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Hedge Funds: Have you missed the boat?

Inside: Executive Summary

There seems to be no lack of opinions on the future of hedge funds. While hedge I. What are hedge funds? funds have been around longer than most investors realize, their recent expansion II. Hedge fund returns: Have we has raised their profile. Articles on hedge funds permeate nearly every financial killed the goose that laid the publication, but the story is almost always the same. The tone of the commentaries golden egg? are most often vague or skeptical, pointing to increasing assets and managers, III. Does active portfolio disappointing returns, high fees, or, perhaps worst of all, scandal or fraud as management add value? indications of the imminent demise of hedge funds. Understandably, many investors IV. In the Headlines: Fees, who have been disappointed with recent hedge fund returns are asking, “Have I leverage, scandals missed the boat? Is it too late to gain the benefits of hedge fund investing?” To and regulation answer this question, we believe it is imperative to take a fresh look at the investment category and re-assess return, risk and correlation expectations. V. The future of hedge funds There is no doubt that hedge funds are vehicles for delivering active risk and return. But the decision to include them in a portfolio hinges on your belief in the ability of active management to deliver returns. Our view is that despite what you may read in the papers today, the ship has not sailed for hedge funds. A diversified portfolio of hedge funds can still add value to a portfolio.

KENT A. CLARK Managing Director, Chief Investment Officer Hedge Fund Strategies [email protected] (212) 855 9928

The material in this publication is for your private information and should not be construed as financial advice and it is not intended as an offer or solicitation to buy or sell any securities. NOVEMBER 2005 Perspectives | Hedge Funds: Have you missed the boat?

Author

KENT A. CLARK Managing Director, Chief Investment Officer, Hedge Fund Strategies

Kent is a Managing Director and Chief Investment Officer of Goldman Sachs Hedge Fund Strategies (HFS). Kent joined Goldman Sachs Asset Management in 1992 as a member of the Quantitative Equity team, where he managed Global Equity portfolios and Equity Market Neutral trading strategies. In this capacity, he also developed risk and return models. Kent became a managing director in 1998 and partner in 2004. Kent’s research has been published in the Journal of Financial and Quantitative Analysis and in Enhanced Indexing. He co-authored A Strategic Role for Hedge Funds and Active Risk Budgeting in Action: Understanding Hedge Fund Performance and contributed a chapter to Modern Investment Management: An Equilibrium Approach. Kent serves on the Board of Governors of the Graduate Faculty at the New School University, on the board of the Managed Funds Association, and he is a member of the Chicago Quantitative Alliance. Formerly, he was president of the Society of the Quantitative Analysts. Kent joined Goldman Sachs from the University of Chicago Graduate School of Business where he completed all but dissertation in the PhD program and received an MBA. He holds a Bachelor of Commerce degree from the University of Calgary.

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Introduction

Hedge funds have grown to Hedge funds have captured increasing attention over the past few years, as evidenced by be a significant investment strong asset growth. Hedge fund assets have doubled over the past five years to over one category. But, at the same trillion dollars by mid-2005. Not surprisingly, with this growth has come an increased focus time, investors seem on hedge funds among financial journalists, academics and commentators. Although many disenchanted with returns. articles written during the equity bear market years of 2000 through 2002 were focused on Is it too late to invest in hedge funds? the benefits of hedge funds for investors’ portfolios, popular opinion has increasingly become more skeptical.

I just finished reading one of many gloomy hedge fund articles that cross my desk. It raised all the issues I have recently come to expect when reading about hedge funds: disappointing returns, too many managers, decreased risk-taking, best-in-class managers retiring from the business, changing fee structures, scandal and the threat of SEC regulation. The major difference is that this article, entitled “Hard Times Come to Hedge Funds,” was published in the January 1970 issue of Fortune.

Apparently, 1969 was a tough year for hedge funds. At the time, the industry was focused on executing equity long/short strategies. Weak equity markets found many funds without enough short exposure and with the wrong stocks held short. There were suggestions that the US$1 billion in assets, approximately 150 managers, represented too much capital in the strategy. Some managers discussed adjusting their investment approach to take less risk, treating their assets as if they represented 100% of an investor’s wealth. One of the “oldest, largest and most successful investment partnerships, Buffett Partnership, Ltd.,” run by Warren Buffett, was expected to close down. Mr. Buffett’s investment partnership commanded a 25% incentive fee over a 6% hurdle rate. Managers were starting to charge a fee to pay base salaries in addition to participating in partnership profits, thereby increasing fees. Some hedge fund reputations were tarnished because managers had been implicated in an insider trading scandal in 1968. And finally, the article states that “SEC staff members have made it supremely clear that they believe the [hedge] funds should be brought under some form of regulation.”

