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ANALYSIS OF HEDGING EFFECTIVENESS OF INDEX FUTURE AGAINST STOCK INDICES MOVEMENT

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## ABSTRACT

in terms of reducing portfolio variance.ratio is also an essential factor. It’s found that in longer term hedging, the time varying hedge ratios outperform the constant hedge ratio it Some of the financial instruments include future, forwards and options. The aim of hedging is not to make a profit rather it is to preserve transactions from market volatility. This can only be achieved through taking an offsetting or what is called reverse position. In the market, there are majorly two forms of hedging position or transaction. The long hedge should be used in case the risk is that of prices or when the rate has chances of going up. Conversely, if the risk is that price or rates will go down or decrease, the selling or the short hedge should be applied. 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 these competing model to estimate the effectiveness of the hedging. 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. The use of GARCH adds value to the overall discussion and we can conclude that it is among the effective methods of establishing the stock movement using hedging. Hedging is important. It suggests that return and variance are not the only variables that determine the appropriate hedge ratio, the investor’s preference for

## ABBREVIATION AND ACRONYMS

Autoregressive Conditional HeteroskedasticityARCH:

ASX: Australia Stock Exchange

EFP exchange for physical

Generalized Autoregressive Conditional HeteroskedasticityGARCH:

OLS: Ordinary Least Square

SPI share price index

Vector Error Correction Model VECM:

## LIST OF TABLES

Table 4.1: Descriptive statistics………………………………………………………………….33

Group unit root test: Summary………………………………………………………..34Table 4.2

Table 4.3: Null Hypothesis: ASXF_LN has a unit root………………………………………….35

Table 4.4: Null Hypothesis: STOCK_INDICES_LN has a unit root……………………………36

Table 4.5.0: OLS Regression results……………………………………………………………..37

Table 4.6: The Bivariate VAR Model Estimates………………………………………………..38

Table 4.7: Optimal Hedge ratio using Bivariate VAR Model……………………………………39

Table 4.8: The Vector Error Correction Estimates Model………………………………………39

Table 4.9. Optimal Hedge Ratio from the VEC Model………………………………………….40

Table 4.10: GARCH Model of Estimation………………………………………………………41

Table 4.11: Mean Return for within sample……………………………………………………..42

Table 4.12: Average Variance Reduction for within sample…………………………………….45

Table 4.13: Average variance reduction outside the sample…………………………………….46

CERTIFICATION ii

ABSTRACT iii

ABBREVIATION AND ACRONYMS iv

LIST OF TABLES v

CHAPTER ONE: INTRODUCTION OF THE STUDY 1

Introduction 1 1.0

Background of the study 1 1.1

Characteristic of future contract 3 1.2

Future trade on organized exchange 3 1.2.1

Existing of standardized contract terms 4 1.2.2

Subjected to clearing house 4 1.2.3

Need for margin payment and daily settlement 4 1.2.4

Closing of future position 5 1.2.5

Function of the future contract market 5 1.3

Price discovery 5 1.3.1

Hedging. 6 1.3.2

Speculative purposes 6 1.3.3

Australia Derivative market 7 1.4

Purpose of the study 9 1.5

Objective of the study 10 1.6

Hypothesis of the study 10 1.7

Scope of the study 11 1.8

Benefits of the Study 11 1.9

Policy makers 11 1.9.1

Investors 11 1.9.1

Financial Managers 12 1.9.2

CHAPTER TWO: LITERATURE REVIEW 13

Introduction 13 2.0

Literature on future contracts 13 2.1

Dynamic hedging 15 2.2

Static hedging 17 2.3

Empirical Review 20 2.5

CHAPTER THREE: ECONOMETRIC METHODOLOGY 23

Introduction 23 3.0

Unit Root Tests 23 3.1

ADF Test for Unit Roots 25 3.2

Hedging models 26 3.3

VECM 26 3.4

Regression model 28 3.5

Bivariate VAR Method 29 3.6

The Multivariate (GARCH Method) 29 3.7

The Data 30 3.8

CHAPTER FOUR: ANALYSIS AND RESULTS 30

Introduction 30 4.0

Descriptive statistics 31 4.1

The regression model 34 4.2

ARCH and GARCH Effect 38 4.3

CHAPTER FIVE. SUMMARY AND CONCLUSION 42

Summary 42 5.0

Conclusion 42 5.1

Bibliography 45

## 1.0 Introduction

This chapter provides introduction and background of the study. It provides details background of the study, objectives of the study, study questions. Purpose of the study and the summary of the study.

## 1.1 Background of the study

. (Stoll and Whaley 2015). The new advancements in the time run econometrics have also contributed in juggling around with on the conventional ways used so far and revamped the whole gamut of experimental research to establish the hedge ratio successfully. The traditional knowledge suggests that the optimal hedge ratio is supposed to have 1:1 situation to successfully hedge a single unit of spot location to have a single unit of a future contract Arouri, Jouini and Nguyen 2012)he successful use of contracts in future for matters hedging has become the primary concern and center of discussion on getting the finest hedge ratio and hedging helpfulness in experimental financial research (. Apart from the efficiency of the future market, the choice of the effective hedging strategy is crucial for those who are hedging. It should be noted that for effective hedging t (Stoll and Whaley 2015)Hedging is one of the most important functions of any stock index future as it helps in reducing and controlling the risk which may cause unfavorable changes in price on the spot market while at the same time increases the value of the relevant stock index

. (Kara, Boyacioglu and Baykan 2011). Some of the financial instruments include future, forwards and options. The aim of hedging is not to make a profit rather it is to preserve transactions from market volatility. This can only be achieved through taking an offsetting or what is called reverse position. In the market, there are majorly two forms of hedging position or transaction. The long hedge should be used in case the risk is that of prices or when the rate has chances of going up. Conversely, if the risk is that price or rates will go down or decrease, the selling or the short hedge should be applied. The effect of this is that the company will go long on the assets and other receivables while short on the liabilities and other payablesArouri et al., 2012)(; hedging is one of the common and effective ways of managing systematic risk in the derivative markets. The main concept of hedging is to help in fixing the price level of the future transaction of the financial instruments to acceptable level JohnsonHedging is one of the common characteristics of the derivative marketsThis approach frequently referred to as naïve-hedging strategy botched to deliver as the progress between the place and prices in future are not harmonized. This has, therefore, resulted in a transformed interest at the level of theoretical by works. They used a portfolio method to determine the most favorable hedging through the use of expected utility maximization that cuts down to the lowest variance analysis as the best case.

