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Academics All Over The World Finance Essay

Academics all over the world have in recent years, carried out extensive research in the fields of Business, Finance and Economics in order to better understand the catalysts of the recent global financial crisis. Quite a number of studies speculate that the quick and easy lending and borrowing practices of some the world’s wealthiest financial institutions, led to the economic and financial meltdown experienced by several nations around the world; There have also being suggestions that a substantial increase in savings available for investment during this period from developing nations entering global markets, led to quite a few investors seeking a better return globally, than those offered by the United States of America.

This study seeks to unveil the opportunity realised or lost by certain global investors during the recent crisis period in South African equities specifically through the Single Equation Method of hedging. The first chapter will include a literature review on the topic of hedging and will give a brief insight into the possible reasons or factors that affect investing in equities. The reason for this is to allow scholars interested in the field to gain a better understanding of the complexities involved in the market and why hedging is so important. The second chapter will take a deeper look into direct un-hedged investment strategies in the Johannesburg Stock Exchange (JSE) Top 40 companies and compare the returns and yields on that to hedged investments in the JSE Top 40.

Chapter 3 will focus on the formulation of a regression model and a study into the concepts involved in regression modelling to better understand the use of the Single Equation Method to estimate the Optimal Hedge Ratio. Chapter 4 will look at volatility as a measure risk to give basis for Ederington’s use of the reduction in volatility as a measure of effectiveness when comparing the hedged versus the un-hedged as an investment strategy. Chapter 5 will look at some actual data analyses and the implementation of the Single Equation Method to find the Optimal hedge ratio on the JSE Top 40 actual spot and futures price dat.. This study will focus on the British and American investor in South African equities, with consideration for local investors and the use of Ederington’s measure of hedging effectiveness to decide on which hedge ratio reduces the exposure to risk of the investors mentioned above, the most. Hedge ratios for in sample and out of sample data from the 2006 to 2011 currency spot and futures data for the British and American investor in South African equities will be compared in this study to determine the optimal hedge ratio used to calculate the returns of the hedged and un-hedged investment strategy.

Chapter 1

Literature Review

A vast number of empirical studies on the estimation of the optimal hedge ratio have being brought to light over the years in hedging literature. These widely used methods of estimating the optimal hedge ratio originated or was first started by Johnson in 1960 and Stein in 1961. The former wrote and deliberated around the idea that using futures contracts to hedge one’s vulnerability to risk by minimizing the unconditional variance of portfolio returns could maximise the utility of portfolio holders.

This idea has proved to be invaluable because if one is able to use futures contracts effectively then one could hedge underlying exposure. After carefully studying the relationship between sport and futures prices Stein however felt that all of one’s entire exposure to risk should not be hedged. His research revealed that some portion of one’s vulnerability to risk should be hedged while some should remain un-hedged. He discussed that the portion of the portfolio in question that was hedged should follow a one to one ratio; That is to say that for every single spot exposure one finds oneself in, there is a single futures exposure to hedge one’s risky position. This idea is now more popularly known as the “naïve hedging strategy”. This strategy is said to be naïve for the mere fact that one could hold futures contracts covering less exposure than the exposure the sport presents and still be able to maximise my utility if my variance of portfolio returns is minimized.

This study will showcase and support some of Ederington’s ground breaking study on the optimal hedge ratio and specifically the role it plays in maximising one’s utility. The use of the optimal hedge ratio from the Single Equation Method will be focused on in this study and was implemented by Ederington in order to estimate the hedge ratio using parameter estimates obtained by the method of Ordinary Least Squares. Time Series Regression is used with historical data on spot and futures prices and in Ederington’s study, Treasury Bills futures were used as hedging instruments in the application of the Single Equation Method to determine the optimal hedge ratio.

This study seeks to expand on Ederington’s use of out of sample data as a hedging strategy and compare in-sample data hedge ratios with out-of-sample hedge ratio’s and determine effectiveness. Ederington’s study was able to show that the method of Ordinary Least Squares produced much better results than the one-to-one idea or method of thinking, through a reduction in the risk exposure of portfolios.

