Hedge funds as portfolio supplements for German pension funds

¶ … Performance Evaluation of How Hedge Funds Can Be Used to Augment the Overall Efficiency in German Pension Funds

Much attention has been given to hedge funds over the last few years, but the industry itself remains to a large degree, opaque. A lack of clarity and understanding of how these funds work, what they do, and how they can be used in conjunction with other kinds of funds is at the forefront of the knowledge and beliefs of most people when it comes to these funds.

High and unseen risks are involved when investing in these vehicles. However, the returns generated have attracted the attention of a growing number of institutional investors, including those who work with pension funds. Past studies have suggested that investments in these risky vehicles can improve the return expectation of a portfolio.

For pension funds, the results have shown that even small investments in hedge funds can generate a more efficient portfolio, but the numbers of hedge funds that fail each year is high. In the current financial crisis, the growth trend in the hedge fund industry has halted and is now showing signs of decline. This puts into question whether investing in hedge funds really is a wise decision. Some investments will bear fruit whilst others will have to be written off as losses.

This study looks at pension funds and how hedge funds can be used in order to augment and supplement their efficiency. Whether this can be done is a topic for debate, because hedge funds have not performed as well in recent years as they did in the past. In addition, they can be confusing and hard to understand for a lot of people, so many individuals are not comfortable using them as an investment vehicle.

The objective of the study is to look carefully at hedge funds and how they work, as well as pension funds and how they work, in order to determine whether they are actually a good fit for one another.

In order to do this, data will be analyzed that will show the performance of both of these vehicles and explain their inner workings more carefully. From that data, both quantitative and qualitative information can be collected and conclusions can be drawn.

TABLE OF CONTENTS

iiiABSTRACT

vLIST OF ILLUSTRATIONS

1 CHAPTER ONE: INTRODUCTION

Statement of the Problem

Problem Driver

Importance of the Study

Hypothesis

Objectives

Rationale for the Study

Methodology and Overview

10 CHAPTER TWO: REVIEW OF LITERATURE

What are Pension Plans?

What are Pension Funds?

What are Hedge Funds?

Using Hedge funds in pension funds

Investment Risk

Pension Funds, Hedge Funds, and Risk Management

Type and Number of Assets

Management Risk

Hedge Fund Databases

46 CHAPTER THREE -- RETURN AND RISK MEASUREMENT METHODS

Measuring Returns

Modern Portfolio Theory

Standard Deviation / Variance

Coefficient of Variation

Sharpe Ratio

Volatility Attribution Model

Marginal Contribution to Volatility

Inclusion of New Assets in a Portfolio

57 CHAPTER FOUR: EMPIRICAL ANALYSIS

Types of Pension Funds

Types of Hedge Funds

Method

63 CHAPTER FIVE: CONCLUSION

Findings

Limitations

Conclusion

Suggestions for Future Research

72 BIBLIOGRAPHICAL REFERENCES

80 APPENDICES

Table 2.1 The use of leverage by the different hedge fund styles as of December 2001

3

Table 5.1 Preliminary Calculations

69

Table 5.2 Sharpe ratio and 1 / Coefficient of Variation comparison

71

LIST OF ILLUSTRATIONS

Figure 2.1.1

The master / feeder structure

39

Figure 2.2

Security market line (SML)

44

Figure 3.1

Removing unsystematic risks through diversification

54

CHAPTER ONE: INTRODUCTION

Statement of the Problem

The issue of hedge funds is one that has been misunderstood for many years. There are individuals that study these funds and discuss how significant they are for investing, and there are others that see them as some kind of risky endeavor that is really not important enough to focus on or that should be avoided. Both of these are valid points-of-view but, in recent years, it has generally been accepted that hedge funds are growing in popularity, and that the study of them is important, especially when it comes to considering them as investment vehicles that tie into pension funds. For a study such as this one, it is important to discuss hedge funds, but it is more important to look at how hedge funds affect pension plans and whether they are a good or bad investment vehicle. To that end, both hedge funds and pension funds must be discussed and understood well.

There has been dramatic growth in hedge funds over the last ten years. This growth is shown both in terms of assets under management and in the number of funds. The assets under management in hedge funds have grown from U.S.$40 billion in 1990 to U.S.$600 billion in 2003 (Schachter, 2004) to over U.S.$2.65 trillion as of April 2008, according to Hedge Fund Intelligence (2008). The numbers of hedge funds that currently exist, however, is difficult to obtain. In 2003, industry reports estimated that there were around 6,000 hedge funds worldwide. Both Schlachter (2004) and Lhabitant (2004) concurred with those figures. According to Hamilton (2008), there were 10,000 registered hedge funds in the Cayman Islands alone as of June 2008.

Over the last few years the growth of hedge funds has been dramatic, and the hedge fund industry has experienced a number of changes as the motives to invest in these vehicles have evolved over time. In the 1990s, according to Borla and Masetti (2003), money managers from big institutions defected to the world of hedge funds in pursuit of an ostentatious life style. They invested a large portion of their own financial wealth into their own funds in the hopes of generating a high return by finding niches to generate so called 'absolute returns' while limiting their portfolio risk. The effectiveness of these processes however is questionable due to the opacity of the hedge fund industry.

As hedge funds invest in a vast array of different instruments which include securities, options, futures, and other derivative instruments, standards for risk and return measurement have yet to be defined. Furthermore, the existing hedge fund databases are affected to a greater or lesser degree by several biases and inaccuracies. This raises the question of whether hedge funds are suitable investment vehicles for pension funds, or whether they subject the pension fund owners to too much risk.

Problem Driver

The issue driving this study is to not only show the seriousness of the problem in question, but to come up with ideas that will help to show how this problem can be reduced in size. The best way to do this is to first analyze the problem to determine just how serious it actually is, and then use that seriousness as a wake-up call for those who have been looking the other way and avoiding dealing with the issue. Many pension fund managers are believed to have done this because they want to ensure that they get good commissions, but when they do not fully inform their clients about hedge funds it can end up being detrimental to all of the parties involved.

Hedge funds are relatively unregulated, as they are typically structured in such a way to benefit from the majority of regulatory exemptions. This allows those who work with hedge funds to pursue broad investment policies and encompass a wide variety of asset classes, with no strict limits on leverage, shorting, and the use of derivatives. The financial regulations set in place for other types of institutional markets essentially pursue three objectives:

To protect the investors from abuse and default through licensing / registration, minimum disclosure requirements and increased transparency.

To reduce systemic risks while ensuring soundness and integrity of the financial system by imposing capital adequacy and margin requirements.

To ensure market price stability though position limits / trade practice restrictions (Lhabitant, 2002).

Only a few advanced countries, such as the U.S. And Europe, have basic regulations for hedge funds. These regulations encompass aspects such as which investors are allowed to invest in hedge funds and the size limits that are placed on unregulated hedge funds. Due to the lack of regulation, hedge fund managers are accorded broad freedoms with respect to transparency as well as the risk and return profile of the hedge fund strategy to be pursued, potentially to the detriment of those who are expecting to see their pension funds continue to grow (Lhabitant, 2002).

Hedge funds are often associated with the pursuit of absolute return strategies. The term 'absolute return' refers to managers exploiting investment opportunities, while protecting their principal investment from potential financial loss. Long positions are secured by selling short, buying futures, options or by using other financial instruments to secure their investments (Ineichen, 2003). The combination of the misnomer 'hedge fund' and the idea that hedge funds will produce returns regardless of the direction of the larger market can greatly deceive investors. As the number of funds multiplies, the quest for earning absolute returns means taking aggressive positions that leave the fund exposed to sudden shifts in the market (Fortson, 2007). As a consequence, investors may suffer.

Importance of the Study

It is necessary and pertinent to discuss the importance of any study, and this particular study is important to many people across many countries. Not only does it have importance for people who are trusting people with their pension and hedge funds in Germany, but it also has importance for people who are considering a career working with these funds and those who are currently serving in the capacity of brokers and advisors. The reason behind this is that hedge funds are not going to disappear, and people have to understand how they work and what they are for so that they do not harm their own investments or others' investments moving forward. It is possible that, in the future, new and better ideas for pension funds and hedge funds will come about.

Also important is being able to identify the people who are most at risk for losing money (i.e. losing their pension funds) when they involve themselves with hedge funds. Not all fund opportunities work in the same way, and people with pension funds should certainly understand that hedge funds may not work in the same way that they expect them to, and that those who are brokers for hedge fund opportunities may not spell out all of the specifics.

