# History of mutual funds

### CHAPTER 1: INTRODUCTION

### Objective of the dissertation

Mutual funds are the common name for open end companies. This is the dominant investment company today, accounting for more than 90% of investment company assets. Assets under management in the US mutual fund industry were approximately $9.5 trillion in mid-2006 and more than $8 trillion was held in non-US funds. Mutual funds have come to play a dramatically increased role in financial markets in recent decades. Although the growth of the mutual fund industry started in the US, where the industry plays an extremely important role in stock markets, this trend has spread more recently to other countries around the world. It is a topic which is of enormous interest not only to researchers all over the world, but also to investors. Mutual funds as medium-to-long term investment options are preferred as a suitable investment option by investors. However, with several market entrants the question is the choice of mutual fund. While the investment actions of fund managers are not directly observable by investors, the latter tend to look at the fund attributes. With the rising popularity of mutual fund investing among individual investors, the information on what fund attributes contribute to fund performance is more relevant than ever for investors facing with the decision of selecting fund for investment. This study focuses on this problem of mutual fund selection by investors by analysing the effect of fund attributes on performance of large growth mutual funds. Four important fund characteristics, namely fund size, fund age, expense ratio and management tenure, are considered and three performance measures are used to assess performance of the funds.

### Structure of the Dissertation

The remainder of this study is structured as follows: Chapter 2 gives an overview of mutual funds in the US and some important definitions pertaining to mutual funds, Chapter 3 provides a literature relating fund attributes to performance, Chapter 4 outlines the various steps undertaken to carry out the research and gives details regarding the two different approaches adopted and the sample used, Chapter 5 presents the analysis of the findings and the final chapter concludes the study

### A brief history of mutual funds

There are many theories as to where and when the evolution of mutual funds originated. The concept of pooling money together for investing purposes started in Europe in the mid-1800s. These early pooled-funds (trusts) resembled closed-end mutual funds. The creation of the Massachusetts Investors' Trust in Boston, which went public in 1928, is cited as the arrival of the modern mutual fund in the U.S. Roughly a year later, the Trust already had 200 shareholders and assets amounting to almost $400,000.00. In 1929, there were 19open-ended funds competing with nearly 700 of the closed-end variety.

By the end of 2006, the mutual fund business was still growing and mutual funds in the U. S. numbered more than 8,000 with asset holdings of $10.4 trillion and new markets opening up around the world.

Mutual funds have become extremely popular over the last 20 years. More than 80 million people, or one half of the households in America, invest in mutual funds. That means that, in the United States alone, trillions of dollars are invested in mutual funds.

### Definition of mutual funds

A mutual fund is an investment company that brings together a group of people and invest their money in a pool of securities of several corporations. These corporations receive dividends on the shares that they hold and realize capital gains or losses on their securities traded. Investors purchase shares in the mutual fund, which represent a portion of the holdings of the fund. After paying operating costs, the earnings (dividends, capital gains or losses) of the mutual fund are distributed to the investors, in proportion to the amount of money invested. Investors hope that a loss on one holding will be made up by a gain on another. Heeding the adage "Don't put all your eggs in one basket" the holders of mutual fund shares are able collectively to gain the advantage by diversifying their investments, which might be beyond their financial means individually. A mutual fund may be either an open-end or a closed-end fund.

### Open-End Mutual Funds

Most mutual funds are open-end funds, which sell new shares continuously or buys them back from the shareholder (redeems them), dealing directly with the investor (no-load funds) or through broker-dealers, who receive the sales load of a buy or sell order. They do not have a set number of shares; it may be considered as a fluid capital stock.The purchase price is the net asset value at the end of the trading day. However this price is influenced greatly by the fund managers.The number of shares of an open-end fund varies throughout its existence, depending on how many shares are bought or redeemed by investors.

### Closed-End Mutual Funds

A closed-end mutual fund sells shares of the fund in an initial public offering (IPO). After the offering, no more shares are created or redeemed. Therefore, less money is needed to manage the fund, since there is no need to deal directly with individual investors, such as sending periodic statements, and it also eliminates the need to redeem shares to pay investors who want to cash out, such as occurs in open-end mutual funds.

### Net asset value

Net asset value (NAV) represents a mutual fund's per share market value at the end of each trading day. It is the total assets of the fund minus its liabilities divided by the number of shares outstanding for that day. NAV also determines the actual value of the securities under management represented by each mutual fund share. Net asset values are like stock prices in that they give investors a way to compare a fund's performance with market or industry benchmarks (such as the Standard & Poor's 500 or an industry index). The change in NAV, reported at the end of every market day, reflects the increase or decrease in the value per share. This is usually used to measure mutual funds. However, some analysts argue that comparing long-term changes in a fund's NAV is not as meaningful as comparing long-term changes in its share price because funds periodically distribute capital gains to their fund holders, thus reducing their NAV.

### Fees

There are numerous fees associated with specific activities of the fund, the total of which can vary from 0.5% to 8.5%, the legal maximum. Management fees are annual charges for administering the fund, which can vary from about 0.5% to 2%. Distribution and service fees (12b-1 fees) cover marketing expenses to bring in new investors, and may be used to pay bonuses for employees. Redemption fees, sometimes referred to as a deferred sale load or back load fees, are charged when shares of the fund are sold, to discourage frequent trading, unless the investor has held the shares for a minimum of time, specified in the prospectus. Reinvestment fees can be charged if the investor reinvests his profits in the fund. Exchange fees can be charged if an investor transfers his money from one fund to another within the same company. A no load fund is one which does not charge a front-end sales charge or a deferred sales charge. Mutual funds are usually divided into different classes where each class will have different shareholder services and/or distribution arrangements with different fees and expenses.

### Types of mutual funds

Most mutual funds have a particular investment objective that will customize the fund's assets, regions of investments and investment strategies. Each mutual fund has different risks and rewards. In general, the higher the potential return, the higher the risk of loss. Although some funds are less risky than others, all funds have some level of risk - it's never possible to diversify away all risk. This is a fact for all investments. For instance, some invest only in Blue Chip companies that are more established and are relatively low risk. On the other hand, some focus on high-risk start up companies that have the potential for double and triple digit growth. At the fundamental level, there are three varieties of standard mutual funds:

### Money market funds

Money market funds have relatively low risks, compared to other mutual funds and most other investments. Thus they are considered the safest investments but have the lowest payouts. By law, they are limited to investing only in specific high-quality, short-term investments issued by the U.S. government, U.S. corporations, and state and local governments as a way to secure a return. Typically these funds will pay you more than the average bank savings account.

### Fixed income funds

Fixed income funds or bond funds are created strictly for cash flow. They invest normally in bonds which are government and corporate debt. While the types of mutual funds holdings may increased in value, the objective of these funds is to provide a steady cash flow to investors. However they are associated with a certain level of risk, they can range in risk from low, such as a U.S.-backed Treasury bond, to very risky in the form of high-yield or junk bonds, which have a lower credit rating than investment-grade corporate bonds.