The use of the Single Equation Method by method of Ordinary Least Squares to obtain the optimal hedge ratio, has being criticized by Kroner and Sultan because of its inability to be unbiased if a co-integrating relationship exists between the spot and futures prices. The study provided by Kroner and Sultan, recommended a model criticized firstly for its derivation of the optimal hedge ratio from the unconditional second moments and secondly for the use of a constant hedge ratio. This method is known as the Vector Error-Correction method and the reason for the first criticism stems from the fact that the minimum variance hedge ratio is based on the conditional second moments. The validity of the second criticism lies in the fact that the use of a constant hedge ratio does not take into account variations over time of the joint distribution between the spot and futures prices. This study therefore focuses on the Single Equation Method by method of Ordinary Least squares as suggested by Johnson and Stein coupled with Ederington’s measure of effectiveness to estimate the optimal hedge ratio and supports Ederington’s, Bartosz Czekierda and Wei Zhang’s notion of it being one of the best if not the best method of estimating the optimal hedge ratio for spots and futures data. It is theoretically sound and is frequently referred to as the minimum variance hedge ratio. Many empirical studies have expanded on Ederington’s study including studies by Franckle and Figlewski that built their theories on fixed-income securities from the theories of Ederington. This study by Franckle and Figlewski shed light on a very important discovery that stock portfolio hedged by futures had basis risk in them and needed to be kept under control by reducing hedges to periods. The use of static hedges worked for shorter periods of time but for long hedging periods where static hedges were used, they proved highly ineffective. Several studies after this ended up adopting Ederington’s method of measuring the hedge ratio effectiveness, some include Yang and Allen; Myers; Ghosh and Chou et al; Park and Switzer; Wahab; Holmes and Laws and Thompson.

The next to build on this theory was Meyer and Thompson who sought to answer the question posed by the Franckle and Figlewski theory as to whether it was possible for a position or a portfolio position to remain hedged forever with the same hedge ratio. Their study revealed that the basis risk will exist if the changes in spot and changes in futures prices are not perfectly correlated. The inevitable consequence of this study and methodology is that the optimal hedge ratio cannot remain constant throughout the hedging strategy anymore and must be updated and recalculated when futures contracts expire and in some cases even before the contracts expire. Three to four years later Myers and Thompson’s research and study focused primarily on commodities futures hedging in the United States of America and used a combination of two of the methods mentioned above, namely the Single Equation Method by Ordinary Least Squares and the bivariate VAR method. Their study gave insight into the fact that the prices of futures contracts do not always predict the prices of spots in the future. This directly implies that the hedge ratio is essentially inefficient in the information it supposedly provides thus contesting declarations made by Stein and Johnson.

Besides issues of cointegration when using the Single Equation Method by method of Ordinary Least Squares to estimate the optimal hedge ratio, it is a very effective method to use to minimize the variance of a portfolio’s returns and maximise utility. David A Dickey and Wayne A Fuller in 1979 developed a test known as the Dickey Fuller test or the Unit root test to test whether a unit root exists in an auto regressive model. Challis and Kitney November in 1991 defined stationarity as “a quality of a process in which the statistical parameters (mean and standard deviation) of the process do not change with time.” The Augmented Dickey Fuller test is an augmented version of the Dickey Fuller test and was created to combat time series of a larger and more complex nature and is a good test for stationarity when using the Single Equation Method by method of Ordinary Least Squares.

The South African economy has proved to be one of the fastest growing economies in Africa in recent years and as such has acquired eminence all over the world as an emerging market. Its inclusion in BRIC (Brazil,Russia, India and China) in 2010 to form BRICS placed a defiant stamp on any doubts surrounding its rising economy and influence on global and regional affairs. This giant leap however, has not resulted in extensive studies by researchers and global investors into the various types of risks investors would face placing their money in South Africa’s very well developed equity market. The implementation of any sort of risk analyses and risk exposure minimization techniques and methods for hedging equities in the South African market is at this point in time still unavailable. This is an area of worry because proper research and analyses in this field could increase the rate of foreign investments in the South African equity market. There is very little research into this field of study in the South African context especially in stock index futures hedging in equity markets in South Africa.

In the South African context this study is the first on of its kind. There are hardly any studies that have dealt with methods of calculating the optimal hedge ratio for equity investments in South Africa and none have taken into consideration hedging for global investors investing in South African equities through currency futures

Lambrechts, H A, (1989/1990), A Snell and E vd Smith (1992) and Degiannaikis and Floros 2010 are amongst the few in financial research to have written anything on this study.

CHAPTER 2

ESTIMATING THE OPTIMAL HEDGE RATIO FOR SOUTH AFRICAN EQUITIES.

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