.(Stoll and Whaley 2015)One of the derivatives instruments used for hedging is futures. A future contract can be defined as standardized agreements on the future delivery of the underlying assets of a given quantity and quality for a given price agreed today. The future is generally traded on the exchange with the exchange acting as the go between. The underlying asset to the future contract can either be a commodity, security, currency or any other financial instruments like a stock index

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 the determination of the hedging ratio. The main objective of this study is to investigate hedging effectiveness of index future against Stock Indices movement in Australia Stock market.Arouri, Lahiani & Nguyen (2015) states that for efficiency and effectiveness of the hedging, then the future price needs to be efficient as the inefficiencies in the market would result into higher cost of hedging which may undermine the effectiveness of the future markets. Stoll & Whaley (2015) For the future stock index to reduce the risk of any unfavorable changes in price, hedging is very essential. Hedging helps in increasing the value of the relevant stock index. For portfolio managers, the selection of an effective strategy for hedging is critical than the efficiency of the future markets. 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.

## 1.2 Characteristic of future contract

When concentrating on future contracts, they contain five major characteristics which distinguish them from other financial instruments which exist in the market. These characteristics are discussed below:-

## 1.2.1 Future trade on organized exchange

Ciner et al., 2013). The trade is organized in a manner that they can take place during the official trading hours and this can take place either in a physical location and or on the floor of the exchange. In contrast to other instruments and specialist system which is used in stock exchange, the future contracts trade by a system of open outcry. In most cases, the pit traders are speculators who normally get into these future contracts to pursue profit by carrying risk in their investment. Hedging, therefore, comes on hand to help the traders who are mostly speculators to mitigate risk which they might have been exposed to in the market ( (Ciner, Gurdgiev and Lucey 2013)One of the characteristics of the future contracts is that they are traded on an organized exchange. The exchange members have right to trade on the exchange and to be able to have a voice in the exchange operation

## 1.2.2 Existing of standardized contract terms

The future contract specifies the quality and quantity of the good to be delivered and specific description, date of delivery and method of delivery the minimum and maximum price fluctuations which can be accepted of the commodity. (Mensi et al. 2013) The future contract in most cases have terms which are highly consistent and well-structured commitments and describe the good or commodity which is being delivered at a given time and in a specific manner

## 1.2.3 Subjected to clearing house

. They normally substitute their credibility for the promise of each trader in the market and ensure the smooth running of the business in the future market. (Arouri, Lahiani & Nguyen 2015)The primary function of the clearing house is to facilitate the trade in the derivative market. Every future exchange market has an associated clearinghouse. It is the body they help in enforcing the commitments and obligations that have been entered by different parties. They serve the role by adopting the position of the buyer to every seller and seller to every buyer and indication that every seller or buyer in the future market has an obligation to the clearance house only

## 1.2.4 Need for margin payment and daily settlement

. It is done to a level which is lower than the maintenance margin, the trader then will get what is called margin call from the clearing house to help in replenishing the margin account to the level of initial margin and the amount deposited is what brings the variation margin in the future contracts.(Mensi et al. 2013). For most future contract the first or initial margin is usually 5% of the underlying commodity price or sometimes less depending on the agreement. On the other hand, the maintenance margin is around 75% of the amount of the initial margin. Then after that the future contract prices normally settle on a daily basis and once the cumulated loss of the day brings the deposit of the trader from the initial margin Arouri, Lahiani & Nguyen 2015)The margin of payment and the daily settlement help in ensuring that traders will perform on their contract obligation which they have entered in. In the market, there are three main types of margin which include the initial margin, maintenance margin and the variation margin

## 1.2.5 Closing of future position

. One of the essential characteristics of a future contract is that they are written to call for completion for the future contract through what is known as physical delivery of a given good. There are sometimes when the future contracts are completed through the offset or via reversing trade. To compete for future contract obligation through the offset or reversing trade, the traders need to transact in the future market through selling the same contract that was bought or sold earlier to bring it back to a particular future contract back to zero. This is the main essence of future contract buying through offset reversing trade. These are the five major characteristics of the future contract. (Li 2010)This is another common characteristic of a future contract. There are three ways of closing future contract which is delivery which can either be cash settlement, the offset or exchange for physical commonly known as EFP

## 1.3 Function of the future contract market

There are three main functions of the future contract market. They include:-

## 1.3.1 Price discovery

. The participant in the market when they participate either by buying or selling a future contract, they either agree to receive or deliver a given commodity in future at agreed price now. (Irwin and Sanders 2011)Price discovery can be defined as the process of revealing information concerning the future contract and cash market prices through various communication channels in the market

. The future markets normally serve a social purpose by assisting traders to make an informed decision concerning the future prices as this will help them make their consumption and investment decision in a more accurately manner using informed decision process like price forecasting.(Irwin and Sanders 2011)Through this, there is a relationship which is being created between the expected price and the price that currently prevail in the market. This information is very important, and investors and analyst alike can use this information to predict future prices

## 1.3.2 Hedging.

. (Arouri, Lahiani and Nguyen 2015)This is another function of the future markets, and this is the mostly known function of the future markets. Hedging is used mostly for risk management purposes. Future contracts allow risk to be transferred from those people who are having high-risk exposure to those who are seeking benefit from the existence of risk in the market. Future markets allow the participants to hedge against the risk by protecting the value of their asset against the risk that might exist in the market by taking a position in the future market opposite to the physical position they hold to benefit from the adverse price movement in the market. This is the vital function of hedging as used in the future contract market

## 1.3.3 Speculative purposes

.(Stoll and Whaley 2015)The future contract markets give participants opportunity to speculate. This is the trading where there is unlike hedging or no physical commodities or the financial instruments which are held by traders are a high-risk investment, and they are seeking to reduce risk. The traders will then taking future risk trading purely to profit from favorable price movement. For the efficient market operation, there is a need for the existence of speculators. The speculators perform the important role of often being the counter-party to a position that a hedger may need to take effect through the risk that helps hedgers to seek to escape. In modern operations, the derivative markets are significant for growth and development of the general economic growth. The players in the derivative market are mostly speculators who seek to take advantage of risk averse investors in the market, and they always make their profit out of speculation

