: American Economic Review, Vol. 52, pg. 431-459. M.P.BIRLA INSTITUTE OF MANAGEMENT EFFECTIVENESS OF HEDGING AND HEDGE RATIO ESTIMATION 5. Ederington, L. H. (1979), The hedging performance of the new futures markets, Journal of Finance, Vol.34, pg.157-170. 6. Howard,C, and D’Antonio, L. (1984), A risk-return measure of hedging effectiveness,Journal of Financial and Quantitative Analysis, Vol.19 pg.101 -111. 7. Figlewski, S. (1984), Hedging performance and basis risk in stock index futures, Journal of finance, Vol 39. pg. 657-669. 8. Lindahl, M. (1991), Risk-return hedging effectiveness measure for stock index futures, Journal of futures markets, Vol. 11 , pg. 399-409. 9. Hsin, C, W., Kou, J, . and Lee, C.W. (1994), Anew measure to compare the hedging effectiveness of foreign currency futures versus options, Journal of futures markets, Vol. 14, pg. 685-707. 10. Park, T.H. and Switzer, L.N. (1995), Time-varying distributions and the optimal hedge ratios for stock index futures, Applied financial economics, Vol.5, pg.131-137. 11. Pennings, J.M.E., and Meulenberg, M.T.G. (1997), Hedging efficiency: a futures exchange management approach, Journal of Futures Markets, Vol.17, pg.599-615. 12. Kavussanos, M.G., and Nomikos, N.K. (2000), Constant Vs. Time-varying hedge ratios and hedging efficiency in the BIFFEX market, Transporatation research Part E, Vol.36 pg. 229-248. 13. Chou, W.L. Denis, K.K.F. and Lee C.F (1996), Hedging with the Nikkei index futures: the conventional model versus the error correction model, quarterly Review of Economics and finance Vol.36, pg.495-505. M.P.BIRLA INSTITUTE OF MANAGEMENT

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