Reaction Paper

COMPARATIVE ANALYSIS OF MUTUAL FUNDS IN GHANA

USING BETA AS THE DETERMINANT FACTOR.

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LIST OF TABLES

LIST OF CHARTS

LIST OF ACRONYMS AND ABBREVIATIONS

ABSTRACT

The development of our Nation, Ghana, lies in our own hands.

Reliance Mutual Fund

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English: The Mutual Fund Store office, 37308 Six M...

Our contribution to economic development goes a long way to secure us in the future. The objective of this research is to compare the various equity funds in Ghana using beta and alpha as the determinant factors. The awareness of the benefits of investment is gradually spreading among the Ghanaian population. However, many who venture into many forms of investment lack the concept of that particular investment.

Ghanaian Investors are gradually increasingly getting interested in mutual fund selection, demanding detailed mutual fund information and investment advice. Many authors have tried to clarify the performance of mutual funds, which is a critical aspect in investor fund selection. Several fund characteristics have been analyzed as potential determinants of future fund performance, including fund size, age, fees and expenses, loads, turnover, flows, and returns.

Portfolio theory teaches us that investment choices are made on the basis of expected risks and returns. For the aggregate supply of all securities in the market to equal the aggregate demand for these securities, their expected returns must compensate investors for systematic risk. These returns tell an investor how much he can expect to be rewarded for bearing the systematic risk of a given security or fund. This approach has led to the use of risk-adjusted excess return alpha and beta as a measure of performance. The excess return implies that the manager of that fund has delivered a return over and that which is required to compensate investors for bearing market risk, where the market is represented as a broad-based index such as the GSE.

TABLE OF CONTENT

DECLARATION

DEDICATION

AKNOWLEDGMENT

ABSTRACT

LIST OF TABLES AND CHARTS

LIST OF ACRONYMS AND ABBREVIATION

CHAPTER ONE

INTRODUCTION

BACKGROUND OF STUDY

PROBLEM STATEMENT

OBJECTIVES OF THE STUDY

SIGNIFICANCE OF THE STUDY

SCOPE AND LIMITATION OF THE STUDY

LITERATURE REVIEW

RESEARCH METHODOLOGY

ANALYSIS AND IMPLICATION OF DATA

STRUCTURE OF STUDY

CHAPTER TWO

LITERATURE REVIEW

SECTION A

INTRODUCTION

INVESTMENT THEORIES

COLLECTIVE INVESTMENT WORK

ADVANTAGES OF COLLECTIVE INVESTMENT SCHEMES

OBJECTIVES OF COLLECTIVE INVESTMENT SCHEMES

BENEFITS OF INVESTING IN MUTUAL FUNDS

SECTION B

COLLECTIVE INVESTMENT SCHEMES IN GHANA

MUTUAL FUND IN GHANA

MUTUAL FUND BETA AND ITS IMPORTANCE TO INVESTORS

PERFORMANCE OF MUTUAL FUNDS IN GHANA (2010)

CHAPTER 3

RESEARCH METHODOLOGY

INTRODUCTION

RESEARCH DESIGN

POPULATION AND SAMPLING

SCOPE OF LIMITATION

DATA COLLECTION TECHNIQUES

DATA PROCESSING

REGRESSION

CHAPTER 4

DATA ANALYSIS AND RESEARCH FINDING

INTRODUCTION

CORRELATION

REGRESSION OUTPUT RESULT/SCATTER PLOT

EXPLANATION OF REGRESSION OUTPUT

CHAPTER 5

SUMMARY, CONCLUSION AND RECOMMENDATION

INTRODUCTION

SUMMARY OF FINDINGS

CONCLUSION

RECOMMENDATION

REFERENCES

APPENDICES

CHAPTER ONE

INTRODUCTION

Background to the Study

One of the fastest growing segments of the financial industry in Ghana is the Collective Scheme industry. By December, 2010, the Security and Exchange Commission (SEC) had licensed twenty-four collective investment schemes. The increasing number has resulted in great competition amongst the managers. Since mutual funds have gradually gained popularity on the Ghanaian financial market, it has become necessary to know what characterizes a remarkable mutual fund. Academics incessantly seek to find characteristics influencing mutual fund returns. These characteristics keep the investor well informed while evaluating which manager to invest with as selecting the right mutual fund can have a considerable effect on the investor's return.

Out of the numerous characteristics that distinct mutual funds, this study focuses on the beta and alpha of the equity funds in Ghana to evaluate the volatility of a particular fund in relation to the stock market and to know the performance of a manager compared to others on the same stock respectively.

1.1.1 Collective Investment Scheme in Ghana

Collective Investment Schemes (CIS) in recent years have become a very popular investment vehicle in Ghana due to the fact that they are, among other things, easily accessible, liquid and more transparent in relation to regulation. The growing investor knowledge, liquidity, higher market returns and its aptness for diversification which minimizes risk, also contributes to its popularity. In Ghana, the collective investment scheme comprises of Mutual Fund and Unit Trust Fund, which represent one of the fastest growing sectors in the financial industry in the country.

CIS, as the name implies, is an avenue provided by a company or firm for collection of funds from a wide range of investors. The funds collected form a pool which the Fund Manager invests in a portfolio of securities to earn returns. The collective schemes also serve as a flexible saving vehicle for individuals, corporate bodies, organizations like churches and schools, social and investment clubs, and so forth to amass funds for future needs

The company that collects the pool of funds from investors or contributors is known as the Manager. The Manager offers professional management for the funds collected and invests the funds into securities for high returns.

Under section 142 of PNDCL 333 as amended, a mutual fund is defined as "a public or external company incorporated solely to hold and manage securities or other financial assets and which has made satisfactory arrangement for ensuring that if any invitation is made to the public to subscribe to its shares the price at which the shares are offered shall be based on the net value of its assets at the time of the offer with no addition except for a reasonable service charge subject to the proviso to section 37 (1)(b) and is willing at any time to repurchase any of its shares from the holder at a price based on the net value of its assets at the time of repurchase without any deduction except for a reasonable service charge."

By the end of 2010, a total of twenty four (24) collective investment schemes were licensed to operate by the SEC up from 15 in 2009. They comprised 12 mutual funds and 12 unit trusts. Out of these 24 funds, eight (8) Collective Investment Schemes operated as Equity Funds, 2 as Money Market Funds, 7 as Balanced Funds and only one (1) as a Real Estate Investment Trust (REIT) (Komla, 2010). The remaining though licensed were yet to undertake their Initial Public Offering (IPO). Collectively, these funds have provided small investors the opportunity to participate in and reap the benefits of investing in the financial market.

By the end of 2006, a total of eight (9) collective investment schemes were licensed to operate with five (5) being mutual fund and the remaining four (4) as unit trusts. The total net asset value under management grew from GH¢16.49 million in 2003 to GH¢67.97 million by the end of 2006, representing a percentage growth of 312.19%. (SEC of Ghana, 2006 Annual Report)

In 2008, the total net asset value under the management of eleven (11) of the licensed Collective Investment Schemes (seven mutual fund and four unit trusts fund) in operation amounted to GH¢149 million, representing an increase of 120.0%over that of 2006. (SEC of Ghana, 2008 Annual Report).