## 1.4 Australia Derivative market

(Sagaram and Wickramanayake 2012). The CBOT is one of the world largest future markets currently. Initially, the future markets were majorly concerned with the commodity product which was mostly agriculture goods. Nevertheless, in the modern world today, 99% of the future markets trade on financial instruments which include but not limited to shares, government bonds among other foreign exchange rates instruments available globally (Cairns et al. 2011)Future contracts can be defined as legally binding agreements to buy or sell commodities whether gold, wheat, oil in future or any other financial instruments like government bonds, treasury bills or shares in a fixed time frame in the future at a given agreed upon price today. The history of the future markets can be traced in Chicago when the Chicago Board of Trade was opened in 1848 to help in standardizing the quantities and qualities of grains which were being traded in Chicago

(Sagaram and Wickramanayake 2012)In Australia for instance, In Australia, the future and options on the future contracts are usually traded at the Sydney future exchange. This market was found in 1960 mostly to provide a hedging facility for the wool industry. By the end of the year 1970, the market was diversified by introducing more product to be traded listing steel future contracts, the gold future contract was introduced in 1978, and 1979 financial instruments were introduced in the market. In the year 1983 the share price index (SPI) was introduced and by the year 1995, this market was among the best across the globe and was ranked number thirteen globally. This was a good performance for the market

. By December 2010 it was estimated that market value of cross sectorial bought or sold close to all derivative classes and the volume of the transaction was close to \$350 billion. This only indicates the level of growth and development of this market and also its efficiency. Other sectors like financial and public sector are also heavy users of the derivatives market, and this is a good indication of a growing market. The market is currently one of the international markets with participants across the globe, and it meets international standards.(Irwin and Sanders 2011)Resulting from the financial crisis, many market players have paid close attention to the derivative markets as this is one of the reforms which have been put in place to improve risk management process, practices and transparency in the market operations. The Australia derivative market can be traced back in 1987 when the Australia stock exchange was formed after a debate in parliament which was a great mile regarding development share trading in Australia. With Sydney future exchange, the Australia stock exchange merged in 2006, and for some years they operated under the Australian stock exchange before the new name could be launch. To improve trade efficiency, the ASX was launched with a new group structure. In August 2010 the name was permanent and called ASX group. The group has a rich history rolling to decades, and currently, the ASX group is one of the most active derivative markets across the globe trading billions of volumes of assets. Just like any other international markets, the Australian market has concentrated on few currencies. This is one of the factors that limit trade in the market. The derivatives are frequently used most extensively by several sectors of the Australian economy

## 1.5 Purpose of the study

It is important to note that hedging is one of the major reasons why the existence of the future markets. For efficient portfolio construction, most hedgers combine cash asset and future contracts which give them many challenges as every unit should have a cash asset hence bringing the question on the best optimal way to calculate hedging ratio. The common portfolio theory argues that the main objective of hedging is to reduce the portfolio variance by achieving optimal ratio which some other authors call minimum variance ratio. Some theorist further argues that the estimation of the optimal hedge ratio suffers from serial correlation which exists in the OLS residuals and further argues that simple regression model is quite inappropriate in estimating the best ratio because it ignores the heteroskedasticity which in most cases are encountered in cash future prices series.

. Nevertheless, since there is a basic risk which exists in the market, it is not possible to 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. Hedging helps in increasing the value of the relevant stock index. For portfolio managers, the selection of an effective strategy for hedging is very important than the efficiency of the future markets. 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) argue that there should be a continuous adjustment of hedge ratio which is based on limited information which is calculated from the conditional variance. There for this paper aims at solving this problem by using multiple approaches to the calculation of optimal ratio. Normally derivative instruments, stock index future contracts provide the traders in the stock market or investors with risk diversification and management opportunity. 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 otherIrwin and Sanders (2011)

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 the determination of the hedging ratio. The investors and other player’s aims at improving the hedging effectiveness of index future against stock indices movement hence this study aim at investigating this course.Arouri, Lahiani & Nguyen (2015)states that for efficiency and effectiveness of the hedging, then the future price needs to be efficient as the inefficiencies in the market would result into higher cost of hedging which may undermine the effectiveness of the future markets. Stoll & Whaley (2015)

## 1.6 Objective of the study

The primary objective of this study is to find out the hedging effectiveness of index future against stock indices movement in Australia stock exchange.

## 1.7 Hypothesis of the study

The null hypothesis of this study is that:-

There is no relationship between hedging effectiveness of index future against stock indices movement in Australia stock exchange.

## 1.8 Scope of the study

The range indicates the limits of the study regarding geographical, theoretical aspect and area within which study will investigate. In this study, we will focus mostly on hedging effectiveness on stock indices movement. The study will limit itself to Australia and Sydney stock or derivative market concentrating on a time series data over a given period let’s say ten years or 20 years. The study will not study any other sectors apart from the banking sector and will limit itself to selected indicators which are stock hedging effectiveness of index future against stock indices movement.

## 1.9 Benefits of the Study

This study will be important to various parties which will use it as a reference point.

## 1.9.1 Policy makers

This study will contribute to policy makers by giving them a clearer picture and close look on the financial as well as the performance hedging in derivative markets, Based on this financial information, policy makers can make a decision on how much of and effective a given hedging techniques are effective, and also decision makers have to prioritize the use hedging as a means of risk diversification.

## 1.9.1 Investors

The investors will be able to understand the effectiveness of hedging policy which is being advanced by the financial institution and how hedging mitigate risk. They will be able to choose which type of hedging they should go for and furthermore the best way of calculating the optimum hedging ratio which can help in reducing risk to a minimum level.

## 1.9.2 Financial Managers

Companies are facing difficulties in making a profit because risk brought by globalizations and privatizations issues. While it is important for a corporate to formulate a Hedging policy which can bring value added to the company. Therefore, this study will be able to give guidelines to financial managers to have more understanding on how that firm competes in such type of modernized framework of businesses and best ratio for hedging for the company and how effective international companies can effectively hedge their stock against unforeseen risks.

