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    Hedge Funds: Quantitative Insights
    Hedge Funds: Quantitative Insights
    Hedge Funds: Quantitative Insights
    Ebook703 pages5 hours

    Hedge Funds: Quantitative Insights

    By Francois-Serge Lhabitant

    3.5/5

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    About this ebook

    "An excellent and comprehensive source of information on hedge funds! From a quantitative view Lhabitant has done it once again by meticulously looking at the important topics in the hedge fund industry. This book has a tremendous wealth of information and is a valuable addition to the hedge fund literature. In addition, it will benefit institutional investors, high net worth individuals, academics and anyone interested in learning more about this fascinating and often mysterious world of privately managed money. Written by one of the most respected practitioners and academics in the area of hedge funds." -Greg N. Gregoriou, Professor of finance and research coordinator in the School of Business and Economics at Plattsburgh State University of New York.

    "This is a landmark book on quantitative approaches to hedge funds. All those with a stake in building hedge fund portfolios will highly profit from this exhaustive guide. A must read for all those involved in hedge fund investing." -Pascal Botteron, Ph.D., Head of Hedge Fund Product Development, Pictet Asset Management

    "François-Serge Lhabitant's second book will prove to be a bestseller too - just like Hedge Funds: Myths and Limits. He actually manages to make quantitative analysis 'approachable'- even for those less gifted with numbers. This book, like its predecessor, includes an unprecedented mix of common sense and sophisticated technique. A fantastic guide to the 'nuts and bolts' of hedge fund analysis and a 'must' for every serious investor." -Barbara Rupf Bee, Head of Alternative Fund Investment Group, HSBC Private Bank, Switzerland

    "An excellent book, providing deep insights into the complex quantitative analysis of hedge funds in the most lucid and intuitive manner. A must-have supplement to Lhabitant's first book dealing with the mystical and fascinating world of hedge funds. Highly recommended!" -Vikas Agarwal, Assistant Professor of Finance, J. Mack Robinson College of Business, Georgia State University

    "Lhabitant has done it again! Whereas most books on hedge funds are nothing more than glorified marketing brochures, Lhabitant's new book tells it how it is in reality. Accessible and understandable but at the same time thorough and critical." -Harry M. Kat, Ph.D., Professor of Risk Management and Director Alternative Investment Research Centre, Cass Business School, City University

    "Lhabitant's latest work on hedge funds yet again delivers on some ambitious promises. Successfully bridging theory and practice in a highly accessible manner, those searching for a thorough yet unintimidating introduction to the quantitative methods of hedge fund analysis will not be disappointed." -Christopher L. Culp, Ph.D., Adjunct Professor of Finance, Graduate School of Business, The University of Chicago and Principal, Chicago Partners LLC

    LanguageEnglish
    PublisherWiley
    Release dateAug 20, 2009
    ISBN9780470687772
    Hedge Funds: Quantitative Insights
    Author

    Francois-Serge Lhabitant

    François-Serge Lhabitant is the C.E.O. and C.I.O of Kedge Capital, a Professor of Finance at the EDHEC Business School, and a visiting Professor of Finance at the Hong Kong University of Science and Technology.

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      Book preview

      Hedge Funds - Francois-Serge Lhabitant

      Part I

      Measuring Return and Risk

      1

      Characteristics of Hedge Funds

      I don’t play the game by a particular set of rules; I look for changes in the rules of the game.

      A global macro manager

      While their mainstream popularity seems to be a new phenomenon, hedge funds have been around for more than 50 years. Indeed, Alfred Winslow Jones, journalist, sociologist and fund manager, is credited with establishing the first hedge fund as a general partnership in 1949.⁴ He operated in complete secrecy until 1966. Then, an article penned by Carol J. Loomis in the April edition of Fortune Magazine, entitled The Jones that Nobody Keeps Up With, exposed to the public his unique and highly successful strategy (speculative instruments for conservative purposes), along with his truly astounding return rates. Since then, the number of hedge funds and the size of their assets have soared, particularly since the early 1990s. Estimates suggest there are now over 6000 active hedge funds managing around $600 billion in assets, compared with the 68 funds that existed in 1984.

      Several factors may explain the extraordinary development of hedge funds over recent years. First of all, there was the unprecedented wealth creation that occurred during the equity bull market of the 1990s. That significantly expanded the base of sophisticated investors, especially high net worth private investors, and fundamentally altered the way people in the workaday world viewed their money and finances.

