### An Analysis Of Companies Portfolio Performance Using Sharpe Ratio: –

### A Study On The Differences Of Performance Between Malaysian Conventional And Islamic Equity Mutual Fund In 2007

### 1.0 Introduction

### 1.0.1 Chapter Description

In this chapter, explaining the background of the study, problem statement, objectives of the study, hypotheses, significance of this study, as well as the scope and limitations during the process of completing this study.

### 1.0.2 Background of the Study

Portfolio evaluation is on the time before 1960. Investors evaluated portfolio performance almost entirely on the basis of the rate of return. They were aware of the concept of risk but did not know how to quantify or measure it, so they could consider it explicitly. Developments in portfolio theory in the early 1960s showed investors on how to quantify and measure risk in terms of the variability of returns. Still, because no single measure combined both return and risk, the two factors had to be considered separately as researchers such as Friend, Blume, and Crockett (1970).

Specifically, the investigators grouped portfolios into similar risk classes based on a measure of risk (such as the variance of return) and compared the rates of return for alternative portfolios directly within these risk classes. Before 1960, investors evaluated portfolio performance almost entirely on the rate of return, although they knew that risk was a very important variable in determining investment success. The reason for omitting risk was the lack of knowledge on how to measure and quantify it.

After the development of portfolio theory in early 60s, and CAPM in subsequent years, risk, measured as either by standard deviation or beta, was included in evaluation process. However, since there was not a single measure combining return and risk, two factors were to be considered separately that were researchers grouped portfolios into similar risk classes and compared rates of return of portfolios in the same risk class.

There are many kinds of measurement such as Jensen, Treynor and also Sharpe to evaluate the company’s portfolio performance. Jensen’s alpha has been a popular performance measure because it is a return concept. Related to Dr. William F. Sharpe’s contribution to style analysis of investment performance, the Sharpe’s alpha is related to the Jensen’s alpha in the sense that both measures excess returns. They differ, however, in the selection and construction of benchmarks.

Sharpe (1966) developed a composite index which was very similar to the Treynor measure, the only difference was that it was being used as standard deviation, instead of beta. To measure the portfolio risk, the researcher needs the average rate of return for Portfolio during a specified time period, the average rate of return on risk-free rate during the same period, Sharpe performance index and the standard deviation of the rate of return for Portfolio during the time period. Sharpe preferred to compare portfolios to the capital market line (CML) rather than the security market line (SML). Sharpe index, therefore, evaluated funds performance based on both rate of return and diversification (Sharpe 1967). For a completely diversified portfolio Treynor and Sharpe indices would give identical rankings.

Although the mutual fund industry in Malaysia started as far back as 1959 with the establishment of the Malayan Unit Trust Ltd, the development of the industry did not take-off until the 1980s with the launching of the Amanah Saham Nasional (ASN).

In 2004, the Commission approved 17 new Syariah-based unit trust funds, bringing the total number of such funds to 71 or 24.4% of the total 291 approved funds in the industry as at the end of 2004 (2003: 55 funds or 24.3% of the total industry). Of the 71 Syariah-based unit trust funds, 14 were balanced funds, 14 were bond funds, 39 were equity funds, 2 two were fixed income funds and two were money market funds. The number of units in circulation for Syariah-based unit trust funds also increased from 8.59 billion units as at the end of 2003 to 13.16 billion units in 2004. The number of accounts registered an increase of 23.4% or 80,848 accounts, with a total of 427,000 accounts in 2004.

One conventional fund made changes to its investment objectives and operations which enabled it to comply with the requirements of Syariah-based unit trust funds. In terms of value, the NAV of Syariah-based unit trust funds grew to RM6.76 billion representing 7.7% of the industry, an increase of 0.9% from the previous year. Over a 10-year period (1995-2004), the NAV of Syariah-based unit trust funds grew at a compounded annual growth rate (CAGR) of 26.18% while the overall industry CAGR was 7.89%.

The recognition of the increasing dominance and importance of unit trusts as an investment instrument has spurred researchers to devise appropriate techniques to assess portfolio performance. The earlier works by Sharpe (1966), Treynor (1965) and Jensen (1968) represented significant contributions to the evaluation of portfolio performance.