Lastly, add to the body of knowledge to academicians of the impact of hedging policy on risk minimization and investment diversification. They will be able to do further research on this area of study to contribute more details about the effect of hedging policy towards minimizing risk and the best formula and methodology of calculating hedge ratio. The study will also explain how hedging behaves with the movement of stock indices in the market and for crucial literature body to be added to the existing literature on the topic. It will be precious in the area of international finance and financial management in general.

## 2.0 Introduction

This chapter gives theoretical framework and literature of what other people have said concerning the topic of the study.

## 2.1 Literature on future contracts

. 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 prospects 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 the spot market. (Rao & Srivastava, 2014)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 the ratio of some 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

still stands with the traditional objective of maximizing risks as the main focus of hedging but gives a definition of risks as the variance of a two-asset hedged portfolio.Rao & Srivastava (2014) Used current portfolio theory to the problem of hedging. This was the first time that risks definition and return on variance and means were used to solve this problem. Gupta & Kaur, 2015). 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. The beta hedge is majorly known as portfolio beta, their objectives and that of traditional method are the same which does give a position in the future that is the same in size but parallel in sign position spot (

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 (2016) while investigating the dynamism and the problems with hedging resolve that as a percentage reduction found in the variance linking the un-hedged and hedged returns. Gupta & Kaur (2015) developed measures of hedging efficiency The imperfection in the traditional hedging methods,

Modern advances in the progression econometric techniques have come up with some solutions to help address the problem. In light with this, there are two main hedging which includes:-
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 final 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 the joint distribution of spot and prices in the future over a period. has had a lot of 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. Chkili, Aloui & Nguyen (2014)

1. Dynamic hedging

2. Static hedging

## 2.2 Dynamic hedging

further investigated the dynamic hedging problem employed the use of Treasury bond and the currency markets in different analysis. The findings of these studies suggested that rebalancing the hedging portfolio usually depends on the marginal utility of being positive as you carrying out such diversification. The above findings further show that dynamic hedging performs better than static dynamic when it comes to portfolio risk management.Zanotti, Gabbi and Geranio (2010) states that the problem with static hedging ratio is its lack of capturing risk return fully hence the development of dynamic hedging to help in solving this problem. It is noted that dynamic hedging is likely to reduce the variance of the return on a given hedging portfolio. Psychoyios, Dotsis and Markellos (2010)

x R). Where Qti is a number of the units like shares of the primitive assets S which is held at time ti, t0< ti<tn and Bti are the cash balances which are held in a default free interest bearing money market account that can satisfy the following conditions.n, (Rn defines dynamic hedging as that strategy that involves rebalancing the hedge positions as market conditions change. It seeks to insure the value of a given portfolio is using a synthetic option. The dynamic hedging usually corresponds to any discrete time self-financing strategy pair which is in countable sequence (Qti, Bti) i=0Krollner, Vanstone and Finnie (2010)

they question the reliability of dynamic hedging and how effective the dynamic hedging is capable of reducing the portfolio risk after the financial crisis which took place in Asian countries in 1997. They further argue that the existence of different financial contagion over different assets or markets and high-frequency trading may be some of the reasons of inefficiencies existing in the dynamic hedging. Rao and Srivastava (2014)In a study by

indicated that including the GARCH effect help in reducing the variance hedging portfolio which cannot be found in static hedging portfolio. They further concluded that combining the two models that is ARCH and GARCH help in including all the volatility clustering in most financial data.Syriopoulos, Makram and Boubaker (2015) suggested that a wider approach should be used and suggested that GARCH is the most appropriate by adding past volatility shocks in the ARCH volatility equation. They empirically validated the two models that are ARCH and GARCH for the currency rates and stock indices data. Hood and Malik (2013) initially used the autoregressive conditional heteroskedasticity (ARCH) model to help in including the past return shocks when describing the current volatility existing in the market portfolio. Fattouh, Kilian and Mahadeva (2012)Most of the literature on the dynamic hedging is developed around the conditional volatility models in the financial data.

introduces APACH in the model. All these models are some of the empirical findings to help improve the findings using the GARCH and ARCH model in the analysis.Olson, Vivian and Wohar (2014) proposes EGARCH while Chkili and Nguyen (2014) indicated that it is important for the GARCH model to include asymmetric volatility response in the analysis by including GJR-GARCH model and Alagidede and Panagiotidis (2010)Though GARCH model also presents some difficulties like the normality assumptions in the standardized residues. Most of the financial data usually reveal the existence of asymmetry and kind of leptokurtosis leading to some defect in using the model hence need to use some of the t-distribution in standardized residues or applying extreme value theory in the standardized residues. The leverage effect also is not accounted for in the GARCH model, and the volatility does increase with an increase in negative shock in the market, this is opposing the symmetric assumption of the GARCH model in volatility shock in the data.

## 2.3 Static hedging

There are several types of financial derivatives, and future contracts are one of the basic ones which can be used to hedge against fluctuation in the spot market. Theoretically, it is possible to eliminate all the risk in the market using hedging while practically this is not possible. Perfect elimination of risk through hedging does not exist because differences in contract specification and price dynamics between the underlying asset and the future contracts make it difficult. The concept of hedging was first used in spot price position, and later it was applied in the derivative of the underlying asset. Some scholars have used index futures to cross hedge equity portfolio through constructing a portfolio with the weight on index future being the minimal variance hedge ratio. The static hedge ratio can be calculated, and the formula to the effect is given as:-

It should be noted that static hedging is not as effective as dynamic hedging and most people are using dynamic hedging in their analysis due to its perceived effectiveness.

