Efficient Market Hypothesis

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Methodology & Applied Method

The following chapter presents the methods chosen and the different stages for developing the research strategy, how to use the data collected and a discussion regarding problems and weaknesses that can be identified with the chosen methodology.
Methodology
The purpose of this study is to provide further information to investors regarding the two types of investments. When assembling necessary data and presenting numerical relativeness, the method and methodology is vital to be as accurate and comprehensive as possible to satisfy the purpose of the study. This methodology is characterized by how the quantitative research is done that evaluates the differences in the attached risks and performance of hedge and mutual funds (Saunders, Thornhill, & Lewis, 2016).
Theory Development
When engaging in research, the assumptions and beliefs by the researchers will have impact on the process and the interpretation of the conclusions. The research matrix developed by Saunders et al. (2016) illustrate the different problems when choosing the way, a researcher gather data and what analytical techniques that will be implemented. The first part of the matrix emphasizes the research philosophies of the researchers. There are five main philosophies that will address the characteristics of the researchers’ assumptions and beliefs in the study (Saunders et al., 2016).
The aim of this study is to compare the relative performance and attached risks to US hedge-and mutual funds. The gathered data, testing and analysis will be based on a sample of large hedge- and equity mutual funds and therefore will not provide an exact measure of what to expect from these investments. The conclusions will rather aim to provide an indication of what to expect from investing in hedge and equity mutual funds in the US to being able to evaluate the attached risks and returns so the separate investments. By excluding the fact that one measurement will provide a complete image and instead incorporating several measures will increase the relevance and comprehensiveness of the study (Kelemin & Rumens, 2008). These assumptions and beliefs about the study are therefore categorized under pragmatism.
The purpose and the conclusion of the study are connected by procedures and the methodology. How the research satisfies the purpose of the study is based on the theory development. Is the study based on a theory that is tested by already existing theories or is the study’s aim to develop a new theory through gathered data? The theory development previously mentioned is referred to as deductive and inductive, respectively. By combining induction and deduction there is a third way, abduction, which focuses on moving from applying the deductive approach and, at times applying the inductive approach. (Saunders et al., 2016). When measuring the relative performance and risks of hedge- and mutual funds in the US, a deductive approach to theory is used due to its origin from existing theory. It was vital to create an understanding of previous research to be able to measure and examine hedge and equity mutual fund performance through the application of quantitative models using historical data (Bryman, 2012). The study is based on already existing theories that enables the quantification of the attached risks and the relative performance to obtain the expected risks and returns for the evaluation of the hedge and mutual fund market. The application and usage of already existing theories facilitated the evaluation and analysis to test these theories when using up-to-date data on net asset values from the sample of hedge and mutual funds. The obtained results from integrated models were then to be compared with previous studies to evaluate the consistency in results.
When conducted the research of this study, the research design was vital to clarify how the questions are answered in the study. To satisfy the purpose of the study, it was important to clarify whether the research design is quantitative, qualitative or a mixed method. Quantitative research is the process of integrating numbers into a research. Quantitative research is commonly demonstrated graphically, in numbers or in a statistical agenda to observe connections between different variables. Qualitative research is research not expressed by including numbers and aims to expand or establish theory. Qualitative research is often expressed by conducting experiments or surveys to explain values and connections about the people participating in the study. A mixed method design is research that integrates both quantitative and qualitative attributes to either come up with new theory or to test existing (Saunders et al., 2016). When comparing hedge funds to equity mutual funds, the application of already existing theories to spot relationships emphasizes the use of a deductive approach to the study while incorporating quantitative data. The integration of historical returns of the included funds enabled the application of existing theories to assess the performance and risks attached to a specific fund category. The integration of quantification and analysis of gathered data, along with the deductive approach emphasises the quantitative strategy’s usage and application on this study.