Therefore, the primary aim of this paper is to present new evidences for the analysis of companies’ portfolio performance using Sharpe ratio by studying the differences the performance between Malaysian conventional and Islamic Equity Mutual Fund in 2007.

### 1.0.3 Overview of Conventional and Islamic Mutual Fund

Mutual fund or better known as unit trust in Malaysia is an investment vehicle created by asset management companies specializing in pooling savings from both retail and institutional investors. Individual investors seeking liquidity, portfolio diversification and investment expertise are increasingly choosing unit trust funds as their investment vehicle. However, these investors do differ in their preferences based on their risk threshold, liquidity needs and their needs to comply with religious requirement.

In the Malaysian context, the performance of mutual funds or more popularly known as unit trust funds as reported by Shamsher and Annuar (1995), Tan (1995), Leong and Aw (1997), Annuar et al,. (1997) and Low and Noor A. Ghazali (2005) concluded that on average, funds were unable to beat the market.

The number of unit trust has grown dramatically in recent years. Unit trusts are now the preferred way for individual investors and many institutions to participate in the capital markets, and their popularity has increased demand for evaluations of fund performance.

Muslims are not allowed to invest in standard mutual funds since their religion prohibits them from investing in certain equities, like those of banks or companies that deal in pork, alcohol, pornography and certain entertainment related products.

An Islamic mutual fund is similar to a “conventional” mutual fund in many ways; however, unlike its “conventional” counterpart, an Islamic mutual fund must conform to the Sharia (Islamic Law) investment precepts. The Sharia encourages the use of profit sharing and partnership schemes, and forbids riba (interest), maysir (gambling and pure games of chance), and gharar (selling something that is not owned or that cannot be described in accurate detail; i.e., in terms of type, size and amount) (El-Gamal 2000).

The Sharia guidelines and principles govern several aspects of an Islamic mutual fund, including its asset allocation (portfolio screening), investment and trading practices, and income distribution (purification). When selecting investments for their portfolio (asset allocation), conventional mutual funds can freely choose between debt-bearing investments and profit-bearing investment, and invest across the spectrum of all available industries. An Islamic mutual fund, however, must set up screens in order to select those companies that meet its qualitative and quantitative criteria set by Sharia guidelines.

### 1.1 Problem Statement

At some levels, people are always interested in evaluating the performance of their investments. Having to spend the time and incurred the expense to design an asset allocation strategy and select the specific set of securities to form their portfolios, investors – whether they are individuals, corporations, or financial institutions. It must be periodically determined whether this effort is worthwhile. Investors in managing their own portfolios should evaluate their performance, as should those who pay one or several professional money managers to make these decisions for them. It is imperative to determine the realized investment performance which justifies the additional costs of engaging professional management.

Comparing a portfolio’s historical returns to those produced by other managers or indexes can be instructive; such comparisons do not produce a complete picture of the portfolio’s performance. Indeed, the central tenet of the modern approach to performance measurement is that it is impossible to make a thorough evaluation of an investment without explicitly control the risk of the portfolio. Given the complexity and importance of the issues involved, it is not a surprise to learn that there is not a single universally accepted procedure for risk-adjusting portfolio returns. Nevertheless, there are several techniques that are commonly employed.

Some previous studies found results that are inconsistent with Chua’s findings. These studies include Ewe (1994), Shamsher and Annuar (1995), and Tan (1995). Shamsher and Annuar (1995), focused their study on the performance of 54 unit trusts covering the period of late 80s to early 90s. They found out that the returns on investment in unit trust were well below the risk free and market returns. Furthermore, the results indicated that not only the degree of portfolios diversification was below expectation but the actual returns and risk characteristics of funds were also inconsistent with their stated objectives. Tan (1995) analyzed performance of 12 unit trusts over a 10-year period, 1984-1993. He concluded that unit trusts in general perform worse than the market portfolio. Consistent with Chua’s findings, Tan also concluded that government sponsored funds performed better than private funds.