Future markets are perceived as a primary vehicle for hedging as they help in risk minimization through the use of different hedging strategies with the existing future instruments on the market. Many scholars have research on different hedging strategies used in minimizing risk. The estimation of the optimal hedge ratio is one area which has been researching extensively with mixed findings. Traditional hedging theory usually emphasizes on the risk avoidance approach of the future markets. It argues that spot and future contracts normally move together and hedgers only have to take future markets positions which are equivalent to the amount of opposite sign to their won position in the cash market.

respectively, the gain or loss on an unhedged position will be given by U of the X units can be calculated using the formula:-t2 and pt1 are p2 and t1In case the cash prices at time t

However, the gain or loss on the hedged position H is given by:-

From the equation, the f subscript indicates the future prices. Because the traditional hedging theory believes that spot and future prices normally move together so that the absolute value of H is lower than that of U. This can be demonstrated by the equation below:-

et al. (2013) states that a hedger is nor a risk averter as tradition would have it rather a risk selector. A hedger usually prefers to profit from a skillful prediction of changes in the basis rather than from the predictions of the price levels. In so doing, the hedger becomes exposed to the basis risk hence the view of the hedging is purely speculating on the basis.Chen criticized the traditional method and approach which they are using terming it the naïve approach of testing the hedging effectiveness. He argued that realistically, merchants or the so called dealers in hedging are only determined by the inventory level and usually expected by the change. Contrary to this argument, optimal hedge ratio research articles by other authors argue that discretionary hedging which is based on the predictable basis change. It is important to note that the discretionary hedging usually reduces cash speculation and lower the inventory if unfavorable basis changes are expected. The essence of the workings view of hedging is that hedging is a form of arbitrage between cash and future prices. It helps in undertaking the profit from a predictable changes in the relationship between the cash future prices and not generally to reduce risk in the portfolio. Lin, Wesseh and Appiah (2014)

also uses the same methodology of regression od spot market returns on the future markets returns where the returns according to that research was defined as the proportional price change from time to time. They both concluded that the issue of change or returns should always be used in simple regression approach to optimize the hedge ratio.Krollner, Vanstone and Finnie (2010) uses regression analysis where they regress the spot changes on the future price changes to remedy the problem of non-stationarity in the price levels. Chen, et al. (2013)In a study by

## 2.5 Empirical Review

March 2012. The results of this study indicate that portfolio risk management help in reducing not only the risk in the portfolio but also the profitability of the portfolio. Therefore, inoculation with the aim of risk management has no additional profit in it.th April 2017 to 30nd used Markowitz measures to investigate the effectiveness of hedging strategy that helps in determining the efficiency relation in reducing the standard deviation of the portfolio return. The aim of this study was to investigate the efficiency hedging on the future market security and also to help in identification of the relationship which exists between spot and future markets using the Romanian case study. This study used the data which consisted of 1,243 daily observations, concerning the stock evolution of SIF5 and the future SIF5 which was dated 2Syriopoulos et al. (2015)

they investigated the legality of the financial derivatives which were specifically based on the Islamic commercial law and the confidence from the demand for the different risk management tools that existed in a different business in the Pakistan industrial park. This study used over 600 questionnaires to the randomly selected population within industrial and business section within the Pakistan. The results of this study show that the demand for collateral, the future contracts and the guarantee for credit risk management which required the market risk management of forwarding contracts, the future contract, and the foreign exchange future contract rates. The study further reveals that the future of foreign exchange and the foreign exchange options is demanded specifically for risk reduction of the foreign exchange rate.Ciner et al., (2013)In another study by

in their study established the scope of the use of the derivatives by companies in the country of Bosnia and that of Herzegovina mainly for the risk management purposes. In this research dissertation, they aimed at giving some suggestion to the companies of these two countries ways of improving their risk management practices to ensure a more efficient and effective financial risk hedging through the use of the derivatives instruments mostly with the available through financial markets. The data used for this research was provided by the foreign trade chamber of BiH financial statements of the chosen companies and other interbank agencies with equivalent data on the same. The study reveals that currency forwards has the highest demand among the users of derivative markets in risk mitigation process, this was followed by the currency Swaps and the smallest for the interest rates swaps. Lack of adequate information was cited in this study as one of the reasons why there is low usage of derivatives instruments, and this was coupled with the inadequate knowledge on the usage and the benefits the instruments come with regarding risk management. The study further reveals that a low number of business operations is one of the main limiting factors for large or extensive usage of derivatives among business in the BiH companies.Sagaram and Wickramanayake (2012)

on the importance of risk management using hedging, they stated that the principal purpose of hedging is to manage risk and not to gain profit as perceived by some people. The concept of hedging needs a more comprehensive discussion due to its various interpretations on the meaning of hedging. This study used the content analysis approach where qualitative research method was deployed in the analysis of the documents. The findings of this study reveal that the concept of hedging as per Islamic financial concept gives a different meaning. Furthermore, the objective of Islamic hedging is to reduce risk and must in one way or the other relates to the economic activity. Therefore misconception regarding the idea surrounding hedging should be removed by clear and concise discussion as to what is hedging and the main functions of hedging in the derivative markets.Mensi et al. (2013)In a study by

. Nevertheless, since there is a basic risk which exists in the market, it is not possible to 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. (Stoll & Whaley 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 the determination of the hedging ratio. Normally derivative instruments, stock index future contracts provide the traders in the stock market or investors with risk diversification and management opportunity. 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 otherArouri, Lahiani & Nguyen (2015) states that for efficiency and effectiveness of the hedging, then the future price needs to be efficient as the inefficiencies in the market would result in higher cost of hedging which may undermine the effectiveness of the future markets. Stoll & Whaley (2015)

## 3.0 Introduction

For time series analysis, it is important for checking the stationarity of unit root, and Cointegration characteristics in the given data before the modeling could be started. In case there is the presence of Cointegration in the data or the relationship, then it is important for an error correction term to be incorporated into the model to help in bringing long run equilibrium relationship between the series. This section introduces the various mathematical and econometric techniques which are going to be used in this study. They include methods like unit root test of the time series, the augmented Dickey-Fuller test (ADF), VECM, ARCH and GARCH method.