Thirty-five years later, although the exact facts are different, the setting is familiar. After some very solid years of hedge fund returns, many investors are disappointed with recent returns and are now wondering whether they have missed the hedge fund boat. Is it too late to achieve the benefits of hedge fund investing? Absolutely not. Let’s look more closely at exactly what a hedge fund is and what our expectation should be for their returns going forward.

Goldman Sachs Asset Management | 3 Perspectives | Hedge Funds: Have you missed the boat?

I. What are hedge funds?

Hedge funds are simply investment vehicles. These vehicles have some common characteristics, including a lack of investment constraints, an incentive-based fee structure and limitations on the types of investors who are eligible to participate.

The lack of investment constraints means that a hedge fund’s investment portfolio should represent the purest expression of the manager’s investment views. The manager can be either long or short a security. He can be fully invested, leveraged or may tactically allocate capital to cash. The absence of a benchmark allows the manager to invest, or not to invest in any asset without constraints.

The investment consequence of being largely unconstrained is that hedge funds offer investors the opportunity to maximize exposure to skill, where skill exists. The hedge fund structure does not, however, create manager skill. Nevertheless, relaxing constraints may create opportunities that do not exist within traditional investment mandates. Indeed, some opportunities are created by traditional investment mandates.

Whether we think hedge funds add value is, at its core, a question of our belief in active management. If we believe that taking informed active risk has the potential to generate active returns, then it would stand to reason that hedge funds have the potential to generate active returns as well.

More specifically, we know that among long-only investments, the average manager returns something like their benchmark less management fees and transaction costs. In other words, their average skill is zero. Therefore, in order to earn active returns, investors must be able to select above-average managers. The same should be true for hedge funds. Skill matters – and must be identified regardless of the investment category.

II. Hedge fund returns: Have we killed the goose that laid the golden egg?

The main complaint about hedge funds seems to be that recent returns have been “disappointing,” which, in investment parlance, is a euphemism for “bad.”

Disappointed investors are Of course, disappointment can be the result of either a bad outcome or unrealistic comparing hedge funds to expectations. For example, Exhibit 1 shows hedge fund returns for each year, starting equity markets. Is this an in 2000, as well as returns through July 2005. In addition, it shows returns for the MSCI appropriate comparison? World Index, a broad-based global index of large capitalization stocks. Although absolute returns for hedge funds were higher in 2003 and 2004 than they were from 2000 to 2002, disappointment seems to have taken hold in 2004. One explanation for this is that investors are implicitly comparing hedge funds to equity markets. But are equities the appropriate comparison? Before being disappointed, we should make sure we set realistic expectations for returns. To do this, we put forth a simple and familiar framework for thinking about returns.

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Exhibit 1: Hedge Fund Returns Compared to Equity Markets — Jan-00 through Jul-051

40% CSFB-Tremont HFI Index 33.1% MSCI World Index 30%

20% 15.4% 14.7% 9.6% 10% 4.9% 4.4% 3.0% 3.3% 2.8% 0%

-10% -13.2% -16.8% -20% -19.9% 2000 2001 2002 2003 2004 2005

CSFB-Tremont HFI Index MSCI World Index Annualized Return 7.2% -1.7% Annualized Volatility 5.2% 15.0%

Past performance is not indicative of future results, which may vary.

Simply stated, a portfolio’s return can be decomposed into three components:

1. Return to a risk free asset. This is both the cost of funding and, of course, the return an investor can obtain without taking any risk, whether passive or active.

2. Return to passive exposure to markets, or return to beta. These are measured in excess of the risk-free rate. These risks and returns are typically inexpensive to achieve. For example, broad equity market returns can be replicated at close to zero cost.

3. Return to active management. This is generated in excess of the other two and is typically referred to as alpha. Alpha is the measure of skill-based return.

What are the implications of this framework for understanding hedge fund returns? First, we need to consider excess returns over the risk-free rate. Why should this be our starting point? Any action by a manager must be taken with the expectation of generating return from either asset class risk or active risk. Consequently, we should have different total return expectations in a world with 5% risk-free money than those we have in a period where the risk-free rate is 1%.

1 Indices are unmanaged. The figures for the index reflect the reinvestment of dividends but do not reflect the deduction of any fees or expenses which would reduce returns. Investors cannot invest directly in indices. Goldman Sachs Asset Management | 5 Perspectives | Hedge Funds: Have you missed the boat?