With that in mind, two people may go through the same basic hedge fund manager, but one may be perfectly fine afterward and one may have many problems associated with the experience. The difference between the two could be caused by many things, including the person's view of the hedge fund opportunity, what the market has done, and whether the fund manager was actually clear in explaining how hedge funds and pension funds work, as well as countless other issues.

This study is important to the future of this kind of research because it will give a great deal of insight into the topic and discuss many of the concerns that exist now and the different options that are being used to address those concerns, as well as what is being considered for the future of the field where both pension funds and hedge funds are concerned. It will also show similarities and differences between hedge funds and pension funds so that there is a clearer understanding of the issues surrounding the study. One of the main reasons why this comparison is so important is that individuals can sometimes easily misunderstand the differences between the two, and if they are not clearly explained by a knowledgeable person, the investors financial future can be put at risk.

Naturally, it can be seen how this would be a concern, and therefore hedge funds must be carefully studied and separated from pension funds, which may seem similar in many cases to those who are not trained in these matters. The literature review will look more closely at the comparison thereof, among many other things.

Hypothesis

The unregulated nature of hedge funds allows for management freedom with regard to the investment strategies, asset classes, leverage, shorting, and derivative use. On the other hand the low transparency, lack of standards measuring risk and return, and serious data problems involved in the hedge fund databases masks the risks involved in investing in hedge funds (Schachter, 2004). Based on that information this paper will look at the following hypothesis to determine whether it is valid or invalid:

Since risks with hedge funds are unclear hedge funds cannot be used to lower the overall risk in a pension fund portfolio, therefore, they are not suitable investment vehicle for pension funds.

Objectives

The objectives of this thesis include defining 'hedge fund' and 'pension fund' and showing what is hiding behind those generic terms. Here the structural configurations of both hedge funds and pension funds will be explained along with their different restrictions. The researcher will continue by demonstrating why pension funds seek to invest in hedge funds and what benefits can be gained from doing so in terms of risk and return. In addition, the researchr will mention the variety of risks involved in investing in hedge funds, and illustrate the variety of database biases that plague the hedge fund industry. Once the basis of understanding has been established, different methods to calculate risk will be illustrated.

In the empirical section, a case study will be conducted to show how hedge funds can be used to optimize the pension funds risk and return profile. To begin, one risk parameter and a series of different hedge funds following different investment strategies will be selected. The thesis will continue by analyzing the results of the case study with respect to risk and return.

The researcher will conclude the thesis by exploring whether hedge funds can be used to lower the overall risk of pension funds. Should the research show that hedge funds do lower the overall risk, the extent to which the hedge fund has lowered the overall risk of the pension fund will be addressed. Though hedge funds appear to have the tools for following absolute return strategies, they may not be as low-risk as their name suggests. Therefore the researcher will conclude with whether it is believed that hedge funds are suitable investment vehicles for pension funds based on the evidence presented in this study, thereby effectively addressing the hypothesis.

Rationale for the Study

An important part of the rationale behind this study is that there have not been any other studies done specifically like this one. Doing a study like this therefore provides new and unique information, but it can also be difficult, since there is really no precedent for this type of study that the researcher can follow. The potential problems that a study like this could have will be dealt with further in the methodology section, since they are important concerns that must be pointed out and discussed.

Methodology and Overview

This thesis will provide an overview of hedge funds and pensions funds. The historical development of hedge funds will be presented followed by its definition. Pension funds will be introduced using a similar structure. Reasons for pension fund interest in hedge funds will be given, and the different risks that may be encountered by investing in hedge funds will also be explained. The thesis is based on secondary research of existing literature regarding hedge funds, pension funds, the stock market, and international financial market regulations, as well as official online newspapers and official online information portals published in Europe and the United States.

The portfolio theories and different methods of calculating risk and return will then be introduced. As each risk calculation method targets specific risk criteria, the methods will be differentiated. This discussion will be based on secondary research of existing literature regarding hedge funds, pension funds, the stock market, and international financial market regulations, as well as official online newspapers and official online information portals published in Europe and the United States.

Using the introduced portfolio theory and risk calculation methods, the researcher will describe how hedge funds can be added into pension funds to reduce their overall risk level for an expected return. Some examples using the different methods will be given. This overview will be based on secondary research of existing literature regarding hedge funds, pensions funds, and the stock market published in Europe and the United States.

In the empirical section, the researcher will present the types of pension funds and hedge funds that will be used. Their characteristics and overall strategy will be presented and a brief explanation will be given as to why the data is anonymous. The information for that section will be based on primary sources from BNP clients and Bloomberg. The research will be complemented by secondary research of existing literature regarding hedge funds, pensions funds, official online newspapers, and official online information portals published in Europe and the United States.

The empirical section will continue with a methodology explanation. The different calculations will be presented through the use of graphs and tables. The results will be complemented by secondary research of existing literature regarding hedge funds, pensions funds, official online newspapers, and official online information portals published in Europe and the United States.

The research limitations of this paper will also be stated and the paper will conclude with the presentation of the researcher's findings showing if hedge funds can be used to reduce the risk of pension fund portfolios. Furthermore, the paper will address whether, in the opinion of the researcher, pension funds should invest in hedge funds before concluding with suggestions for future research.

CHAPTER TWO: REVIEW OF LITERATURE

Reviewing the literature is one of the best ways to learn about a subject and to determine where there are gaps that should be addressed. With that being the case, pension plans will be discussed first so that the reader can have a better understanding of what pension funds are used for and how important they are. After that, pension funds themselves, as well as hedge funds, will be addressed to show how they both work and whether they are capable of complementing one another.

What are Pension Funds?

To be able to understand pension funds and their role in society, it is important to first explain the pension system, which was partially done in the previous section with the information regarding pension plans, what they are designed for, and how they have been neglected and abused in many cases. In this section the researcher will be concentrating on the German pension system and pension funds, as both topics can vary significantly from country to country. This limit has been set so as to maintain the correct scope.

Pension plans in their most basic forms date back to the Middle Ages. People who were unable or unfit to work were usually taken under the care of the nobility or the church. The church typically provided alms and shelter; however, further support could only be expected from professional associations. Each association had its own individual professional activity. The best-known professional associations enjoying relative freedom were the miners' fraternities.

Unlike the other professional associations, the miners' guilds were not bound by strict guild rules, because their profession was significant toward the enhancement of their ruler's wealth (i.e. finding and mining gold for their king). Furthermore, large communities made up the mining guilds, which was something that was not typical in the Middle Ages. Monarchs and private entrepreneurs provided this profession with Miners' Codes. These codes helped maintain injured or impoverished miners when they were unfit to work. (80 years of social insurance, 2004)

In Germany, the miners' guilds had their origins in the Saarland. Should fellow miners be injured or too old to mine, their friends would provide them with a small savings known as "Notgroschen" (Geschichte der Betriebsrente, n.d.) or 'savings for a rainy day.' According to Brill (2008), this principal of the Notgroschen lead to the creation of the "bruderbuchse," a social welfare fund, in 1769. The first real steps in the foundation of the German social security system were, according to Deroy (1994), established by Bismark in the 1880's. This system was later renewed in the years 1957 and 1989.

In Germany today the pension system has greatly evolved and now offers a large variety of pension plans. All employees benefit from an obligatory pension plan to which they are required to make payments until a prescribed ceiling has been reached. In addition to this obligatory pension plan, enterprises may establish their own additional pension plan(s). These plans may be set up to target certain categories of employees, or all employees.

Many pension fund systems today are facing ever-growing financial problems. These problems are a direct result of the pension distribution structure and the country's demographic evolution.

Numerous developed countries have pension plans that are based on a repartition system, and they face problems due to the country's demographic evolution, longer life expectancies, and falling fertility rates. According to Sleiman (2003), the main reason is that the baby-boomer generation is now entering retirement. The longer life expectancy means that the current workforce will have to support the retired generation for a longer period of time, and the falling fertility rate means that a smaller workforce is paying the retirement of a growing number of pensioners. Thus, the ratio of worker to pensioners is imbalanced. As a result, the required retirement contribution payments are increasing to an unsupportable level, and they risk impairing the international competitiveness of many different enterprises. (Le Floch-Prigent, 1998)

The German law provides basic norms and guidelines that are needed for the different pension plans. These norms, however, allow these plans a great amount of flexibility and give them the opportunity to take on a variety of different forms to suit the needs and wants of the employees. Therefore, there are no fixed structures in German pension funds. This can further be seen in terms of the legal forms and diversity of payment, all of which indicate that:

The legal forms of these contracts may be in the form of an agreement between the employer and employee, a clause in the employment contract, or a conventional agreement.

The retirement payment can be made either in full (a onetime payment) once the employee has retired, or in monthly installments.

The additional pension plans offered by enterprises may use different vehicles. The main vehicles offered are:

A life insurance company' selected by the employer

A pension fund support agency.

A direct commitment plan by the enterprise to pay out to the employees. This last type, according to Deroy (1994), represents 70% of the additional pension plans.

The large variety and availability of these pension plans can be explained by the tax and treasury benefits offered to enterprises by the German legal system. The benefits an enterprise and its employees' receive through the 'life insurance company' and 'pension fund support agency' vehicles are as follows:

Enterprise, offering its employees the additional investment into a 'life insurance company' or 'pension fund support agency' will receive benefits in forms of tax deductions. The payments made by the enterprise in both of these vehicles are tax deductible up until a certain ceiling has been reached.

For the employees, the payments made into a 'pension fund support agency' by the employer will not be taxed. Meaning, if an employee deposits 100 € per month via his employer into his or her 'pension fund support agency', the government will not tax these deposits.

Once an employee has retired and receives his monthly retirement earnings, the government will only tax 60% of the monthly payout. The other 40% will be paid free of tax (Deroy, 1994).

What are Hedge Funds?

In their original concept, hedge funds are designed to systematically reduce risk with respect to the direction of the market. The term 'hedge' means to address this by pooling investments in a mix of short and long market positions (Pichl, 2001). The term 'hedge fund' has become a misleading concept and is often criticized due to the array of securities investment strategies that are used, as well as the fact that there is no generally accepted definition of a 'hedge fund'. The definition even varies between Europe and the U.S. (Lhabitant, 2004).

Lhabitant (2004), states that most of a hedge fund's defining characteristics stem from its private nature. Regulators state that hedge funds are not thought to be traditional investment vehicles as long as the general public has no access to the private pool. Only high net worth individuals and institutions have access to these pools through private placements, as they are deemed educated enough to be able to assess the risks involved in their investments. As a result:

The fund is not subject to regulatory requirements. Managers may pursue any type of investment strategy and may use any type of derivatives at their disposal.

The manager of the fund has a goal to achieve absolute returns as he has the ability to go short during falling markets.

Management fees and performance fees are offered to attract the most skilled managers in the industry. To disincline poor managers with poorly executed strategies to manage a hedge fund, managers are required to invest a large portion of their wealth in the fund as well.

There are a variety of commitment measures that can be imposed on the investor to allow the manager to focus on investment rather than cash management. These commitment measures include long-term commitment and minimum notice time for any redemption.

Hedge funds do not have to report and disclose their holdings and positions, as they are unregulated. Today, institutional investors are pressuring hedge funds to become more transparent and with this increasing transparency there is more involved in investing in hedge funds (Lhabitant, 2004).

The terms 'hedge fund structure' and 'hedge fund strategy' differ in definition. Therefore, a distinction needs to be made. Hedge fund structure is the legal structure of the fund that allows the pooling of assets and gives the manager the right to invest in assets, while the hedge fund strategy is the manager's plan to exploit the markets in order to generate return. The legal structure stipulates how the manager is to be rewarded, what the rights of the investors are, how many investors and what type of investors will be permitted in the fund, and the taxes and reports the funds will be subjected to. The hedge fund strategy contains issues such as the markets the manager will be investing in, which market segments will be targeted, and what investment style will be adopted (Das, 2002).

Generally, hedge funds adopt the structure of a private investment pool, yet they can be differentiated by their legal location and also by the types of investors the funds choose to target. Hedge funds that are domiciled, for example in the U.S. Or Germany, are known as 'onshore' funds, and those which are located inside tax havens are known as 'offshore' funds.

The transparency of both onshore and offshore funds depends solely on the manager. Typically a performance report is offered to the investors on a monthly basis in most cases, and on a quarterly basis for some (Das, 2002). When describing hedge funds, the researcher will be looking at their different structures from a U.S. perspective. The reason for this is that there are currently insufficient German sources focusing on hedge fund structures which are available to the researcher.

Hedge funds domiciled in the U.S. are usually structured as U.S. Private investment partnerships under the Securities act of 1933. Under this act the SEC limits the U.S. hedge funds to 99 investors of which at least 65 need to be 'accredited' investors and up to 35 'sophisticated investors' (Das, 2002).

According to Section 3(c)(1) of the Investment Company Act of 1940, hedge funds can be exempted from registration as a hedge fund if the securities are not being publicly offered and that not more 99 investors are involved in the fund. Hedge funds relying on Section 3(c)(1) of the Investment Company Act of 1940 may only offer their securities under Rule 506 of Regulation D. Of the Securities Act of 1933, which means that the securities may only be sold to 'accredited investors' and up to 35 'sophisticated investors' (Geffner, 2007).

The National Securities Markets Improvement Act, signed by Bill Clinton on the 11th of October 1996 amended the Investment Company Act of 1940. This effectively allowed a new type of private fund to be created which could be sold to an unlimited number of 'qualified purchasers' (Neuman, 1997).

Also designed during that time was the master / feeder structure. The master / feeder structure allows investors residing in the U.S. And investors residing offshore to invest, indirectly, in the same master fund. Through this structure the critical mass can be developed in the central fund (master fund) by being fed from different distribution channels (feeder funds). A depiction of the master feeder structure can be found in Figure 2.1.

Typically the master fund is created as a limited partnership where the feeders are the partners. The master fund holds a portfolio of securities in which the feeder funds invest some or all of their assets. The feeder funds performance is thus derived through the performance of the master fund and periodically the funds gains and losses are allocated to the different feeder funds (Geffner, 2007).

There are numerous benefits to be gained from this structure. Feeders that are organized under various jurisdictions may participate in a single pooled investment vehicle. Furthermore, these feeders can adopt any legal structure and still participate in the master fund. The different feeder funds may adopt different fee or capital structures as they are not bound by the master fund, thus each feeder may have its own governing board representing the interests of the investors in the feeder fund (Das, 2002).

Figure 2.1

The master / feeder structure

Note:

A simple depiction of a master feeder structure

Source:

Geffner, R.S. (2007). Forming a hedge fund. Retrieved October 29, 2008, from Hedge fund world: http://www.hedgefundworld.com / forming_a_hedge_fund.htm

Hedge funds that are legally domiciled in offshore jurisdictions are known as offshore hedge funds. These funds usually adopt the structure of a corporate entity rather than an investment partnership and are usually domiciled in the tax havens. The most frequently used places are the Caribbean tax havens. These include the Bahamas, the Cayman Islands, and Bermuda. Investing in an offshore fund is similar to investing in a mutual fund, where the investors purchase shares in the corporation. In offshore hedge funds, contrary to mutual funds, the minimum required contribution margin is higher. Additionally, there are no limits on the number of non-U.S. investors joining the fund. For the fund to accept U.S. investors, the funds have to meet the requirements set forth by the U.S. Securities and Exchange Commission (SEC) (Das, 2002).

The offshore jurisdictions compete against each other to provide an optimal regulatory landscape. Today, the Cayman Islands have become the most successful tax haven for hedge funds. They offer hedge fund companies the opportunity to set up in as little as two weeks, for a fee of around $35,000. The Cayman-based corporations and partnerships are legal and allow investors to avoid up to 35% in taxes that are levied by the Internal Revenue Service on unearned business income. Additionally, the Cayman tax laws help the American fund managers to defer domestic taxes on their personal profits by channeling them offshore through their funds in a legal manner. According to the New York Times, around three-fourths of the world's hedge funds are legally domiciled on the Cayman Islands (Browning, 2007).

There are problems with offshore funds, which are often 'open-end'. Investors are allowed to make capital contributions on a regular basis, which causes problems when determining the incentive fees to be paid. The problem stems the fact that all investors are usually offered one class of shares. A fixed number of shares have to be issued each time a new investor invests. Calculating the incentive fees can become complex as soon as investors subscribe to shares, which are also used to calculate the fund's performance, at different net asset value levels.

Due to this, investors may have a differing percentage of appreciation or depreciation for his or her shares relative to others, at the end of any measurement period. The calculations involved in calculating the incentive fees according to the appreciation or depreciation have to be adjusted accordingly (Lhabitant, 2004).

Using Hedge Funds in Pension Funds

The tremendous growth the hedge fund industry has felt over the last few years can, according to Stewart (2007), be attributed to the increase in investment from institutional investors -- in particular, pension funds. Furthermore, Stewart (2007) states that "[t]hough estimates vary, up to 20% of European and American pension funds and 40% of Japanese pension funds are thought to invest in hedge funds" (Stewart, 2007, p 6). However, Stewart (2007) indicates that the total amount of pension fund assets being dedicated to hedge funds is still rather small. According to the IMF (as cited in Stewart, 2007) few funds allocate more that 5-10% of their total assets to hedge funds. From this allocation, most of the exposure comes via other funds.

The question then becomes: what has allowed pension funds to increase their asset allocation towards the hedge fund industry? According to Frush (2008), the decision makers of the pension funds are constantly searching for top managers to invest their funds, and their hunt has in the past brought them to hedge funds. Though the funds in pension funds come from individual investors, the decision-making process is done on an institutional level. Therefore, according to Frush (2008), it is the investment decision-making structure that has allowed pension funds to invest in hedge funds.

According to both Lhabitant (2004) and Stewart (2008), many pension funds began adopting a new method of investing following the poor performance period after March 2000, due to the low returns offered by the equity market and the low bonds yields reflected by the low interest rates.

According to Stewart (2007), pension funds began attempting to match assets and liabilities more closely to avoid under-funding in the future. Stewart (2007) states that this trend was being supported by regulatory and accounting changes. Pension funds saw in hedge funds the possibility of managing, reducing, and hedging their liability risks, as well as a vehicle to diversify away from traditional equity market holdings.

Hedge funds following absolute return strategies aim to generate positive returns regardless of falling, rising or neutral markets, by seeking absolute returns through the generation of alpha and diversification of the portfolio risk (Ineichen, 2003). But, how are these returns measured? According to Dawson (2007), in traditional investments, returns are measured against a benchmark index. Here an investor hires an asset manager to outperform a chosen benchmark by a certain percentage. In absolute return strategies, the return objective can be stated in one of three ways:

1) The return is measured against a cash rate such as LIBOR, with an added premium.

2) The strategy is given a real return objective, or a particular return objective over the rate of inflation.

3) The return objective can be declared as an absolute, nominal return target of for example 10% or a range target of 10 -- 12%. (Dawson, 2007)

There are a number of different methods for achieving absolute return exposures. Ineichen (2003), demonstrates one method where managers exploit investment opportunities while protecting their principal investment from potential financial loss. Long positions are secured by selling short, buying futures or options, or by using other financial instruments to secure their investments. (Ineichen, 2003)

Dawson (2007), states two other different methods to achieve absolute return exposures. Investors can enter long positions in a number of different asset classes such as fixed income, commodities, real estate, or any other asset classes of their choice. Investors may also decide to concentrate on one particular asset class and rotate their investments among the different sectors. Ideally this method requires active managers who allocate the resources in the right sectors at the right times. This first method may be looked at as a more traditional asset allocation model (Dawson, 2007).

In hedge funds, interest in determining alpha and beta has grown as measures to determine the skill of the manager (alpha) and the market return (beta). "Investors increasingly try to get market exposure through derivatives to meet a targeted asset allocation consistent with their long-term risk/return goals. Then they decide on an active manager as a separate source for alpha to outperform markets, for example through an absolute return strategy" (Dawson, 2007).

Both the Jensen's alpha and Treynor ratio are based on the Capital Asset Pricing Model (CAPM), which is calculated according to this formula (Lhabitant, 2004):

where is a regression residual and where beta is defined as:

According to asset pricing theory, beta represents the systematic risk that cannot be diversified away. It is possible to distinguish several cases of beta:

1) If

1 then the portfolio is riskier than the overall market;

2) If

1 the portfolio is as risky as the market;

3) If the portfolio is less riskier than the market.

4) If

0 the portfolio is uncorrelated with market;

5) If

-1 the portfolio is inversely related to the market risk

Equation 2.3.1, can be rewritten according to the risk premium:

In the case of a portfolio with (or the market as a whole), the equity risk premium is simply the excess of return of the market over the risk-free rate. However, if, the risk premium must be adjusted for the risk taken.

This gives the security market line (SML). Graphically, the SML is the line crossing the y-axis (average returns) at the risk-free rate and rising according to the additional market risk accepted (see Figure 2.2). According to CAPM, any well-diversified portfolio should plot exactly on this line.

Figure 2.2

Security market line (SML)

Note:

Any well-diversified portfolio construction should fall exactly on the SML.

Source:

Lhabitant, F., S. (2004). Hedge funds: Quantitative insights.

West Sussex: John Wiley & Sons Ltd. p 71

Fund managers search for assets that deviate from the SML in the hope of making a profit from the mispricing. As a consequence, their portfolio will be located above the SML. Unsuccessful managers will achieve lower returns than should be expected; as a consequence, their portfolio will be located below the SML. This is the basis for Jensen's alpha which measures performance between the realized return and the return predicted by the CAPM and is calculated as such (Lhabitant, 2004):

or According to the CAPM the Jensen's alpha should be zero, as only market risk should be rewarded. The Jensen's alpha can be used to indicate superior or poor performance when positive or negative respectively. Therefore, when selecting funds according to the Jensen's alpha, the fund with the highest alpha is of interest (Lhabitant, 2004, p 74).

Investment Risk

Defining risk is difficult as different investors have different perceptions of what risk is. Furthermore, depending on the nature of the portfolio and the nature of the institution, the perception of risk can vary greatly. For pension funds, hedge funds exhibit several desirable properties. The historical performances of hedge funds available to investors suggests that even a modest allocation can increase the efficiency of the investors' portfolios. Despite the hedge fund industry's growth in terms of the number of hedge funds and the asset under management, the hedge fund industry remains extremely opaque and behind some of the hedge funds' high returns hide a variety of risks. Understanding these risks remains difficult. Schachter (2004) divides the hedge fund risks in four categories: Investment, operational, liquidity, and business risks.

For Schachter (2004), the most significant characteristic of a hedge fund is its 'investment risk' profile. Investment risk deals with how the assets in the hedge fund portfolio are allocated. He states that when allocating the assets to the portfolio, quantitative measures alone fail at encompassing all the risk, and therefore qualitative measures should be included in the assessment. According to Schachter (2004), a number of studies have shown that hedge fund returns cannot be adequately approximated by widely used statistical distributions. Hedge funds exhibit skew and excessive kurtosis that vary across the different trading strategies. Furthermore, past performance does not account for changes in investment styles. Pension fund investors therefore should not mechanically use only quantitative methods when assessing the hedge funds asset allocation.

There are other ways of studying risk, and even then it is often not clear how much risk there is in a particular hedge fund portfolio. It is unfortunate that this is seen to be the case, because hedge fund managers, pension fund managers, and investors can have a lot of trouble determining which choices are the best choices when it comes to maximizing profits and minimizing risks. It becomes a guessing game in many ways, because one cannot use the statistical analyses that would be used for other funds with the high degree of reliability that would otherwise be expected of them.

One study has shown that most hedge funds collapse due to operational flaws rather than poor performance (Capco, as cited in Schachter, 2004). Ineicher (2003) agrees with Schachter and goes on to say that manager evaluation of a fund is also the most important step. Operational risk, according to Schachter (2004), is the lack of adequate support for, or the breakdown of, existing infrastructure supporting the investment process of a hedge fund. This includes any breakdown in communication between hedge funds and third parties or hedge funds and their investors. These breakdowns in communications can take form in the mispricing of underlying positions, siphoning, and embezzlement of fund assets. In order to avoid these types of breakdowns, pension fund investors should understand the fund administrations procedures and the information flow between the hedge fund, prime brokers, administrators, auditors, and custodians (Schachter, 2004).

A further risk that investors are exposed to is liquidity risk. This risk is separated into two categories:

The liquidity of the underlying securities in a hedge fund portfolio.

The inability of an investor to redeem his or her own shares upon request.

The business risk that is seen with pension funds is also a problem, and it includes the risk of getting a reputation for being associated with fraudulent hedge funds. The reason behind this is that it can be a career-limiting move for pension fund investors to be associated with such a fund (Schachter, 2004). They need to keep their reputations high, and they cannot do that if their names are tied to funds that are questionable. It can be hard to tell, however, which of these funds are good and which are not. For that reason, some investors are reluctant to get involved with any pension funds that involve hedge funds.

Pension Funds, Hedge Funds, and Risk Management

The risks that Schachter (2004) describe can be minimized, according to Pichl (2001), through the use of a risk management system. Hedge funds generally do not regard the risk management system as highly as other financial services companies that have firmly integrated this tool in their business administration, but recently, changes have occurred and risk management has become a critical tool in the hedge fund universe (Lhabitant, 2004). The aim of this tool is to observe, limit, and remove risk in these different areas:

Leverage

Type and number of assets

Fund volume

Liquidity

Portfolio construction (Pichl, 2001)

Risk management helps managers in several ways. Some managers adopt risk management as a tool to add value from a proprietary perspective by using advanced risk measurement techniques to both formulate quantitative strategies and manage the portfolios' liquidity and leverage. Other managers use risk management as a means to better communicate with their clients and give them confidence (Lhabitant, 2004)

Leverage is also very important, and it falls under the investment risk category. It is of concern to investors, as most financial disasters in history in one way or another are associated with excess leverage, or to be more appropriate, the misuse of leverage, according to Ineichen (2003).

Lhabitant (2002) states that "Leverage denotes an investment that is higher in value than the available equity capital. Leveraging is an aggressive strategy because it magnifies both profits and losses." The risk of using leverage can be great as the high dynamic of the market is difficult to predict. Should a financial decision result in a loss, it is much more difficult to achieve a positive result in the future. Investors are at risk if managers borrow more money to try and quickly compensate and cover their losses by investing in a rising asset. With such behavior a fund can quickly become illiquid and face the prospects of closing the fund and losing most or all of the investors' capital (Pichl, 2001).

Other strategies -- concentrating long/short equity, distressed securities, short selling, and emerging markets (seen in Table 2.4.1) make little use of financial leverage above the 2:1 ratio (Pichl, 2001). Ineichen (2003) states that only around 24% of the hedge funds used leverage above 2:1 ratio. In comparison, banks are leveraged 10-15:1 and residential real estate is typically leveraged at 5:1. When looking at these figures, the leverage of the hedge fund industry is rather low.

Figure 2.3

The use of leverage by the different hedge fund styles as of December 2001

Note:

The table shows the situation in 2000

Source:

Borla, S., & Masetti, D. (2003). Hedge funds: A resource for investors.

West Sussex: John Wiley and Sons Ltd. Page 16

However, over the last five years the hedge fund has gone through a boom period where the economy offered low interest rates and easy access to money (Gatinois, 2008). These statistics should therefore be viewed with caution and one should assume that the amount of leverage used has risen up until the subprime crisis started to manifest itself in the global markets, which took place around the second and third quarters of 2007.

Leverage can be defined in two ways; it can be defined under accounting or balance sheet terms as the ratio of total assets to equity capital and alternatively it can be defined in terms of risk as the measure of economic risk relative to capital (Ineichen, 2003).

Type and Number of Assets

Pension funds should be wary of how managers utilize derivative instruments such as futures, forwards, and options, as such instruments are great potential risk factors if not used to secure a particular position. Therefore, pension fund investors should review how these particular instruments are being used in the funds strategy and what percentage of the funds' portfolio will be dedicated to such assets (Pichl, 2001). Though it is true that pension funds seek a greater return when investing in hedge funds, risk limits should be put into place to avoid excessive losses.

Risk management may reduce the pension fund investors' risk by ensuring the assets employed are used to secure particular asset positions or to conform with the funds' strategy. The percentage of the funds that are to be dedicated to such derivative instruments should therefore also be regulated through risk management (Pichl, 2001).

With the number of funds under management growing every year, the fund volume can also become a potential risk factor or return delimiter. Should the transaction volume be too great, the fund could become inflexible and certain strategies, such as arbitrage investment, can no longer be employed efficiently. Should the fund be too small, the fund faces the risk of not being diversified enough. Therefore, funds which are either too small or too large are at risk should they employ the wrong strategy. Risk management can help avert such problems by stipulating the minimum and maximum fund size. Investors, when investing in hedge funds following a particular strategy, should inform themselves of the minimum/maximum required amount the particular strategy will need to run efficiently (Pichl, 2001).

Lhabitant (2002) agrees with Pichl (2001) in stating that the size of the fund is not the factor of success. Hedge funds crucially depend on manager skill and available investment opportunities. These are two factors which are not scalable. Lhabitant (2002) continues to mention several funds that failed though they were large in size: Julian Robertson's Tiger Fund, Jeff Vinik's fund, and George Soro's Quantum Fund.

Management Risk

According to Ineichen (2003) and Lhabitant (2002), the manager is considered one of the major keys to success. Ineichen (2003) goes on to state that investing in a hedge fund is essentially a people and relationship business. The pension fund investors' decision to invest in a hedge fund means that the investor expects to participate in the skill of the manager or managers and not necessarily in a particular investment strategy or a mechanical process. Therefore, manager evaluation is not only the most important step, according to Ineichen (2003) but also the most difficult. There are several problems involved when researching managers, as finding information is difficult. Commercial databases are a starting point yet the information offered is often incomplete.

For pension fund investors, the due diligence process is the single most important aspect of the investment process. Reason being, this process includes both quantitative aspects and qualitative judgments. During the due diligence process, the fund is thoroughly analyzed as a business and the manager information is validated. The operational infrastructure is presented along with financial and legal documentation, affiliates, investment terms, investor base, reference checks, and more (Ineichen, 2003).

Lhabitant (2002) warns, however, that though hedge fund managers share both the up and downside risk by having a significant personal stake in the fund, the personal wealth commitment is not necessarily a good indicator of motivation. At the beginning of a manager's career, for example, a manager has little to lose and may be tempted to increase the risk knowing that in case of a disaster he can go back to a traditional asset manager and recover quickly, while an extremely successful manager at the end of his career may have such large commitments in the fund that he will refrain from taking risks, even though these are often well-rewarded.

Managers are one of the most important factors in the fund as they are the ones who assess the market and the risk, pick the securities in which to invest, and are thus responsible for the investors' assets. For these reasons and more, the evaluation of managers is a key step that needs to be undertaken before investing in a hedge fund.

Hedge Fund Databases

Hedge funds, unlike mutual funds, are not required by law to report their daily net asset value (NAV). As a result, obtaining adequate information on hedge funds is problematic (Schachter, 2004). Recently there have been changes in the hedge fund industry, and as a result, information on the different hedge funds has become more readily available. A number of hedge fund databases have emerged, collecting information and selling it to anyone interested. As hedge funds are not allowed to publicly advertise themselves, hedge fund managers have found that reporting on their monthly returns can greatly improve their chances of attracting additional investors (Lhabtiant, 2004).

Both Schachter (2004) and Lhabitant (2004) agree that the two main sources for hedge fund biases comes from the differing hedge fund database structures and the voluntary reporting of hedge fund data.

Bias in the hedge fund data occurs because the number of non-reporting funds cannot be quantified. There are many reasons why hedge funds choose not to report their performance data, including:

Well-performing hedge funds with sufficient capital under management may not find any added value to reporting their performance data and therefore choose not to (Schachter, 2004).

Poor-performing hedge funds have no incentive to report their fund's performance and choose to hide it instead. This gives the hedge fund manager the option to liquidate the unsuccessful fund and start a new one (Schachter, 2004).

Some fund managers "are afraid that if they communicate their performance to a data vendor, they will be included in that data vendor's index and automatically raise the performance of that index, so their individual performance will appear less differentiated." (Lhabitant, 2004, p 89).

The self-selection bias, according to Lhabitant (2004), may be positive or negative. The impact this bias has on the hedge fund data cannot be quantified. However, it can be assumed that the number of poor-performing funds outnumber the well-performing funds. The unfortunate issue for investors is that there is no real way to determine which of these funds are which, and that leaves them with a trust issue that can be hard to overcome.

In other words, trusting a hedge fund or pension fund manager with a large amount of money when there is no guarantee of return or even of retaining the initial investment is difficult enough, but it becomes much more complex when there is no way to show statistical probability or what kinds of funds a particular portfolio is really invested in. Information that is reported is also only on current funds, so those that have done poorly in the past and been excluded from the report might paint a much different picture if they were seen.

According to Schachter (2004), hedge funds have a short life expectancy. This short life expectancy, in combination with the survivorship bias, blurs the return profile of the hedge fund industry. Gregoriou (as cited in Lhabitant, 2004), found that hedge funds have a high failure rate after the first year. This failure rate remains high before eventually decreasing. The reasons for the funds disappearing from databases are numerous:

A series of large and sudden losses can lead to the liquidation of the fund.

The fund is unable to regain its previous high water mark, for the performance-based fees, after a period of poor performance and is therefore closed.

Funds that are performing poorly may merge with another fund and is therefore absorbed.

Funds may decide to stop reporting yet still be active.

(Lhabitant, 2004).

CHAPTER THREE -- RETURN AND RISK MEASUREMENT METHODS

Any investment requires that risk and return be weighted. Risk and return, however, are two different things and each have to be measured and assessed to understand past performances. Furthermore, risk and return have to be predicted in order to make intelligent investment decisions for the future.

The problem that the hedge fund industry faces is that there is a lack of standards on how to measure risk and return. There is a multidimensionality of hedge funds in terms of descriptive statistics and a lack of agreement on what constitutes an appropriate benchmark. Thus, the hedge fund industry is so diverse that it is impossible to define a small number of sectors that are homogenous enough to ensure an apples-with-apples comparison (Lhabitant, 2004).

In this section, the thesis will concentrate on the most commonly used calculation methods in the hedge fund industry today and explain what these different calculation methods show and why they are effective at showing what they offer to indicate but not really effective at addressing the actual risk and return comparison issue. This section will not include all of the different types of calculations methods as there are far too many and they would not bring with them additional added value concerning the hypothesis that was presented in Chapter One. Presenting only a few options for calculations will also allow for more analysis of the information, which will better showcase what the study is focused on.

Measuring Returns

A common tool used by hedge fund managers when measuring the returns of their funds is to quote their 'Net Asset Value' (NAV). Due to the recent movement of viewing returns rather than net asset values or prices, the NAV formula is often adjusted to show returns rather than prices. The reason for the shift towards viewing returns rather than net asset values or prices is that return has standardized the evolution of a price by considering price as a 'per unit investment'. Furthermore, using returns in statistics is more attractive in comparison with prices (Lhabitant, 2004, 27).

Before comparing NAV results, it should be ensured that the data has taken into account all realized and non-realized capital gains, accrued dividends and interest income, capital distributions, splits, and all the impacts of equalization and crystallization. The return of the NAV data can be transformed using the following formulas (Lhabitant, 2004):

The simple net return of a fund between any time and is defined as:

This formula measures the relative change in the fund's net asset value over the considered time period. The simple net return formula can be used to express future net asset value as a function of the present net asset value:

The term is known as the simple gross return.

To annualize the simple returns the number of holding periods must be expressed as a ratio with respect to one year. The annualized return is calculated as follows:

Where HPR = Holding period return

(Lhabitant, 2004)

Modern Portfolio Theory

Prior to Harry Markowitz's development of the modern portfolio theory (MPT), investors assessed securities by focusing on the securities' individual risk and return characteristics when constructing their portfolios. This approach to portfolio construction could have lead an investor to construct a portfolio based solely on railroad stocks and would lead to the construction of an inefficient portfolio. (Portfolio theory, 1996). Markowitz's theory attempted to quantitatively demonstrate the benefits that could be gained by not placing all one's eggs in one basket, as well as how portfolio diversification could reduce the risk for investors while still retaining a strong level of expected return. (Modern Portfolio Theory, 2008)

The theory behind MPT was that a portfolio of diverse stocks would, as a group, be less risky than holding any one of them individually. Two types of risks are described in the MPT theory: systematic and unsystematic risk (see Figure 3.1).

Systematic risk is a measure of the market risks, such as interest rates, recession, wars and more, that cannot be diversified away.

Unsystematic risk, or specific risk, is the risk specific to a particular security. According to the MPT, this type of risk can be diversified away. This particular risk represents a component that is not correlated with the general market movement.

(McClure, 2008)

Figure 3.1

Removing Unsystematic Risks Through Diversification

Note:

A simple depiction of unsystematic risk elimination through diversification

Source:

Mclure, B. (2008). Modern Portfolio Theory: An Overview.

Retrieved November 22, 2008, from investopedia:

http://www.investopedia.com/articles/06/MPT.asp?Page=1

The MPT model assumes that the investors are risk averse by nature and will select for the same expected return the security with the lower risk. Investors accepting higher levels of risk will only do so if compensated with higher levels of return. The investors in the MPT model are rational investor and will not invest in a portfolio should another portfolio exist that shows, for the same level of risk, higher expected returns. (Modern portfolio theory, 2008).

Standard Deviation / Variance

Mathematically, Markotwitz calculated a portfolio's expected returns by treating single period returns for the various securities as random variables. The random distribution of the possible return, or expected return, is calculated using this formula:

Where is the individual securities return and is the weight of the security.

(Portfolio theory, 1996)

The risk in the MPT model is calculated using the standard deviation of returns. Today there are a number of different methods of calculating and measuring risk, and the standard deviation of returns is a frequently used method for risk measurement in securities and portfolios. It measures the variability of returns based on the mean, and the greater the standard deviation the greater the risk over any given period. The standard deviation is calculated using this formula:

The variance is "[a] measure of dispersion of a set of data point around their mean value" and is calculated by squaring the standard deviation:

(Modern Portfolio Theory, 2008)

Coefficient of Variation

The standard deviation of two variables cannot be meaningfully compared to determine which variable has the greater dispersion as both variables may vary greatly in terms of units and the means around which they are located. To be able to compare the standard deviations of two variables, the correlation coefficient (

) has to be calculated. The formula for this is:

(FAQ: What is the coefficient of variation?, n.d)

Where is the standard deviation, and is the mean or average return, this formula effectively allows comparing the standard deviation generated for each unit of return. In the empirical section however, the researcher will be inversing the formula to:

This formula effectively allows the comparison of the return generated for each unit of standard deviation. The larger the, the greater the return for each unit of standard deviation in the variable and vice versa. The allows the standard deviation of two variables to be compared, as both the standard deviation and the mean are expressed in the same units. By calculating their ratio, the units are cancelled out. This method has its disadvantages. When the standard deviation nears zero, the becomes more sensitive to changes in the mean.

Sharpe Ratio

The sharp ratio is one of the most commonly used risk-adjusted performance measures. It measures the excess of return per unit of volatility in a fund and is calculated according to this formula (Lhabitant, 2004):

is the average return on portfolio P. The risk free rate is denoted as

. The standard deviation of the portfolio return is denoted as

. Interpreting the Sharpe Ratio is relatively simple: the larger the ratio, the higher the return the fund delivers for its level of volatility. A Sharpe ratio of 1.0 indicates that the funds return is proportional to the risk taken. A Sharpe ratio below 1.0 indicates that the fund's return is lower than the risk taken (Lhabitant, 2004).

In that case the fund would be a high risk investment and it might be best to avoid it in favor of a fund that was easier to work with and that did not provide so much risk for the rate of return. High-risk funds can certainly bring high rewards but they can also bring great risk, and with the argument that the standard calculation models do not clearly indicate whether hedge funds are volatile -- and which hedge funds are most volatile -- more investors are turning toward investment vehicles that are easier to work with and that are a lower risk for their money.

Volatility Attribution Model

The standard deviation using historical returns is able to quantify the total risk of a portfolio. What the standard deviation is not able to show is which holdings, trades, or exposures account for the level of volatility. The marginal contribution to volatility, contrary to the standard deviation, is able to show, to a certain extent, where the level of volatility comes from. As previously mentioned, the variance of a portfolio is calculated using the formula which can be rewritten as:

Where

is the holding in asset

or asset class I;

is the covariance of asset with asset or the variance if equals

. The variance in this formula is either ex-post or ex-ante.

Ex-post means that the calculation is based on historical performance of the portfolio.

Ex-ante on the other hand means that the performance is based on the volatility of single assets in the portfolio.

For ex-ante, the matrix of variance-covariance has to be forecasted with know weights. This is difficult to achieve with a degree of reasonable accuracy with a small portfolio. However, with an increasing portfolio size, the number of forecasts necessary grows (Bacon, 2007).

With an ex-post basis and constant weights, the formula is a 'bottoms up' approach. This means that the historical volatility of the portfolio is calculated from the constituent elements. The variance-covariance matrix is extracted from the historical data. This approach, however, can be difficult to implement, as a large number of estimations for the variance-covariance matrix are required. According to Bacon (2007), in a portfolio of 100 assets 5,050 estimations would be needed when calculating the variance-covariance matrix.

Marginal Contribution to Volatility

To be able to calculate the marginal contribution to the fund volatility, it is necessary to have the variance-covariance matrix of the securities returns. Once the variance-covariance matrix has been created, calculating the contribution of asset to the portfolio variance is done using the derivative of the volatility relative to the holdings / portfolio (Bacon, 2007).

Therefore the marginal contribution of asset can be expressed as:

Or simply:

Marginal contribution of asset I is equal to the correlation between the asset and the portfolio multiplied by the volatility of the asset. Thus, if the correlation of the asset I with the portfolio is negative, the volatility can be lowered by increasing the weight of the asset. Finally, it is interesting to note that the weighted sum of each marginal contribution gives the volatility of the portfolio:

The two formulas above are expressed in actual holdings, expected correlations and volatilities. To estimate the impact of increasing the weight of an asset

on the portfolios volatility, a linear approximation can be used:

(Bacon, 2007)

Inclusion of New Assets in a Portfolio

Marginal contribution to volatility is a useful tool. However, it tells nothing about the efficiency of increasing the weight or adding a new class of asset to the portfolio. In fact, an increase in the portfolio volatility could be the result of an increase in the expected return. How can it be proven if this increase is optimal on a risk-adjusted basis? In general, adding a new asset class to the portfolio is optimal if the following condition is met:

The Sharpe Ratio of the new asset class must be greater than the Sharpe Ratio of the portfolio multiplied by the correlation between the two. If both Sharpe Ratios are positive, it is always optimal to add asset classes that are negatively correlated with the portfolio (Maginn, 2007).

CHAPTER FOUR: EMPIRICAL ANALYSIS

Types of Pension Funds

The funds used in the empirical analysis will be comprised of five different equity pension funds. These funds hold only equity assets. All of the pension funds contain derivative instruments for hedging purposes in their portfolios, and all of the funds are actively managed private German pensions funds run by different fund managers for two different BNP Paribas clients. The returns presented are net returns and these funds have been selected due to their longer track records, comprising almost five years. The longer track records were selected for the following reasons:

To be able to more accurately determine the funds' true risk profile.

To better evaluate the performance of the fund through a complete market cycle with both bear and bull phase. In bull phases, the markets gain can mask the risk profile of funds using aggressive investment approaches. These aggressive strategies can be identified in bear periods through the funds' substantial losses.

To allow the longer track records to have moderation effects on the funds that have unusually good and/or bad short-term performance periods (Newsome, 1997).

Types of Hedge Funds

Due to the vast number of different hedge fund strategies available in which to invest, the researcher was required to choose among the different strategies. The types of hedge funds comprised in the empirical analysis will be five different 'funds of hedge funds' or 'fund of funds' following a multi-strategy approach, as well as five different hedge funds from each of the following strategies:

Directional equity / Equity market neutral strategies

Global macroeconomic strategies

Emerging market strategies

The data source of the funds of funds are BNP clients and were selected due to their lower risk structure. The fund of fund structure seeks to invest in other strategies and management styles to better diversify itself. By definition, multi-strategy funds engage in a variety of investment strategies to earn smoother returns, reduce their volatility, and decrease asset-class and single-strategy risks. Their aim is therefore to deliver consistently positive returns regardless of the directional movement of the markets (Starr, 2008). The official objective of these funds of funds is to attempt to generate long-term capital growth consistent with the principles designed to minimize risk of capital loss through investments in alternative investment strategies globally.

The source of the different hedge funds was Bloomberg. The monthly net asset values, valued in euros, were used to calculate the different hedge funds' monthly performance. As these are not BNP clients, the provided values can be verified using the tickers.

The hedge funds following directional equity strategies and market neutral strategies were selected to examine the extent of risk diversification and return maximization that could be achieved by incorporating them into the portfolio of equity-only pension funds. Both directional equity strategy and market neutral strategy can involve either long or short investments in equities. Traditionally, these strategies purchase stocks that are perceived as undervalued and sell stocks that are perceived as overvalued. Therefore, in a particular sector, hedge fund managers may hold both long and short positions in different stocks (Long & short equity or directional equity, n.d.)

The Global macroeconomic strategy hedge funds were selected because the portfolios of these strategies are globally diversified and have long and short positions in securities as well as in both currencies and derivatives. The selections were made based on the overall economic and political views of various countries (Global macro strategy, n.d.)

The Emerging market strategy hedge funds were selected due to the potentially higher levels of risk and return that could be earned, compared to the other strategies. The higher expected returns were one of the important criterions for pension funds when investing in hedge funds. The emerging market strategies invest in traditional fixed income, value, and growth equity investments located in developing economies. These economies are located in areas like Asia, Africa, the Mediterranean, and the American continents -- with the exception of the United States and Canada. These markets are characterized as being highly volatile, as information regarding the securities being traded is difficult to obtain. As a result, these markets are inefficient but offer the potential to generate large returns (Emerging markets, n.d.)

As with the pension funds, these fund of funds were selected due to their longer track records, comprising five years. The returns presented are net returns, after all performance fees and management fees have been deducted.

In this thesis, numerous hedge funds have been selected and they pursue a multitude of various strategies. One of the assumptions made for the study was that the hedge funds managers did not deviate from their defined strategy. In other words, throughout the funds' lifetime, the strategy did not change.

As there is a lack of defined standards on how to measure returns in the hedge fund industry, the researcher presumes that both the pension funds' and hedge funds' NAVs have been calculated in the same manner, and that the NAV's are net returns.

The different pension funds and hedge funds that have been selected all have different start dates. In order to compare them the researcher has artificially shortened the different track records to the same date: the 31st of January, 2004.

The Sharpe Ratio calculation requires the risk free rate. As this thesis uses German pension funds, the researcher has selected as a measure for the risk free rate: the 5-year yield of the German bond. As a start date the researcher chose the 31st of January, 2004, as this is the same start date for all the pension funds and hedge funds.

Method

The empirical analysis will begin by calculating the pension funds, hedge funds, and fund of funds average return, volatility, Sharpe Ratio, variation coefficient, and the various other correlations between pension funds and hedge funds. Calculating the variation coefficient will effectively allow the comparison of the volatility per unit of return among the different funds. The pension funds will be compared by their coefficient of variation. The fund with the lowest coefficient of variation will be selected, as in terms of volatility to return this fund is the most efficient.

The empirical study will continue by selecting the most efficient hedge fund from the different hedge fund strategy samples, once again looking at the coefficient of variation. Once the hedge funds have been selected, the most efficient hedge funds from each strategy group can be compared with the most efficient pension funds. The aim is to show that a mix between a pension fund and a hedge fund will generate a greater return with lower levels of volatility.

According to a survey by the OECD (Survey of investment regulations of pension funds. 2006), German state-owned pension funds are only allowed to invest 5% of their assets into hedge funds, while other German non-state-owned pension funds have no investment limit. According to Stewart (2006), another OECD paper that was published a year later stated that the limit of 5% on German state owned pension funds will increased to 10%. Though the pension funds being analyzed in this thesis are not state-owned, the researcher will be calculating the Sharpe Ratio of the selected pension funds and comparing them with the Sharpe Ratio of the pension funds with both 5% and 10% investments in the different selected hedge funds.

The reason for this is that the researcher wishes to demonstrate what effects a small investment in hedge funds will have on a pension fund's risk / return profile. An increase in the Sharpe Ratio will suggest that the portfolio of the pension fund and hedge fund will be more efficient.

The marginal contribution to volatility will also be calculated for the selected hedge funds. On an absolute basis, and without considering additional return, if marginal contribution is positive the composite portfolio volatility will be higher if there is an increase in the weight of the hedge fund in the composite, and vice versa. Because marginal contribution does not tell if there is a potential improvement in return by adding volatility, the researcher will use the formula to show whether, by adding a new asset class to a portfolio, the new Sharpe Ratio will improve. Once again, a higher Sharpe Ratio will suggest an improvement in the fund's risk / return profile. The calculation methods used for the empirical section have been described in Chapter Three of the thesis.

CHAPTER FIVE: CONCLUSION

Findings

Using the net returns of the pension funds, the pension funds benchmark, and the hedge funds, the average return, standard deviation, and variation of coefficient were calculated. The different net returns of the funds can be viewed by opening the excel file accompanying the thesis. The researcher has not added them in the annex of the thesis itself, as the data is too long to be displayed correctly in a meaningful manner.

As previously stated, all calculations are based on the funds' net monthly returns over the same time period, January 2004 -- August 2008. By viewing the average returns and standard deviations of the different funds, one can see that the pension funds have similar returns and standard deviation. The results for the variation coefficient show the standard deviation for each unit of return generated by the fund. The most efficient fund in terms of risk and return has the lowest variation coefficient.

In order to clearly see where the researcher is going with his information and what kind of information is being worked with, it is important to show the preliminary calculations for the different pension funds, benchmarks, emerging markets, and other information. All of those are included in the table below.

Table 5.1

Preliminary Calculations

Note:

The different funds average return, standard deviation and variation of coefficient calculations

Source:

BNP clients and Bloomberg

Using Figure 5.1, it can be seen that all the fund of funds (FoHF), except for FoHF 5 are completely efficient along the slope. The starting point of the efficiency frontier, or the global minimum variance portfolio for FoHF 5, is when 30% investment is made in the PF and 70% are invested in the FoHF 5. An additional manner of verifying the most efficient fund would be by determining the trend lines gradient. The slope of the trend line that is the least steep is an indicator that the fund is the most efficient. With the use of leveraging, the slope of the curve can be move upwards along the y-axis.

The most important thing to address here is that all of these different types of calculations are designed to show which fund is more efficient -- and therefore better for an investor. However, since hedge funds are difficult to address and categorize statistically, there is no real consensus as to what 'efficient' or 'better' is. Logically, these terms would mean that an investor would have a low risk and a high return. Everyone wants these things when they invest their money, and that is true of small-time investors as well as big companies that are investing to ensure that their employees can keep their pension plans.

Of the different efficient hedge funds the most efficient hedge fund based on risk and return according to the coefficient of variation is EQ 5. Though EQ 5 has a low portfolio return it benefits from having a low level of standard deviation. To obtain higher levels of return, the pension fund would need to leverage EQ 5. Though EM 5 offers the greatest returns, it does so at the price of much higher levels of volatility. When viewing the table information, one can discern that EM 5 is the least efficient hedge fund of this current selection. In addition, one can see that alone, the PF 4 is not as efficient as it could be with any investments in the hedge funds.

The researcher also verified, using the Sharpe Ratio, that if PF 4 has an excess return per unit of volatility that will increase with the addition of the above-used hedge funds. This will be compared with the same percentages of 1/Cv.

The scale for rating Sharpe Ratios are as follows:

1.0 the risk taken is in direct proportion to the return earned

1.0 -- 2.0 is considered good

2.0 -- 3.0 is considered excellent

Table 5.2

Sharpe ratio and 1 / Coefficient of Variation comparison

Note:

A table showing the minimum efficiency level in the mix of pension fund 4 and the sample of equity hedge funds.

Source:

BNP clients and Bloomberg

In Table 5.2, above, one can discern that, alone, PF 4's return per unit of volatility, or Sharpe Ratio, is extremely low, as are those of the hedge funds. The Sharpe Ratio for all funds increases greatly with just 5% of the pension fund's portfolio dedicated to hedge funds. This is in line with the 1/Cv. Here, too, adding hedge funds into the pension fund's portfolio has improved the fund's efficiency.

By adding hedge funds to the pension funds' portfolio, PF 4's marginal contribution to volatility is positive for all 4 funds, meaning that the volatility of the funds has increased. The increase, however, for both 5% and 10% investment in hedge funds from the pension fund is marginal. This would appear to indicate that, not only do hedge funds not increase the volatility of the pension fund by a dangerous amount, but the difference in having a pension fund with 5% hedge funds and one with 10% hedge funds is relatively negligible, at least with the funds that are used for analysis.

By calculating the Sharpe Ratio for PF 4 and the different hedge funds, and finding their correlation to the pension fund, the researcher was also able to statistically deduce that adding hedge funds to the pension fund will improve PF 4's Sharpe Ratio. Using the formula it can be seen that the excess of Sharpe ratio for hedges funds is greater for EQ 5. However, this is not meaningful because the formula used may indicate that a mean-variance improvement can be affected at the margin by adding a positive amount to the hedge fund, but it offers no information about how much of the hedge fund asset to add. In fact, in spite of the fact that EQ 5 has a greater excess of Sharpe Ratio, the table shows that for different weights (5% and 10%), EQ 5's Sharpe Ratio at 5% and 10% investment is the lowest among all the other hedge funds.

Limitations

There are several limitations to what has been done here. The limitations of the findings in this thesis start with the opacity of the hedge fund industry. Limited amounts of information are available on the different hedge funds. As has been stated earlier in the document, hedge funds are not required to report their daily net asset values and they do so only if they choose to. Furthermore, the data that is published is subjected to a variety of biases that distort the performance data.

The average return and volatility calculations were done on a monthly basis. In the Bloomberg database, among the different hedge funds, the only data consistently present are the hedge funds' monthly NAVs. It is, therefore, impossible to determine if strong inter-month volatility has occurred and how this would affect the calculated standard deviation of any of these funds.

Because the hedge fund industry is opaque, assumptions had to be made on the strategy followed by the hedge funds. Though the hedge funds offer a name for the strategies that they pursue, their management methods are not guaranteed, nor are they required. Therefore, if the opportunity arises, they may switch strategies or styles. They can do this without warning, without acquiring permission from anyone, and without being required to notify investors or anyone else. In other words, an investor may not know that the hedge fund that he or she has put money into has changed.

The pension funds that were chosen were rather correlated and did not allow for deeper analysis. Furthermore, the time frame of the research was just under five years. A longer time period would be necessary in order to be able to draw stronger conclusions. Overall, insufficient funds, both hedge funds and pension funds, were used to be able to draw an overall conclusion of the hedge fund industry. In addition, the researcher used past data as a predictor of future data. However, the future does not necessarily follow past results, and it is quite possible that there would be or will be other factors occurring in the future that will cause the trends in the hedge fund market to change.

Conclusion

The findings indicate that on a mathematical level, adding small levels of hedge funds (5 -- 10%) into pension funds, does in fact improve (or at least not appreciably harm) the efficiency of the pension funds in terms of the risk and return profile. According to the marginal contribution calculation the pension funds gain in volatility is only marginal compared to the excess return gained per unit of volatility. The gain in average return with investments of 5 -- 10% in hedge funds ranged from 0.747% to almost 1%. It should be noted, however, that the pension funds' average return to begin with was extremely low, as were those of the hedge funds.

What were not taken into account in the researcher's findings were the data biases that still persist in the hedge fund industry. Due to the hedge fund biases mentioned in an earlier section of this thesis, great care should be taken when interpreting hedge fund industry information. It is reasonable to assume the self-selection bias, survivorship bias, database/sample selection bias and backfill bias that are often seen will distort the performance data upwards. The degree of distortion varies depending on the database being used (Lhabitant, 2004). The term 'hedge fund' is actually a misnomer in itself. When combined with pursuing absolute return strategies, hedge funds should not be mistakenly associated as a risk-limited investment vehicle.

Reviewing the recent, major turmoil in the financial markets should, in theory, allow hedge funds to earn positive returns in the falling markets. Where other investment vehicles generate negative performances, hedge funds should be generating positive performances, however low those performances may be. Yet, according to Nouriel Roubini (as cited in Gatinois, 2008), around 20% to 30% of the hedge funds worldwide are condemned to close and are not generating any positive returns at all. Peter Douglas (as cited in Burton, 2008) states that, as of October, 2008, eighteen percent, or U.S. $300 billion; of hedge fund industry assets were being subjected to withdrawal restrictions. Citadel Investment Group LLC has, for example, subjected its investors to such a strong investment withdrawal that the U.S. $10 billion funds under management have lost 49.5% of their value over the last year.

Funds that lose almost 1/2 of their value in one year are clearly not good vehicles for investment, regardless of the problems that are being seen in the markets and regardless of economic conditions and concerns. Many pension funds that used hedge funds for part of their investment have lost more than pension funds that chose not to use hedge funds. Of course, there are hedge funds that are still doing well and that have done well in the past, but, as has been pointed out, there is no guarantee that past performance will equal future performance.

These closings of funds and withdrawal restrictions are not new to the hedge fund industry. There are many examples of large funds that have collapsed in the past for diverse reasons. These funds include Granite Partners, Lipper Convertible Arbitrage, and Bear Stearns (Lhabitant, 2004; Hoffmann, 2007). In 2005 alone there were approximately 1,000 out of a presumed total of 8,000 of the kinds of funds which collapsed (Fortson, 2007).

The researcher is of the opinion that, though certain hedge funds demonstrate acceptable risk and return profiles, investing in hedge funds is riskier than its name suggests. There are numerous hidden risks involved that even a more savvy investor might not be aware of because of the lack of disclosure required for these kinds of funds. Though pension funds may be tempted by the higher returns, they should keep in mind the fact that with the higher returns that hedge funds can provide come greater risks, especially when alternative investments and leverage are misused.

Suggestions for Future Research

While writing this thesis, the researcher came across numerous ideas for further research. The first of these is that there should be an analysis of which hedge fund strategy provokes consistently higher returns, and which of the strategies perform (on average) better in bull and/or bear markets. A further research idea would be to analyze just how effective hedge funds are in times of crisis compared to the number of hedge fund closures. Another topic for research would be which strategies consistently earn the highest returns and why this appears to be the case. Which hedge fund strategy types do better in bull and bear periods should be considered, as well as how effective hedge funds really are in times of turmoil and crisis.

BIBLIOGRAPHICAL REFERENCES

80 years of social insurance. (2004). eska sprava socialniho zabezpe-eni. Retrieved October 29, 2008, from: www.cssz.cz/NR/rdonlyres/4A1C1E3E-2A27-49F6-A9BD-F863C843731A/0/publikace_80letSP_aj.pdf

Accredited investors. (2000). U.S. securities and exchange commission. Retrieved October 29, 2008, from: http://www.sec.gov/answers/accred.htm