### Equity funds

Equity funds or stock funds are one of the types of mutual funds representing the largest category of the types of mutual funds. Generally, the investment intention of this class of types of mutual funds is long-term capital growth with some income. There is, however, a variety of types of equity funds because there are many different types of equities. Because equities give off the best long term investments these funds are typically outperform the rest. But they also have the greatest risks.

### Classification of funds

Mutual funds can further be classified under size and investment style. For this purpose, Morningstar, which is a famous website providing information on mutual funds, has created a tool called the Style Box. This box can represent the investment characteristics of the mutual funds:

The vertical axis of the Style Box defines three size categories, or capitalization bands-small, mid, and large. Large-cap stock refers to almost the same thing as large-company stock. A company's capitalization is the total value of all its stock—that is, the price of a company's stock times the number of shares it has sold. Large-cap companies are usually very big corporations, like IBM or Microsoft whereas small-caps are generally defined as companies with less than about $800 million in capitalization. Many successful small-cap companies eventually grow into large-cap corporations. Mid-cap stocks are those between large and small cap stocks.

The horizontal axis defines three style categories, value, blend and growth. Value stocks are stocks from firms with relative low Price to Earning (P/E) Ratio which usually pay good dividends. The investor is looking for income rather than capital gains whereas growth stocks are stocks from firms with higher low Price to Earning (P/E) Ratio which usually pay small dividends. The investor is looking for capital gains rather than income. The central column of the style box represents the blend style that is a mixture of growth and value stocks or mostly core stocks.

The different classifications are thus as follows large value, large blend, large growth, mid value, mid blend, mid growth, small value, small blend and small growth. For example a fund investing in large growth companies will seek capital appreciation and the fund will normally invest in securities of large-sized growth companies with a large capitalisation.

### Introduction

Our understanding of the determinants of the performance of mutual funds is still quite broad, as there is no specific model which could reliably explain why some mutual funds perform better than others. Moreover most past studies are rather concerned with the measures of the performance of mutual funds or on a specific factor that may drive the success of mutual funds. Literature shows that there are a number of factors that may determine the performance of mutual funds. The purpose of this paper is to study the impact of the main factors that previous research has found to be important in the performance of mutual funds. The sample consists of 30 large growth mutual funds in the U.S. Performance is evaluated using the three most important and widely used measures; the Jensen Measure, the Treynor Measure and the Sharpe Measure. Then fund performance is studied using a list of determinants, including fund attributes like size, age, fees and management tenure.

The significance of this literature review is to provide a brief discussion of research concerning:

- Performance evaluation
- Fund attributes

### Performance Evaluation

Measurement of a mutual fund's performance is of extreme importance to investment managers. Performance evaluation of mutual funds is one among the preferred areas of research where a good amount of study has been carried out thus literature on mutual fund performance evaluation is enormous. The most widely used overall performance measure for investors picking their funds are like the Sharpe measure, Treynor measure and the Jensen Measure.

Evaluating performance based on average return alone is not very useful. Returns must be adjusted for risk before they can be analysed meaningfully. The simplest and most popular way to adjust returns for portfolio risk is to compare rates of return with those of other funds with similar risk characteristics, however this proved to be misleading. This suggested that a more precise means for risk adjustment was desirable. Methods of risk-adjusted performance evaluation using mean-variance analysis criteria came on stage simultaneously with the capital asset pricing model (CAPM). Treynor (1965, 1966), Sharpe (1966) and Jensen (1968) recognized immediately the implications of the CAPM for evaluating performance of mutual funds.

Treynor and Mazuy (1966) used a quadratic term of the excess market return to test for market timing ability. It can be viewed as the extension of the Capital Asset Pricing model (CAPM). If the fund manager can forecast market trend, he will adjust the proportion of the market portfolio in advance. However the CAPM is subject to the criticisms such as inappropriate assumptions, its reliability is dependent on the benchmark relevance to a particular portfolio.

Roll (1977) has forcefully argued that the use of the CAPM as a benchmark in performance evaluation is logically inconsistent under the assumptions of the model since any measured abnormal performance can only occur when the market is inefficient. This has led researchers to explore alternative theory of asset pricing. One theory which has stimulated much research is the Arbitrage Pricing Theory (APT). The APT-based performance measure was then formulated by Connor et al. (1986).

Lehmann and Modest (1986) examined whether different methods for constructing reference portfolios lead to different conclusions about the relative performance of mutual funds and showed that alternative APT implementations often suggested substantially different absolute and relative mutual fund rankings. The fund ranking based on alpha is very sensitive to the method used to construct the APT benchmark.

Fama and French (1992, 1993, 1995, 1996) have highlighted two important factors that characterise a company's risk, as a complement to the market beta: the book-to-market ratio and the company's size measured by its market capitalisation. They therefore proposed the Fama and French's three-factor model. The Carhart's four-factor model (1997) is an extension of Fama and French's three-factor model. It includes an additional factor, momentum which enables the persistence of the returns to be measured. This factor was added to take the anomaly revealed by Jegadeesh and Titman (1993) into account.

The theory developed by Sharpe (1992), the Sharpe's style analysis model, stipulates that a manager's investment style can be determined by comparing the returns on his portfolio with those of a certain number of selected indices. Intuitively, the simplest technique for identifying the style of a portfolio involves successively comparing his returns to those of the different style indices. The goodness of fit between the portfolio returns and the returns on the index is measured with the help of a quantity called R2 which measures the proportion of variance explained by the model.

### The Treynor Measure

Jack Treynor (1965) conceived an index of portfolio performance measure called the reward to volatility ratio, based on systematic risk. He suggested a way of evaluating the performance of a portfolio by adjusting the mean excess return (i.e. mean return less the risk-free rate of return in the economy) for the degree of market (systematic) risk and thus calculating the performance of the portfolio. Systematic risk could be estimated by regressing the mutual fund's returns on the returns to a market benchmark index.

The Treynor ratio is particularly appropriate for appreciating the performance of a well-diversified portfolio, since it only takes the systematic risk of the portfolio into account, i.e. the share of the risk that is not eliminated by diversification. It is also for this reason that the Treynor ratio is the most appropriate indicator for evaluating the performance of a portfolio that only constitutes a part of the investor's assets. Since the investor has diversified his investments, the systematic risk of his portfolio is all that matters.

Srivastava and Essayyad (1994) proposed Treynor's index, where beta is a composite measure generated by combining the expected asset returns from the traditional CAPM and the mean-lower partial moment CAPM. Their argument is that a composite forecast is more accurate than separate forecasts: valuable information missing from one model may be captured by the other model. They tested this measure on U.S.-based international funds and found that the composite beta is a statistically significant and meaningful parameter. They also ranked the performance of the funds using the Treynor index with three models (the CAPM, the mean-lower partial moment CAPM and a combination of the two), but their sample, which was made up of 15 funds, was too small to test whether the difference in ranking obtained with the different models was significant.