      In addition, there was an unprecedented generational shift of wealth through inheritance, as the parents of baby boomers progressively left their assets to their children. These new investors were typically more sophisticated and had a higher tolerance for risk than the previous generation, but were also more demanding in terms of investment performance. This boded well for hedge funds and other alternative investments, which generally targeted higher absolute returns thanks to their flexibility and lack of constraints.

      It was also at this time that the first institutional investors started showing a greater interest in hedge funds. In particular, in September 1999, the pension fund CalPERS raised the ceiling on its alternative investments allocation to $11.0 billion, that is, 6% of its total assets. This amount included about $1.0 billion specifically allocated to hedge funds.

      After March 2000, the growth of the hedge fund industry continued. However, the motives for investing had changed dramatically: investors were then looking for an effective means of diversification to protect their capital from falling equity markets and depressed bond yields. In addition, sub-par performance in traditional asset categories started luring institutional investors toward absolute return strategies, and more specifically hedge funds. Until then, alternative investments had primarily focused on private equity and real estate.

      The needs of these new investors - quite different from those of the wealthy private clients - triggered a process that led to several changes in the hedge fund industry. Many hedge funds became more mature, and put in place stable investment processes, lower leverage, improved transparency and effective risk management to satisfy the high standards and rigorous selection processes of large institutions. In addition, many traditional financial institutions began to develop funds of hedge funds as part of their global product range, and offered them to their retail and affluent clients.

      The total assets now managed by hedge funds may still seem small with respect to the $3.8 trillion allocated to more traditional strategies by institutional investors alone, or the $6.3 trillion of assets under management in the mutual fund industry. But the double-digit growth in asset size and the increasing popularity of hedge funds have also brought about a change in the attitude of regulators, who now regularly scrutinize the secretive world of alternative investments on both sides of the Atlantic Ocean. Nevertheless, the increased market volatility, the corporate activity and the extreme valuations (both on the upside and on the downside) continue to offer unrivaled opportunities for talented portfolio managers to exploit anomalies in the markets. As a consequence, the number of hedge funds should keep growing, and their strategies become more prominent and more popular in the near future.

      1.1 WHAT ARE HEDGE FUNDS?

      Originally, hedge funds were so named because their investment strategy aimed at systematically reducing risk with respect to the direction of the market by pooling investments in a mix of short and long market positions. However, in today’s world, many hedge funds are not actually hedged, and the term has become a misnomer.

      Surprisingly, though, there is no commonly accepted definition of what exactly a hedge fund is. To confuse matters further, the term hedge fund has different meanings on each side of the Atlantic. In Europe, a hedge fund denotes any offshore investment vehicle whose strategy goes beyond buying and holding stocks or bonds and that has an absolute (i.e. non-benchmark-related) performance goal. In the United States, a hedge fund is typically a domestic limited partnership that is not registered with the Securities and Exchange Commission (SEC) and whose manager is rewarded by an incentive fee and has a broad array of securities and investment strategies at his disposal.

      In this book, we have adopted the following pragmatic definition as a starting point:

      Hedge funds are privately organized, loosely regulated and professionally managed pools of capital not widely available to the public

      The private nature of hedge funds is the key issue in this definition, and we believe that most of the other characteristics of hedge funds follow directly from it. Indeed, as long as the general public has no access to a private pool,⁵ regulators do not consider the pool as a traditional investment vehicle (e.g. a SICAV, an OPCVM, a mutual fund, etc.) and conclude that there is no need to regulate it or require regular specific disclosure. This makes sense, because the pool only caters to high net worth individuals and institutions through private placements, and these investors are likely to be educated enough to assess the risk of their own investments.

      Consequently:

      • The pool is not subject to the requirements imposed on registered investment companies and, therefore, its manager may pursue any type of investment strategy. In particular, he may concentrate its portfolio in a handful of investments, use leverage, short selling and/or derivatives, and even invest in illiquid or non-listed securities. This is in total contrast to mutual funds, which are highly regulated and do not have the same breadth of investment instruments at their disposal.

      • The pool manager has the primary goal of achieving a target rate of return, whatever happens on the market. This is what is meant by absolute return. Falling markets are no more an excuse for poor performance, as the manager has the latitude to go short if he wants to.