In 2010, the total net asset value of the funds under management of Collective Investment Schemes was GH¢ 193 million representing a growth of 30% over the 2008 amount. Mutual funds contributed GH¢ 149.95 million whereas unit trusts contributed GH¢ 43.4 million. The number of shareholder and unit holders increased from 71,960 in 2006 to 178,764 in 2010, an increase of over 148% (SEC Annual Report, 2010).

The statistics over the years has shown a tremendous increase in net asset value as well as in the number of shareholders. Nonetheless not much study has yet been conducted to evaluate the performance of these Funds on the Ghanaian Financial market. The basic aim of any investor is to maximize his or her returns at a reasonable risk to his investment. According to Clive Granger, there is the need to analyze the performance of mutual funds using various parameters such as beta, alpha and standard deviation. This is necessary and relevant to investors because analyzing and evaluating the performance of a fund pinpoint the strong points and weaknesses of mutual fund schemes

1.2 Problem Statement

In many parts of the world, collective investment schemes are becoming more and more popular in recent times and more accessible to the individual investor. Investors are thus looking beyond traditional investments for such opportunities that will give them higher return on their capital. However, it is very important for investors to realize that there is no guarantee that one particular scheme will give them an "above average return". They need to carefully evaluate all facts concerning a particular scheme. Most investors are tempted into believing that a scheme will do well because it did well in the past and as such invest in such a scheme. It is not certain that a scheme will in the future repeat its past performance. The share prices might have already reached their peak with no prospect for further significant growth.

A number of academic literatures have reviewed mutual funds in general. According to Peterson et al. (2001), one area of research in mutual fund performance is whether it is possible to find predictive characteristics explaining fund performance. Finance professional frequently claim that different mutual fund characteristics are useful tools in either selecting the top-performing funds or rejecting the worst performers (Peterson et al., 2001).

It is in view of the above that investors need to evaluate and analyze fund's performance using appropriate parameters. Assessment of fund's performance is very important however, the parameters to use and their interpretation are not known to many investors in Ghana. This research seeks to compare the Equity Mutual funds in Ghana in terms of their sensitivity to the stock market and the performance of their managers. This will be a stepping stone in the right direction in establishing a platform for more complex analysis of the mutual fund industry of Ghana in the near future. This will inform Ghanaian shareholders in mutual funds to make decisions based on quantitative analysis instead of mere hearsay from others.

1.3 Objectives of the Study

The objectives of the study are outlined as:

To compare and evaluate the sensitivity of the returns of the mutual funds have been in existence for more than at least five (5) years in Ghana to the GSE stocks returns by determining their beta.

To establish the performance of these equity funds by calculating their alpha.

To find out if beta influences the returns of the funds and whether they can be used to predict fund's future performance.

Ascertain the importance of beta in the mutual fund market.

Significance of the Study

Mutual funds per its features presents itself as the most suitable investment for investors who are risk adverse as it offers an opportunity to invest in a diversified , professionally managed portfolio at a relatively low cost. Its shareholders usually comprise of investors of different financial literacy levels. A study of this nature that performs a comparative analysis of these managers with quantitative parameters will go a long way to inform both existing shareholders and potential ones of the performance of each manager as well as their risk level.

More importantly, with these parameters established and published, many managers will step up their games so as to give a better image to their shareholders or stand the risk of losing some of their shareholders.

Furthermore, as shareholders make more informed decisions the financial market of Ghana becomes more active with vibrant investors. This consequently leads to a healthy competition among managers thus grow the economy.

The measurement of beta gives some more details of a fund and therefore is of much importance. From the beta, the funds risk is established which can inform shareholders of the kind of securities the fund invests in and subsequently the fund's investment style. It is also used in comparing two funds. This study will help make the general public aware of the factors that cause the fluctuation of mutual funds

This study can serve a stepping stone into investigating some more parameters of the CIS on the Ghanaian financial market and not just on Equity funds as is done in this study.

1.5 Scope and Limitations of the Study

The scope of the study is to analyze the returns on the equity funds in Ghana. The study is limited to these five mutual funds. The focal point of this study is returns made on mutual fund which is a fast growing type of investment in the financial institutions in Ghana. Due to time and budget constraints, this study will only analyze the returns of these five schemes from 2004-2010. As previously stated, I would have loved to analyze all twelve mutual funds but due to the latter inception of most of the funds, I decided to concentrate on five of the mutual funds.

The next chapter looks at the various means of analyzing the performance of funds. Chapter three outlines how data was collected for the case study, the design, population and sample size. It also outlines sampling techniques used. Chapter Four gives a comparative analysis of the betas of the equity funds and that of the money market fund and further discusses the main findings of this paper in relation to the objectives and research questions it seeks to address. Chapter Five concludes with a summary of the findings and furnishes all especially Ghanaians on how to assess the performance of mutual funds.

CHAPTER TWO

LITERATURE REVIEW

INTRODUCTION

This chapter delves into related research on Mutual funds conducted in other parts of the world with some more emphasis placed on the few conducted in Ghana. A critical study and review is carried out to appreciate what these researchers sought to look out for and the various methods they adopted to obtain the results. This is to ensure that the wheel is not reinvented but rather existing works are used to serve as a guide to obtain a meaningful outcome. In searching for the most relevant literature, Google search engine and the University of Ghana Business School library were the main source of information.

INVESTMENT THEORIES

Investment can be defined as the commitment of funds to one or more assets that will be held over some future time period for return that is commensurate with risk (Arbor, 2009). The basic aim therefore, of any investor is to obtain a better than "average market" return from an investment, either by income or capital growth, or a mixture of both at a reasonable risk to their investment.

Investment theory includes the body of knowledge used to support the decision-making process of choosing investments for various purposes. It includes Portfolio Theory, the Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT) and finally the Efficient Market Hypothesis (EMH). In this chapter of the research paper, the author will concentrate on the portfolio theory Capital Asset Pricing Model (CAPM) which support the arguments made by Harry Markowitz.

In 1952, the Journal of finance issued an article titled "Portfolio Selection" authored by Harry Markowitz. The ideas later became a foundation of financial economics and revolutionized investment practice (Bernstein, 1992). Harry's work earned him a share of 1990 Noble Prize in Economics. This theory allows both investment professionals to better serve the needs of their clients, and investors to monitor and evaluate the performance of their investment.

In addition to that, he argued that an investor should maximize expected portfolio returns while minimizing portfolio variance of returns. Investment decision is not merely which securities to own, but how to divide the investor's wealth amongst securities. Markowitz's paper is the first mathematical formalization of the idea of diversification of investment: the financial version of "the whole is greater than the sum of its parts". He had the brilliant insight that, while diversification would reduce risk, it would not generally eliminate it. He believed that diversification is a powerful means of achieving risk reduction. Thus, mean-variance analysis gives an exact mathematical meaning to the saying "don't put all your eggs in one basket". Markowitz framework of developing the mean-variance analysis is to select a portfolio of stocks which over the last decade has become an analysis which is applied to asset allocation.

Asset allocation is an investment strategy that attempts to balance risk versus reward by adjusting the percentage of each asset in an investment portfolio according to the investors risk tolerance, goals and investment time frame. Basically the component is an asset class rather than an individual security. This makes asset allocation a suitable application of mean-variance than stock portfolio selection. In traditional Markowitz inspired investing, mutual funds and index funds; there is a discipline around variables such as asset classes and models of covariance. Furthermore, he reasoned strongly that risks that are not correlated with one another work best while investment that move together, example owning both FORD and GM stocks are way riskier.