### The Sharpe Measure

William F.Sharpe (1966) devised an index of portfolio performance measure, referred to as reward to variability ratio denoted by SP. He assumes that a small investor invests fully in the mutual fund and does not hold any portfolio to eliminate unsystematic risk and hence demands a premium for the total risk. He computed mean excess return and adjusted for the degree of total risk involved in the portfolio. Total risk was estimated by the standard deviation of returns. This ratio measures the return of a portfolio in excess of the risk-free rate, also called the risk premium, compared to the total risk of the portfolio, measured by its standard deviation. It is drawn from the capital market line, and not the Capital Asset Pricing Model (CAPM). It does not refer to a market index and is not therefore subject to Roll's (1977) criticism concerning the fact that the market portfolio is not observable.

Since this measure is based on the total risk of the portfolio, made up of the market risk and the unsystematic risk taken by the manager, it enables the performance of portfolios that are not very diversified to be evaluated. This measure is also suitable for evaluating the performance of a portfolio that represents an individual's total investment.

The superiority of the Sharpe ratio over the Treynor ratio is that it considers the point whether investors are reasonably rewarded for the total risk in comparison to the market. A mutual fund scheme with a relatively large unique risk may outperform the market in Treynor's index and may underperform the market in Sharpe ratio. A mutual fund scheme with large Treynor ratio and low Sharpe ratio can be concluded to have relatively larger unique risk. Thus the two indices rank the schemes differently.

### The Jensen Measure

Sharpe and Treynor ratios rely mainly on ranking of portfolios in comparison to the market portfolio. They are unable to answer question like: Has fund given more than/less than/ equal to expected returns? Hence there is a need for a better performance measure.

Michael C. Jensen (1968) has given different dimension and confined his attention to the problem of evaluating a fund manager's ability of providing higher returns to the investors. He measures the performance as the excess return provided by the portfolio over the expected (CAPM) returns. He assumes that the investor expects at least CAPM returns. He devised a method of determining whether the deviation of portfolio returns from market returns was statistically significant, and, therefore, determining whether the excess return could be attributed to superior management, or purely to chance. The Jensen alpha can be used to rank portfolios that are managed in a similar manner and therefore have comparable levels of risk.

The Jensen measure is subject to the same criticism as the Treynor measure: the result depends on the choice of reference index. In addition, when managers practice a market timing strategy, which involves varying the beta according to anticipated movements in the market, the Jensen alpha often becomes negative, and does not then reflect the real performance of the manager.

### Fund attributes

Investors are increasingly interested in mutual fund selection, demanding detailed mutual fund information and investment advice. Expansion in the number of choices can make evaluating and selecting funds particularly challenging. Selecting a mutual fund that is able to offer high returns with acceptable risks is a complex task. The purpose of this second part of the literature review is to identify the factors that previous research has found to be important in the performance of mutual funds.

The most common determinant of mutual fund performance to study is fund size. Grinblatt and Titman (1989, 1994) and Prather et al (2004) found that performance is negatively related to size. However Israelsen (1998) found that as a fund becomes larger the better it will perform. Liljeblom and Loflund (2000) also detect a positive relationship between size and performance over long time periods. They were not able to prove the same over shorter time periods. Chen et al (2004) developed a theory which says that the most obvious and most cited reason why performance is eroded by fund size is transaction costs.

Mutual fund expenses, is also an important factor to consider when determining performance. Sharpe (1966) was among the first researchers to investigate this. He found that funds with lower management fees tend to perform better than those with higher fees. However the results of Ippolito (1989) were the complete opposite of that of Sharpe (1966). Elton et al (1993) also document that management fees have a negative effect on performance but later on, most precisely in 2003, they found that incentive fees may increase performance. On the other hand, Grinblatt and Titman (1994) were unable to find any relationship between management fees and performance. The transaction costs involved in buying and selling of mutual funds or what is known as expense ratio has also been considered by several studies. Blake et al (1993), Carhart (1997), Dellva and Olson (1998), Israelsen (1998) and Liljeblom and Loflund (2000) found negative relationship between expenses ratios and fund performance however Chen et al (1992) reported a positive relationship. Golec (1996) suggested that investors should avoid funds with high expenses ratios.

A factor that has received as much attention in previous literature is past performance because it is seen to be the simplest and most direct method to determine the performance of a mutual fund. Grinblatt and Titman (1992), Hendricks et al (1993) and Goetzman and Ibbotson (1994) reported that past performance does have an effect on actual returns. However Blake et al. (1993), Bogle (1992), Brown and Goetzman (1995) and Brown et al. (1992) showed that there was a relatively small relationship between past performance and actual performance of a fund. But, still many investors continue to base themselves on past performances when selecting mutual funds; this might be a reason why some poorly performing funds are still surviving (Harless and Peterson, 1998)

The characteristics of the fund manager, also is an important determinant since that he is the one who will select the stocks in which to invest and who will manage the fund. Studies like that of Jensen (1968), Malkiel (1995) and Gruber (1996) among others documented that managed mutual funds do not outperform their benchmark that is managers do not make a difference in the performance of their funds. However Golec (1996) found that abnormal returns can be forecast using the fund manager education and tenure.

The different investment styles used by the manager may also have a direct impact on performance. During the 1970s only the buy-&-hold strategy seemed to be justified by theoretical and empirical work (Shiller, 2003). In the 1980s, an influential challenge arose in the work of De Bondt and Thaler (1985), which claimed that a contrarian strategy would be profitable over a time period of several years this is because the average individual investor tends to follow a momentum strategy. They buy mutual funds that have performed well in the recent past as it was explained above. Thus studies showed that managers are benefiting from trading in the opposite direction. Finally, Jegadeesh and Titman (1993) and other studies led to research in the 1990s, proving the remarkable and stable profitability of momentum strategies at horizons of around six months.

Asset allocation may help the manager to generate abnormal returns thus a better performance of their funds. Elkin (1999) stated that asset allocation, rather than stock picking or market timing, is by far the most important factor that determines the returns that a portfolio would generate over time. However in this dissertation asset allocation will not be a factor to consider since only large growth mutual fund are being studied.

### Size of the Fund

There have been a lot of studies on whether fund size affects performance of mutual funds but this question is still a dilemma to investors and fund managers. The impact of size on mutual fund performance varies; it can be negative, neutral, or positive. Size affects different types of funds differently; it also affects the manager's ability to achieve objectives. The manager has to monitor size changes and make investment decisions accordingly.

A relatively large amount of assets available to a fund manager presents various economies. The expenses of most funds are reduced as a percentage of net asset value as the fund grows. Expense ratios can have a major impact on performance. However as a fund becomes larger and larger, the transaction costs may become so high that investors are reluctant to invest in the fund. Chan et al (2009) investigated the transaction costs theory by analysing the daily transactions of large and small managers and show that large managers do indeed incur higher costs than small managers. They showed evidence that fund size detracts from performance.

A larger asset base provides more liquidity to a fund. With more assets, the manager can buy more shares and more stocks. Transaction costs are reduced if higher trading volumes are achieved. A larger asset base also can reduce relative tax costs. It also usually attracts high skilled managers to the management team.

Rapid growth or a large asset base can prevent managers from taking meaningful positions in market sectors they believe will outperform others. Smaller funds are more flexible and may take advantage of opportunities or liquidate unwanted positions faster than larger funds. A large fund that owns a significant position will negatively affect a security's market price if it unloads shares all at one time. As Chen et al (2004) described it in their study; liquidity is an important reason why fund size erodes performance since that they found strong evidence that effect of fund size on fund returns is most pronounced for funds that play small cap stocks.