Exhibit 2 compares excess returns of 10 hedge fund strategies in 2004 to those in the prior 10 years. These returns are measured in excess of the risk-free rate (90-day US Dollar LIBOR), which averaged 1.5% in 2004 compared with 4.7% in the previous 10 years.

Exhibit 2: Returns in excess of 90 day US Dollar LIBOR2

Last year’s average † returns were superior to 10-year excess returns (Jan-94 – Dec-04) 2004 excess returns* 15% historical data. 12%

9%

6%

3%

0%

-3%

-6%

-9% Convertible Fixed Equity Event Risk Distressed Equity Global Managed Arbitrage Income Market Driven Arbitrage Long/Short Macro Futures Arbitrage Neutral

Source: Goldman Sachs, CSFB Tremont +Excess returns defined as annualized total returns over three-month US $ Libor. Data from Jan-94 to Dec-04. * Excess returns generated in the trailing 12 months from Jan-04 to Dec-04. Past performance is not indicative of future results, which may vary.

After adjusting for the risk-free rate, just three of the 10 strategies’ returns in 2004 were less than their historical averages, two of which were statistically significant. These two strategies – convertible arbitrage and global macro – accounted for about 18% of hedge fund assets over the period.3 This suggests that, on an asset-weighted basis at least, most strategies had higher excess returns in 2004 than they had in the past. This is even more interesting in light of the survivor and backfill biases in historical hedge fund data. These biases suggest that historical excess returns are likely overstated.

2 Indices are unmanaged. The figures for the index reflect the reinvestment of dividends but do not reflect the deduction of any fees or expenses which would reduce returns. Investors cannot invest directly in indices. Indices used: CSFB-Tremont HFI Convertible Arbitrage, CSFB-Tremont HFI Fixed Income Arbitrage, CSFB-Tremont HFI Equity Market Neutral, CSFB-Tremont HFI Event Driven, CSFB-Tremont HFI Event Driven - Risk Arbitrage, CSFB-Tremont HFI Event Driven –Distressed, CSFB- Tremont HFI Event Driven - Multi-Strategy, CSFB-Tremont HFI Long-Short Equity, CSFB-Tremont HFI Dedicated Short Bias, CSFB-Tremont HFI Emerging Markets, CSFB-Tremont HFI Global Macro, CSFB-Tremont HFI Managed Futures. 3 Survivor bias arises when failed managers are retroactively removed from an index, presumably increasing index returns during the period that the failing manager was doing poorly. Backfill bias is introduced when a new manager’s return history is retroactively included in an index. This benefits index returns by including managers who are known to have survived, an insight that was presumably not possible with perfect foresight. 6 | Goldman Sachs Asset Management Perspectives | Hedge Funds: Have you missed the boat?

Therefore, last year’s average returns are even better in this context. So why were investors disappointed?

The other two components of returns – those that are derived from taking passive and active risk – are potentially much more interesting. If we set reasonable expectations for our risk exposures to markets and to the managers’ active views, then we should be able to generate reasonable expectations for hedge fund returns and risks as well. Our expectations should be based on both how much risk we expect to be taken and how efficiently that risk is turned into return.

As stated earlier, passive market risk is expressed as beta – the degree to which an asset’s return varies with market performance. Beta may be measured for equity and fixed income exposure. While ideally, beta is a relatively small fraction of return for most hedge funds, the degree to which passive risk-taking affects return varies depending on the strategy and manager. Certainly, equity market beta expectations should be different for a fixed income manager, who typically has no equity market sensitivity, than for an equity long/short manager, who may have material and variable equity market exposure.

Whereas the amount of passive risk exposure a portfolio takes varies by portfolio, the risk premium received for taking a unit of passive risk is the same for all assets. So the degree to which hedge fund returns are driven by passive risk is a function of the fund’s risk exposure and the passive risk premium. While risk exposure is presumably measurable, risk premia are not easily observable and are uncertain. Our expectations for both are important inputs into broader return expectations. We will focus on a single source of passive risk and return – equity market beta and the equity risk premium.