As we can see, there are three portfolio performance evaluation techniques that comprise the basic ‘toolkit’ for measuring risk-adjusted performance. Although some redundancy exists among these measures, each of them provides unique perspectives, so that best viewed as complementary measures. In particular, examining the controversy surrounding the selection of the proper benchmark to use in the risk-adjustment process and discussing why these benchmark problems become larger when beginning to invest globally.

From here, how to evaluate the performance of the investments in order to reduce the risk taken? What measurement can contribute to evaluating a good investment? Therefore, it is interesting to analyze the companies’ portfolio performance by studying on the differences in the performance between conventional and Islamic equity mutual fund in Malaysia by using Sharpe ratio.

### 1.2 Objectives of Research

The general purpose of this study is to analyze the companies’ portfolio performance using Sharpe ratio by studying on the differences in the performance between conventional and Islamic equity mutual fund in Malaysia.

A careful review on those questions has led to the development of the following specific research objectives which are:

i. To measure and rank both relative quantitative performances of mutual fund (conventional/Islamic) on the basis of their return, total risk, coefficient of variation and Sharpe ratio. The term performance contains both the return and the risk undertaken by these mutual funds.

ii. To investigate whether both mutual funds (conventional/Islamic) are earning higher returns than the benchmark returns (or market Portfolio/Index returns) in terms of risk.

iii. To determine the relationship between dependent variable and independent variable.

### 1.3 Scope of Study

The study is on the analysis of the companies’ portfolio performance in determining the measure of average daily return, total risk (standard deviation), coefficient of variation and Sharpe ratio. Moreover, to observe the differences in terms of performance between conventional and Islamic mutual fund in the context of Malaysian capital market by comparing them to the stock market index or Kuala Lumpur Composite Index (KLCI) benchmark.

### The scopes of the study are stated as follow:

§ The relationship between two variables: the return on equity mutual fund as the dependent variable whereas the return on stock market index (KLCI) as the independent variable for conventional and Islamic fund.

§ The period of study will cover one (1) year starting from January 2007 to December 2007 using the daily basis collected from The Star and New Straits Times newspapers and also from the internet.

§ This research will also focus on the conventional and Islamic Equity Mutual Fund companies available in Malaysia.

### 1.4 Theoretical Framework

The theoretical framework shows the relationship between the independent variables and dependent variable. The independent variable is the return on KLCI while the dependent variable is the return of Equity Mutual fund companies in Malaysia.

Schematic diagram for the theoretical framework in this study is as follows:

Market Index Equity Fund

Market Index Islamic Equity Fund

Independent Variable Dependent Variable

### 1.5 Hypotheses

According to Uma Sekaran (2003), a hypothesis can be defined as a logically conjectured relationship between two or more variables expressed in the form of testable statement. Hypothesis can be divided into two categories which are Ho which is a Null Hypothesis and Ha which is an Alternate Hypothesis. The term “null” can be thought of as meaning “no change” or “no difference”. The second hypothesis is called alternative hypothesis. It is summary of the case if the null hypothesis is not true. It is stated that Ha, the alternative hypothesis is a statement of a view that has been prepared to be accepted if Ho is rejected. The hypotheses of this study are:

Hypothesis 1:

Ho: There is no relationship between the return on KLCI and the return on

Conventional equity mutual fund.

Ha: There is a relationship between the return on KLCI and the return on

Conventional equity mutual fund.

Hypothesis 2:

Ho: There is no relationship between the return on KLCI and the return on

Islamic equity mutual fund.

Ha: There is a relationship between the return on KLCI and the return on

Islamic equity mutual fund.

### 1.6 Limitations of the Study

### Data Collection and Cost Limitation

The major source of data gained is from the secondary sources. The data is only available at certain places and it requires cost to obtain the data. Besides, it also requires costs in the process of printing, photocopying, data services and transportations to obtain the information. The information about the topic studied is also difficult to search in the library because of the limited information. As a result, it causes problems to the researcher to gather and collect the information. The information and data related to the study is rather difficult to obtain. Thus, the accuracy of the study depends on the accuracy of the data available and may not perfectly precise. In addition, data is also limited since it relies on the secondary sources alone.

Lack of Experience and Expertise

Since this research is the first research experience for the researcher, undoubtedly there are still lots of things to improve. The lacks of experience especially in data collection and time management have been the limitations to the researcher. Moreover, the researcher has limited knowledge on the topic and needs more understanding on the topic studied.