Thus from Markowitz's portfolio selection theory, collective scheme is an excellent means of diversifying your investment over a period of time so as to receive a befitting reward. Most authors conclude that mutual funds underperform the market, but some others find that managers display some skill. In particular, there is evidence of short-term persistence in funds' performance and that money flows to past good performers. Investors display some fund selection ability as they tend to invest in funds with subsequent good performance ("smart money" effect). There is also evidence that fund performance worsens with fund size (Chen et al., 2004)) and fees (Gil-Bazo and Ruiz-Verdu, 2009). Although the literature focuses on the U.S. mutual fund industry, several authors study fund performance in individual countries. Few, however, examine cross-country mutual fund performance.

Theory of Mutual Funds

The mutual fund is one of the more ingenious inventions of the financial industry. It allows small investors to participate in virtually any part of the financial world. Many of us think mutual funds as a relatively modern invention but the mutual funds have been around for a long time, at least since King William I set one up in the Netherlands in 1822.

The first mutual fund, or open-end fund, the Massachusetts Investors Trust, was started in the United States in 1924. But during the bull market of the 1920s, mutual funds were eclipsed by their sister investments, the closed-end funds. These funds tumbled during the 1920s stock market frenzy when the market crashed. The SEC cleaned up the mutual funds industry after the Investment Company Act of 1940 was passed. The stock market performed well during the 1950s, then came the 1969-70 bear market. Investors again deserted mutual funds in droves but this time mutual funds companies began looking for alternatives to funds that invested only in stocks.

Explanation of Indicators

After the development of the Modern Portfolio Theory (MPT), Asset Pricing Theory (APT), Capital Asset Pricing Model (CAPM), the acceptance of the five major indicators of investment risk is widely used all over the world by financial analyst, portfolio managers, etc. The five major indicators of investment risk are Alpha, Beta, R-Squared, Standard Deviation, and the Sharp Index. These statistical measures historical predictors of investment risk/volatility and are all major components of MPT. In addition to that, these indicators are intended to help investors determine the risk-reward parameters of their investment

Analyzing Mutual Fund using the following parameters:

Alpha:- Using Alpha as a parameter, tells you how particular mutual fund schemes performed related to what it was expected to do

Beta: - By comparing mutual fund on the basis of beta, you will come to know how volatile a particular mutual fund as related to the stock market or stock index is.

Standard Deviation: - The standard deviation of a fund measures the risk by measuring the degree to which the fund fluctuates in relation to its mean return.

Treynor Ratio: - Using Treynor ratio as a parameter utilizes "market" risk (beta) instead of total risk (standard deviation).

Sharpe Ratio: - The Sharpe ratio is a risk-adjusted measure of return that is often used to evaluate the performance of a portfolio. The ratio helps to make the performance of one portfolio comparable to that of another portfolio by making an adjustment for risk.

Clive, evaluated the performance of different schemes (Equity fund, balanced fund, money market fund and liquid fund) by using the afore-mentioned parameters and came to the conclusion that, investors should always study the risk and returns relation of funds before investing in them. If the risk and returns is been matched with their planning, then the investor should invest in that mutual scheme or fund. A number of lessons can be learned from that study. First of all, the study showed that an investor is not rewarded for choosing a fund with high expenses and turnover ratios. Secondly, the regression with beta, alpha, treynor ratio, sharpe ratio and standard deviation as a parameter in evaluating the performance of a fund, provides a diverse results; high beta funds perform better than those having low beta whereas funds with high standard deviation perform worse than those with low standard deviation.

Alpha

Alpha is the intercept of that regression and can be interpreted as the "extra" return for the fund's level of systematic risk, or the "value added" by the fund's manager. This interpretation of alpha as a measure of performance adjusted for systematic risk was first suggested by Jensen (1968). However, it is important to be careful in the way one interprets this measure in the CAPM framework. In theory, any alpha other than zero is inconsistent with the CAPM because, if the market portfolio is efficient, then the expected return on every security or portfolio of securities is completely determined by its relationship to the market portfolio, as measured by beta. Thus, it is logically inconsistent to apply the CAPM to measure a mutual fund's return over and above the return required to compensate investors for the fund's systematic risk.

Alpha is a reward to risk measure but uses a different concept of risk. The concept of this measurement is taken from the capital asset pricing model. Alpha measures an investment's performance on a risk-adjusted basis. Which means, alpha measure the deviation of a portfolio's return from its equilibrium level, defined as the deviation of return from the risk-adjusted expectation for that portfolio's return. Alpha is often considered to represent the value that a portfolio manager adds or subtract from a fund portfolio's return. A positive alpha of 1.0 means the fund has outperformed its benchmark index by 1%. Correspondingly, a similar negative alpha would indicate an underperformance of 1%.

Beta

The beta can be estimated empirically from a time series of the historical returns on a given investment and the historical returns on the market portfolio. Five years of monthly returns (60 months) are commonly used to estimate beta. The return on the market portfolio is traditionally represented by the return on the S&P 500, though a value-weighted index of all securities in the market may be preferable, given the definition of the market portfolio. The most common way to estimate beta is a linear regression of the excess return of the given portfolio on the excess return of the market portfolio, where, beta is the slope of the regression line: Rp = Rf + (Rm - Rf)

Beta, also known as the "beta coefficient," is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is calculated using regression analysis, and you can think of it as the tendency of an investment's return to respond to swings in the market. By definition, the market has a beta of 1.0. Individual security and portfolio values are measured according to how they deviate from the market. A beta of 1.0 indicates that the investment's price will move in lock-step with the market. A beta of less than 1.0 indicates that the investment will be less volatile than the market, and, correspondingly, a beta of more than 1.0 indicates that the investment's price will be more volatile than the market. For example, if a fund portfolio's beta is 1.2, it's theoretically 20% more volatile than the market.

R-Squared R-Squared is a statistical measure that represents the percentage of a fund portfolio's or security's movements that can be explained by movements in a benchmark index. For fixed-income securities and their corresponding mutual funds, the benchmark is the U.S. Treasury Bill, and, likewise with equities and equity funds, the benchmark is the S&P 500 Index.

R-squared values range from 0 to 100. According to Morningstar, a mutual fund with an R-squared value between 85 and 100 has a performance record that is closely correlated to the index. A fund rated 70 or less would not perform like the index.

Standard Deviation

Markowitz (1952) suggested the use of standard deviation as a measure of risk. This metric measures the dispersion of returns from a central average value. In plain English, the more that data is spread apart, the higher the difference is from the norm. The greater the standard deviation, the greater the fund's volatility.

Sharpe Index or Ratio

Sharpe Index is a risk-adjusted measure developed by the Nobel Laureate William Sharpe. Sharpe used Markowitz's concept to create the ratio which later became known as the Sharpe Index. The ratio is calculated by subtracting the risk-free rate of return (U.S. Treasury Bond) from the rate of return for an investment and dividing the result by the investment's standard deviation of its return. The higher the Sharpe Ratio, the better the fund's historical risk-adjusted performance. In theory, the Sharpe ratio tells investors whether an investment's returns are due to smart investment decisions or the result of excess risk. This measurement is very useful because although one portfolio or security can reap higher returns than its peers, it is only a good investment if those higher returns do not come with too much additional risk. The greater an investment's Sharpe ratio, the better its risk-adjusted performance.