However Rao (2009) studied 244 equity mutual funds in India for a time period of 3 years (1st April 2006 to 1st April 2009). They found that the correlation coefficients of fund size and performance variables are not significant and also their hypothesis that "There is no conclusive evidence that the fund size affects performance of equity/growth funds, be it micro-, small-, medium- and large sized funds." was not rejected. They also pointed out that the Indian Fund Managers of Medium- and Large sized Equity/Growth Funds were unable to outperform the stock market and also did not leverage the advantage of relatively large amount of funds at their disposal.

### Age of the fund

The age of a mutual fund must also be considered before investing. Very often newly created funds have excellent short-term performance records since these funds may invest in only a small number of successful stocks, this can have a large impact on their performance. But as funds grow larger and increase the number of stocks they own, each stock has less impact on the fund's performance. This may make it more difficult to sustain initial results. Ferreira et al. (2007) study a large sample of actively managed open-end equity funds in nineteen countries and find evidence for a negative relation between fund age and abnormal performance, in particular for foreign and global funds. Moreover older funds on average benefit from a stronger brand and market position, this decreases the incentive of performing well, resulting in worse investment performance. Petersen et al. (2001) and Prather et al. (2004) report no significant difference in the performance of new and existing mutual funds.

However the effect of age on performance can also run in the other direction. Younger funds may suffer from a lack of experience and from higher costs. Blake and Timmerman (1998) who study a large sample of U.K. open-end mutual funds find weak evidence for a superior performance of new funds and report an average, risk-adjusted excess return of 0.8% over the first year.

### Expense Ratio

The expense ratio is a measure ofwhat it costs aninvestment company to operatea mutualfund. It is charged annually to shareholders of all funds. It expresses the percentage of assets deducted each fiscal year for fund expenses, including management fees, administrative fees, operating costs, and all other asset-based costs incurred by the fund.

The relation between mutual fund returns and expense ratio provides a good indicator whether it is worthwhile investing in active management since that mutual fund fees can be seen as the price that uninformed investors pay to managers to invest their money.

Ferreira et al (2009) study the determinants of mutual fund performance around the world using a new data set of 16,316 open-end actively managed domestic and international equity funds in 27 countries. They used six different benchmarks to measure performance and found a statistically significant negative relation between the expense ratio and net-of-fees performance.

Haslem et al (2008) provided extensive evidence on the performance and characteristics of 1,779 U.S. domestic, actively managed retail equity mutual funds. Their results also indicated that funds with low expense ratios outperform those with higher expense ratios.

### Management tenure

Management tenure is the length of time a mutual fund has been under the guidance of the current manager. As a result of managerial experience, managers with longer tenure could perform better than others and, consequently, investors would prefer to invest in funds run by experienced managers. Ferreira et al (2007) supported this idea, they found a significant positive relationship between management tenure and performance using a sample of 10,568 open-end actively managed equity funds from 19 countries between 1999 and 2005.

To test the effect of manager experience on the performance and characteristics of a mutual fund, Ding and Wermers (2005) sorted all funds, at the end of each calendar year, on the level of career experience of the lead manager of the fund Their resulting measures also showed that more experienced managers generate higher levels of performance than their less-seasoned counterparts, even though they manage larger funds.

However, managers that run a fund for a shorter period are usually more alert and have more incentives to perform better. Petersen et al. (2001) find that there is a an average negative return premium associated with management tenure as managers underperform two years prior to departure and they also present higher portfolio turnover and management fees. On the other hand, Chevalier and Ellison (1999) find no significant relationship between mutual funds performance and management tenure.

### Formulating the Research Objectives

The research question identifies the factors that may eventually determine the performance of mutual funds. The study focuses on the most common fund characteristics as the main determining factors.

The specific research objectives are:

- To find out if performance depends on the size of a mutual fund.
- To test whether the age of a mutual fund is a determining factor in explaining its performance.
- To identify whether funds with higher expense ratio could effectively produce a better performance than funds with a lower one.
- To determine if a manager with a longer experience can make a fund perform better or worse.
- To assess whether the relationships between fund's performance and fund's characteristics are similar when using the three different measures of performance, the Jensen Index, the Treynor Index and the Sharpe Ratio.

### The Data Sample

All the data is secondary and was obtained from the Morningstar website and the Yahoo Finance website and the respective home pages of the Asset Management Companies. These three websites provide information on fund performance information and fund characteristics. The data sample in this study is made up of 30 U.S. mutual funds.

In order for a mutual fund to be included in the data sample there are four requirements that the mutual fund must satisfy:

- The fund has to be classified as a large growth fund.
- The fund normally invests at least 80% of net assets in equity securities of companies that have a large market capitalization.
- The fund is 3-star rated by Morningstar.
- The fund has at least 5 yrs of return data since that a 5-year average return is being computed for the calculation of the performance measures.

These requirements are to ensure that the funds have more or less a similar risk profile and invest in a similar portfolio of assets.

### Measuring fund performance

The performances of the mutual funds are estimated using the three different risk-adjusted performance measures: the Treynor measure, the Sharpe measure and finally the Jensen measure. The three measures are being calculated for the period 09 February 2005 to 08 February 2010.

### Average return of fund

A five-year average return on each fund is calculated using daily net asset values (NAV) from 09 February 2005 through 08 February 2010 as follows:

(NAVt - NAVt-1)

NAVt-1

Where,

NAVt is the net asset value of today and

NAVt-1 is the net asset of the previous day

The daily closing prices of the funds, or their net asset values, are already adjusted for dividends therefore the returns obtained are net of dividends.

### Beta of fund

The following equation was regressed, under the graphical method with the use of excel, to find beta:

Y = a + βX

Where,

Y, the dependent variable = Daily returns of fund,

X, the independent variable = Daily returns of the market index and

β, the coefficient = Beta of the fund

### Average market return

For the purpose of this study, the Russell 1000 Growth Index has been taken as the market index since that most of the funds in the sample invest in equity securities of companies that have a market capitalisation more or less similar to the market capitalisation of companies included in the Russell 1000 Growth index. The method used to calculate the market return is the same as that used to calculate the five-year average return of the funds.

### Average return of the risk free rate

The average return of the risk free rate, Rf, was calculated using the five-year average yield on the US Three month Treasury Bill, as it is commonly used to represent the risk free rate in the US. Daily rates of the T-Bill are collected from the period 09 February 2005 to 08 February 2010 and then an average is done to obtain the five-year average yield.

### Standard Deviation of fund

While beta compares a fund's returns with a benchmark, standard deviation measures how much the return on the fund is deviating from the expected normal returns. A large standard deviation supposedly shows a more risky fund than a smaller one. In this study, standard deviation is being computed for the calculation of the Sharpe ratio. It is calculated on spreadsheet using daily returns of the five year period, the daily results are then annualised using the following equation:

σ × √252

Where,

σ = Standard deviation of daily returns

The annualised standard deviation obtained is called volatility of return.