### Time Constraint

Time is very limited for the researcher to complete the research. The researcher has to be very smart in scheduling the time to make sure the research is completed in time. Thus, time constraint has been identified as one of the limitations for the researcher.

### 1.7 Significance of the Study

This research analyzes on the companies’ portfolio performance using Sharpe ratio by studying on the differences in the performance between conventional and Islamic Equity Mutual Fund in Malaysia. Therefore this study will provide some information that can be useful because the data and findings from this research will help other researchers to produce better result in their research. This research is also significant to:

### To Researcher

As a finance student, issues in measuring portfolio performance are so much important and crucial. By studying about measurement of portfolio performance in depth, a better understanding and knowledge is gained. This research has given the researcher the opportunity to get the experience in practice as well as in theories.

### To other researcher

This study also can be a useful reference to other researchers who are keen to carry on the study regarding the performance of mutual fund in Malaysia. There are several fruitful areas in this study that can be further examined by other researchers. Further study will give an opportunity to other researchers to expand their view and knowledge. To do so, they need to refer to numerous literatures and hopefully, this research can come in handy for them.

### To Finance Students

This research will be very useful for finance students in having more knowledge about the company’s portfolio performance and the differences in the performance between conventional and Islamic Equity Mutual fund in Malaysia. They can use this research as a guide and as references in their studies in portfolio management and mutual fund in Malaysia.

### To Businesses

This research is very important to businesses in realizing the effects of portfolio management on their performance. This is important so that they will have clear direction in deciding their investment.

### To Investors

This study plays an important role in decision making since it gives the investors a prior knowledge of which Equity Mutual Fund companies is the best to invest and whether those companies provide high returns on investment. Moreover, revealing the specific volatility patterns in returns might also benefit investors in risk management and portfolio optimization. This research is also important to investors so that they can have a clearer picture of their investment choices. For investors the study can help them to know the risk and return of their investment transaction.

### 1.8 Definition of Terms

Portfolio

A collection of investments are all owned by the same individual or organization. These investments often include stocks, which are investments in individual businesses; bonds, which are investments in debt that are designed to earn interest; and mutual funds, which are essentially pools of money from many investors that are invested by professionals or according to indices.

Sharpe Ratio

A risk-adjusted measure developed by William F. Sharpe, calculated using standard deviation and excess return to determine reward per unit of risk. The higher the Sharpe ratio, the better the fund’s historical risk-adjusted performance.

Mutual Fund (Unit Trust)

A form of collective investment constituted under a trust deed or a pooled investment plan where the capital contributions of investors are combined into a legally formed trust fund.

Equity fund

Equity fund or stock fund is a fund that invests in Equities more commonly known as stocks. Such funds are typically held either in stock or cash, as opposed to bonds, notes or other securities.

Return

Based on Investopedia definition, return can be defined as the gain or lossof an investment over a specified period, expressed asa percentage increase over the initial investment cost. Gains on investments are considered to beany income received from the security, plus realized capital gains.

Risk

The quantifiable likelihood of loss or less-than-expected returns

Risk-adjusted return

A measure of how much an investment returned in relation to the amount of risk it took on. Often used to compare a high-risk, potentially high-return investment with a low-risk, lower-return investment.

Benchmark

A standard, used for comparison. For example, the Nasdaq may be used as a benchmark against which the performance of a technology stock is compared.

Regression Analysis

A statistical technique used to find relationships between variables for the purpose of predicting future values.

Coefficient of Determination

A measure of the correlation between the dependent and independent variables in a regression analysis.

R-squared

A measurement of how closely a portfolio’s performance correlates with the performance of a benchmark index, such as the S&P 500, and thus a measurement of what portion of its performance can be explained by the performance of the overall market or index. Values for r-squared range from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation.