Hedge funds typically have low beta, certainly less than most active managers that are benchmarked to a passive index. In the extreme case, a hedge fund that is truly zero beta will be unaffected by stock market gyrations. When equity markets are falling, low beta works in a fund’s favor, dampening its decline. Of course, when equity markets rise, there is no reason for the fund to follow suit. It is no accident that hedge funds gained tremendous favor during the time when equity markets were dropping like a rock. And it is likely no coincidence that they are falling out of favor in the wake of two very good years for equity markets. In fact, the MSCI World Index returned 33.1% in 2003 and 14.7% in 2004. However, despite strong returns in 2003 and 2004, annualized returns to the MSCI World Index over the three- and five-year periods ending December 2004 are 6.9% and 2.4%, respectively.4

These returns should serve as a reminder that equities are a relatively high-risk asset. As measured by the MSCI World Index, both the volatility of returns (a standard deviation of about 17% over the very long term) and the dramatic losses experienced in the last five years substantiate this fact. Exhibit 3 shows return, volatility and peak-to-trough losses for equity markets and a broad hedge fund index from January 1994 though July 2005.

4 Source: Bloomberg Goldman Sachs Asset Management | 7 Perspectives | Hedge Funds: Have you missed the boat?

Exhibit 3: Hedge Fund and Equity Market Risk

Index CSFB-Tremont HFI Index MSCI World Index Annualized Return 10.7% 7.7% Annualized Volatility 8.0% 14.0% Beta to MSCI World 0.3 1.0 Maximum Drawdown -13.8% -46.8% Current Drawdown 0.0% -10.1% Peak Jul-05 Apr-00

All of this is interesting, but what are reasonable expectations for future equity market returns? After adjusting for expansion in price-to-earnings multiples in the last quarter of the twentieth century, US equity markets delivered about 4% over the risk-free rate.5 Supposing that we will experience a similar equity risk premium in the future, then with the risk-free rate at around 4%, we could expect returns of 8% for equities.6

III. Does active portfolio management really add value?

This is the fundamental question we need to answer to determine whether the hedge fund ship has sailed. As already discussed, if you believe active management has the potential to generate returns, then hedge funds are the purest means for investors to capture those active returns. If, however, you don’t believe in active management, you should reconsider all the active exposure in your portfolio, whether it is in hedge funds or attached to a market index in a traditional investment portfolio.

Active risk is simply the risk that a manager takes in expressing his investment views. Active return is a function of the amount of active risk taken and the portfolio manager’s ability to convert that active risk to return, or alpha. Active risk is independent of any passive market exposure created, whether intentional or not. Ideally, hedge funds are vehicles for delivering active risk and return. In reality, however, many combine some amount of market exposure with active risk. In traditional benchmark-oriented portfolios, active risk is created by deviating from benchmark asset weights. For hedge funds, where there is no benchmark, all portfolio positions presumably result from the manager’s active views. These positions may create some market exposure as well. For example, a bullish outlook for equities and resulting long positions would create exposure to the equity market.

There are many reasons to believe active portfolio management can effectively transform active risk into active returns. These are well documented in investment literature and include time-varying risk premiums, the tendency of investors to under- react and over-react to different types of information, the existence of investors with motives other than pure risk/return optimization, and a variety of frictions and pockets of illiquidity.7

5 Roger Ibbotson and Peng Chen, “Stock Market Returns in the Long Run: Participating in the Real Economy,” Yale International Center for Finance working paper no. 00-44, Mar 2002. 6 Expectations, including forecasts of conditions, are estimates as of the date of this material and are based on a number of assumptions. Expectations are subject to revision and may vary as economic and market conditions, models, or other matters change. These expectations should not be relied upon to make predictions of actual future performance. There is no guarantee that the above results can or will be achieved. 7 A compact overview related to Global Tactical Asset Allocation, including both theory and evidence, is provided Mark M. Carhart, “Global Tactical Asset Allocation” in Modern Investment Management: An Equilibrium Approach, John Wiley & Sons, Inc., 2003, chapter 25, pp. 455-482. 8 | Goldman Sachs Asset Management Perspectives | Hedge Funds: Have you missed the boat?

A portion of active return may be attributable to “exotic” or hedge fund betas.8 These returns are derived from passively investing in strategies most closely associated with hedge funds, such as merger arbitrage or convertible bond arbitrage. Exposure to these risks and returns is more difficult to achieve than asset class exposure, and exotic betas represent drivers of return that are not found in traditionally managed active portfolios. Consequently, we typically consider these risk and returns as a subset of the active component of portfolio risk and return. Skilled managers may be able to add alpha above the return to exotic beta.

Even if we agree that there have been opportunities to generate active returns, skeptics point to inflows of capital and the apparent demise of a few strategies as indicators that hedge funds are finished. While inflows have been very strong, totaling approximately US$74 billion in 20049 alone, we need to consider this in the context of overall market size.

First, let’s consider the assets in hedge funds that short stock relative to the overall market size. Approximately 35% of hedge fund assets, or US$350 billion, is invested in equity long/short and equity market neutral strategies.10 If the average hedge fund has US$1 long and US$1 short for each dollar of equity in the fund, then these managers would control about US$700 billion in equities. In fact, this may overstate the amount of capital at work, but is a good starting point. As a rough approximation, then, equity long/short and equity market neutral hedge funds account for less than 2% of global equity market capitalization, which is about US$40 trillion.11 Short interest on the New York Stock Exchange represents about 2.3% of listed shares.12 If this is a good proxy for the global average, then there are about US$1 trillion of stock sold short. This suggests that these two hedge fund categories account for about 35% of short interest. Looking at turnover, an average of about US$100 billion of shares trade each day,13 so hedge funds would hold seven days of trading volume. It seems unlikely, at these levels, that there is too much capital in long/short and equity market neutral hedge funds.

Hedge funds trade in many other markets, and several of these markets are also very large. For example, approximately US$1.2 trillion of currencies are traded each day.14 Hedge funds participating in these markets are also small relative to market size.

Of course, even considering the simple numbers we present, hedge funds could seem to represent a significant proportion of activity in a position or market at times. But, broadly speaking, hedge funds do not currently seem to be dominating market activity.

8 Two pieces on this topic are: Thomas Dunn, “Hedge Fund Investing – A Taxonomy of Alpha”, ABP Investments US, Inc., 2004 and Cliff Asness “An Alternative Future” Journal of Portfolio Management, 30th Anniversary Issue, 2004. 9 Hedge Fund Research, HFR Q2 2004 Industry Report 10 Hedge Fund Research, HFR Q2 2004 Industry Report 11 Goldman Sachs, BIS, Bloomberg 12 Source: NYSE website 13 Goldman Sachs, BIS, Bloomberg 14 Goldman Sachs, BIS, Bloomberg Goldman Sachs Asset Management | 9 Perspectives | Hedge Funds: Have you missed the boat?

IV. In the Headlines: Fees, leverage, scandals and regulation

One way to think about hedge funds is as businesses that generate revenue by trading securities. They have a very well-defined expense structure combining fixed and variable costs in the form of asset-based and performance-based fees. Like other businesses, hedge funds employ leverage, based on the risk of the underlying assets. Unlike most businesses, however, hedge funds trade at a price-to-book ratio of one. Hedge funds fail, usually because of an inability to generate revenues sufficient to sustain the business, often because customers are dissatisfied with the product (returns) and occasionally because of a lack of controls or fraud. All of this makes hedge funds seem more familiar than the usual definition of “secretive, highly levered, investment vehicles for the very rich.”

Fees. Hedge fund fees are typically 1% to 2% of assets plus 20% of trading profits. While these seem rich relative to fees for traditional actively managed portfolios, the comparison is really not fair. As we know, a traditional portfolio bundles a large exposure to inexpensive beta as well as exposure to alpha. An appropriate analysis would compare fees paid for the amount of active risk and return the investor expects.

Ultimately, whether hedge fund fees are too high really depends on whether investors are receiving an attractive risk-adjusted return. We know that some hedge funds turn away capital, in spite of fees that are much higher than average. These funds have demonstrated the ability to generate attractive returns over a long period and investors are willing to pay higher fees to receive these returns. Conversely, investors seldom receive value for fees paid, regardless of how low they are.

Leverage. Hedge fund investors often attribute failures and losses to leverage, which serves to amplify returns, both positive and negative. In this respect, during bad performance periods, a more highly levered fund will have steeper losses and find its business in a more precarious state than a less levered fund will. Of course, leverage is only half the story. Risk ultimately depends on both leverage and the volatility of a hedge fund's unlevered strategy. But leverage is not unique to hedge funds. On average, hedge funds probably put two to three dollars to work for every dollar invested in the fund, with many managers operating with less leverage. And while some hedge funds may operate with higher leverage, we should remember that many traditional financial institutions operate with debt/equity ratios of 10x to 15x or higher.

Scandals and Frauds. Many businesses, both small and large, experience various forms of fraud or scandal each year. Some are very public, such as WorldCom, Enron, Tyco and Adelphia. Rarely is it suggested that investors should completely avoid debt and equity markets as a result. Hedge funds are also the subject of deception, theft, or slightly less glamorously, poor controls, all of which may result in losses and failure. When hedge funds are at the center of the story, however, lurid headlines often prevail.

Thorough analysis of a firm’s infrastructure, process and controls helps reduce the probability of investing in a fund with shaky operations or one that is particularly susceptible to fraud. And while it may be impossible to completely ensure against investing with a fraudulent fund, diversification can mitigate the economic impact of such an investment.

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Regulation. All this leads quite smoothly to the topic of hedge fund regulation. While regulation remains apparently quite shocking to US domiciled hedge funds, readers outside the US will be excused for wondering what all the fuss is about. The Financial Services Authority oversees hedge funds based in the UK and it seems to have neither discouraged the creation of funds nor impeded their ability to generate returns.

V. The future of hedge funds – you haven’t missed the boat

We believe active management generates active returns, and active risk and return have a place in all investment portfolios. As long as there are active returns to be made, the hedge fund ship has not sailed – you have not missed the boat. Uncorrelated sources of return are powerful additions to portfolios. And thoughtfully chosen portfolios of hedge funds can offer access to uncorrelated returns. Of course, it is the nature of risk that there will be periods when active returns will be below or above our expectations. Importantly, generating active returns is not easy and selecting managers who will reliably generate active returns in the future should not be taken for granted.

Realistic expectations for return, risk and correlation are critical to any successful investment program. Investors can be misled by making investments in any asset based on unrealistic hopes of heroic returns. In the case of hedge funds, after properly adjusting for risk-free rates, it is difficult to argue that recent returns for many strategies have been worse than historical experience. Nevertheless, some investors continue to expect absolute returns higher than those generated in the past, in spite of currently lower risk-free rates, while still taking minimal risk. However, the importance of reasonable expectations doesn’t stop with hedge funds. Unrealistic hopes for returns to the available alternatives can lead to equally misguided investment allocations. For example, investors with long-term expectations for equity market returns greater than the risk-free rate plus 4% are likely to be disappointed.

Finally, hedge fund investing is an active process. New strategies are created by financial innovation and an evolving marketplace. Returns to existing strategies change as traders enter and exit the market and as underlying risks evolve. Some strategies dissipate as pricing anomalies are arbitraged away and liquidity flows to where it is needed. Hedge fund managers are drawn to the market by the opportunity to create independent investment organizations, to prove their ability and to build wealth. And hedge funds shut down as victims of unfortunate timing, poor management and bad luck. Although there may be some return to investing in “exotic beta” strategies, which offer exposure to risk factors that are difficult or expensive to access, earning above-average returns requires finding above-average managers. As long as investors have resources, judgment and access, the hedge fund boat will stay afloat for years to come.

Goldman Sachs Asset Management | 11 This presentation has been prepared and given by Kent Clark of Goldman Sachs Asset Management LP. Pursuant to an instrument issued by the Australian Securities and Investments Commission, Goldman Sachs Asset Management, LP is exempt from the requirement to hold an Australian Financial Services License provided the only financial service it conducts in Australia is the provision of general advice to wholesale clients (as those terms are defined in the Corporations Act 2001 (Cth)). Accordingly, in Australia, this presentation is intended to only be given, and may only be given, to wholesale clients. To the extent that this presentation contains any financial product advice, that advice is general advice only. This document may not be reproduced or distributed to any person in Australia or New Zealand without the express prior written consent of Goldman Sachs Asset Management, LP. The opinions expressed in this material are those of the author, and do not necessarily represent the opinions of Goldman Sachs. The investments and returns discussed in this paper do not represent any Goldman Sachs fund, separate account, or product. This material is provided for educational purposes only and should not be construed as investment advice or an offer to sell or the solicitation of offers to buy any Goldman Sachs product or service. The information contained in this paper is not intended to be used as a general guide to investing, or as a source of any specific investment recommendations. This paper makes no implied or express recommendations concerning the manner in which any client’s account should or would be handled, as appropriate investment strategies depend upon the client’s investment objectives. This material is for the general information of our clients. It does not take into account the particular investment objectives, restrictions, tax and financial situation or other needs of any specific client. Expected returns are statistical estimates derived from statistical models. Actual returns are likely to vary from expected returns. Expected return models apply statistical methods and a series of fixed assumptions to derive estimates of performance. Reasonable people may disagree about the appropriate statistical model and fixed assumptions. These models have limitations, as the assumptions may not be consensus views, or the model may not be updated to reflect current economic or market conditions. Accordingly, these models should not be relied upon to make predictions of actual future account performance. Goldman Sachs has no obligation to provide recipients hereof with updates or changes to such data. 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