MEASURING FUNDS PERFROMANCE

Many researchers have assessed the performance of CIS either with countries or across the continent. While aiming that, different methods were used in the assessment. A few of these are reviewed to serve as a guide in the attainment of the objectives of this study.

Katerina Simons in her article, Risk adjusted performance of mutual funds, stated "The two major issues that need to be addressed in any performance ranking are how to choose an appropriate benchmark for comparison and how to adjust a fund's return for risk. Her article further describes a number of performance measures which she believes have a common feature. That is they all measure funds' returns relative to risk. However, they differ in how they define and measure risk and, consequently, in how they define risk-adjusted performance. The two measures of risk-adjusted performance based on the standard deviation, are the Sharpe ratio and the Modigliani measure. However the Morningstar ratings, are based on downside risk

Markowitz identified the trade-off facing the investor: risk versus expected return.

The investment decision is not merely which securities to own, but how to divide the investor's wealth amongst securities. This is the problem of "Portfolio Selection," where he argues that the critical line algorithm identifies all feasible portfolios that minimize risk (as measured by variance or standard deviation) for a given level of expected return and maximize expected return for a given level of risk. When graphed in standard deviation versus expected return space, these portfolios form the efficient frontier. The efficient frontier represents the trade-off between risk and expected return faced by an investor when forming his portfolio.

Most of the efficient frontier represents well diversified portfolios. This is because diversification is a powerful means of achieving risk reduction. A common technique for selecting a portfolio is to maximize a linear function of expected return and variance, namely the Investor's Utility:

U = EP - VP/RT

where:

U = the utility of the portfolio for the Investor EP = the expected return of the portfolio VP= the variance of the portfolio return RT= the Investor's risk tolerance

Here, "RT" represents the investor's marginal rate of substitution of variance for expected value. Moreover, u, the measure of portfolio utility, can be interpreted as a risk-adjusted expected return, since it is computed by subtracting a risk penalty (VP/RT) from the expected return (EP).

The goal is to find the best portfolio -- here, the one with the maximum possibility utility.

The issue with this methodology is the inconsistency in data inputs as it is subject to one's discretion. Historical statistics should not be blindly fed into an optimizer. Inputs should be adjusted to reflect a sound understanding of capital markets.

Cuthbertson et al (2010), addressed the issue of the Measurement of Mutual Funds in mainly UK and USA. The main aim of the paper was to provide a critical review of empirical findings on the performance of mutual funds. It critically appraised rival theoretical, methodological and practical issues in evaluating mutual fund performance, place particular emphasis on providing quantitative (rather than just qualitative) results and on standardizing results across studies (where possible) - the reader can then more easily compare results across somewhat diverse approaches.

The Euler equation (first order condition) for any asset is:

[1] E[mi+1Rit+1|It]=1 The projection of the managed fund (excess) return rp+1 on the benchmark return R(t+1, Rp+1

Rpt+1 = α pt+1 + β pt R(t+1 + εpt+1

Where it is important to note that alpha and beta are conditional on public information available to the investor It (and not any superior private information available to the managed fund).

The SDF (and the no-arbitrage) approach makes clear that it is the conditional alpha and beta that we are trying to measure and the benchmark portfolio in this approach is not the market portfolio of all tradable assets (as in the CAPM) but is the mean-variance efficient portfolio of investors who use only public information.

Separating out the two distinct sources of performance attribution has been attempted by explicit modeling of the signals used by portfolio managers (Admati et al 1986) but it can be shown that the TM regression does not resolve the performance attribution problem unless additional "strong restrictions" are placed on the model (Lehmann and Timmermann 2007).

From Cuthbertson et al, the average managed funds, (US or UK) fund underperforms its benchmarks by around 1% p.a. (Kosowski et al 2006, Barras et al 2009, Cuthbertson et al 2008 ) but the average US fund does earn a positive risk adjusted return in recession periods (Kosowski 2006)

Fama (1972) developed a methodology for evaluating investment performance of managed portfolios. Fama suggested that return on a portfolio could be subdivided into two parts; the return for security selection (selectivity) and return for bearing risk (risk).

Gohar et al, in their journal sought to analyze and compare the performance of different types of mutual funds in Pakistan, and concluded that equity funds outperform income funds. He also discussed the four models which are used worldwide for the performance evaluation of mutual funds: Sharpe measure; Treynor measure; Jenson differential measure; information ratio. Certain hypotheses were developed upon which conclusions were made for the research. Statistical Package Social Sciences (SPSS) also employed for the analysis of data. The funds outperformed the market on all four measures.

Ferreira et al, in their cross country study of the determinants of Mutual fund performance. We study how the performance of equity mutual funds relates to fund characteristics and country characteristics around the world for 27 countries over 1997 -2007. We study fund performance using an extensive list of fund characteristics, including fund and family size, age, fees and expenses, front-end and back-end loads, flows, past returns, management structure, and number of countries where a fund is sold. The mean and standard deviation of monthly factor returns (percentage per month) in U.S. dollars of the Carhart model in 1997-2007 was calculated for all 27 countries for RM, SMB, HML and MOM. RM is the excess return on the domestic market, SMB is the difference in return between the small and big portfolios, HML is the difference in return between the high and low book-to-market portfolios, and MOM is the difference in return between last year's winner and loser portfolios.

We estimate the mutual funds (risk-adjusted) performance using several benchmark models. Fama and French (1992) propose a three-factor model that improves average CAPM pricing errors by including size and book-to-market factors. Carhart (1997) proposes adding a factor that captures the Jegadeesh and Titman (1993) momentum anomaly. The four-factor model regression is given by:

R= α + β0i RMt+ β1iSMBt + β 2i HMLt + β 3i MOMt + ε

Where R is the return in U.S. dollars of fund in excess of the one-month U.S. Treasury-bill in month.

SBM = (Small value + Small Neutral + Small Growth - Big value - Big Neutral - Big Growth)/3

HML = (Small value +Big value - Small Growth - Big Growth) /2

MOM = (Small High +Big High - Small low - Big Low) /2

Mohammed et al, in 2010 conducted a research to evaluate CIS in Ghana by determining the factors that affect the performance of mutual funds from 2005 to 2009 in Ghana and running simple and multiple regressions for the Standard deviation, beta, fund size, NAV, Fund age and Management tenure. For simple regression Y = a + Bx was used and for multiple regression Y = a + bX + cX + Dx.

Table 2.1 Difference between a Unit Trust and Mutual Fund

NATURE OF COLLECTIVE SCHEMES IN GHANA

The Ghana Securities and Exchange Commission website describes Collective Investment Schemes (CIS) as "pools of funds that are managed on behalf of investors by a professional money manager. The manager uses the money to buy stocks, bonds, or other securities according to specific investment objectives that have been established for the scheme. In return for putting money into these funds, the investor receives shares or units that represent his/her pro-rata share of the pool of fund assets. In return for administering the fund and managing its investment portfolio, the fund manager charges a fee based on the value of the fund's assets". In Ghana, the Collective Investment Schemes takes the form of either a Mutual Fund or a Unit Trust. This means that the law has combined both the British and American systems of collective investment scheme.