Kuala Lumpur Composite Index (KLCI)

The Kuala Lumpur Composite Index (KLCI) is a stock market index generally accepted as the local stock market barometer. KLCI was introduced in 1986 to public the need for a stock market index which would serve as an accurate performance indicator of the Malaysian stock market as well as the economy. It is used to be the main index, and is now one of the three primary indices for the Malaysian stock market which the other two are FMB30 and FMBEMAS, Bursa Malaysia. It contains 100 companies from the Main Board with approximately 500 to 650 listed companies in the Main Board which comprise of multi-sectors companies across the year 2000 to 2006 and is a capitalization-weighted index.

### 2.0 Literature Review

### 2.1 Chapter Description

Literature review is the documentation of a comprehensive review of the published and unpublished work from the secondary sources of data in the areas of specific interest to the researcher. The reason of the literature review is to ensure that no important variable that has in the past been founded repeatedly to have an impact on the problem is ignored. (Uma Sekaran, 2005 page 63).

### 2.2 Literature Review of Evaluated Portfolio Performance

Craig W. French (2003) discussed on what is involved in evaluating portfolio performance, including the need to adjust for differential risk and differential time periods, the need for a benchmark, and constraints on portfolio managers. It also considered the difference between the portfolio’s performance and the manager’s performance. For measurement this paper used well-known risk-adjusted (composite) measures of Sharpe portfolio performance. Investors who had all (or substantially all) of their assets in a portfolio of securities should rely more on the Sharpe measure because total risk is important.

Joel Owen and Ramon Rabinovitch (1998), for the last four decades, numerous authors have been suggesting methods to evaluate portfolio performance. Sharpe (1966) proposed performance measures which had produced a score for every portfolio being evaluated. These scores were used to compare the performance of any two portfolios or rank the performance of all portfolios in a given set. The earlier works by Sharpe (1966), Treynor (1965) and Jensen (1968) represented significant contributions to the evaluation of portfolio performance.

### 2.3 Literature Review of Sharpe Ratio

Francisco Peñaranda (2007) in her paper commented on developments beyond mean-variance preferences to some alternatives to the Sharpe ratio. The main goal of those measures was to give a similar ranking to Sharpe ratios when returns were symmetrically distributed and showed a preference for skewness when they were not. Moreover, performance measures could be used to guide asset allocation since they can be used as the criterion to maximize with portfolio.

Raphie Hayat (2006), the attractiveness of the Sharpe Ratio came from its intuitiveness and simplicity. The Sharpe Ratio are simple because it could rank funds on the base of a single and intuitive since it only rewarded funds with a higher ratio if their returns were higher with the same level of risk or if the risk was lowered while keeping the same level of return.

Zhidong Bai, Keyan Wang, and Wing-Keung Wong (2006) stated that the asset performance evaluation was one of the most important areas in investment analysis. In order to compare the performance among assets, several statistics had been developed and among them, the Sharpe-ratio statistic was the most prevalent. However, the major limitation of the Sharpe-ratio statistic was that its distribution is only valid asymptotically, but not valid for small samples. Nevertheless, it was important in finance to test the performance among assets for small samples.

Tzu-Wei Kuo and Cesario Mateus (2006), the Sharpe ratio was well known risk-adjusted performance measures and easily understood by an individual investor. Thus, investors could evaluate the exchange-traded funds (ETF’s) performance, based on the Sharpe ratio. However, the Sharpe ratio relied on the assumption that returns were normally distributed having these measures difficulty in evaluating the performance with skewed return distributions.

Martin Eling and Frank Schuhmacher said that the classic Sharpe ratio was adequate in evaluating investment funds when the returns of those funds were normally distributed and the investor intended to place all his risky assets into just one investment fund. Because hedge fund returns differed significantly from a normal distribution, other performance measures had been proposed and encouraged in both academic and practice-oriented literature. The Sharpe ratio measured the performance of an investment fund by considering the relationship between the risk premium and the standard deviation of the returns generated by a fund. The Sharpe ratio were an adequate performance measure if the returns of the investment funds were normally distributed and the investor wished to place all his risky assets in just one investment fund.

Andreas G Merikas, Anna A Merikas and Ioannis Sorros (2005) examined the exact relationship between the Sharpe ratio and the information ratio. Sharpe in 1994 asserted that the information ratio was a generalized Sharpe ratio. Sharpe ratios had been estimated for each fund in each category, and an average ratio for each category. The Sharpe ratio would generally be positive since excess returns of funds over the risk free rate would be positive, unlike excess returns of funds over the market, which could be negative, as the return of the risk free bond was smaller but at the same time less volatile than the return of the market.