## 3.1 Unit Root Tests

violates the three basic conditions (unbiased, consistent and efficient) required for a valid estimate. In consequence, economists have been intrigued by the prospect of retesting these models in the theories. In the first modem attempt to do so using a unit roote1 yet they are related. In situations where the variables in the regression model are not stationary, then it can be proved that the standard assumption for asymptotic analysis will not be valid. That is to say the t-ratio fail to follow t-distribution hence we are not able to validly undertake hypothesis tests concerning the regression parameters. McAleer (1999) pointed out that «the single topiC in the 1980s that attracted the most attention and to which most econometricians have devoted their energies is that of testing for unit roots.» It has also been found that most empirical applications of unit root testing have been in the field of economics and finance. One reason why economists became interested in the existence of unit roots is that, for economic time series, nonstationarity behaviour is often the most dominant characteristic. If that is the case, then those models that are estimated using OLS are mis-specified in that the error term 2 even though the two variables are not related and in some cases may have lower R2The unexpected change in a variable in a value of a variable is called shock. This behaviour of data is common in the time series data. In situations when we have stationary system, effect of a shock will die out with time while in time when we have a non-stationary system, effect of a shock is permanent. It should be noted that the stationarity or otherwise of a series can strongly influence the behaviour of a data like persistence shock which will be infinite for nonstationarity. There are circumstances where trend over two variables on the regression would have higher R

noted that one of the most important characteristics of any economic variable impacting on the behavior of statistics in an econometric model is the extent to which that variable is stationary or not. Given an autoregressive description with the formula below:-Gupta & Kaur (2015)

= α +Ƴys-I +ƐttY

that testing for a unit roots as a topic is common in economics and finance, and one of the reasons why economist became interested in the existence of the unit roots is due to the economic time series non-stationary behavior which was not exhibited in most of the data. Suppose that is the case, it is important to note that there is misspecification of the models which are estimated using the OLS since the error term Ɛ in the model violates the three primary conditions of unbiased, consistent and efficient which is required for a valid estimate. As a result, economist has intervened by the prospect of re-testing the models in the theories and unit root test is one such model.Chkili (2016) Is having a root on its unit circle, that is the autoregressive coefficient generates a random walk of (Ƴ = 1), then this equation can be said to have a unit root, and the stationarity is violated in the equation. As pointed out by

:-tUnit root test is important in testing the stationarity and non-stationarity of the data. Consider the following trend cycle decomposition of a time series Y

In this case, TDt is the deterministic linear trend, and Zt is an AR (1) process. The autoregressive unit test is commonly based on the null hypothesis that Ø = 1 against the alternative hypothesis that states that the polynomial of Zt, Ø (z) = (1- Øz) = 0 which indicates it has a root equal to unity. The stationarity takes the opposite direction.

## 3.2 ADF Test for Unit Roots

The Augmented Dickey-Fuller for unit roots is a more advanced Dickey and Fuller findings. ADF deals with the situation that error term is not having white noise and adds F-test to help in testing hypothesis on the coefficient. In ADF test, three different regression equations are used to test for the presence of the unit root. The following are the three common formula:-

The main distinction among the three equation above is the presence of the deterministic elements of α0 andα1. A close look at the first equation, it indicates the random walk model while the second equation shows the presence of the drift term which is the equation intercept. The third equation contains the drive and linear time trend elements in it. The main factor in the three equation is the beta and the sequence of a unit root. Suppose the null hypothesis is rejected in the series, (y1) is stationary otherwise the equation (b) above is tested for the null hypothesis which is given by β =α0 = 0 using the static concept. Also, if the null hypothesis is rejected, then the series (y1) is stationary drift, otherwise the third model (c) plus a time trend is estimated with the joint hypothesis β =α2 = 0 is tested using the Øs. If the null hypothesis is rejecting during the testing period, we can confidently conclude that the series (y1) is stationary with a time trends. Otherwise, the series considered is non-stationary.

Augmented Dickey-Fuller t-test help in testing the stationarity of data similar to unit root test. Using the case of a flat time series and potentially slow turning around zero. The following equation can be used:-

Where the number of lags in augmentation (p) is determined by minimizing the Schwartz Bayesian information criterion or minimizing the Akaike information criterion. Using the software EVIEWS allows the option for you to choose from. Using Eviews, will give correct critical values for the test and using the following hypothesis:-

= 0 (the data needs to be differenced to make stationary)Ø: 0H

Versus alternative hypothesis of

< 0 (The data is stationary and doesn’t need to be differenced)Ø: 1H

In circumstances where the time series is flat and potentially slow-turning around a non-zero value, uses the following equation:-

As opposed to the initial equation, this equation has the intercept term in it but no time trend is given. The number of lags further is given. Eviews allows all of these options for you to decide from. The final aspect is to use the T-test on the coefficient to test whether you need to difference the data to make it stationary or not. The test in this case is left tailed.

The null hypothesis of the augmented Dickey- Fuller t-test is given by

= 0 (The data needs to be differenced to make it stationary)Ø
0H

< 0 (The data is stationary and doesn’t need to be differenced. In circumstances where there is series trend and it is potentially low turning around, a trend like would be drawn through the data. This is shown in chapter four.Ø: 1Alternative hypothesis. H

## 3.3 Hedging models

defines hedging ratio as the proportion of future holdings to a spot position in the hedging portfolio. The variance of the hedging can be calculated using the formula below:-Chkili (2016)

In computing the first order condition of heteroscedasticity of the equation 1 with respect o h, we can get the static minimum variance hedge ratio h as therefore we have:-

This is the static equation with respect to h; the dynamic optimal hedge ratio at a given time t, given as per the information give and time is set at t-1, is given by:-

The third equation shows that one approach in estimating the dynamic hedge ratio is by using the bivariate GARCH models. Nevertheless, since this study concentrates mostly on the movement of stock indices and the future index, the model should be in a position to account for the long run cointegration dynamic between the two-time series. Therefore, including the EC terns in the equation indicate the presence of bivariate GARCH model which will be more accurate and authentic in the analysis.

## 3.4 VECM

Log prices of the spot and the future log prices are usually non-stationary, however, the continuously compounded returns or what is referred to the first differences of either of these series are stationary. On the other hand, the linear combination of two series is stationary, since the future prices at maturity usually tend to converge if not coincide to the spot price, by the theory of no arbitrage. According to Engle and Granger (1987), the log-prices of spot and futures are cointegrated. Granger (1981) studied the relationship between EC models and cointegrating series. The Granger representation theorem (1983) allows us to model the log prices of spot and futures using the following EC model. This can be presented in the equation below:-

From the equation above, it is clear that the long run dynamics of spot and future returns are restricted by eth EC terms, while the short run adjustments are captured by the AR-terms of the lagged returns.

In conditions where the level of the 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)

as the adjustment variables in the study. 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 as compared to the first two ratios discussed above.f and λsis the correction of the error term the (1-δ) as the cointegrating vector and λt-1 — δFt-1Where in this case we have Z t-1 = S

## 3.5 Regression model

A conventional method of calculating an evaluating an optimal hedge ratio is 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.