The objectives remain the same; however, the only difference between the two is the form of ownership or corporate structure. Mutual funds in Ghana are organized by corporate entities registered under the Companies Code. A Mutual fund in Ghana may either be Open-ended fund or a Close-ended fund. The following definitions about these funds are derived from the official website of the Ghana SEC website.

While the Open-ended fund is a collective investment scheme which can issue and redeem shares at any time the Close-ended fund is a collective investment scheme with a limited number of shares. An investor will generally purchase shares in the fund directly from the fund itself rather than from the existing shareholders. The price of a share in an open-ended fund is determined by the net asset value per share of the fund, where net asset value per share refers to the total value of the assets in the fund's portfolio, less any fund liabilities, divided by the number of shares outstanding.

The closed-ended funds issue a fixed number of shares and do not stand ready to repurchase their shares from their shareholders when they decide to sell them.

Mutual Funds and Unit Trusts are generally categorized according to their investment objectives and their investment policies. Some funds focus on stocks, others on bonds, and money market instruments. On the international scene, some funds invest primarily in their countries, others invest internationally, and some specialize in specific countries.

As reported by the Security and Exchange Commission on their web site www.secghana.org/investor/cischemes.asp. (March 24, 2010), Collective Investment Schemes are categorized as;

1. Money Market Funds,

2. Fixed Income Funds,

3. Growth or Equity Funds,

4. Balanced Funds,

5. Global and Foreign Funds,

6. Specialty Funds,

7. Index Funds.

Mutual Funds in Ghana

As defined previously, mutual funds are collective investment schemes that are mostly managed by professionals for their unit holders. They often have different classes of assets drawn together by many different investors. Operating mutual funds requires professional knowledge and expertise and are regulated by the Ghana Securities and Exchange Commission for investor protection. This type of investment is very liquid since investors can convert their investment upon request at the net asset value per share. Like corporations, mutual funds have boards of directors to oversee fund management and the boards appoint registered investment advisers for its portfolio management.

Five (5) out of the twelve (12) mutual funds in Ghana was chosen for this study. The five mutual funds comprises of four equity funds (Anidaso Fund, Epack Fund, SAS Fortune Fund, and NTHC Horizon Fund) and one (1) money market fund (MFUND). As previously stated, there are 12 mutual funds in Ghana, six (6) are equity funds, four (4) are balance funds and the remaining two (2) are money market fund. Due to the latter inception of most of the funds, I have decided to concentrate on four equity funds and one money market fund. In addition to the inception years, regression may give a poor result or meaningless result with just few observations. These mutual funds are managed by different firms in Ghana. The following is a brief history about the company managing these funds under study.

Source: SEC, Annual Report 2010

ADVANTAGES OF COLLECTIVE INVESTMENT SCHEMES

They allow ordinary people to invest in shares that would normally be out of their financial reach if their money had not been pooled with that of other investors in the fund.

They provide a means to beat inflation, as returns are normally higher than the inflation rate.

CIS are a flexible form of investment, as you can either invest a lump sum or you can make a regular investment each month.

CIS offers liquidity. In other words, the unit holder may choose to cash in a portion of the CIS or all of it. This means that your money is always accessible, which is not the case with all long term investments.

They can also be transferred to another party, and you can even invest on somebody else‛s behalf.

You can monitor the performance of your CIS on a daily basis as it appears in the newspapers‛ business reports.

Experts in the field of managing money, invest your money on your behalf.

You can choose a CIS to meet your needs.

You may invest in markets all over the world, and reap the benefits of rand hedging.

Capital gains are taxed in the hands of the individual investor in respect of Capital Gain Tax (CGT)

OBJECTIVES OF MUTUAL FUNDS

Income: Income funds emphasize on dividends and interest that provides income to investors. This is a relatively fixed source of money, but the fund's NAV can still fluctuate

Growth: Growth funds concentrates on increasing the value of the principal or amount invested through capital gains and net assets value. Growth funds are usually more risky but offer greater potential returns.

Stability: Stability funds focus on protecting the amount invested from loss so the fund's NAV does drop. This is the least risky type of fund but may make the least amount of money

BENEFIT OF INVESTING IN MUTUAL FUNDS

The advantages are traditionally associated with investing in mutual funds:

Liquidity: Mutual funds are highly liquid, meaning that they are easily converted to cash by redeeming the shares with the investment company.

Professional Management: Investors of Mutual funds employs the service of professional managers to monitor and manage their investments. These skilled professionals backed by their team of investment research team analyses the performance of various funds or schemes and closely monitors each investment made with the view to making rational and timely decision so as to enhance the performance of the fund under management.

Diversification: The main idea of diversification of portfolio is to reduce risk by allocating investments among various financial instruments. It aims to maximize return by investing in different areas that would each react differently to the same event. In other words, the more stocks and bonds you own, the less any one of them can hurt you. Large mutual funds typically own hundreds of different stocks in many different industries.

Return Potential: Over a medium to long-term investment, Mutual Funds have the potential to providing higher returns as they invest in diversified basket of selected

Low Costs: Mutual Funds are less expensive way to invest compared to some investing in securities in the capital markets because the benefits of scale in brokerage, custodial and other fees translate into lower costs for investors

Transparency: Mutual Fund industry is well regulated worldwide and as an investor you can get regular information on the value of your investment in addition to release on the specific investments made by the scheme. In the mutual fund industry, there are rules and regulations designed to benefit investors such as the issuing the fund prospectus, statement of additional information, and annual report so as to help investors make right decisions.

Taxes: Mutual funds in Ghana, under the current legislation, are not subject to taxes on interest income nor to any taxes on income distribution

MUTUAL FUND BETA & ITS IMPORTANCE TO INVESTORS

What is a fund beta?

A fund's beta basically measures the fund's risk. A fund's beta tells us what kind of securities the fund invests in, I.e. a stock fund's size beta tells us whether the fund invests in large, medium or small cap stocks while the fund's valuation beta tells us whether the fund invests in value, blend or growth stocks. Similarly, a bond fund's duration beta indicates whether the fund invests in short, intermediate or long term bonds while the fund's quality beta indicates whether the fund holds high credit quality (low yield) or low quality (high yield) bonds (EMA Softech, 2004).

Therefore, because betas tell us what sort of stocks or bonds a fund invests in, they measure a fund's investment strategy or investment style

Why is beta important?

Funds' betas tell us what kind of securities funds invest in and hence measure the funds' investment styles and knowing funds' styles is important for:

Finding a fund with a particular investment style. It is straightforward to select a fund with a particular style if the styles of all the available funds are measured accurately.

Checking the consistency of a fund's investment strategy. Drift or shift in a fund's style may signal an inconsistent strategy. Also, investing in a fund with style shift or drift may raise the risk of the investor's overall portfolio. It is easy to determine whether a fund is suffering from style drift or shift by looking at a plot of its betas over time.

Comparing two funds. A side-by-side comparison is more meaningful if both funds have the same style.