Reliability and Validity of the Research

When conducting research, it is essential to consider the value of the research. The value of the research emphasizes the range of how reliable and valid a study is. Therefore, the value of the conducted research can be summarized into two segments, the reliability and validity. Reliability emphasises the importance of being able to consider research to be reliable, which can be verified by if the research replicates previous studies and obtains consistency in terms of the same results. If these requirements about the conducted research are being fulfilled, the research is considered reliable (Saunders et al., 2016). The application of reliability in this study is reflected in the consistency in applied methods.
The second segment supporting the value of research is validity. Validity directs the focus on how the research is being conducted, how parameters are quantified by using the suitable measures and if the obtained results and conducted analysis contains any accuracy to previous research. In this study, the validity of the measures used to assess risk and performance will be able to satisfy this part of the value and quality of the research.
In terms of the measures used to assess the risk-adjusted performance we apply the Modigliani’s M-squared measure, which differs slightly from the Sharpe ratio and is a commonly applied measure by investors. To further assess the risk-adjusted performance, the Sortino ratio is integrated to account for the downside risk. This is also a measure previously integrated in journals in the assessment of performance with respect to downside risk. When measuring the performance by hedge and equity mutual funds, the validity and reliability in terms of consistency will also be justified by integrating the Fama-French three factor model. Due to its wide application and integration in previous studies, the conclusion of the study contains an increased credibility for being interpreted as reliable. By also separating the different strategies applied by hedge funds, the replication of previous research ensures reliability and consistency to the research in this study. Therefore, the integration of previously applied procedures in this study verifies the validity, while the replication of previous comparisons in the area and outcome of the quantifications account for the reliability.
Method
Risk-Adjusted Return
Historical data concerning risk and returns are useful in financial analysis and therefore becomes natural areas of emphasis. Return on any given fund can be calculated with the net asset value and is defined as = ln(       ) − ln(        ₊₁). The returns have been calculated with continuous compounding using natural logarithms to get accurate and precise rates of returns.
To evaluate risk-adjusted performance, the commonly applied Sharpe ratio is integrated. The integration of additional measures gave the performance evaluation increased accuracy and strength. Risk-adjusted performance measures used independently, can be, as illustrated by McLeod and van Vuuren (2004) and Lo (2002), hard to interpret and give inaccurate results. By integrating the Sharpe ratio, along with M-squared and the Sortino ratio, the results of the performance measures gave a broader picture allowing for a righteous and comprehensive performance evaluation. By applying multiple measures, the possibility of applying these to each asset class and strategy and foreseeing differences among the investment vehicles is given to derive relative performance. Integrating the M-squared measure allowed for a more straightforward interpretation of the risk-adjusted performance. The M-squared, expressed in percentage terms, provides the most justifiable return adjusted for risk to be used for any given financial asset, as stressed by Scholz and Wilkens (2005).
Additionally, the Sortino ratio was applied to evaluate performance as it only focuses on downside risk i.e. when deviation falls below the rate of risk-free interest. This measure helps to evaluate risk-adjusted performance of the included funds, with only bearing downside risk in mind and acknowledging standard deviation not only as something negative. When applying these measures, the risk-free rate was integrated to quantify the return that is risk-bearing. The measures are calculated on an annual basis to identify fluctuations in the risk-adjusted performance of all funds. In calculating performance measures annually, the risk-free rate was signified by the one-year US Governmental bond as counterpart to the one-year performance measurements. The risk-adjusted performance was also measured for the entire ten-year period, which accounted for a different risk-free interest rate equivalent to 2.41 per cent, signified by the ten-year US Governmental bond (Bloomberg, 2017).
The standard deviation generated monthly from the NAVs was annualized by calculating the standard deviation over each year respectively, multiplied by the square root of 12.
When obtaining annual returns to provide an accurate return for each year for all fund categories, with the respect to changes in value, the accumulated return for each year was used. The accumulated return was obtained by dividing the end value of each year by the beginning value minus one. The return of each year illustrated the actual return for each fund category and better portray the risk-adjusted performance over the period. The risk-adjusted performance was also calculated for the entire period by taking the end value of the ten-year period and divide with the beginning value. The standard deviation for each fund category was also calculated over the entire ten-year period, to measure the performance over the longer time horizon, by multiplying with the monthly number of observations equal to 119.
The Sharpe ratio was calculated for all fund categories annually by taking the accumulated return subtracting the risk-free rate and dividing by the standard deviation for each year. The same principle was used for the measures signifying the entire period with the difference in using the accumulated ten-year return, subtracting the ten-year risk free rate, divided by the ten-year standard deviation. The applied formula for the Sharpe ratio is illustrated in equation 1.
The M-squared ratio was calculated on an annual basis with accumulated returns and standard deviation for respective periods. Integrating the S&P 500 enabled the comparison of hedge and equity mutual funds by using an equivalent deviation as a common denominator to measure what return to be expected if hedge and equity mutual funds possessed the deviation of the benchmark index. The M-squared was calculated annually by applying the risk premium multiplied with the ratio of the market standard deviation divided with the standard deviation of fund category , lastly adding the risk-free rate. The applied formula for the M-squared measure is illustrated in equation 2.
The Sortino ratio integrates the downside deviation to only consider the volatility that is viewed as harmful. The risk-free rate of a one-year US governmental Bond was applied as the minimum acceptable return and the deviation below this level was deemed downside deviation. The accumulated return for each fund category and its standard deviation below the monthly risk-free rate was applied to obtain the risk-adjusted return to harmful volatility.
The accumulated return subtracting the risk-free rate for each year was divided with the downside deviation for each year respectively. The measure was also calculated for the entire ten-year period by applying the same principles. The formula applied is demonstrated in equation 3.