+Ɛ………………………………………………………………………………. (1)ft = α + βrstr

In this case we have:-

• – Is the spot rate of the returnstr

• — is the future returns ftr

• t- is the time

• will help us to provide an estimate of the required optimal hedge ratio.β

The regression model is simple and direct to use, and this beta value will be important to understanding the required ratio of the hedge used in getting the required optimal and effective hedge.

## 3.6 Bivariate VAR Method

Due to shortcomings of the regression model like the presence of autocorrelation of residual. 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 is fully eliminated from the data. The following formula will be used in the calculation of the VAR model.

## 3.7 The Multivariate (GARCH Method)

Which will be the varying time ratio.fft. / heft Due to the 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. 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 Bollerslev eta l 1988 will be used. This model is useful in this it can 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 h

………………….. (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

## 3.8 The Data

The data which will be used in this study will be downloaded from the data stream database. In include all ordinary share prices index and the corresponding share prices index future prices on a daily basis for a period of stock index future and ASX index for the period of 1990 to 2016. The data will be collected from the ASX 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 Introduction

This chapter gives the results of the findings on how hedging effectiveness of index future against stock indices movement. The chapter first give descriptive analysis of the variables after converting them to log form then moves on to test all the four test in the study.

## 4.1 Descriptive statistics

Table 4.1: Descriptive statistics

 STOCK_INDICES_LN 7.608337 7.121472 Median 7.618713 7.106721 Maximum 7.663069 7.347622 Minimum 7.511568 6.936255 Std. Dev. 0.038376 0.101808 Skewness -0.561411 0.397305 Kurtosis 2.158327 2.346816 Jarque-Bera 16.49156 8.861192 Probability 0.000262 0.011907 1529.276 1431.416 Sum Sq. Dev. 0.294536 2.072971 Observations

It is important to note that the statistics for the Kurtosis are different from 3. As they fall below 3. This in essence tell us the problem of non-normality may come from the heavy tails in the distribution of the series or what is called the leptokurtosis. The descriptive statistics on the ASX Index and ASX Index Futures returns for the whole research period is represented in table above. The descriptive statistics analysis describes the data in terms of central tendency, variability and distribution normality. One of the most pertinent values for the current research is the simple measure of the central tendency that is the mean or an arithmetic average. As the sample data comprises rather low figures, the mean is small as well and equals 0.00062 and 0.00060 for the ASX and ASX Futures returns respectively. One of the variability measures reported in the descriptive statistics is the standard deviation that shows the spread of the values around the central tendency, which are 0.025 and 0.031 for ASX index and future ASX respectively. Other variables include mean, median and standard deviation from the descriptive analysis in table 4.1 above.Jarque-Bera normality test indicate that we have to reject null hypothesis that the two series follow normal distribution. That is to say P (0.000262) < 0.05 and p (0.011907) < 0.05. Therefore, it can be concluded that both the logged of stock price indices and future prices are not normally distributed. From the table above, the value indicates that the largest test statistics of the

Group unit root test: Summary Table 4.2

 Statistic sections Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -0.33889 0.3673 Null: Unit root (assumes individual unit root process) Im, Pesaran and Shin W-stat -0.15673 0.4377 ADF — Fisher Chi-square 3.42247 0.4898 PP — Fisher Chi-square 3.64170 0.4567 ** Probabilities for Fisher tests are computed using an asymptotic Chi -square distribution. All other tests assume asymptotic normality.

Table 4.2 above gives the overall summary of the group unit test and the result of Fisher Chi-square is shown above in the table.

 Table 4.3: Null Hypothesis: ASXF_LN has a unit root Exogenous: Constant Lag Length: 0 (Automatic — based on SIC, maxlag=14) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.216448 0.6674 Test critical values: -3.463067 -2.875825 10% level -2.574462 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(ASXF_LN) Method: Least Squares Date: 07/24/17 Time: 09:16 Sample (adjusted): 2 201 Included observations: 200 after adjustments Variable Coefficient Std. Error t-Statistic Prob. ASXF_LN(-1) -0.012248 0.010069 -1.216448 0.088934 0.071706 1.240260 R-squared 0.007418 Mean dependent var 0.001716 Adjusted R-squared 0.002405 S.D. dependent var 0.014426 S.E. of regression 0.014408 Akaike info criterion -5.632093 Sum squared resid 0.041104 Schwarz criterion -5.599110 Log likelihood 565.2093 Hannan-Quinn criter. -5.618746 F-statistic 1.479746 Durbin-Watson stat 2.155796 Prob(F-statistic) 0.225262

-1.216448 and the associated one sided p-value for the 200 observation with 14 lag is 0.6674. The critical values are tested also at 1%, 5% and 10% levels. It is clear from the analysis that the statistics t value is greater than the critical values so that we do reject the null hypothesis at the conventional test sizes for the ASX future. The second part shows the coefficient and the equationIn the first table, of the index future, it shows that the ADF statistic value is

 Table 4.4: Null Hypothesis: STOCK_INDICES_LN has a unit root Exogenous: Constant Lag Length: 0 (Automatic — based on SIC, maxlag=14) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.037582 0.2707 Test critical values: -3.463067 -2.875825 10% level -2.574462 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(STOCK_INDICES_LN) Method: Least Squares Date: 07/24/17 Time: 09:16 Sample (adjusted): 2 201 Included observations: 200 after adjustments Variable Coefficient Std. Error t-Statistic Prob. STOCK_INDICES_LN(-1) -0.042349 0.020784 -2.037582 0.322257 0.158131 2.037913 R-squared 0.020538 Mean dependent var 5.64E-05 Adjusted R-squared 0.015591 S.D. dependent var 0.011338 S.E. of regression 0.011250 Akaike info criterion -6.127016 Sum squared resid 0.025058 Schwarz criterion -6.094033 Log likelihood 614.7016 Hannan-Quinn criter. -6.113669 F-statistic 4.151740 Durbin-Watson stat 1.854358 Prob(F-statistic) 0.042922

-2.037582 and the associated one sided p-value for the 200 observation with 14 lag is 0.2707. The critical values are tested also at 1%, 5% and 10% levels. It is clear from the analysis that the statistics t value is greater than the critical values so that we do reject the null hypothesis at the conventional test sizes for the stock movement. The second part shows the coefficient and the equation.it shows that the ADF statistic value is STOCK_INDICES_LN has a unit root For