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MUTUAL FUND PERFORMANCE ON THE GHANAIAN MARKET

Table 2.3 Performance of Collective Investment Schemes in 2010

Source: Security and exchange Commission, 2010 Annual Report

Mutual Fund Performance on the Ghanaian Market

Table 2.4: Market Share and Performance of Collective Investment Schemes Industry 2010

Chart 2.1: Performance of Funds as of the end of 2010

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We focus on the sample of funds that invest in their local market (domestic funds), but we also perform some tests using funds that invest outside their local market or globally (international funds). We use the Carhart (1997) four-factor model to measure risk-adjusted performance, but we also consider several alternatives including benchmark-adjusted returns,

market-adjusted returns, and the market model.

CHAPTER THREE

RESEARCH METHODOLOGY

Introduction

This chapter clearly shows an in depth direction into the way data gathering and data analyses are structured in this study. The study probes into the performance of FUNDs in Ghana using beta as its main parameter for evaluation and analysis. The study also reviews existing research on Collective Investment Schemes which comprises of Mutual Fund and the need to analyze the performance of the schemes using various parameters. Thus both primary and secondary data are collected for analysis

Research Design

The term "research design" refers to how a researcher puts a research study together to answer a set of research questions. Research design works as a systematic plan outlining the study, the researchers' methods of compilation, details on how the study will arrive at its conclusions and the limitations of the research (Wills, 2009). The plan is geared at collecting and utilizing data so that desired information can be obtained.

The research approach adopted for this study is the case study approach. A case study is a research approach that is used to generate an in-depth, multi-faceted understanding of a complex issue in its real-life context. According to Garger (Gromisch, ed., 2010), one of the biggest disadvantages of using the case study method has to do with external versus internal validity. Case study research excels at bringing us to an understanding of a complex issue or object and can extend experience or add strength to what is already known through previous research (Stake, 1995). Case studies emphasize detailed contextual analysis of a limited number of events or conditions and their relationships. A key strength of the case study method involves using multiple sources and techniques in the data gathering process. Tools to collect data can include surveys, interviews, documentation review, observation, and even the collection of physical artifacts (Wills, 2009). According to Yin, case studies can be used to explain, describe or explore events or phenomena in the everyday contexts in which they occur.

In order to develop a thorough understanding of the case, the case study approach usually involves the collection of multiple sources of evidence, using a range of quantitative (e.g. questionnaires, audits and analysis of routinely collected data) and more commonly qualitative techniques (e.g. interviews, focus groups and observations). The use of multiple sources of data (data triangulation) has been advocated as a way of increasing the internal validity of a study (i.e. the extent to which the method is appropriate to answer the research question). An underlying assumption is that data collected in different ways should lead to similar conclusions, and approaching the same issue from different angles can help develop a holistic picture of the phenomenon (Crowe, 2011)

Case study research excels at bringing us to an understanding of a complex issue or object and can extend experience or add strength to what is already known through previous research. Case studies emphasize detailed contextual analysis of a limited number of events or conditions and their relationships. Researchers have used the case study research method for many years across a variety of disciplines. Social scientists, in particular, have made wide use of this qualitative research method to examine contemporary real-life situations and provide the basis for the application of ideas and extension of methods.

SAMPLING FRAME

In this section, we first describe our sample, and then we describe the methods for computing alpha and beta of the equity funds.

SAMPLE DESCRIPTION

Data on equity mutual funds come from the SEC of Ghana database, which covers all the CIS in Ghana from 2005 - 2010 periods. The database is survivorship bias-free, as it includes data on both active and defunct funds. Although multiple share classes are listed as separate funds in Lipper, they have the same holdings, the same manager, and the same returns before expenses and loads. We eliminate multiple classes of the same fund to avoid multiple counting of returns.

We have checked the coverage of funds by Lipper with the aggregate statistics on mutual funds (European Fund and Asset Management Association (2008), EFAMA). Total numbers of equity funds reported by SEC are, as of December 2011. Total net assets of equity funds (sum of all share classes) reported by Lipper and EFAMA are, respectively, $10.9 trillion and $12.5 trillion as of December 2007. Thus, our initial sample of equity funds covers 87% of the total net assets of the CIS in Ghana running for more than 3 years.

We also require a fund to have at least two years of reported returns because we need to estimate fund factor loadings based on past fund returns. The final sample includes 16,316 funds in 27 countries (12,577 active funds and 3,739 dead funds as of December 2007). We believe this is the most comprehensive data set ever used to study mutual fund performance in terms of both number of funds and countries.

The target population in this study consists of all equity and money market mutual funds in Ghana that were in existence at the end of the 2004 fiscal year. I employed their annualized returns, NAV, daily prices, number of shareholders from January 2005 to December 2010.

SCOPE OF LIMITATION

As previously stated, the study included all equity and money market fund that were in existence by the end of 2004. The study covers the period from 2005-2010. The data used in the analysis was the yearly returns of the funds from 2005-2010. This study would have loved to analyze all twelve mutual funds but because the mutual fund industry in Ghana is young compared to its global counterparts, this limited the amount of element we could include in our target population. This therefore narrowed the amount of mutual funds we could employ in the study. In addition to that, the study overlooked all mutual funds whose inception dates were after 2005.

DATA COLLECTION TECHNIQUES

Data collection techniques allow us to systematically collect information about our objects of study (people, objects, phenomena) and about the settings in which they occur.

Data-collection techniques permit us to systematically gather information about our objects of study (people, objects, phenomena) and about the settings in which they occur.

Qualitative technique was used to allow for the triangulation of data. Qualitative methods include the researcher's experience through techniques such as focus groups, case studies, interviews, existing research and personal observations (Smith, 2008).

Denzin, et al (ed. 2005) defined qualitative research as a method of inquiry aimed to gather an in-depth understanding of human behaviour and the reasons that govern such behavior. The qualitative method investigates the why and how of decision making, not just what, where, when. Hence, smaller but focused samples are more often needed, rather than large samples.

In this study the main source of our data will be the annual reports of the collective investment schemes reported to the Ghana Securities and Exchange Commission. We also reviewed different relevant research paper in relation to the performance of collective investment scheme. Advantages of using the primary sources include it uniqueness and the fact that it has not been collected (Lawrence, 2007).

DATA ANALYSIS

The primary data collected from annual report of the SEC in relation to mutual funds was analyzed using excel simple linear regression method. In order to compare the different mutual equity funds, annualized returns of the funds and GSE-All Share Index was used to run the regression analysis

REGRESSION ANALYSIS

One use of capital asset pricing model (CAPM) is to analyze the performance of mutual funds and other portfolios. The method is used to relate the historical risk-adjusted returns (that's the return minus the return of risk-free cash) of the fund against those of a suitable index, and then use least-squares regression to fit a straight line through the data points:

Each data point in the graph shows the risk-adjusted return of the portfolio and that of the index over one time period in the past.

The general equation of this type of line is given by

r - Rf = beta x ( Km - Rf ) + alpha

Where r is the fund's return rate, Rf is the risk-free return rate, and Km is the return of the index.

Note that, except for alpha, this is the equation for CAPM - that is, the beta got from Sharpe's derivation of equilibrium prices is essentially the same beta got from doing a least-squares regression against the data. Beta is the slope of this line. With this the sensitivity of the return of the investment in question can be determined and therefore the risk level. Alpha, the vertical intercept, tells how much better the fund did than CAPM predicted (or maybe more typically, a negative alpha tells how much worse it did, probably due to high management fees).