Cheryl J. Frohlich, Anita Pennathur and Oliver Schnusenberg in their research, Sharpe reward-to-variability ratio was used if total variability was thought to be the appropriate measure of risk, a stock’s (portfolio’s) risk-adjusted returns could be computed using the Sharpe Index. The Sharpe and Treynor Index eliminated the problem of only considering return as a measure of performance. However, neither ratio was independent of the time period over which it is measured. This means that the ratio can change from one period to another with different results. Moreover, both ratios also ignored the correlation of a fund with other assets, liabilities, or previous realizations of its own return.

Mario Onorato (2004), the Sharpe Ratio of any investment was defined as its excess return, it is return in excess of a benchmark return divided by the standard deviation of excess return. The benchmark represents a risk free investment alternative. Moreover, although the Sharpe ratio has become part of the modern financial analysis, its applications typically did not account for the fact that it was an estimated quantity, subject to estimation errors that would be substantial in some cases. The statistical properties of Sharpe ratios depended intimately on the statistical properties of the return series on which they are based. This suggests that a more sophisticated approach to interpreting Sharpe ratios is called for, one that incorporates information about the investment style that generates the returns and the market environment in which those returns are generated.

Wei Zhen (2004), in his paper said that the Sharpe (1966) and Treynor (1965) performance measures were widely accepted in both academia and industry to assess the Risk-adjusted value of a particular portfolio. It could be shown, after some mathematical treatment, that the Sharpe performance measure was useful when the portfolio of interest represented all of the investor’s investment, while Treynor’s measure was preferred when the portfolio under discussion was only a portion of the whole investment package.

Robert McCauley and Guorong Jiang (2004), through the Sharpe ratio it compared the returns of portfolios in relation to their risk by dividing their returns in excess of the riskless rate of return by the volatility of their returns. A portfolio with a higher Sharpe ratio was preferred in that it offered a higher return per unit of risk, as measured by return volatility.

William Goetzmann, Jonathan Ingersoll, Matthew Spiegel and Ivo Welch (2002), the Sharpe ratio is one of the most common measures of portfolio performance. It was used as a tool for evaluating and predicting the performance of mutual fund managers. Since then the Sharpe ratio, and its close analogues the Information ratio, the squared Sharpe ratio and M-squared, have become widely used in practice to rank investment managers and to evaluate the attractiveness of investment strategies in general. The appeal of the Sharpe measure was clear. It was an affine transformation of a simple t-test for equality in means of two variables, the first variable being the manager’s time series of returns and the second being a benchmark. The Sharpe ratio was also ubiquitous in academic research as a metric for bounding asset prices.

Andrew Worthington and Helen Higgs (2002), the Sharpe ratio (also known as the reward-to-volatility ratio) indicated the excess return per unit of risk and was calculated by dividing the return in excess of the risk-free rate by the standard deviation of returns. In the current context, the Sharpe ratio was the most appropriate performance measure for an investor whose portfolio was composed wholly of a given artist’s work.

Verena Kugi (1999), the Sharpe ratio measured the change in the portfolio’s return with respect to a one unit change in the portfolio’s risk. The higher this “Reward-to-Variability-Ratio” the more attractive was the evaluated portfolio because the investor received more compensation for the same increase in risk. Graphically, the Sharpe ratio was equal to the slope of a straight line connecting the position of the evaluated portfolio, for example a fund, with the risk-free rate. To determine the quality of performance, the Sharpe index of the evaluated portfolio was compared to the Sharpe index of the market or benchmark portfolio. The portfolio’s Sharpe index being higher than the market’s Sharpe index indicated that the portfolio manager had outperformed the market. Respectively, a lower Sharpe ratio was a sign of underperformance. Any portfolio that was positioned on the capital market line had a Sharpe ratio equal to that of the market and was therefore characterized by neutral performance.

Youguo Liang and Willard McIntosh (1998), the Sharpe’s alpha captured the excess return of