## 4.2 The regression model

The regression model results is shown in the table below:-

Table 4.5.0: OLS Regression results

 Variable Coefficient Std. Error t-Statistic Prob. 0.027849 0.000659 42.26201 0.022863 0.034381 0.665009 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

= 0.984565.20.022863, β = 0.027849 RFrom the table above, α =

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 4.6: The Bivariate VAR Model Estimates

 Equation (2) STOCK_INDICES_LN Equation (3) ASXF STOCK_INDICES_LN (-1) 1.552737 37.76572 (0.58313) (24.1148) STOCK_INDICES_LN (-2) -1.010655 -26.86954 (0.57143) (23.6308) ASXF(-1) -0.011652 -0.070008 (0.01491) (0.61678) ASXF(-2) 0.021983 0.677736 (0.01413) (0.58441) 0.050706 1.262276 (0.09062) (3.74739) 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:-

fƐsƐsf covariance δWhere:-

In order to calculate the hedge ratio here

Will have:-

Table 4.7: Optimal Hedge ratio using Bivariate VAR Model

 f)ƐsƐCovariance ( 0.000195 f)ƐVariance ( 0.000209

The third step is to calculate the hedge ratio using the vector error model from the data of STOCK_INDICES_LN not and future prices. The results are shown in the table below:-

Table 4.8: The Vector Error Correction Estimates Model

 Error Correction: D(STOCK_INDICES_LN ) Coint Eq1 0.668483 56.74549 (0.65994) (25.5853) D(STOCK_INDICES_LN (-1)) 0.886632 28.68181 (0.52491) (20.3501) D(STOCK_INDICES_LN (-2)) -1.860029 -74.80484 (0.52636) (20.4066) D(ASXF(-1)) -0.016662 -0.652466 (0.01430) (0.55435) D(ASXF(-2)) 0.037930 1.416303 (0.01228) (0.47623) -0.096724 -4.010205 (0.04251) (1.64807) 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:-

fƐsƐsf covariance δWhere:-

For the calculation of the hedge ratio using the above formula will have:-

Table 4.9. Optimal Hedge Ratio from the VEC Model

 ) f εs ε(Covariance 0.000194 f)ƐVariance ( 0.000207

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:-

As seen in the graph above, the ASXF residual price index and the future contracts are closely correlated. It is obvious that from the time trend shown in the diagram it is suspected that both have similar series characteristics by non-stationarity in level.

## 4.3 ARCH and GARCH Effect

Table 4.10: GARCH Model of Estimation

 GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1) Variable Coefficient Std. Error z-Statistic Prob. 0.026674 0.001025 26.01631 0.045452 0.020403 2.227714 Variance Equation 0.000108 0.000145 0.749360 RESID(-1)^2 0.615843 0.413277 1.490145 GARCH(-1) 0.388111 0.198727 1.952983 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

=0.045452, p-value in both cases is < 0.05 indicating that the null hypothesis is rejected and acceptance of alternative hypothesis.α0.026674. In addition, =βFrom the table above, we can find

noted 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:-Arouri et al., (2012)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 ratio will be well captured in the GARCH analysis in the table 4.8 above. The same data which has been used in establishing the effective hedge ratio which is the annual returns from 2000 to 2017. 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.

Table 4.11: Mean Return for within sample

 12 months 0.027849 Bivariate VAR Vector Error Correction GARCH model 0.026674

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 4.12: Average Variance Reduction for within sample

 12 months 0.027849 Bivariate VAR Vector Error Correction GARCH model 0.026674

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

The out of sample analysis is shown in the table below:

Table 4.13: Average variance reduction outside the sample

 12 months 0.027849 Bivariate VAR Vector Error Correction GARCH model 0.026674

This further shows the effectiveness of the model used in the hedging. There are several tests for Cointegration, including those developed by Engle and Granger (1987) and then extended to a multivariate version by Engle and Yoo (1987). These two-step cointegration tests have been criticized on various grounds as discussed in Chapter 4. Therefore, in this application the more advanced Johansen and Juselius (1990) cointegration tests are employed. The model selection criteria method is also used as a supplement to cointegration tests in finding the rank of the cointegrating vector,

## 5.0 Summary

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 the determination of the hedging ratio. The main objective of this study is to investigate hedging effectiveness of index future against Stock Indices movement in Australia Stock market. This study has used four methods which include, Unit Root test, AFD, ARCH, GARCH, Regression model, VEC among others to investigate the index future contract on stock movement

## 5.1 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. suggested that a wider approach should be used and suggested that GARCH is the most appropriate by adding past volatility shocks in the ARCH volatility equation. They empirically validated the two models that are ARCH and GARCH for the currency rates and stock indices data. This is in line with the findings of this study and proves that GARCH is more stable than ARCH model. Hood and Malik (2013)ARCH) model to help in including the past return shocks when describing the current volatility existing in the market portfolio. ) who demonstrated that the hedge ratio derived from other models and fails to recognize the Cointegration relationship between the future contract prices and the stock prices are always biased downwards. Kavussanos, Visvikis and Dimitrakopoulos (2014. The analysis of Cointegration shows that it there is relationship hence the use of error correction term in the analysis. In the view of the existence of the ARCH effect which is present in the residuals, the GARCH model was also estimated to cater for the heterocedastic error term in the data. The hedge ratio almost four to find how hedging influence the stock movement. The findings are in conformity with (Su and Wu, 2014) (Padungsaksawasdi and Daigler 2014)From the results, it is clear that the overall effectiveness of hedging ASX index future on the stock movement is over 81% on the monthly basis as it is grouped quarterly, semiannually and annually. It demonstrates that the ASX index future are more efficient to use for hedging. This is captured by high hedging ratio on the stock movement in the market

in terms of reducing portfolio variance. Accurate calculation of hedge ratio will help in reducing risk posed by stock movement volatility in the stock market.ratio is also an essential factor. It’s found that in longer term hedging, the time varying hedge ratios outperform the constant hedge ratio it 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. The use of GARCH adds value to the overall discussion and we can conclude that it is among the effective methods of establishing the stock movement using hedging. Hedging is important. It suggests that return and variance are not the only variables that determine the appropriate hedge ratio, the investor’s preference for (Narayan and Phan 2017).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

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