### The Treynor measure

The Treynor index or Treynor ratio, also referred to as the reward-to-volatility ratio, is an investment measurement index that indicates how much an investment that involves some level of risk has earned over a risk-less investment per unit of market risk (given in the following calculation as the beta coefficient):

(R-Rf)/β

Where,

R = Average Return of fund,

Rf = Average return of the risk free rate and

β = Beta of the fund

The beta coefficient comprises the risk arising from the fluctuations of individual securities and the risk produced by fluctuations in the market. The Treynor index assumes a suitably diversified portfolio, as it only takes into consideration systematic risk. Unsystematic risk is not accounted for and therefore the results of a Treynor Index calculation for an undiversified portfolio are misleading. When comparing different funds, the one with the higher Treynor index has the best performance.

### The Sharpe measure

The Sharpe ratio is a measure of the excess return (or Risk Premium) per unit of risk in an investment asset. It measures a ratio of return to volatility. The Sharpe ratio is calculated as follows:

(R-Rf)/σ

Where,

R = Average Return of fund,

Rf = Average return of the risk free rate and

σ = Standard deviation of the fund

The Sharpe ratio is similar to the Treynor measure with the same assumption of a diversified portfolio. The only difference is that compared to Treynor measure that accounts for systematic risk only, the Sharpe ratio takes into consideration the total risk. The greater a portfolio's Sharpe ratio, the better its risk-adjusted performance has been. A negative Sharpe ratio indicates that a risk-less asset would perform better than the security being analyzed.

### The Jensen measure

The Jensen alpha is a measure that represents the average return on a portfolio over and above that predicted by the capital asset pricing model (CAPM). It is calculated as:

R - [Rf + β*(Rm - Rf)]

Where,

R = Average Return of fund,

Rf = Average return of the risk free rate,

Rm = Average market return and

β = Beta of the fund

The Jensen measure also uses systematic risk only as the Treynor measure. The Jensen measure is analysed by its sign, a positive alpha will imply that the fund is earning excess returns over the market return, a negative one will imply that no excess return is being earned and lastly a zero figure alpha will mean a neutral performance.

### Fund characteristics

As discussed in the above literature review, many factors may drive the performance of mutual funds. However for the purpose of this dissertation only the following most common determinants have been chosen, these are namely fund age, fund size, expense ratio and management tenure. The details of these characteristics are as follows:

- Fund size is measured by total assets in US dollars and in millions as at 08 February 2010. The details were obtained from the website of Morningstar.
- Fund age is measured in years and is calculated to the nearest month. It is as from the date of the inception of the fund till 08 February 2010.
- Expense ratio is measured in percentage. The annual report of the fund and the prospectus of the fund usually display different expense ratios, however in this study, it is the one found on the prospectus that is taken into consideration.
- Management tenure is also measured in years and calculated to the nearest month. It is as from the date the current manager has started to manage any fund till 08 February 2010.

### Research approach

Two approaches will be used in this study, the first one is by using Correlation Coefficients and the second one is the Regression approach.

### Correlation coefficients approach

From the data collected and the calculations made, relevant findings are extracted. Correlation coefficients are computed to assess the degree of relationship between fund characteristics and performance. Covariance of fund characteristics and the four parameters of performance (Return, Treynor measure, Sharpe Ratio, Jensen measure) are then computed to assess how the fund characteristics and each of these parameters move together. Furthermore hypothesis testing is conducted to ascertain these relationships.

Correlation coefficients: A measure of the relation between two or more variables. Correlation coefficients can range from -1.00 to +1.00. The value of -1.00 represents a perfect negative correlation while a value of +1.00 represents a perfect positive correlation. A value of 0.00 represents a lack of correlation.

Covariance: A measure of the degree to which two variables move in tandem. A positive covariance means that they move together while a negative covariance means theymove inversely.

For the hypothesis testing, a two-tailed tests is conducted at 5% significance level with degrees of freedom n-2 (where n is the number of funds) of the Correlation coefficients, denoted by r, using the table of the 'Critical Values of the Pearson Product-Moment Correlation Coefficient'. The null hypothesis is defined as there is no relationship (r=0) and the alternate hypothesis is defined as there is relationship (r?0). If r is greater than the critical value of r in the table, then the null hypothesis is rejected.

### Relationship of fund size with performance

The correlation coefficients and the covariance between funds size and the four parameters of performance of the 30 funds are computed and then the following hypothesis is tested:

Null Hypothesis: There is no relationship between Fund Size and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Fund Size and Performance of Funds (r ≠ 0)

Afterwards the 30 large growth mutual funds are classified as follows:

Small sized funds: Funds with total assets between $30 millions and $150 millions.

Medium sized funds: Funds with total assets between $151 millions and $550 millions.

Large sized funds: Funds with total assets of more than $550 millions.

For each of the three different classifications, correlation coefficients and covariance are again computed and hypotheses are tested.

### Relationship of fund age with performance

To detect any relationship between the 30 funds' age and their four performances parameters, correlation coefficients and covariance are measured and this hypothesis is tested:

Null Hypothesis: There is no relationship between Fund Age and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Fund Age and Performance of Funds (r ≠ 0)

To assess how funds in different age groups may affect performance, the 30 mutual funds are further classified as follows:

Young age funds: Funds aged between 2 years old and 7.5 years old.

Middle age funds: Funds aged between 7.51 years old and 12.5 years old.

Old age funds: Funds aged above 12.5 years old.

The correlation coefficients obtained are then tested for the three age groups.

### Relationship of expense ratio with performance

Firstly, the correlation coefficients and the covariance between expense ratio of the sample of the 30 mutual funds and their performance measures are obtained and then the following hypothesis is tested:

Null Hypothesis: There is no relationship between Expense Ratio and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Expense Ratio and Performance of Funds (r ≠ 0)

Secondly the funds are classified as follows:

Low expense ratio funds: Funds with expense ratio between 0.25% and 1.05%

Moderate expense ratio funds: Funds with expense ratio between 1.06% and 1.25%

High expense ratio funds: Funds with expense ratio above 1.25%

Then finally hypotheses of the correlation coefficients of each of the three classifications are tested.