Quantifying Alpha Through Multi-Factor Models

To be consistent with previous research, it has been determined that the use of the Fama-French three-factor model fits best in explaining and measuring excess returns. The foremost reason being the ten-year period applied in this study. The indications of persistence in returns found by Grinblat and Titman (1992) are weak and determines that, when evaluating funds over a longer period, the explanatory power of using a momentum factor arguably does not contribute. Additionally, the argument for using the three-factor model strengthens with Grinblat and Titman (1992) attributing the indications of persistence in funds returns not to momentum, but to the information strength of historical data and individually successful stock picking. An implication highly vital when considering hedge funds is the fact that such funds apply more flexible strategies and thus making short-term investments a greater emphasis in the asset allocation. Arguably, in such an environment, a momentum factor is of less relevance (National Association of Pension Funds, 2005).
The variable − is defined as the excess return of the market derived from a value weight portfolio consisting of all firms noted on the New York stock exchange (NYSE), NASDAQ or AMEX subtracting the risk-free interest rate defined by the one month Treasury bill rate. To make estimations on the size variable and book-to-market variable used, a combination of six portfolios based on size and book-to-market ratios were constructed for all stocks noted on the NYSE, NASDAQ or AMEX. Firstly, individual stocks were split into two groups, divided at the median in terms of market equity. The group clustered below the median consists of the returns for all stocks with smaller market equity values and firms above the median high market equity. These two groups are subsequently split depending on book-to-market ratio separated at the 70^th and 30^th percentile. Firms above the 70^th percentile are denoted small value or big value, depending on the individual firms’ market equity measure, firms between the two percentiles denoted small neutral or big neutral and firms below the 30^th percentile are denoted small growth or big growth. The six portfolios were subsequently created as: small value stocks, small neutral stocks, small growth stocks, big value stocks, big neutral stocks and big growth stocks. The portfolio constructing is illustrated in figure 4.2a.

1. Introduction 
1.1 Background
1.2 Problem Discussion
1.3 Purpose
2 Theoretical Framework
2.1 Mutual Funds
2.2 Hedge Funds
2.3 Efficient Market Hypothesis
2.4 Previous Research
2.5 Expected Rate of Return
2.6 Risk-Adjusted Return
2.7 Hedge Fund Strategies
2.8 Survivorship Bias .
3 Data
4 Methodology & Applied Method 
4.1 Methodology .
4.2 Method
5 Empirical Results 
5.1 Fund Performance by Category
5.2 Risk-Adjusted Return
5.3 Multi-Factor Model Regression
6 Analysis
6.1 Fund Performance by Category
6.2 Risk-Adjusted Return
6.3 Alpha by Fund Category
7 Conclusion
8 Discussion 
References
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Actively Managed Investments A comparison of US hedge and equity mutual funds