The quality of the fit is given by the statistical number. An r-squared of 1.0 would mean that the model fit the data perfectly, with the line going right through every data point. More realistically, with real data, an r-squared of around 0.85 is obtained. From the above analysis, a conclusion can be drawn that 85% of the fund's performance is explained by its risk exposure, as measured by beta.

The method adopted is Simple Regression analysis. Regression analysis is the statistical technique that identifies the relationship between two or more quantitative variables: a dependent variable, whose value is to be predicted, and an independent or explanatory variable (or variables), about which knowledge is available. The technique is used to find the equation that represents the relationship between the variables.

A simple regression analysis can show that the relation between an independent variable X and a dependent variable Y is linear, using the simple linear regression equation Y = α +βx (where α is the Y intercept and β is the slope of the line or beta of the fund).

Regression analysis is used to understand the statistical dependence of one variable on other variables. The technique can show what proportion of variance between variables is due to the dependent variable, and what proportion is due to the independent variables.

It is necessary to note that the Ghana Stock Exchange All Share Index (GSE) was considered as the benchmark for the market index.

Beta also known as the beta coefficient is a measure of the volatility, or systematic risk of a security or a portfolio in comparison to the market as a whole. Using regression analysis to calculate beta gives you a better responds to the relationship between the security and the market. Beta is calculated using regression analysis, and you can think of it as the tendency of an investment's return to respond to swings in the market. By definition, the market has a beta of 1. Individual security and portfolio values are measured according to how they deviate from the market. In order for us to run a regression analysis, we have to use the returns of the all four equity fund (dependent variable or Y) and the returns of GSE-ASI

Reason for GSE-All Share Index

The study employed GSE-ASI to proxy for Ghana stock market returns. The index which is the broad market indicator of the stock market measures the overall performance of the stock market. The index is computed by the Ghana Stock Excahnge and it is calculated as the natural logarithms of GSE-ASI at month t. In January 2011, the Ghana Stock Exchange changed the name of the GSE-ASI into Ghana Stock Exchange Composite Index (GSE-CI). In addition to the change of name, the base index value was changed to 1000.

GSE-CI) is based on the volume weighted average closing price of all listed stocks. All ordinary shares listed on GSE are included in the GSE-CI at total market capitalization, with the exception of those of listed companies which have shares listed on other markets. The GSE-CI is a market capitalization weighted index, i.e. each constituent is given weight according to its market capitalization.

CHAPTER FOUR

DATA ANALYSIS AND RESEARCH FINDINGS

INTRODUCTION

The study is a comparative analysis of mutual funds in Ghana using beta as the determinant factor over the past six years. The study seeks to come out with findings that will assist investors and readers to which of the funds is less risky over the stated years.

In this chapter, we will first run a correlation analysis on three different variables (Net Asset Values, No. of Shareholders and annualized returns) on all five funds. After which we will run a regression analysis on all five mutual funds (four equity fund and one money market fund) over the period of five years. These funds and their regression analysis output are shown below

CORRELATION

Before we run a regression analysis using the dependent and independent variables, I decided to run a correlation between the NAV and the no. of shareholders, the NAV and the annualized returns of CIS in Ghana and that between the no. of shareholders and the annualized returns in 2010. The reason is to find out if there is a relationship between the two variables. The importance of correlation in the finance world comes from the simple insight that since investors naturally seek to minimize risk, a low correlation with each other is much favorable or preferred. The correlation coefficient between the NAV and the no. of shareholder returned a positive value (0.93901) close to 1 which means that as one of variable gets larger the other gets larger. It can also be said that, there is a positive relationship between the NAV and the no. of shareholders.

The two other correlation coefficients are -0.18670 and -0.055162 which shows that, as one variable get larger, the other gets smaller. Also since those values are closer to zero (0), we can also conclude by saying there is no relationship between those variables.

Table 4.1: Various CIS with Number of Shareholders and Annualized returns of the funds

Source: Securities and Exchange Commission, 2010 Annual Report

Table 4.2: Correlation output result of Net Asset Value, No. of Shareholders and the annualized returns of listed Collective Investment Schemes above

REGRESSION OUTPUT RESULT/SCATTER PLOT

Table 4.3: Annual returns of four equity funds and the GSE-ASI

Source: Ghana SEC, Annual Report 2010

The following returns of all four equity funds and GSE-ASI in Table 4.3 were obtained from the SEC annual report from 2005-2010 fiscal years. In this exercise, we will be using the returns of all four equity fund as the dependent variable or Y variable (Y1, Y2, Y3, Y4) and the returns of Ghana Stock Exchange All Share Index (GSE-ASI) as the independent variable or X variable.

Although the annualized returns of the equity funds were obtained from the annual report of the SEC, calculation of the returns is as follows:

Since returns are calculated from one period to the next, the return for the EPACK for example is calculated as

Return of EPACK= (Current price-Previous price) Previous price

OR

Return of EPACK = (Current price) - 1

(Previous price)

Table 4.4: Annual MFUND returns and the 91-Day T-bill Interest Rates

Source: Ghana SEC, Annual Report 2010

In the table above, there are five columns of data. In column 1 has dates of the data. In the second and third column, are closing prices for the year ending for the MFUND and the interest rate for the 91-day Treasury bill rate. MFUND return is the dependent variable (Y) whiles the X variable or independent variable is the 91 days Treasury bill rate.

Return on MFUND is computed with the bid prices only. It is equal to the change between the bid prices of the relevant date and that of the bid price of the previous year end and then annualizes the result.

Return of MFUND = ((Current bid price / Last year ending bid price) - 1)*(365/number of days current bid price correspond to)

In this exercise, we are going to create a scatter plot of both variables (X and Y) for each fund and also run a simple regression analysis using the same variables (X and Y) for each fund. The scatter plot or diagram is made up of an X axis (the horizontal axis), a Y axis (the vertical axis), and a series of dots. Each dot on the XY chart represents one observation from the data set. Using the returns, we generate a scatter plot and identify the slope of the "best line" fit which is the beta. The following charts below are the output results of the scatter plot and regression analysis.

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Table 4.5: Regression Output result of EPACK returns and GSE-AS1

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Chart 4.2: Scatter Plot of SAS Fortune's returns (Y) and GSE-ASI returns (X)

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Table 4.7: Regression Output result of NTHC Horizon's returns and GSE-AS1

Chart 4.3: Scatter Plot of NTHC Horizon's returns (Y) and GSE-ASI returns (X)

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Chart 4.4: Scatter Plot of Anidaso's returns (Y) and GSE-ASI returns (X)

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Chart 4.5: Scatter Plot of MFUND's returns (Y) and 91 -Day Treasury-Bill (X)

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EXPLANATION OF REGRESSION ANALYSIS OUTPUT

Table 4.11: Regression Analysis Output Results

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Beta also known as the beta coefficient (X Variable 1) is a measure of the volatility, or systematic risk of a security or a portfolio in comparison to the market as a whole. Using regression analysis to calculate beta gives you a better responds to the relationship between the security and the market. The following betas from the simple regression analysis listed in Table 4.11 denotes the nature of the relationship between the dependent variable (Fund's annualized returns) and the independent variable (GSE-ASI returns) and more specifically denotes the slope of the linear equation that specifies the model. Epack's fund recorded the least beta whiles that of SAS Fortune had the highest. If the fund's price experiences movements that are greater or more volatile than the market, then the beta value will be greater than 1. In our case, the betas for the four equity funds and one mutual funds are all less than one. That means the fund's price movement's swings below that of the market thus recording a beta values less than 1 during the six year period (2005-2010). In theory, we can conclude by saying Epack's fund is less volatile, and therefore gives a lower overall returns.