### Relationship of management tenure with performance

For the last characteristic studied, the same method is used as before, correlation coefficients and covariance are found for the 30 funds and then tested as follows:

Null Hypothesis: There is no relationship between Management Tenure and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Management Tenure and Performance of Funds (r ≠ 0)

The 30 funds are then classified as follows:

Low management tenure funds: Funds managed by a manager having tenure between 0.5 years to 4.05 years

Moderate management tenure funds: Funds managed by a manager having tenure between 4.06 years to 6.25

High management tenure funds: Funds managed by a manager having tenure above 6.25 years

### Regression Approach

The next step consists of testing whether the four fund characteristics affect performance through the regression approach. While correlation gives an estimate of the degree of association between the variables, regression attempts to describe the dependence of a variable on one (or more) explanatory variables; it implicitly assumes that there is a one-way causal effect from the explanatory variable(s) to the explained variable, regardless of whether the path of effect is direct or indirect. To determine to what extent fund performance is related to fund characteristics, the three performance measures calculated above are regressed on the fund characteristics variables in the following three regressions:

First regression:

treyi = β0 + β1log_sizei + β2log_agei + β3expi + β4log_mgti + βi

Second regression:

shari = β0 + β1log_sizei + β2log_agei + β3expi + β4log_mgti + βi

Third regression:

jensi = β0 + β1log_sizei + β2log_agei + β3expi + β4log_mgti + βi

Where,

treyi = Treynor measures of the thirty funds

shari = Sharpe measures of the funds

jensi = Jensen measures of the funds

log_sizei = log of the sizes of the funds

log_agei = log of the ages of the funds

expi = expense ratios of the funds

log_mgti = log of number of years of management tenure of the funds

εi = error terms

### Performance of mutual funds

The performance measures and the fund characteristics statistics summary for the sample of the 30 large growth funds over a 5 year period are given below:

As it can be observed from the table, the four performance parameters (Average return, Treynor index, Sharpe index and Jensen index) are not indicating that funds have well performed during the past five years. This is because of the financial crisis that took place in 2008; the US was amongst the countries that were the most affected by the crisis. Because of the effect of the financial crisis, funds' average annual returns were negative and as such all the three performance measures. Moreover, it must be noted that over the 5 year period the average return of the risk free rate and the average return of the market were 2.7071% and 2.1337% respectively.

### Analysis of the effect of fund characteristics on performance

In this part of analysis, each of the fund characteristics, fund size, fund age, expense ratio and management tenure, will be studied to find if they have any relationship with performance. For that purpose correlation coefficient, covariance and hypothesis testing will be used.

### Analysis of Fund size

Correlation coefficients and covariances of the 30 sampled funds:

It is observed from Table 2 that the Correlation Coefficients of Return (R), Sharpe index (s), Treynor index (t) and Jensen index (j) with Fund size (S) are not significant for the sample of the 30 funds implying that the Fund size does not affect fund performance significantly. However, the Covariances (a measure of how much two variables change together) of fund size with return; fund size with Jensen index and fund size with Treynor index are positive indicating that the fund size and these three performance variables moved in the same direction, while the opposite has been observed in the case of Covariance of Fund size with Sharpe index (due to negative covariance) implying that if the fund size increases fund performance would go down in terms of total risk (since that the Sharpe index takes into account total risk).

### Analysis of Small sized funds

Details of fund size and of the performance of small sized funds are given below:

Correlation coefficients and Covariances:

The correlation coefficients in the above table are very low and insignificant. Regarding the covariances, only the Sharpe ratio indicates that fund size move in opposite directions with performance of small sized funds.

### Analysis of Medium sized funds

The summary statistics of the performance of medium sized funds are as follows:

Correlation coefficients and Covariances:

The four correlation coefficients above indicate moderate positive relationships between fund size and performance of medium sized funds. The covariances also show the same. This implies that as fund size increases performance of medium sized funds will tend to increase also.

### Large sized funds:

The details of the 10 funds classified as large sized funds are given below:

Correlation coefficients and Covariances:

Very low negative relationships can be detected between fund size and performance when analysing the above correlation coefficients and covariances.

### Hypothesis Testing

Null Hypothesis: There is no relationship between Fund Size and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Fund Size and Performance of Funds (r ≠ 0)

For the thirty sampled funds:

At 5% significance level (Alpha=0.05), degrees of freedom 28 (n-2, where n= No. of Funds), and 2-tailed test, referring to the Critical Values of the Pearson Product-Moment Correlation Coefficient Table in appendix I, the critical value of r (correlation coefficient) is found to be 0.361. Since that the correlation coefficients in Table 2 do not fall in the rejection region we do not reject Null Hypothesis. Therefore it is concluded that there is no relationship between fund size and fund performance.

For the three classifications under fund size:

Two-tailed tests, at 5% significance level and degrees of freedom 8 (n-2, where n=No. of funds), were conducted for each of the three classifications under fund size, namely small sized funds, medium sized funds and large sized funds. The critical value of r is found to be 0.632. Since that the correlation coefficients in Table 4, Table 6 and Table 8 do not fall in the rejection criteria the null hypotheses are not rejected for the three tests and it is concluded that fund size does not affect performance of small sized funds, medium sized funds and large sized funds.

### Conclusion

According to the hypothesis tests, fund size is not a determining factor of performance. No relationships are found between fund size and performance neither for the 30 sampled large growth funds nor for the three different classifications of the funds.

### Analysis of Fund age

Correlation coefficients and covariances of the 30 sampled funds:

The correlation coefficients of Return, the Treynor index, the Sharpe index and the Jensen index with Fund age (A) for the sample of the 30 funds demonstrate moderate positive relationships meaning that older funds tend to perform better than younger ones. The covariances of fund age with the performance parameters indicate that fund age and performance move in the same direction.

### Analysis of Young aged funds

The following table give the summary statistics about the performance parameters of young aged funds:

Correlation coefficients and covariances:

The four correlation coefficients indicate that fund age has a positive relationship with performance of young aged funds. The older funds tend to perform better than the younger ones in the classification of young aged funds. As far as covariances are concerned, all the performance parameters seem to move in the same direction as fund age of young aged funds.

### Analysis of Middle aged funds

Performance measures of middle aged funds:

Correlation coefficients and covariances:

When analysing the correlation coefficients, low negative relationships are found between middle aged funds' performance and fund age. The covariances also confirm this opposite movement.

### Analysis of Old aged funds

The details of the performance measures of old aged funds are presented in table below:

Correlation coefficients and covariances:

The above correlation coefficients are found to be low and insignificant and the covariances are positive indicating that age and performance move in the same direction for old aged funds. However the covariances are also very low.

### Hypothesis testing

Null Hypothesis: There is no relationship between Fund Age and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Fund Age and Performance of Funds (r ≠ 0)

For the thirty sampled funds:

A two-tailed test at 5% significance level (Alpha=0.05), degrees of freedom 28 (n-2, where n= No. of Funds), the critical value of r is found to be 0.361 according to the Critical Values of the Pearson Product-Moment Correlation Coefficient Table in appendix I. Since that all the four correlation coefficients in Table 9 are greater than the critical value of r, they fall in the rejection region. Therefore the Null Hypothesis is rejected and it is concluded that a relationship does exist between fund size and fund performance.

For the three classifications under fund age:

Two-tailed tests, at 5% significance level and degrees of freedom 8 (n-2, where n=No. of funds), were conducted for each of the three classifications under fund age. The critical value of r is found to be 0.632. Since that the correlation coefficients in Table 11, Table 13 and Table 15 do not fall in the rejection criteria the null hypotheses are not rejected for the three tests and it is concluded that fund age does not affect performance of small sized funds, medium sized funds and large sized funds.

### Conclusion

The results above give evidence that a positive relationship does exist between fund age and performance of the 30 sampled funds. However, when analyzing the results of young aged, middle aged and old aged funds, no evidence is found of any relationship between age and performance.

### Analysis of Expense ratio

Correlation coefficients and covariances of the 30 sampled funds:

The correlation coefficients of Return, the Treynor index, the Sharpe index and the Jensen index with Expense ratio (E) report that funds with high expense ratios perform better than funds with lower expense ratios, however the relationships found are low. Regarding the covariances, they are almost zero but still they are positive, this indicates that expense ratio move in the same direction as performance.

### Analysis of Low Expense ratio funds

Details of the performance measures of low expense ratio funds are as follows:

Correlation coefficients and covariances:

As it can be observed, a high positive relationship is found between expense ratio and performance of low expense ratio funds since that all the correlation coefficients between the four performance measures and expense ratio are above 0.7. However the covariances are near to zero, but they are positive, this means that performance of low expense ratio funds and expense ratio move in the same direction.

### Analysis of Moderate Expense ratio funds

The summary statistics of the performance of moderate expense ratio funds are as follows:

Correlation coefficients and covariances:

The correlation coefficients and covariances above are indicating very low and insignificant relationship between expense ratio and performance of moderate expense ratio funds.

### Analysis of High Expense ratio funds

Performance measures of high expense ratio funds:

Correlation coefficients and covariances:

The four correlation coefficients are around -0.5; this indicates that expense ratio has a negative relationship with performance of high expense ratio funds. Funds with lower expense ratios tend to perform better than funds with higher ones in the classification of high expense ratio funds. As far as covariances are concerned, all the performance parameters seem to move in the opposite direction as expense ratio.

### Hypothesis testing

Null Hypothesis: There is no relationship between Expense ratio and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Expense Ratio and Performance of Funds (r ≠ 0)

For the thirty sampled funds:

Referring to the table in appendix I, a critical value of 0.361 is obtained for r, for the two-tailed test at 5% siginificance level and degrees of freedom 28 (n-2, where n=No. of funds). Since that all the correlation coefficients in Table 16 do not fall in the rejection criteria, the null hypothesis is not rejected meaning that no relationship exists between expense ratio and performance.

For the three classifications under expense ratio:

Two-tailed tests, at 5% significance level and degrees of freedom 8 (n-2, where n=No. of funds), were conducted for each of the three classifications under fund age. The critical value of r is found to be 0.632. Only the correlation coefficients In Table 18 of expense ratio of low expense ratio funds with performance measures fall in the rejection criteria. For moderate expense ratio funds and high expense ratio funds, the null hypothesis was not rejected since correlation coefficients in Table 20 and Table 22 were less than the critical value of r.

### Conclusion

As it is concluded above for the 30 large growth funds, performance and expense ratio are not related, there is no significant difference in the performance of a fund with a high expense ratio and fund with a low expense ratio.

However as far as the three classifications are concerned, the results are different, no relationships are found between expense ratio and performance of moderate expense ratio and high expense ratio funds whereas a positive relationship is found between expense ratio and performance of low expense ratio funds.

### Analysis of Management tenure

Correlation coefficients and covariances of the 30 sampled funds:

It is observed from the above Table that the Correlation Coefficients of Return, Sharpe index, Treynor index and Jensen index with Management tenure (M) are not significant for the sample of the 30 funds implying that the Management tenure does not affect fund performance significantly. However, the four Covariances are positive indicating that management tenure and these four performance variables moved in the same direction.

### Analysis of Low Management tenure Funds

Performance measures of low management tenure funds are as follows:

Correlation coefficients and covariances:

The correlation coefficients above indicate a low positive relationship between management tenure and performance of low management tenure funds and the positive covariances indicate that management tenure and performance of low management tenure funds move in the same direction.

### Analysis of Moderate Management tenure Funds

The statistics of the performance parameters of moderate management tenure funds are presented in the table below:

Correlation coefficients and covariances:

The correlation coefficients of management tenure with the four performance parameters all indicate low negative relationships for the moderate management tenure funds. The covariances also demonstrate that management tenure and performance of moderate management tenure funds move in opposite directions.

### Analysis of High Management tenure Funds

The performance parameters details of the 10 funds classified as high management tenure funds are as follows:

Correlation coefficients and covariances:

According to the above results, we can observe that management tenure has a negative impact on high management tenure funds. The covariances also indicate the opposite movement between management tenure and performance of high management tenure funds.

### Hypothesis testing

Null Hypothesis: There is no relationship between Management tenure and Performance of Funds (r=0)

Alternate Hypothesis: There is relationship between Management tenure and Performance of Funds (r ≠ 0)

For the thirty sampled funds:

At 5% significance level, degrees of freedom 28 (n-2, where n= No. of Funds), and 2-tailed test, the critical value of r is found to be 0.361 (refer to table in appendix I). Since that all the four correlation coefficients in Table 23 do not fall in the rejection region we do not reject Null Hypothesis. Therefore it is concluded that there is no relationship between management tenure and fund performance.

For the three classifications under management tenure:

Two-tailed tests, at 5% significance level and degrees of freedom 8 (n-2, where n=No. of funds), were conducted for each of the three classifications under fund age. The critical value of r is found to be 0.632. Since that the correlation coefficients in Table 25, Table 27 and Table 29 do not fall in the rejection criteria the null hypotheses are not rejected for the three tests and it is concluded that fund age does not affect performance of low management tenure funds, moderate management funds and high management tenure funds.

### Conclusion

According to the above hypothesis testing, management tenure does not affect performance at all. And this is also the case for low management tenure, moderate management tenure and high management tenure funds. This implies that the experience of the manager managing a fund does impact on the fund performance.

### Regression analysis

The second approach used is the regression analysis where it will be investigated whether the four fund characteristics are driving factors of fund performance.

After running the first regression, using the Treynor measure as performance measure, the following output is generated:

The results of the second regression, using the Sharpe measure as performance measure:

The results of the third regression, using the Jensen measure as performance measure:

Testing the overall significance of the model:

The F-test is used to test whether the model as a whole is significant.

Null hypothesis: β1=β2=β3=β4=0

Alternate hypothesis: β1≠β2≠β3≠β4≠0

For the first regression:

F = 3.37; p-value = 0.024 <0.05

For the second regression:

F = 3.26; p-value = 0.028 <0.05

For the third regression:

F = 3.03; p-value = 0.037 <0.05

Using 5% significance level, the null hypothesis is rejected since that the p-values for the three models are less than 0.05. It can be concluded that the three models are significant at the 5% significance level.

In addition to the F-test, the adjusted R-squared, which measures the proportion of the variation in the dependent variable accounted for by the explanatory variables, can also be used to look at the overall significance of the model. Adjusted R-squared lies between 0 and 1; an adjusted R-squared of 1.0 indicates that the regression line perfectly fits the data. The adjusted R-squared for the three models are 0.2466, 0.2379 and 0.2185 respectively. It can be observed that these values are not so near to 1. However this does not mean that the regressions poorly fit the data since that the data used in this study is cross sectional data and for this type of data, it is very unusual to obtain high adjusted R-squared. Values of adjusted R-squared around 0.2 to 0.3 can be considered as satisfactory.

### Testing the significance of beta

The beta coefficient represents the estimated average change in standard deviation units. The significance of the betas of the variables is tested, using a two tailed t-test at 5% significance level, as follows:

Null hypothesis: βi = 0

Alternate hypothesis: βi ≠ 0

For the first regression:

β1: p=0.128 >0.05

β2: p=0.003 <0.05

β3: p=0.679 >0.05

β4: p=0.498 >0.05

For the second regression:

β1: p=0.118 >0.05

β2: p=0.003 <0.05

β3: p=0.780 >0.05

β4: p=0.532 >0.05

For the third regression:

β1: p=0.181 >0.05

β2: p=0.005 <0.05

β3: p=0.670 >0.05

β4: p=0.501 >0.05

For the three regressions, at 5% significance level, the null hypothesis is accepted for the variables fund size, expense ratio and management tenure. This means that the beta coefficient of these variables is statistically insignificant in explaining the relationship between these variables and performance.

However, the beta coefficient of the variable fund age is statistically significant since at 5% significance level, the null hypothesis is rejected for the three models.

### Testing for normality of residuals

Many researchers believe that multiple regression requires normality. This is not the case. Normality of residuals is only required for valid hypothesis testing, that is, the normality assumption assures that the p-values for the t-tests and F-test will be valid. Normality is not required in order to obtain unbiased estimates of the regression coefficients. OLS regression merely requires that the residuals (errors) be identically and independently distributed. Furthermore, there is no assumption or requirement that the predictor variables be normally distributed. Below the kdensity command is used to produce a kernel density plot with the normal option requesting that a normal density be overlaid on the plot:

### Testing for heteroskedasticity

One important assumption of the regression is that the equal variance of the error terms. When the variance of the errors is different, varying depending on the value of one or more of the independent variables, the error terms are heteroskedastic.

Heteroskedasticity has serious consequences for the OLS estimator. Although the OLS estimator remains unbiased, the estimated standard error is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. To test for heteroskedasticity, the White's General Test for Heteroskedasticity is used and the resuts are shown below:

### Null hypothesis: homoskedasticity

Alternate Hypothesis: unrestricted heteroskedasticity

For the first regression:

chi2 (14) = 11.30

Prob > chi2 = 0.6622

For the second regression:

chi2 (14) = 10.00

Prob > chi2 = 0.7624

For the third regression:

chi2 (14) = 9.54

Prob > chi2 = 0.7948

Since that the p-values are greater than 0.05, under 5% significance level, the null hypothesis is accepted and the presence of homoscedasticity in the three models can be concluded.

### Testing for multicollinearity

Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated. In this situation the coefficient estimates may change erratically in response to small changes in the model or the data. Multicollinearity does not reduce the predictive power or reliability of the model as a whole; it only affects calculations regarding individual predictors. To test for multicollinearity, the VIF and tolerance statistics are estimated and is presented below:

A VIF of less than ten shows that multicollinearity is not a cause of concern in a model. The VIF for the four variables is less than ten therefore it can be concluded that there is no multicollinearity in the three models.

### Interpretation of results

According to the results above, it is found that only fund age has a relationship with fund performance, the other three variables do not have any relationship with fund performance. Moreover the three performance measures used in the three regressions give rather the same results. It is also interesting to note that the results obtained from the regression analysis confirm the findings of the first approach that is Correlation coefficients and Covariances.

Israelsen (1998) and Liljeblom and Loflund (2000) found that large funds tend to perform better than smaller funds. However in this study, no relationship is found between fund size and performance. As fund size increases, the manager is presented with a significantly large amount of cash. The risk that arises in this situation is how to invest that cash, some managers may purchase additional instruments that are profitable to the fund. Therefore size does not really matter, most importantly is how the assets under management were placed, that is which stocks the manager has invested in and in which company he has invested in. As Rao (2009) pointed out that the Indian Fund Managers of Medium- and Large sized Equity/Growth Funds did not leverage the advantage of relatively large amount of funds at their disposal. This could explain the lack of any link between size and performance.

A significant positive relationship is found between fund age and performance in this study. Ferreira et al. (2007) found that newer funds tend to perform better than older ones, however it should be noted that these findings were mostly on a short term basis that is young funds usually perform well during their first years from their inception, this performance does not persist on a long term basis. In this study, only funds above five years old are considered this might be a possible reason for the positive relationship. Moreover older funds tend to have more experience and have less transaction costs compared to young funds. Blake and Timmerman (1998) also found weak evidence for a superior performance of new funds.

Ferreira et al (2009) and Haslem et al (2008) found that funds with low expense ratios outperform those with higher expense ratios. But this is usually the case when different types of funds are being studied. In this case, only large growth mutual funds are being studied therefore there are not large differences in the expense ratios of the thirty funds under observation, which might explain the insignificant relationship between expense ratio and fund performance. Moreover expense ratios can be important when analysing funds that require high active management, it will help to determine how well the fund is performing according to the fees he is charging for the funds. Thus in the case of large growth funds, no high active management is needed, the fund manager only has to invest in large market capitalisation companies.

A highly experienced manager is expected to have very good investment abilities, thus a positive relationship is usually expected between management tenure and fund performance, however, in this study, no relationship was found. Chevalier and Ellison (1999) also did not found any significant relationship between mutual funds performance and management tenure. A possible reason is that the experience of the manager does not really matter nowadays. The education and the age of the manager are also important factors of fund performance. Another important factor might be management change, though a manager may have a long tenure in managing funds, when he switches funds, that is, he leaves one fund to start managing another he may not be able to produce the same high returns.

### Findings

This study examines the relationship of fund characteristics and fund performance. Since mutual fund investing has become a much more popular choice for investors, it would certainly be of interest for investors to know how fund performance relates to fund's fundamental characteristics such as fund size, fund age, expense ratio and management tenure. Using daily returns for a sample of thirty large growth mutual funds from 09 February 2005 through 08 February 2010, this paper uses the Treynor measure, the Sharpe measure and the Jensen measure as performance measures of the funds. The estimated performance measures are then used in three different cross-sectional regressions performance on fund characteristics variables.

The results indicate that funds' performance measures are not significantly related to fund size. A fund may be large or small, but if the fund has invested in successful stocks, the fund will perform well. However, there is evidence that the fund age is positively and significantly linked to fund performance, suggesting that as funds grow older, they tend to become more efficient in their operations. Presumably younger funds are usually faced with high transactions which may hinder performance. This paper finds no significant relation between performance and expense ratio. However it must be noted that only one type of fund is considered in this study therefore there are not big differences in the expense ratios of the funds. There is also no evidence that management tenure is related to funds' performance. The most probable reason is that performance of mutual funds depends on all the characteristics of the manager such as education, age, etc and not only on his experience.

### Limitations and recommendations

- The data sample has been taken in the US rather than in Mauritius due to the lack in the number of funds in Mauritius. A minimum of thirty funds were needed for the regression approach and there is less than thirty funds in Mauritius. Also the sample consisted of large growth funds only, further research can be done using other types of funds.
- Data was collected in the period 2005 to 2010. Therefore the financial crisis of 2008 to early 2009 forms part of this period. It should be noted that the financial crisis had a big effect on US and the fund's return were negative during the financial crisis. The results may be distorted because of this.
- There are other fund characteristics that have not been considered in this study due to lack of information and to the limit of number of words. Therefore these characteristics can be included in further research.