      • To attract the most skilled managers in the industry, the pool offers some performance fees (typically 20% or more of the hedge fund’s annual profits) rather than asset-based fees (typically 1% or 2% of the assets). Assuming a 5% net trading profit for a hedge fund, the total fee would be equal to 200 basis points (1% management fee, plus 20% of the 5% performance) per annum. This would amount to more than five times the fees for most traditional, active equity products. But high fees will also attract managers with poorly established and executed strategies, potentially resulting in grim surprises for their investors. Hence, most hedge funds request their manager to invest a large fraction of his personal wealth in the fund alongside other investors. In addition, a hurdle rate of return must usually be achieved or any previous losses recouped before the performance fee is paid.

      • To allow managers to focus on investments and performance rather than on cash management, the pool may impose long-term commitments and a minimum notice time for any redemption by its investors. This feature also provides the hedge funds with the flexibility to invest in securities that are relatively illiquid from the long-term point of view.

      • Finally, as it is almost unregulated, the pool does not have to report and disclose its holdings and positions.⁶ This feature contributed significantly to the mystery that surrounded hedge funds, a trait that attracted individual investors while at the same time keeping institutional investors away. However, institutional investors are gaining ground in obtaining greater transparency and thus are getting increasingly involved in hedge fund investing.

      1.2 INVESTMENT STYLES

      Although the term hedge funds is often used generically, in reality hedge funds are not all alike. In fact, there exist a plethora of investment styles with very different approaches and objectives, and the returns, volatilities and risk vary enormously according to the fund managers, the target markets and the investment strategies. Some hedge funds may be non-directional and less volatile than traditional bond or equity markets, while others may very well be completely directional and display a much higher volatility. Many managers even pretend to have their own, unique investment styles. Therefore, one size fits all does not apply in the evaluation process or in the arena of risk management.

      As it is critical to have a basic understanding of the underlying hedge fund strategies and their differences in order to develop a coherent plan to exploit the opportunity offered by hedge funds, consultants, investors and managers alike often segregate the hedge fund market into a range of investment styles. Unfortunately, there is no accepted norm to classify the different hedge fund strategies, and each consultant, investor, manager or hedge fund data provider may use his own classification. In the following, for the sake of simplicity, we have classified hedge funds into four main strategies: tactical trading, equity long/short, event-driven and relative value arbitrage. A fifth category comprises funds that follow more than one strategy as well as funds of funds. We do not claim that this classification is better than existing ones. It is just a working tool that is compatible with most existing classifications.

      1.2.1 The tactical trading investment style

      The tactical trading investment style refers to strategies that speculate on the direction of market prices of currencies, commodities, equities and/or bonds on a systematic or discretionary basis. Global macro investing and commodity trading advisors (CTAs) are the predominant styles in this category.

      Global macro managers tend to make leveraged, directional, opportunistic investments in global currency, equity, bond and commodity markets on a discretionary basis. They usually rely on a top-down global approach and base their trading views on fundamental economic, political and market factors. Their portfolios are large in size but concentrated, relying heavily on derivatives (options, futures and swaps). Global macro managers are by no means homogenous in the specific strategies they employ, but their goal tends to be high returns with a more liberal attitude toward risk than other hedge fund categories. Due to their discretionary approach, the quality of the manager is the sole key to a fund’s success.

      Commodity trading advisors and managed futures managers primarily trade listed commodity and financial futures contracts on behalf of their clients. As with global macro managers, CTAs are by no means homogenous, but are usually split into two groups: systematic traders and discretionary traders. Systematic traders believe that future price movements in all markets may be more accurately anticipated by analyzing historical price movements within a quantitative framework. Hence, they rely heavily on computer-generated trading signals to maintain a systematic and disciplined approach, and often use multiple systems in order to reduce volatility and produce more stable returns. In contrast, discretionary traders base their trading decisions on fundamental and technical market analysis, as well as on their experience and trading skills developed over the years (Figure 1.1).

      1.2.2 The equity long/short style

      As their title indicates, long/short equity managers invest in equities, and combine long investments with short sales to reduce but not eliminate market exposure. Indeed, long/short strategies are not automatically market neutral. Most funds tend to have a net long exposure (more long gross exposure than short gross exposure), which implies that they can have significant correlation with traditional markets, and therefore experience large downturns at exactly the same times as major market downturns. However, a few funds also aggressively use their ability to be net short.

      The long/short equity style can be divided into several sub-strategies:

      • Regionally or industry focused managers specialize in a region (e.g. Asia, Europe), a country (e.g. the United States) or a specific industry (e.g. technology), while global managers can invest worldwide.

      • Dedicated short managers only use short positions. In a sense, they are the mirrors of traditional long-only managers. They suffered greatly during the bull market of the 1990s but put up a better overall performance during the bear market of the 2000s.

      • Emerging market funds invest in all types of securities in emerging countries, including equities, bonds and sovereign debt. While many investors avoid investing in regions where information is scant, accounting standards are weak, political and economic turmoil is prevalent and experienced management is scarce, others see these as opportunities that can result in undetected, undervalued and under-researched securities. Emerging market hedge funds typically tend to be more volatile than developed market long/short equity funds. Because many emerging markets neither allow short selling nor offer viable futures or other derivative products with which to hedge, these funds often employ a long-biased strategy.

      • Market timers vary their long/short exposure in response to market factors within a short period of time.

      Figure 1.1 The various hedge fund strategies

      002

      1.2.3 The event-driven style

      Event-driven strategies focus on debt, equity or trade claims from companies that are in a particular stage of their life cycle, such as spin-offs, mergers and acquisitions, bankruptcy reorganizations, re-capitalization and share buybacks. Distressed securities and risk arbitrage are the predominant styles in this category.

      Distressed securities funds focus on debt or equity of companies that are, or are expected to be, in financial or operational difficulty. This may involve reorganizations, bankruptcies, distressed sales and other corporate restructurings. The securities of such companies generally trade at substantial discounts, because of regulatory issues (many investors are unable to hold below investment grade securities), lack of analysts’ coverage, low market liquidity and irrational fears of private investors. Distressed security specialists analyze and buy these securities when they perceive a turnaround. They take on credit and liquidity risk, and wait for these securities to appreciate in value after a restructuring is complete. Some managers may hedge with put options on the underlying market; others may even take a strategic holding in the firm and become actively involved in the restructuring. Hence, the distressed securities funds are long term in nature and have long redemption periods.

      Merger arbitrage, also referred to as risk arbitrage, involves investments in event-driven situations that include a merger or acquisition, including leveraged buyouts, mergers and hostile takeovers. A typical trade within this style is to buy stock of the company being acquired while shorting the stock of the acquirer. Even though the transaction may be publicly announced, there is still a spread to be made following regulatory acceptance, etc. Hence, the most important risk to this style is deal breakage after the announcement.

      Event-driven multi-strategy funds draw upon multiple themes, including risk arbitrage, distressed securities and occasionally other themes such as investments in micro and small capitalization public companies that are raising money in private capital markets (regulation D). Fund managers often shift assets between strategies in response to market opportunities.

      1.2.4 The relative value arbitrage style

      Relative value arbitrage strategies attempt to capitalize on relative pricing discrepancies between related instruments, including equities, debt, options and futures. The general theme among these strategies is a bet that two securities or market prices will converge over time.

      Arbitrage is usually a two-sided strategy involving the simultaneous purchase and sale of related securities that are mispriced compared to each other. Managers using this strategy may utilize mathematical, fundamental or technical analysis to determine misvaluations. Over time the instrument’s mispricing is expected to return to its theoretical or fair value.

      Managers following the convertible arbitrage style seek to exploit pricing anomalies between convertible bonds and their underlying equity. As embedded options in convertible bonds are often undervalued with respect to their theoretical value, a typical investment is to be long the convertible bond and to hedge a portion of the equity risk by selling short the underlying common stock. The positions are designed to generate profit from the fixed income security as well as from the short sale of the stock, while protecting capital from market moves. Most managers employ some degree of leverage, ranging from zero to 6:1. That is, for every $1 of investor capital, $6 is invested in securities using a margin account. Risk factors, some of which can be hedged, include interest rate, credit,⁷ liquidity and corporate event risk.

      The fixed income arbitrage style encompasses a wide spectrum of strategies that seek to exploit pricing anomalies within and across global fixed income markets. These pricing anomalies are typically due to factors such as investor preferences, exogenous shocks to supply or demand, or structural features of the fixed income market. Typical strategies are yield curve arbitrage, sovereign debt arbitrage, corporate versus Treasury yield spreads, municipal bond versus Treasury yield spreads, cash versus futures (basis trading) and mortgage-backed securities arbitrage. Value may also be added by exploiting tax loopholes, yield curve anomalies and volatility differences. Fixed income arbitrage managers often neutralize interest rate risk in their portfolios and use a large amount of leverage to enhance returns.

      The equity market neutral style (also referred to as statistical arbitrage) is a quantitative portfolio construction technique that seeks to exploit pricing inefficiencies between related equity securities while at the same time exactly neutralizing exposure to market risk. The neutrality is achieved by exactly offsetting long positions in undervalued equities and short positions in overvalued equities, usually on an equal dollar or zero beta basis. The strategy’s profit objective is to exploit mispricings in as risk-free a manner as possible. Returns often come from mean reversion (the undervalued security that has been bought, moving up in price or the overvalued security that has been sold short, declining in price), or from sector/country bets. Pair trading, which involves highly correlated stock pairs that have deviated from their historical pricing relationship, is a popular example of this strategy. Note that market neutral funds should not be confused with long/short investment strategies. The key features of market neutral funds are the low correlation between their returns and those of traditional assets.

      Other relative value arbitrage strategies include:

      • The index arbitrage style, which exploits the relative mispricings of index and index-derivative securities. Usually, this strategy is implemented through long positions in the stocks that underlie an index and short positions in an index-derivative security.

      • The mortgage-backed securities arbitrage style, which seeks to profit from the pricing difference between a mortgage instrument with uncertain prepayment and credit quality characteristics, and a non-prepayable Treasury security.

      1.2.5 Funds of funds and multi-strategy funds

      The different investment styles mentioned so far usually have very different risk-return parameters. Therefore, instead of selecting a single hedge fund manager following a single strategy, it can be more attractive to combine several individual hedge funds in a portfolio. Through diversification, this yields a more efficient portfolio - that is, a portfolio with less risk for potentially more return. The combination of hedge funds minimizes the potential impact of poor performance on the part of any individual manager and provides a more stable long-term investment return than any of the individual funds, much like what happens within traditional diversified portfolios. This idea has given birth to funds of hedge funds (referred to below as funds of funds) that allow investors to access a variety of managers and gain diversification through a single investment. A fund of funds manager may allocate his capital to several managers within a single strategy (style-specific fund of funds), or to several managers in multiple strategies (multi-strategy fund of funds).

      Attracted by the free lunch, several individual hedge funds have also joined the diversification game and started combining several strategies within the same organization. These funds usually fall under the general heading of multi-strategy funds. Most of them claim to implement some sort of dynamic strategy allocation as market conditions change.

      Figure 1.2 Estimated assets under management

      003

      1.3 THE CURRENT STATE OF THE HEDGE FUND INDUSTRY

      It is relatively difficult to obtain statistics on the overall hedge fund industry, as advertising and reporting of hedge fund information is restricted by the Securities and Exchange Commission in the USA, by the Financial Services Authority in the UK, by the Central Bank in Ireland and more generally, by regulatory authorities in most countries. Consequently, most available hedge fund information is either voluntarily submitted or incomplete and therefore may be subject to many biases that we will discuss later. Hence, the conclusions drawn from these statistics should be treated with caution.

      As mentioned previously, the number of hedge funds worldwide is estimated to be over 7000, managing total assets of around $800 billion. Further, it is important to keep in mind that this amount only represents the capital account balances of investors and not the actual number of dollars deployed in the markets. Hence, the amount of money invested by hedge funds in the market, given some of the leveraged strategies employed, could be as large as $1 trillion.

      The average hedge fund has $135 million in assets under management, but 50% of funds have assets under management of less than $38 million, while the largest hedge fund in the world, Caxton Associates, now manages more than $10 billion. An astounding number of new hedge funds have been created in the past few years to meet investors’ demands, and they are now literally starving for assets to manage (Figure 1.2).

      Most of the funds are effectively managed⁸ from the United States (New York), although around 70% are administered and registered in offshore locations. Europe (London) and Asia (Hong Kong and Singapore) are experiencing strong growth, but remain far behind the USA in terms of assets under management and number of hedge funds.

      The majority of the assets under management by hedge funds come from wealthy private individuals. Indeed, high net worth individuals (HNWIs) - individuals with assets in excess of $1 million - account for a large part of the wealth invested in hedge funds, and there are numerous signs that hedge funds are becoming a standard component of HNWI portfolios. In Switzerland, anecdotal evidence suggests that private banks now recommend investing up to 30% of assets in alternative investments. Recent research by Bernstein Research concluded that approximately 5% of high net worth individuals invest through hedge funds, but that approximately 70% of high net worth individuals who invest in hedge funds have done so for at least three years and their average allocation is above 30% of their financial assets. This segment still represents a significant potential source of growth for hedge funds over the coming years.

      Institutional investors (e.g. endowments, foundations, pension funds and insurance companies) still come well down the scale in terms of hedge fund investments, but they are showing increasing interest and now seem to view alternative investments as a necessary part of portfolio management. Participants at the SEC’s roundtable forum on hedge funds confirm that around $175 billion invested in hedge funds comes from institutions, up from $52 billion in 1998. According to another report by industry researchers Greenwich Associates, titled Asset Allocation: US Portfolios Adjust to Difficult Markets, in 2002 nearly 60% of endowments and foundations invested in hedge funds, up from 50% in 2001, and 20% of pensions also allocated to the asset class, up from 15% in 2001. And according to a survey by Goldman Sachs and Frank Russell, the average US plan sponsor anticipates that its strategic allocation to alternative investments will rise to 8% over the next three years. If the forecast proves true, this should constitute a major source of inflows in the near future (Figure 1.3).

      Figure 1.3 Estimated breakdown of hedge fund investors

      004

      Figure 1.4 Breakdown of hedge fund assets by investment strategy

      005

      Figure 1.4 illustrates the breakdown of hedge fund assets by investment strategy. It appears very clearly that long/short equity is now the dominant strategy. This is a direct consequence of the bear market of the early 2000s that resulted in several long-only managers closing their traditional funds to open a new hedge fund in order to be able to sell short and capture performance fees. However, as we shall see, long/short equity is an easy strategy to understand, but picking its best managers is a daunting task.

      An interesting statistic to monitor is the amount of money that has flowed into hedge funds. TASS Research - the information and research unit of Tremont Advisers Inc. - provides this information on a quarterly basis for a universe comprising a broad base of 3775 funds located and managed in the United States and overseas.⁹ The flow of global capital to hedge funds has risen dramatically over the last decade, and not surprisingly, money seems to chase performance.

      Today, the hedge fund industry bears a strong resemblance to the mutual fund industry of 25 years ago. Tremendous inflows of capital combined with reinvestment have fed the growth in assets, but have also resulted in little or no industry structure. Standalone funds each present themselves to investors using different investment styles, benchmarks and performance measures. High fees have attracted managers with poorly established and executed strategies, resulting in potentially grim surprises for the unwary. And while some sophisticated investors have the time, resources and intellect to evaluate and select hedge funds, the lack of transparency and disclosure deprive the average investor of access to comprehensive information about hedge fund performance.

      Fortunately, in the near future, the increasing interest of institutional investors for hedge funds combined with the sophistication and rigor of their investment process should serve as an important catalyst for refining standards of practice. More regulation, more transparency and more risk control should shift the emphasis from the high absolute returns sought by high net worth individuals to the risk-adjusted returns needed by institutions. Considering the size of the capital pool theoretically available for investment and the present allocation to hedge funds,¹⁰ the industry has plenty of room to increase its market share, either through an increase in the number of funds or through an increase in the average size of hedge funds. In both cases, we expect fund selection and portfolio construction methods to come under greater scrutiny. A better understanding of these issues is needed, and we hope that this book will contribute to this understanding.

      2

      Measuring Return

      A stock that fell by 90 percent is a stock that fell by 80 percent and then halved.

      The two basic factors to be weighted in investing, risk and return, are obviously the opposite sides of the same coin. Each must be measured to assess and understand past performance, and convince investors that their money is in the right hands. Both must also be predicted in order to make intelligent investment decisions for the future. Of course, we all know that the future is uncertain and that history may not repeat itself, but understanding what happened in the past is likely to be a guide in formulating expectations about what may happen in the future.

      Measuring the expost return and risk of an investment may sound somewhat trivial. However, the number of hedge fund managers claiming that their fund has superior risk-adjusted returns often amazes me, particularly when we simultaneously hear the dissatisfaction of investors and the tentative explanations of consultants. The reason for this discordance is simply the lack of standards on how to measure risk and return, the multidimensionality of hedge fund returns in terms of descriptive statistics, and the lack of agreement on what constitutes an appropriate benchmark. Today, the hedge fund industry is so diverse that it is impossible to define a small number of sectors that are homogenous enough to ensure apples-with-apples comparisons.

      In the traditional investment world, formal standards of performance measurement were drawn up and adopted in the early 1990s, under the influence of the Association of Investment Management and Research (AIMR). Compliance with the AIMR Portfolio Presentation Standards (AIMR-PPS) and the more recent Global Investment Performance Standards (GIPS) ensures full and fair disclosure of investment results to clients and prospective clients, and guarantees that all managers act on the same level playing field. Unfortunately, we do not have the equivalent yet for hedge funds and alternative investments.

      As long as clearly-defined standards are lacking, performance measurement will have much in common with religion: it means something different to everyone, it results in veneration by some, and it is often the source of disputes and conflict. To make matters worse, smart swindlers take advantage of the lack of consensus by propagating hedge fund statistics that claim to be of value to investors, but which are in reality based on misconceptions, misinterpretations and flawed assumptions.

      This situation is of some concern, particularly when we recall that risk and return - the two keys of performance - play an essential role in comparing different funds as well as in evaluating the compensation of hedge fund managers. It also raises serious doubts about the possibility of evaluating hedge funds from an ex ante perspective. If we cannot agree about what happened in the past, how can we attach any value to our forecasts for the future?

      In order to interpret correctly the statistics of hedge fund performance and separate the wheat from the chaff, the reader must first understand the basic quantitative concepts and know what is hidden behind the notions of risk and return. In this chapter, we attempt to demystify both the statistical analysis of hedge fund returns and result interpretation, in an effort to enhance our future decision-making process. Although we have made every effort to offer a clear and intuitive explanation of the associated issues, we could not avoid a few equations, some of them probably intimidating. But do not worry: the material is covered in the text and in examples, so that most equations do not need to be fully understood in order to clearly grasp the concepts involved.

      You may be tempted at this point to skip this chapter and go straight to the next one. This would not be a judicious move, however, because the rest of the book builds upon what is learnt in this chapter. When the wind blows, a house with no foundations will not resist for long. The same applies to the hedge fund investor without a clear understanding of the material that follows. Without a thorough understanding of risk and return, it would be an uphill task to carry out the necessary quantitative analysis.

      2.1 THE DIFFICULTIES OF OBTAINING INFORMATION

      Investors accustomed to high levels of control and transparency in traditional investments often find the variations in what hedge funds disclose discouraging. In some cases, even the phone number of the hedge fund manager seems to be proprietary information.

      Transparency is obviously a touchy subject for hedge fund managers. After Alfred Winslow Jones had formed the first hedge fund in 1949, he managed to operate his fund in complete secrecy for 17 years. Almost 50 years later, the hedge fund Long Term Capital Management (LTCM) was considered as being the very paragon of modern financial engineering, with two Nobel Prize winners among its partners and Wall Street’s most celebrated trader as its CEO. It shrouded its operations in secrecy, denying lenders and their regulators any data about its positions or its liabilities to other lenders. Do you want us to refund your money? was the usual question to LTCM partners that were too inquisitive about the fund’s activities.

      These two examples, although not recent, are quite representative of the reputation of operating under a cloak of secrecy that most hedge fund managers have today. They still tend to avoid disclosing the securities they hold, their views on the market, the extent to which they are leveraged, or even in some cases their past performance figures. This attitude has often been perceived as hubris and arrogance. The true picture is somewhat different. In reality, there are at least three reasons that may help justify the relative secrecy surrounding hedge fund operations.

      First, one should remember that, unlike mutual funds, onshore hedge funds are privately organized investment vehicles subject to minimal oversight from regulatory bodies. The numerous funds incorporated offshore for tax purposes are even less regulated. As long as smaller, unsophisticated investors do not join the band, regulators do not bother with the situation. Consequently, hedge funds are not required to disclose holdings, returns or even their existence beyond what is spelled out in the contract with their investors. And many hedge fund managers are very happy to remain boutiques catering primarily to high net worth individuals. They do not really care about attracting new investors. Hence, the lack of transparency to non-investors is not surprising!

      Second, most regulators do not allow hedge funds to advertise or solicit money from the general public. Onshore hedge funds are only allowed to target limited groups of accredited investors, and offshore hedge funds are legally debarred from making domestic public offerings. Releasing information about past performance could easily be regarded as advertising, particularly if the figures are good and attract the attention of potential investors. Hedge fund managers will not take that risk and prefer to remain in the shade.

      Third, many hedge fund managers shy away from disclosure, particularly those active in illiquid markets (e.g. distressed securities or merger arbitrage), or who frequently engage in heavy short selling or highly leveraged positions (e.g. fixed income arbitrage or global macro, for example). These managers believe that allowing competitors to see their trades is tantamount to revealing the underpinnings of their strategies and exposing them to disastrous short squeezes and numerous competitive risks. Arbitrage is often based on being the first to find rare market inefficiencies before anyone else has the chance to squeeze profit out of the trade, which effectively irons out the inefficiency. The more secretive you stay, the higher the profit. Furthermore, the market could easily trade against a hedge fund manager once its positions are revealed.¹¹

      For these reasons, among others, it is common practice for hedge fund managers to structure their funds so as not to trigger reporting requirements imposed by regulators¹² and to supply minimal information to their existing investors. This typically includes an estimate of the monthly return, a few statistics such as volatility and correlation, and possibly a quarterly letter from the manager himself. In a sense, the situation could be described as relatively opaque.

      It was only after 1998 and the bail-out of Long Term Capital Management that regulators, investors and prime brokers started requiring greater disclosure, particularly in relation to the risk side. The demand for more transparency strengthened with the interest of institutional investors such as pension funds and insurance companies, which had, and still have, limited exposure in this market, but constitute a large potential source of demand for hedge fund products in the future. Under pressure from these new investors and fearing regulatory controls, the hedge fund industry is progressively institutionalizing itself. Many hedge funds have evolved from the start-up structure of a one-man trading company to a global financial institution, with written policies and procedures, separation of front, middle and back office, succession planning, disaster recovery, independent risk management, etc. This seems to be the new pattern of evolution for hedge funds.

      In parallel, transparency has swept across markets, and while some hedge fund managers may not like it, they will have to live with it. An increasing number of managers are now willing to discuss portfolio information openly and directly with investors, at least on a monthly basis. Many investors are quite satisfied with this approach, as they have confidence in the manager. But some request more information, ranging from the dollar exposure by trader or portfolio manager, asset class, sector/industry, currency, strategy or style, to the leverage, the performance attribution and the complete value at risk analysis. In a few cases, the request concerns the individual position details on a weekly or even daily basis. For the time being, the majority of experienced hedge fund managers are still unwilling to offer this level of transparency, except perhaps through a managed account that they run in parallel with their fund.¹³ But things could change very rapidly, as the demand for increased transparency is still around.

      The question of determining the level of detail beyond net asset values that constitutes adequate or appropriate portfolio transparency still fuels an ongoing debate.¹⁴ A few hedge funds have agreed to provide full transparency by allowing investors to gather position data from prime brokers. But most investors lack the skills and resources to interpret position-level information, so that complete transparency actually makes the job of analyzing risk and return more complicated. The emergence of risk transparency rather than position transparency seems to offer a good compromise, at least for the time being, and provides investors with a meaningful snapshot of a hedge fund’s risks. It addresses investor concerns while avoiding position detail that may be difficult to obtain and overwhelming to receive.

      The next step of risk transparency is the standardization of risk factors, so that the risk exposures can be aggregated across an investor’s portfolio of hedge funds. Riskmetrics™ and other market leaders in the field of risk management are now offering solutions in order to fulfill this task. Value at risk (VaR) in particular has been used by both investors and managers in analyzing their portfolios and provided a common language for risk communication. But this is another topic, which we shall come to later.

      2.2 EQUALIZATION, CRYSTALLIZATION AND MULTIPLE SHARE CLASSES

      Obtaining a time series of historical net asset values for a given hedge fund may be difficult. Unfortunately, it is only the first part of the story. Unlike traditional mutual funds that have a clean way of calculating their net asset values, the world of hedge funds is a real jungle with its particularities and conventions. Hence, several adjustments must usually be made to historical data before performance can be measured. Among these, the most frequent are equalization calculations and crystallizations.

      Equalization calculations are a series of accounting methods used to ensure that incentive fees are charged in a fair and equitable way to all investors in a hedge fund. Conceptually, determining the incentive fee at the fund level should be a fairly straightforward exercise. Incentive fees are typically calculated as a percentage of the annual or semi-annual increase in the gross asset value of the fund, either as a straight percentage of the appreciation or as a percentage of the increase over a certain threshold (hurdle rate). However, computational complications arise when investors are allowed to buy into the fund at different times during the year and, therefore, at different net asset values per share. Indeed, purchases at different times result in differing percentages of appreciation relative to other investors at the end of each measurement period. This raises several potential problems.

      2.2.1 The inequitable allocation of incentive fees

      In the absence of any adjustment, when the fund performance is positive, an investor who buys into the fund in the middle of the measurement period may be charged a full incentive fee, although he has only participated in a part of the performance. In a sense, he will be subsidizing another shareholder.

      As an illustration, consider a hedge fund launched on 1 January at a share price of $100. To keep things simple, say the fund charges no management fee. Its incentive fee is equal to 20% of the performance, charged semi-annually without any hurdle rate. On 1

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