The beta (X Variable) for the MFUND is quoted as 0.0019 implies that the MFUND is less riskier compared to the four equity funds and is approximately risk free but will yield lesser returns.

The Multiple R, also known as the correlation coefficient measures the strength and directions of the linear relationship between the dependent and independent variable for each fund. A value close to -1 or 1 indicates a good linear relationship between the two variables and the least-square regression line will fit the data well. Anidaso's fund and SAS Fortune fund indicated a correlation coefficient value of 0.9474 and 0.9185 respectively which means a positive correlation among the dependent and independent variables. Likewise, a value close to zero (0), means the least-square regression line (which is the best line possible) doesn't fit the data very well.

The multiple correlation coefficient of the MFUND is 0.02533. This confirms that the correlation among the independent variable (91-day T-bill rates) and the dependent variable (MFUND's returns) is positive though not strong.

Coefficient of Determination (R-Squared) is a measure of the proportion of variability in the dependent variable explained by the regression relationship. It shows the goodness of fit of the entire estimating equation to the data set. The coefficient of determination R2 expresses the proportion of the variation in the dependent variable (Y) which is explained by the variation in the independent variable (X). It reveals what percentage of a fund's movements can be related to movements in its benchmark index. An R-Squared of 100 would mean that all of the fund's movements are perfectly explained by its benchmark. In our case, the R2 for Anidaso Fund of 0.897571 means that close to 89% of the variation in Anidaso's return is explained by the GSE-ASI returns.

Adjusted R Square, is a modification of R2 that adjusts for the number of explanatory terms in a model. Unlike R2, the adjusted R2 increases only if the new term improves the model more than would be expected by chance. The adjusted R2 can be negative, and will always be less than or equal to R2. In addition to that, we should note that the statistic is not generally interpreted because it is neither a percentage (like the R2), nor a test significance (such as F-Statistic). A negative value which in our case is Epack's fund (-0.025673) means the relationship between the two variables contains terms that do not help to predict the response.

As stated above the adjusted r square can be a negative value and in the case of the MFUND is -0.199230 which implies that there is no correlation between the MFUND and the 91-Day T-Bill.

Standard Error, is an estimate of the standard deviation of the coefficient. It gives us a first handle on how well the fitted equation fits the sample data. The standard error of Epack's fund recorded the highest value of 0.232383 which is a percentage of the variation of the observed returns of Epack returns in percentage terms, about the regression line.

Note: the standard error is the same unit of the measurement as the dependent variable

T-Test, test for the significance of the coefficients of the independent variables in a regression analysis. A t-test value greater than 2.0 shows 95% certainty coefficient is significant. Since the T-Test for SAS Fortune, NTHC Horizon, and Anidaso Fund shows values greater than 2 and also indicate P-values (Significant F) values less than 0.05, means it is very much significant. Epack's T-Test is 0.935332 which Is less than 2 but has a significant F value greater than 0.05 tells us that, the independent variable (GSE-ASI return) is not a significant predictor of the dependent variable (EPACK's return) beyond the sample. In regression, the t-stat, coupled with its p-value, indicates the statistical significance of the relationship between the independent and dependent variable. The p-value is not an indicator of the generalizability of the model (i.e., will it accurately predict "outside" of the model?), but the probability of getting the result if in fact the null hypothesis is true (i.e., "no significant relationship").

A t-test value of 0.056655 for the MFUND and p-value of 0.957014 shows the coefficient is not significant. This is because the t-test is less than 2, whiles the p-value or the significant f value is greater than 0.05.

Table 4.11, provides the Average Annualized Returns, Effective Returns, Return Standard Deviation and Sharpe ratio for all four equity funds and the money market fund. Money market fund (MFUND) is known to have a low risk fund, therefore generating a low standard deviation of 4.97% with a high Sharpe ratio of 0.42 among all the mutual fund. It also recorded the highest average annualized return of 17.87% and an average effective return of 2.06% after subtracting the risk-free rate which in our case is the 3 month Ghana Treasury bill.

As we compare these statistical measures between the four equity funds, we've observed that the SAS Fund generated the highest average annualized return of 17.64% but also took much large risk than the rest of the funds. NHTC Horizon recorded the least average annualized return of 7.63% and took the lowest risk of 13.05% (standard deviation) than the rest of the funds, and that may actually be the case because the NTHC Horizon Fund has a better risk-adjusted return than the rest of the equity funds.

In addition to that, we know that the greater a fund's Sharpe ratio, the better the risk -adjusted performance has been. However, a negative Sharpe ratio indicated that a risk-less asset or fund would perform better than the security being analyzed. The Sharpe ratio allows comparisons of investments over multiple sets of assumption, meaning there may be instances in which some part of an investment have a given risk-fee rate and another part has a different risk-free rate. The inclusion of the risk-free rate parameter allows one to use the Sharpe ratio to compare these options under the different circumstances

The Treynor measure is similar to the Sharpe ratio in that it is a ratio of the excess return per unit of risk except that in this case, the risk is defined as the non-diversifiable risk. In other words, it gives us the measure of return of return per unit of market risk or systematic risk that the investment earns. A higher Treynor Ratio indicates that the fund has performed well not only in terms of returns but also in terms of volatility (i.e. it has displayed less riskiness. This explains the higher Treynor Ratio for MFUND since money market fund is risk free.

Anidaso fund recorded an average excess return of 0.38% over a short term treasury bill (90-day), whiles that of EPACK recorded an average excess return of 0.28% when we divide the two returns with their respective beta. EPACK yields a higher ratio Treynor ratio of 0.012 than that of Anidaso fund of 0.006. This may because; Anidaso fund is more volatile to the market whereas the MFUND is less volatile to the market

EXPLAIN THE VALUES FOR ALPHA

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Table: 4.12: COMPARATIVE ANALYSIS ON FOUR (4) MUTUAL EQUITY FUND AND ONE (1) MONEY MARKET

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Chart 4.6: Comparative Investment Returns (2005-2010)

Source: Databank Research, Bank of Ghana, Ghana Association of Bankers, Databank Asset Management Services Limited�

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

INTRODUCTION

This chapter draws the link between the objectives of this case study and the findings that were realized in this study as well as in previous research findings. It summarizes the entire case study, draws conclusions and gives recommendations for further study. The objectives of the study were to ascertain parameters that can inform investors as to where to invest.

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Databank Mutual Fund

First Fund

Databank Balance Fund

HFC Future Plan

iFund

Christian Community Fund

Databank ARK Fund

Capital Growth Fund

HFC Unit Trust

Gold Fund

SAS Furture Fund

Horizon Fund

Anidaso Fund

EPA¢K

HFC Equity Fund

Campus Mutual Fund

Heritage Fund Ltd

MONEY MARKET FUNDS

EQUITY FUNDS

BALANCE FUNDS

HFC REIT

SPECIALTY FUNDS

Chart 4.1: Scatter Plot of EPACK's return (Y) and GSE-ASI returns (X)

Table 4.10: