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Risk Analysis of Hedge Funds versus Long-Only Portfolios
Duen-Li Kao1
Correspondence: General Motors Asset Management 767 5th Avenue New York, N.Y. 10153 E-Mail: [email protected] Current Draft: October 2001
1 Tony Kao is Managing Director of the Global Fixed Income Group at General Motors Asset Management. The author would like to thank Pengfei Xie and Kam Chang for their insightful research assistance. The author is grateful for many useful discussions with colleagues in the Global Fixed Income Group and constructive comments from Stan Kon, Eric Tang and participants at the �Q� Group Conference in spring 2001.
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Risk Analysis of Hedge Funds versus Long-Only Portfolios Introduction
Despite the decade-long bull market in the 1990s and liquidity/credit crises in the late
90s, hedge fund investing has been gaining significant popularity among various types of
investors. Total size of reported hedge funds increased four fold during the period 1994
to 20002. The Internet bubble and valuation concerns for global equity markets,
especially among sectors such as telecommunications, media and technology, have
provided additional catalysts for the soaring interest in hedge funds over the last two
years.
Institutional investors often use hedge funds as part of absolute return strategies in
pursuing capital preservation while seeking high single to low double-digit returns. This
strategy is primarily implemented by absolute return investors (e.g., endowments,
foundations, high net-worth individuals). Allocations by corporate and public pension
plans to hedge funds as a defined asset class is a recent phenomenon. A second
application is to use hedge funds as an alternative to long-only investing through an alpha
transfer process. This often involves combining hedge funds with various derivative
overlays. The pension consulting and hedge fund communities have been advocating this
application in view of long-only managers� difficulty in achieving active returns over
benchmarks.
For example, pension plans can overlay an equity market neutral fund with equity index
futures to create a synthetic equity long portfolio. To the extent the hedge fund
component outperforms its funding cost (e.g., LIBOR), the alpha may be transferred back
to a long equity portfolio via derivatives. In theory, one can reverse this process to form
a pseudo-hedge fund. That is, an equity long-only manager�s alpha over an equity index
can be transferred back to an absolute return fund by shorting equity futures. Most likely,
2 See TASS (2000). Estimated market size of hedge fund industry varies greatly. For example, Hennessee Hedge Fund Advisory puts it at $408 billion at the end of 2000 in contrast to $210 billion according to TASS.
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endowments and foundations would not pursue this fantasy strategy. Does a pure
mathematical equivalence fail to convince these institutional investors to �expand� their
hedge fund manager universe?
Since theoretically one can transfer alphas from either long-only or long/short portfolios
to a desired target investment, we can compare these two types of alphas over their
respective benchmarks (index benchmark or LIBOR) on a common basis. It is a general
perception that as a group, hedge fund managers produce just enough active return to
earn their overall fees while long-only managers fail to do so. How different are these
two types of alpha anyway? Do alphas from long-only and long/short investments
present different return distributions? Do these alphas derive from different risk factors?
This article examines these questions by examining empirical evidence of active
performance differences in long-only versus long/short investing. It also provides
potential explanations from the standpoint of compensation and investment constraints.
To further gain insight of how hedge funds incur risks, the article reviews the evolution
of methodologies for analyzing hedge fund risk. It first examines return/risk patterns of
various hedge fund investments and issues related to data reliability. Risk factors related
to market returns and financial markets are examined using performance indices of
several popular hedge fund strategies. The article proposes an alternative method of
analyzing �investment style� as applied to hedge fund investments. It also reviews the
contingent claim approach to hedge fund risk analysis: replicating hedge fund�s option-
like payoffs or trading strategies.
Classification of Hedge Funds
Conventionally, hedge funds are classified into categories according to their trading
strategies or styles. Sub-sectors of hedge funds include trend following, global/macro
strategies, long-only, arbitrage, long-short, etc. Despite attempts by data vendors,
practitioners and academics, no clear standard of classification currently exists as evident
by diverse categories used by various data vendors. In addition, given a variety of
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dynamic investment strategies and multiple capital market instruments utilized within
individual hedge funds, style classification of a hedge fund can be easily mishandled by
data vendors or hedge funds themselves3. For a comprehensive discussion of the nature
of these hedge fund strategies, see Fung and Hsieh (1999).
In a broad sense, we can classify hedge fund styles according to how funds manage the
first or second order of the distribution of systematic risk factors. From the viewpoint of
the first order of factor distribution, hedge funds differ as to whether they are taking
�market directional� bets. That is whether a fund is taking systematic versus
idiosyncratic risk (e.g., credit, spread or event risks). On the other hand, we can examine
how a hedge fund manages against the second order of factor distribution: volatility. For
example, practitioners, for simplicity, often consider commodity trading advisors (CTA)
long volatilities while arbitrageurs short volatilities. Thus, during extreme market
volatilities, these two types of hedge funds tend to offset each other.
Active Performance of Arbitrage Funds vs. Long-Only Portfolios
Do hedge funds or active equity managers produce different types of alpha distributions?
To isolate and compare these two types of alpha, we benchmark the funds� performance
versus their respective benchmarks. Arbitrage funds are measured against LIBOR and
long-only portfolios against equity or bond market indices. We use the Frank Russell
institutional long-only universe to represent long-only portfolios instead of a mutual fund
universe as conventionally done by other studies. Arguably, the clientele of hedge funds
is more likely to resemble institutional long-only portfolios than mutual funds. They both
target more sophisticated and longer-term investors who may not require daily liquidity
and thus, making it easier to pursue desired investment strategies. As for arbitrage funds,
CSFB/Tremont hedge fund indices which are increasingly becoming the industry
standard, are used.
3 In fact, this is one of the toughest problems in style classification. Most of data vendors use the category of multi-sector strategies to group those funds that are not easy to classify.
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It should be noted that the following simulation results make an implicit assumption of
the alpha transfer process being perfect. That is, financing costs for both hedge funds and
derivatives used in the transferring process are identical. As experienced by many
practitioners in recent years, the violation of this assumption can introduce significant
return variance to the transfer process.
Exhibit 1 compares after-fee quarterly alphas of active U.S. long-only equity accounts
versus the equity market neutral index for the period 1994 to 20004. The 45-degree line
represents even performance of these two universes. Scatter points represent paired
quarterly active performance under different equity market environments during the
period. We use different types of points in the scatter plot to represent active
performance under different states of equity markets. Solid points (diamond and square
4 Spear and Wiltshire (2000) also investigate the return differences of equity market neutral managers and long-only equity universe and find similar results.
Exhibit 1: Active U.S. Long-Only Equity vs. Equity Market Neutral for U.S. Equity Asset Class (Data Source: Frank Russell Company, CSFB/Tremont; All figures in %)
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0
1
2
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-5 -4 -3 -2 -1 0 1 2 3 4 5
Market Neutral Excess Return
< -1 Std dev of S&P 500> +1 Std dev of S&P 500+/- 1 Std dev of S&P 500Even Performance Line
After-Fee Quarterly Excess ReturnsOver Respective Benchmarks
Q1/94-Q4/00
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shaped) are for large positive or negative equity market movements (observations outside
of one standard deviation of the S&P 500 quarterly return distribution). Triangle/blank
points represent normal equity market conditions. Below the 45-degree line, active return
from equity market neutral strategy is greater than that of active U.S. equity accounts.
Examining from the direction of x or y-axis, one can see that market neutral strategies
had wider active return distributions than long-only accounts with a few observations at
the extreme. Market neutral strategy outperformed its benchmark on an after-fee basis
much more often than active long-only accounts did as indicated by more points below
the 45-degree line. Furthermore, market neutral strategy performed better than the long-
only accounts at extreme equity market conditions as also depicted by more solid points
among them. Another interesting phenomenon is that long-only accounts produced
negative active returns when equity markets are very strong. This is consistent with the
findings of active performance of equity mutual funds from 1965 to 2000 by Mezrich et
al. (2000). Conversely, market neutral funds generated positive alpha over LIBOR under
these situations perhaps due to their positive exposures to the market risk factor (see the
discussion in the later section).
Turning to bond markets, Exhibit 2 shows similar results for fixed income arbitrage funds
as compared with the active U.S. bond manager universe. However, active returns from
bond portfolios produced a substantially narrower distribution as compared to fixed
income arbitrage strategies. The most noticeable outliers for fixed income arbitrage
performance are from the difficult periods for hedge funds: early 1994 and late 1998.
High volatile outcomes should not surprise arbitrage fund investors since those funds
tend to employ leverage that often averages five to ten times of the fund�s capital. In
general, the investment objective of many fixed income arbitrage funds is to produce
absolute returns comparable to equity markets with lower volatilities or higher return
with comparable volatility. Since potential returns from relative value trades are often
small, leverage is usually employed in order to achieve the return objective. However,
this practice comes with a stiff price during credit or liquidity crises. As such, hedge
funds often incur substantial losses from rapidly rising financial costs of leverage
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positions, forced liquidations stemming from margin calls at the worst market conditions
and demands of true �marking-to-market� by brokers/dealers or from investors� panic
withdrawals.
Another possible reason for fixed income arbitrage funds having a more diverse active
return distribution is attributed to differences in performance benchmarks. Fixed income
arbitrage funds tend to stay within niche market segments where they have substantial
expertise and devise various strategies to exploit investment opportunities. The
performance index reflects various fixed income arbitrage funds employing a variety of
fixed income relative value strategies. When they are measured against a simple and low
volatile return benchmark (e.g., LIBOR, T-bills), the variance of alphas can easily be
magnified. On the other hand, long-only managers tend to emphasize tracking errors
when facing a more diversified and complex market benchmark. In measuring alpha, the
return variance is largely offset by the market benchmark.
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-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
Fixed Income Arbitrage Excess Return
< -1 Std dev of Leh Aggr> +1 Std dev of Leh Aggr+/- 1 Std dev of Leh AggrEven Performance Line
After-Fee Quarterly Excess ReturnsOver Respective Benchmarks
Q1/94-Q4/00
Exhibit 2: Active U.S. Long-Only Bonds vs. Fixed Income Arbitrage for U.S. High Quality Bond Asset Class (Data Source: Frank Russell Company, CSFB/Tremon; All figures in %)
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One approach to deal with arbitrage funds� volatility is to �de-lever� the investment.
This can be accomplished by combining arbitrage investments with either short-term cash
portfolios or a bond index fund depending on the objective of the overall portfolio in
achieving absolute return or broad bond market exposures5. Exhibit 3 depicts the result
of active returns of long-only bond portfolios versus the fixed income arbitrage index de-
levered by a ratio of one to ten. The �de-levered� bond portfolio would invest one-tenth
of the asset in fixed income arbitrage fund with the remaining in a bond index fund. The
hedge fund portion is further overlaid with bond derivatives to create synthetic bond
exposures. As can be seen, a �de-levered� bond portfolio still offers higher alphas with
comparable volatility. Moreover, negative active returns of this fund are generally not as
severe as those of long-only portfolios during extreme bond market conditions.
5 If the investment objective of the �de-levered� portfolio is to achieve cash return, it implicitly assumes 90% of assets invests in LIBOR-based instruments.
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0.5
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-1 -0.5 0 0.5 1
Fixed Income Arbitrage Excess Return
< -1 Std dev of Leh Aggr> +1 Std dev of Leh Aggr+/- 1 Std dev of Leh AggrEven Performance Line
After-Fee Quarterly Excess ReturnsOver Respective Benchmarks
Q1/94-Q4/00
Exhibit 3: Active U.S. Long-Only Bonds vs. Fixed Income Arbitrage for U.S. High Quality Bond Asset Class: Risk �De-Levered� by Ratio of 10 to 1 (Data Source: Frank Russell Company, CSFB/Tremont; All figures in %)
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What type of hedge fund is a better source of alpha for a given asset class?
Exhibit 4 compares excess returns of equity market neutral funds and fixed income
arbitrage funds given equity market performance over the last seven years. The objective
is to evaluate which is the better source of equity alpha if hedge fund�s alpha is
transferred back to the equity asset class? It appears equity market neutral managers
performed significantly better than fixed income arbitrage managers in most equity
market conditions, even in extreme cases. They also had an active return distribution
slightly tighter and less "fat tailed".
So what if alphas from these two types of hedge funds were transferred to the fixed
income asset class? Exhibit 5 compares these alphas in different U.S. high quality bond
market environments. Similar to the results in Exhibit 4, equity market neutral funds
appear to provide more consistent sources of alpha to the U.S. bond asset class than a
fixed income arbitrage strategy.
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Market Neutral Excess Return
< -1 Std dev of S&P 500> +1 Std dev of S&P 500+/- 1 Std dev of S&P 500Even Performance Line
After-Fee Quarterly Excess ReturnsOver Respective Benchmarks
Q1/94-Q4/00
Exhibit 4: Equity Market Neutral vs. Fixed Income Arbitrage for U.S. Equity Asset Class (Data Source: CSFB/Tremont; All figures in %)
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Based on previous exhibits, Exhibit 6 presents statistics of three different sources of after-
fee active returns for equity and bond market asset classes over the last seven years.
Market returns are divided into two states: the top half and bottom half among 28
quarters. A few observations are worth noting:
• Equity market neutral funds provided better and more consistent alphas for both
equity and bond asset classes than other funds as evidenced by high average active
returns and information ratios in all market conditions
• Fixed income arbitrage funds seem more suitable for the bond asset class than for the
equity asset class although information ratios were extremely low, especially without
de-leveraging.
• Both long-only equity and bond portfolios performed poorly compared with hedge
funds, except for long-only bond accounts providing the most consistent alpha for the
bond asset class when the market performed poorly (the bottom-half of market
performance conditions).
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-5 -4 -3 -2 -1 0 1 2 3 4 5
Market Neutral Excess Return
< -1 Std dev of Leh Aggr> +1 Std dev of Leh Aggr+/- 1 Std dev of Leh AggrEven Performance Line
After-Fee Quarterly Excess ReturnsOver Respective Benchmarks
Q1/94-Q4/00
Exhibit 5: Equity Market Neutral vs. Fixed Income Arbitrage for U.S. High Quality Bond Asset Class (Data Source: CSFB/Tremon; All figures in %.)
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• Active returns of equity market neutral funds were positively correlated with the
equity markets (about 0.5). It confirms the general perception of market neutral funds
exhibiting some market directionality.
• Fixed income arbitrage funds had higher correlations with equity markets than with
bond markets. However, they performed poorly when equity market returns were
high.
• Active returns from equity and fixed income arbitrage funds were uncorrelated with
bond markets.
• Active returns of equity and bond long-only accounts showed negative correlations
with their respective benchmarks in all market conditions, especially for long-only
bond portfolios (-0.73).
Exhibit 6: Sources of After-Fee Active Returns, Q1/1994 to Q4/2000 (Data Source: CSFB/Tremont; All figures in %)
Equity Fixed Inc. Equity Equity Fixed Inc. Bond
Statistics Mkt.Neutral Arbitrage Long-Only Mkt.Neutral Arbitrage Long-Only
OverallAvg. Excess Ret. 1.43 0.22 0.15 1.43 0.22 -0.11
Volatility 2.13 2.43 1.53 2.13 2.43 0.59Info. Ratio 0.67 0.09 0.10 0.67 0.09 -0.19
Top Market ReturnsAvg. Excess Ret. 2.08 1.03 0.10 1.32 0.19 -0.47
Volatility 2.41 2.27 1.29 1.76 2.59 0.55Info. Ratio 0.86 0.45 0.08 0.75 0.07 -0.86
Bottom Market ReturnsAvg. Excess Ret. 0.78 -0.60 0.19 1.54 0.24 0.25
Volatility 1.65 2.38 1.79 2.51 2.36 0.37Info. Ratio 0.48 -0.25 0.11 0.62 0.10 0.67
Correlation with Markets Overall 0.50 0.23 -0.16 0.03 0.01 -0.73 Top Market Returns 0.50 -0.60 -0.30 0.13 0.01 -0.45 Bottom Market Returns 0.33 0.56 -0.14 0.13 0.07 -0.59
Equity Asset Class Bond Asset Class
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In the sections that follow, we will examine potential explanations of market hedge and
arbitrage funds appearing to be better sources of active returns than long-only portfolios.
As for the comparison between hedge funds, why did equity market neutral funds have a
more attractive active risk/return profile than fixed income arbitrage strategies?
First of all, even though CSFB/Tremont indices used in this study are considered superior
than most hedge fund data (Lhabitant, 2001), the time period covers only 1994 onward.
The period examined here is not only short but generally regarded as a tough period for
fixed income arbitrage strategies, e.g., 1994, 1997, 1998 and 1999. As shown above,
positive exposures to market risk by equity market neutral funds further enhanced their
performance advantages over fixed income arbitrage funds during equity bull markets.
Furthermore, it should be noted that equity hedge funds (e.g., market neutral, convertible
arbitrage, risk/merger arbitrage) have significant longer histories than fixed income
funds. Many mistakes have been experienced by equity related hedge funds, especially
during 1990 and 1991. Of course, fixed income related hedge funds learned an expensive
lesson from the recent LTCM episode: the danger of accounting-based leverage, the
power of margin calls, the importance of marking-to-market, and the unreliability of
carry trades without proper downside risk hedges.
Since then, fixed income hedge funds and the broker/dealer community have devised
many remedies (willingly or unwillingly) in an attempt to avoid the same mistakes. For
example, more fixed income arbitrage funds are employing leverage constraints,
downside risk analytics, risk budgeting implementation and fund alliance6. Perhaps fixed
income hedge funds will be able to reduce the performance gap versus equity hedge
funds going forward.
6 I thank Eric Tang for pointing out these issues.
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Hedge Funds versus Institutional Long-Only Portfolios
Data Issues
The previous section empirically compares active performance of hedge funds versus
long-only portfolios. The conclusion should be taken carefully since hedge fund data by
itself presents numerous debates among practitioners and academic researchers regarding
its usefulness and reliability. Biases in the construction of hedge fund databases include
survivorship, self-delist, selection and back filling7. On the other hand, even with the
help of stringent disclosure requirements from investors and regulatory agencies, most
performance databases of long-only portfolios also exhibit one or more of these database
biases found in hedge funds8.
The self-delist bias appears to be somewhat unique to hedge funds. Firms may stop
reporting performance data to database vendors for a variety of reasons such as difficulty
in executing trades due to asset capacity and potential liability in reporting errors. In
addition, almost all the databases exhibit a significant selection bias. Most databases do
not even include or gain the support of some large and preeminent hedge funds.
Furthermore, many large hedge funds with impressive performance records catering
primarily to financial institutions and institutional investors are not part of publicly
available hedge fund databases.
Perhaps the more significant issue of data reliability is the practice of stale pricing,
questionable �mark-to-market� and �mark-to-model� employed by prime brokers and
hedge funds (Asness et al., 2001; Tremont, 2000) 9. According to a recent survey of
hedge fund valuation practices, price differences and valuation adjustments made by 7 For comprehensive discussions of issues related to hedge fund data, see Fung and Hsieh (2000a, 2001) and Brown et al. (1999). 8 For example, see Brown et al (1992) and Carhart (1997). 9 Pricing issues are even more severe and common before and during the LTCM debacle. However, we cannot untangle numerous other issues surrounding that market environment including price discovery process and the impact of dealer margin calls.
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hedge funds can be substantial (30%-40%). This is especially problematic for illiquid or
less liquid securities (e.g., high yield and distressed bonds, private securities, over-the-
counter options, structured notes and mortgage derivatives)10.
Stable pricing/modeling practice is essentially an artificial and costless process to smooth
performance variation and �amortize� gains and losses11. It definitely contributes to
hedge funds� low return volatility, low correlation with other asset classes which in turn,
enhances the notion of hedge funds being investment vehicles with high information
ratios and great diversifiers. Stale pricing may well be the key factor underlying
quarterly performance persistence of hedge funds found in Agarwal and Naik (2000).
Despite the efforts by numerous studies in documenting and quantifying hedge fund data
bias, conclusions based on the existing hedge fund databases were diverse and remain
dubious. Thus, it is difficult to conclude the extent or even the direction of performance
differentials between hedge funds and long-only accounts induced by database bias.
Structural Differences
One may argue that what lies beneath performance between hedge funds and long-only
accounts are their differences in compensation structures, investment constraints from
guidelines and regulations, and other structural factors12. These differences may allow
hedge funds to:
• Focus on extracting returns related to idiosyncratic risks rather than relying primarily
on taking systematic risks;
• Serve as liquidity providers to hedgers;
10 Capital Market Risk Advisors, Inc. (2001) 11 Arguably, this is similar to the book value accounting used in insurance community. 12 Ackermann (2000) examine these issues as related to differences in performance persistence of mutual funds versus hedge funds.
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• Effectively execute certain investment strategies via various forms of derivatives; and
• Customize investment/security structures to explore certain properties of return
distributions.
The following table outlines various factors that may contribute the return differentials of
these two types of alphas.
Compensation Investment Constraints Structural Factors
Management fees Leverage Lockup period Incentives Short selling Disclosure requirements Hurdle rate Use of derivatives Asset capacity High watermark Concentrated positions Simple benchmark Management Capital Investment guidelines
One of the common beliefs of hedge funds� perceived outperformance is due to their
unique compensation structure, which generally attracts supposedly more skillful
professionals. Arguably, the most important factor is the setting of higher management
fees in addition to potentially large payoffs from the incentive fee schedule (Ackermann
et al., 1999)13. Furthermore, performance hurdle rate, high watermark14 and fund
management contributing their own capital may provide hedge funds with additional
drivers in achieving superior performance.
Investment Constraints
Another factor often cited for hedge funds� outperformance is the flexibility they have in
pursuing investment strategies. For example, short selling and the use of leverage are
two of the trademarks of hedge fund management. Short selling allows fund managers to
take advantage of their investment views on both sides of factor or security valuation. 13 It is often argued that this feature may encourage managers to take more risk. However, empirical studies indicate that this is not necessarily the case unless the implied option is deep out of money (Carpenter, 2000). 14 Incentive fees are earned only if cumulative performance recovers past shortfalls, if any.
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Grinold and Kahn (2000) develop an analytical framework to quantify the efficiency gain
from loosening the short selling restriction. They find that it can have significant impact
on active management especially if they deal with large sets of assets, low volatilities and
high active risk. However, it is questionable whether this flexibility does generate double
alpha. Alexander (2000) empirically shows that if one considers Regulation T restriction,
liquidity haircut and derivatives availability in short selling, abnormal returns from
popular pricing "anomalies" based on zero investment strategies may not be supportive.
With regard to leverage, it is conventionally defined as a discrete, accounting-based
measure and does not give a complete indication of the type or amount of risk taken. It
does not consider market volatilities and possible diversification benefits within
portfolios. In fact, a fund may be able to reduce its leverage while increasing portfolio
risk. In addition to the lack of actual leverage information, researchers have difficulty in
empirically analyzing whether and how leverage improves a hedge fund's risk-adjusted
return. Recent advances in hedge fund risk management call for risk-based definitions of
leverage instead of conventional accounting measures (even if they include on- and off-
balance sheet items)15. Incorporating value-at-risk and scenario stress tests should help
investors better evaluate the true impact of portfolio leverage. Further research is needed
to understand (1) the relationship between hedge fund return distribution and leverage,
(2) leverage limits and proper leverage for various hedge fund strategies, and (3) leverage
dynamics: what factors influence hedge funds� use of leverage over a market cycle.
Since most hedge funds focus on generating absolute returns with a "below-market"
volatility, they are often measured against a simple performance benchmark: the funding
cost. As a result, unlike long-only fund managers, hedge fund managers do not have to
deal with issues related to benchmark style drift (e.g., Brealy and Kaplanis, 2001) and
investment style boxes. In fact, pension sponsors and the consulting community are
increasingly relying on "style" indices to monitor long-only fund managers and to
construct risk/return profiles of overall asset classes. There is a tendency for investors to 15 See Sound Practices (2000), the President�s Working Group (1999), Norland et al (2000) for excellent discussion on this subject.
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end up with a locally optimized asset class since their focus is often a collection of
�optimized� managers within individual investment styles. Perhaps in response to this
trend in institutional investing, long-only fund managers have shown increasing concern
with tracking error and maverick risk. They tend to stay around the given style
benchmark rather than stay with their supposed investment conviction. Focusing on
"style" products and benchmarking may prove to be detrimental to long-only asset
management going forward.
In sharp contrast to long-only portfolios, hedge funds face few, if any, investment
guideline restrictions. They are not limited by capital markets they can trade, constraints
imposed by the Investment Company Act of 1940, and investment guidelines (e.g.,
sector/security limits and duration/spread duration risk limits) often found in a long-only
portfolio. This may account for the tendency of hedge funds' extensive use of exotic
securities or derivatives, and holding concentrated positions of what is considered "the
best ideas" rather than overly diversified positions often found in a long-only portfolio.
Finally, most hedge funds have investment lockup periods that allow hedge funds to use
illiquid and restricted securities16. Anecdotally, all the flexibility discussed above may
contribute to seemingly better risk-adjusted returns earned by hedge funds versus long-
only portfolios.
Other Issues
Recently, questions have been raised regarding practices supposedly used by some hedge
funds and Wall Street that may distort the true picture of hedge fund performance. These
practices include:
• Potential conflict of interest from trade allocation by a firm managing both long-only
and hedge funds in view of compensation differentials. The possibility of allocating
16 Lockup period is the time restriction of redeeming hedge fund investments. Ackermann (2000) empirically showed that the provision of lockup period and incentive structure are two of the most important contributors to hedge funds� superior performance.
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profitable trades to funds with substantially more profitable compensation structures
has caught regulatory attention17.
• Trader order-handling sequence by brokers/dealers for hedge funds versus long-only
(Santini, 2001). The allegedly preferential treatment of hedge funds is perhaps due to
the tendency of hedge funds to have higher portfolio turnover rates and their
willingness to pay higher commissions in order to obtain information flows from
Street traders.
Understanding Hedge Fund Risk
As hedge funds employ diversified and dynamic trading strategies in a rather loosely
defined operating environment, the return generating process of hedge funds can be
complex and hard to analyze. Most studies show that factors based on market returns of
standard asset classes are not sufficient to describe risk taken by hedge funds, especially
those employing market neutral or arbitrage strategies. So, what are additional
systematic risks that hedge funds incur?
Hedge fund risk is a function of quantity (leverage), instruments/markets traded, market
volatility, strategy diversification within the fund and liquidity. One may argue that
investors can get a better understanding of risk exposures by a hedge fund from
examining portfolio holdings and trades. Value added from this exercise is generally
considered questionable. Hedge funds tend to dynamically and rapidly shift trading
positions and exposures to risk factors daily or intra-day. Portfolio holdings or
transactions are difficult to piece back together to their original tactical or strategic
purposes.
Perhaps the most important aspect of hedge fund risk analysis is to understand the nature
of trading strategies and underlying risk elements of each strategy. By doing so, the
17 See Financial Times (2001), HedgeWorld (2001).
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investor can develop a more reasonable expected risk/return of the fund. He or she will
better understand how and when trading strategies and funds invested are correlated.
Low correlation is also often found between hedge fund categories focusing on different
"style� or �markets". However, within each hedge fund category, correlations vary.
Individual funds within market directional hedge fund categories tend to have higher
correlation while non-directional funds often exhibit lower correlations (Brealey and
Kaplanis, 2001; Martin, 2001). Diversification of trading strategies within a hedge fund
is also a powerful tool for delivering consistent performance in various market
conditions. Exhibit 7 shows paired return correlations of six different investment
strategies employed by a successful capital structure arbitrage fund. Monthly correlations
ranged from -0.35 to 0.41 during the period 1998 to 2000. Notwithstanding, in order for
hedge funds to be able to perform consistently and survive difficult market environments,
it is important for a manager to dynamically manage the optimal mix of these lowly
correlated strategies.
Exhibit 7: Strategy Diversification within a Fund (Monthly Return Correlations, 3/98-12/00)
ConvertArb.
Yld-ToC/P
CapitalStr. Arb.
Multi-CStk.Arb.
PairedTrades
Yield-to-Call/Put 0.34
Capital Structure Arb. 0.11 0.41
Multiclass Stock Arb. 0.33 0.06 0.19
Paired Trades 0.23 0.10 -0.35 0.05
Special Situations 0.06 0.23 0.05 -0.14 -0.08
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Performance Measures
Conventionally, the hedge fund community likes to use singular measures to describe
hedge fund performance and risk. For example, hedge fund marketing materials often
present the fund�s standard deviation of returns, maximum drawdowns (peak-to-trough
performance) and percentage of negative months (or quarters). Various risk adjustment
ratios are also popular -- Sharpe ratio, information ratio (excess returns divided by
volatility of excess returns), efficiency ratio (ex ante risk divided by realized return
volatility) and appraisal ratio (significance of the intercept of a CAPM-type regression).
All these risk/return measures do not express the nature of a fat tail return distribution nor
do they address investors' concern that under certain types of market condition, the �true�
risk of hedge fund investment will appear.
Risk Factors
Exhibit 8 depicts returns of fixed income arbitrage funds under various bond market
performance levels. Monthly returns of the Lehman Aggregate Bond Index from 1994 to
2000 were classified into seven buckets according to their return rankings. As shown,
fixed income arbitrage funds earned positive active returns in all types of bond market
conditions.
Searching for methods to analyze hedge fund risk beyond exposures to various
market/sector portfolios, researchers attempt to identify economic or financial market
factors as additional systematic risk taken by hedge funds. Financial market factors are
primarily based on publicly traded instruments (e.g., changes in levels and volatilities of
market index, index futures, options, swaps and other forms of derivatives). Unlike
information based on economic conditions (e.g., inflation, GDP growth and industrial
production), financial market factors have advantages of higher pricing frequency and are
directly related to trading strategies used. These factors combined with market factors
provide investors with a better analytical framework and empirically explain higher
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portions of return variance than market risk factors alone18. Different hedge fund
strategies may require different sets of factors to describe their risk propensity.
Financial Market Risk Factors
Continuing the example in Exhibit 8, we examine the performance of the fixed income
arbitrage funds in different environments of fixed income volatilities during the period of
1995 to 2000. Volatility is represented by the changes in volatilities implied in the
swaption market. As shown in Exhibit 9, the fixed income arbitrage strategy remarkably
performed consistently in all but the highest volatility scenario. In fact, the only regime
in which fixed income arbitrage funds averaged negative returns is when bond markets
experienced their largest increases in implied volatilities (e.g., October 1997 and August
to October 1998).
18 For example, see Martin (1999), Schneeweis and Spurgin (1998)
-2
-1
0
1
2
3
State of Market Performance (lowest to highest)
FI Arb.
Lehman Aggregate
Exhibit 8: Performance of Fixed Income Arbitrage Funds vs. Bond Market Returns (Monthly, 1/94 to 12/00). All figures in %.
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Exhibit 10 presents other systematic risk factors critical to bond markets: the change in
high yield spreads, Treasury volatility (implied volatility of Treasury options), swap
volatility and equity volatility (implied volatility of the S&P 100 index options).
Monthly excess returns of fixed income arbitrage funds over LIBOR show modest
Most ! Most "
Factors 1 2 3 4 5 6 OverallCorrel.
HY Spreads 0.84 0.62 0.18 0.32 -0.04 -1.07 -0.46
Treasury Vol. 0.54 0.52 0.47 0.19 0.09 -0.95 -0.47
Swap Vol. 0.51 0.34 0.38 0.27 0.37 -1.01 -0.50
Equity Vol.Whole Period -0.72 0.02 0.57 0.56 0.28 0.15 0.23
Excl. 9,10/98 0.31 - - - - - -0.27
Ranks by Changes in Factors
Exhibit 10: Active Returns of Fixed Income Arbitrage Funds Under Different Risk Conditions (Monthly, 1/95 to 12/00). All figures in %.
-3
-2
-1
0
1
2
3
4
State of Factor Risk (lowest to highest)
FI Arb
3x10 Swaption VolChange
Exhibit 9: Performance of Fixed Income Arbitrage Funds vs. Bond Volatility Risk (Monthly, 1/95 to 12/00). All figures in %.
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negative correlations to the first three fixed income related systematic risk factors (about
�0.5). The funds were most vulnerable when systematic risks drastically increased. High
yield spread changes and Treasury volatility had a reasonably linear relationship with
arbitrage funds� active returns. As for the equity volatility factor, arbitrage funds
performed the worst during extreme scenarios (both large declines and increases in the
factor). However, excluding large decreases in equity volatilities following the LTCM
episode (September and October of 1998), the correlation changed from a small positive
to a small negative. This indicates that observations from that period (August to October
1998) have a critical impact on the analysis.
Turning to convertible arbitrage funds, the same four systematic risk factors have similar
impacts on active returns as shown in Exhibit 11. The underperformance of convertible
arbitrage was most pronounced in regimes with the largest increases in three fixed
income factors. At the first glance, the overall correlation of convertible funds and the
changes in equity volatilities were virtually zero. At extreme market volatilities (the first
and sixth states), the funds performed poorly as compared to more normal scenarios.
Significantly negative performance from August to October 1998 (the impact is shown at
Most ! Most "
Factors 1 2 3 4 5 6 OverallCorrel.
HY Spreads 0.95 1.03 0.55 0.94 0.80 -0.55 -0.46
Treasury Vol. 0.66 1.00 0.57 1.32 0.73 -0.56 -0.49
Swap Vol. 0.90 1.11 0.73 1.05 0.62 -0.69 -0.51
Equity Vol.Whole Period -0.34 0.59 1.30 0.88 1.20 0.09 0.00
Excl. 8/98 -0.34 - - - - 0.56 0.41
Excl. 9,10/98 0.48 - - - - 0.09 -0.39
Ranks by Changes in Factors
Exhibit 11: Active Returns of Convertible Arbitrage Funds Under Different Risk Conditions (Monthly, 1/95 to 12/00). All figures in %.
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the bottom of Exhibit 11) further demonstrates the vulnerability of convertible hedge
funds during extremely volatile markets. During and after the LTCM debacle,
convertible hedge funds are believed to have suffered significant "mark-to-market" issues
that may have masked the extent of these relationships (Tremont, 2000).
Exhibit 12 examines risk factor exposures of equity market neutral and long/short
(directional) hedge funds. In addition to equity implied volatility, exposures to three
Fama-French return factors are also analyzed. Market neutral funds show insignificant
relationships to the changes in size and value factors. Their active performance was
essentially flat when equity volatility increased the most.
Despite what the name implies, the funds have positive directionality to the market factor
(i.e., positive excess return increases as the equity market performs well). As for
long/short hedge funds, they show strong correlations to all four systematic risk factors:
short equity volatility and value factors while long market and size factors. Examining
across six regimes, active returns of long/short funds had an almost perfect linear
relationship to these factors.
Most ! Most "
Market Neutral 1 2 3 4 5 6 OverallCorrel.
Equity Vol. 0.82 0.30 1.36 0.43 0.85 0.06 -0.29
Market Factor -0.04 0.39 0.48 0.57 1.04 1.37 0.52
Size Factor (SML) 0.26 0.69 0.49 0.77 0.87 0.74 0.10
Value Factor (HML) 0.62 1.13 0.72 0.92 -0.20 0.62 -0.12
Long/Short
Equity Vol. 2.60 1.16 2.59 1.53 0.71 -1.62 -0.41
Market Factor -3.33 -1.29 2.06 2.28 3.17 4.07 0.76
Size Factor (SML) -2.67 -0.64 1.58 2.07 2.56 4.06 0.62
Value Factor (HML) 5.35 2.34 1.87 1.34 -0.70 -3.23 -0.77
Ranks by Changes in Factors
Exhibit 12: Active Returns of Equity Hedge Funds Under Different Risk Conditions (Monthly, 1/95 to 12/00). All figures in %.
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Style Analysis of Hedge Fund Risk
Style analysis, pioneered by Sharpe (1988 and 1992), uses market/sector benchmark
portfolios as systematic factors to derive the asset mix implied in an active portfolio's
return series. For a long-only portfolio, exposures to these market portfolios are
constrained to be positive and summed to one. Many studies apply style analysis to
analyzing hedge fund risk by relaxing these two constraints (e.g., Fung and Hsieh, 1997;
Brown et al., 1999; Agarwal and Naik, 1999). While most studies employ capital market
or style index portfolios as implied building blocks in style analysis, Lhabitant (2001)
uses hedge fund style indices as risk factors in order to directly derive a fund�s implied
exposures to conventional hedge fund styles/strategies.
Brown and Goetzmann (2001) further extend hedge fund style analysis by allowing factor
loadings on market portfolios (i.e., coefficients) to vary over time19. Using time varying
factor loadings in style analysis is constructive since the method accommodates dynamic
trading strategies with non-linear payoffs. All these studies found that individual fund
returns have lower correlations to standard asset class returns as compared to mutual
funds. Funds with styles of market neutrality, arbitrage or commodity have significantly
low to nil exposures to these asset classes.
Moreover, one of the criticisms of conventional style analysis is that investment risk as
defined by these styles is too narrow and singular. It fails to recognize that investment
risk is often multi-dimensional, asymmetrical and potentially correlated (Michaud, 1998).
This problem becomes even more severe when analyzing hedge fund risk. Active returns
of hedge funds generally exhibit asymmetric sensitivities to risk factors in different
market environments. For example, it has been shown that hedge funds perform
differently in positive versus negative equity markets (Lo, 2000) and in rising versus
declining interest rate scenarios. Previous sections present empirical evidence of how the
changes in implied volatilities in various capital markets may be of importance in 19 Brown and Goetzmann (1997) first present this methodology in studying mutual fund styles.
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evaluating hedge fund strategies. In summary, to analyze hedge fund risks, we not only
have to incorporate various systematic risk factors beyond conventional market return
factors but also employ a multi-dimensional framework.
Risk Style Analysis Under A Long-Only Framework
Kao (2000a) presents a return-based approach to analyze investment styles of fixed
income managers. It involves identifying several systematic risk factors important to
active performance of a fixed income portfolio; e.g., changes in 10-year Treasury rate,
implied volatility of interest rate options, swap spreads, swap volatility and systematic
risks in equity markets20. Exposures to these risk factors in relation to a bond benchmark
are grouped and summarized in two dimensions: interest rate risk and spread risk.
Exhibit 13 compares two distinct long-only fixed income investment styles. The
construction of this risk factor model follows Kon (1999) in which factors are adjusted
for the variable dependence of prominent risk factors such as the level of interest rates.
For example, the changes in implied volatilities are adjusted for directionality of ten-year
Treasury rates. The changes in swap spreads are adjusted for both the changes in interest
rates and the adjusted changes in volatility.
The exhibit shows how portfolios managed active exposures to two risk dimensions
differently with each point covering a rolling 36-month period. The center point
represents a neutral position of risk exposures versus the benchmark. To illustrate the
changes in exposures over time, the largest point is the most recent observation and the
smallest the earliest.
Manager A is a highly risk controlled bond fund of funds (diversified multiple advisors)
as evident by its stable exposures to both risk dimensions. On the other hand, viewing
from both interest rate and spread risk related to their benchmark, Manager B took more
20 See Kao (2000b) for an application to analyzing determinants of the changes in corporate credit spreads.
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active risks with drastic shifts in exposures than Manager A. The bottom table of Exhibit
13 presents average statistics of risk exposures of the bond index and these two portfolios
according to this risk style model.
The risk factor model explains return variances of these three portfolios very well as
evidenced by the significance of T-statistics and R-squares. Manager B had larger
exposures to all risk factors than Manager A and the benchmark except for exposure to
the changes in 10-year Treasury rates. Obviously, two spread risk factors are very
Exhibit 13: Risk Styles of U.S. High Quality Core Bond Managers (8/99-6/00)
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
0.9 1 1.1
Relative Interest Rate Risk
Manager A
Manager B
Benchmark: Salomon BIG IndexMonthly Exposures: 8/99-6/00
Ten-YearRate
Int. RateVolatility
SwapSpread
EquityRisk (t-1)
10-YearRate
Int.RateRisk
FourFacotrs
Bond Index Coef. -3.92 -0.77 -2.41 1.42 0.91 0.94 0.97 T-Stat -31.65 -6.54 -5.48 2.81Manager A Coef. -3.80 -1.40 -2.97 2.80 0.68 0.77 0.83 T-Stat -12.16 -4.71 -2.59 2.25Manager B Coef. -3.87 -1.09 -2.01 1.58 0.87 0.93 0.96 T-Stat -24.62 -7.33 -3.62 2.47
Average Statistics R-Square
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important in explaining the return volatility of Manager B�s performance as R-square
increases from 0.77 to 0.83.
We apply the same risk factor model to examine relative risk exposures of fixed income
arbitrage funds versus the long-only bond fund of funds from June 1998 to December
2000 in Exhibit 14. Monthly excess returns of fixed income arbitrage funds over LIBOR
are assumed to transfer to a bond market index in order to make it comparable to the
Exhibit 14: Risk Styles of Fixed Income Arbitrage Overlay Versus Long-Only Bond Fund (6/98-12/00): Fixed Income Arbitrage de-levered by 10:1
0.5
0.75
1
1.25
1.5
0.8 0.9 1 1.1 1.2
Relative Interest Rate Risk
Long-Only Bond Fund
Fixed Inc. Arb. Overlay
Benchmark: Salomon BIG IndexQuarterly Exposures: 6/98-6/00
Ten-YearRate
Int. RateVolatility
SwapSpread
EquityRisk (t-1)
10-YearRate
Int.RateRisk
FourFacotrs
(b.p.) (10 b.p.) (b.p.) (%)Bond Index Coef. -3.95 -0.71 -2.42 1.25 0.92 0.95 0.97 T-Stat -34.98 -5.59 -4.91 2.58Fixed Inc. Arb. Coef. -3.80 -1.05 -2.01 1.58 0.86 0.91 0.94 T-Stat -22.00 -5.40 -2.73 2.11Long-Only Fund Coef. -3.94 -1.04 -2.09 1.66 0.88 0.93 0.96 T-Stat -25.45 -6.36 -3.16 2.58
Average Statistics R-Square
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long-only portfolio. Furthermore, as in the case of Exhibit 3, to make return volatilities
of these two portfolios more comparable, the performance of the arbitrage fund index was
�de-levered� by investing one-tenth of assets in hedge funds and the remainder in a bond
index fund. Again, the analysis is done on a 36-month rolling basis to explore the funds�
changes in risk exposures (only quarter-end observations are displayed).
Exhibit 14 shows these two investments possess similar and rather consistent exposures
to both directional and volatility risks. The �de-levered� fixed income arbitrage overlay
portfolio had slightly lower relative interest rate and spread risks than the long-only bond
fund. This was achieved through having lower exposures to ten-year interest rate and
equity risk factors. Comparing with the bond market index, however, this portfolio still
had higher exposures to volatility and equity risk factors. Remarkably, hedge fund
overlay and long-only portfolios also changed their exposures over time in a similar
pattern. After the LTCM debacle, both portfolios became more risk neutral versus the
benchmark.
Risk Style Analysis Under A Hedge Fund Framework
If we were to analyze the source of active risk of hedge funds on a stand-alone basis (i.e.,
without an overlay process), the risk factor model requires some modifications. First, we
define risk style dimensions relevant to hedge fund investment risks: directional risk (first
order) and volatility risk (second order). Continuing the example in Exhibit 14,
systematic risk factors important to fixed income arbitrage funds as discussed in previous
sections are categorized into these two dimensions. For example, exposures to the
changes in interest rates and credit spreads are jointly formed to measure directional risk
(correlation of these two factors is considered). Volatility risk combines the changes in
implied volatilities of equity and interest rate options. Again, the model construction
requires the adjustment of variable dependence.
Exhibit 15 compares risk exposures of after-fee active returns of fixed income arbitrage
funds and a long-only bond fund over their respective benchmarks. Fixed income
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arbitrage funds have large and statistically significant active risk exposures to all four
factors, especially to the changes in high yield spreads and equity volatilities as compared
to the long-only fund. Viewing from risk factors important to fixed income arbitrage
funds, volatility risk had significant impact on active returns of the long-only bond fund.
In contrast to fixed income arbitrage funds, the directional risk factor (ten-year rate) had
nil effect on active return variance of the long-only fund.
As indicated by R-square measures in the last three columns of the exhibit, factors related
to directional risk explain about 30% of active return variance of fixed income arbitrage
Exhibit 15: Risk Style of Active Quarterly Returns of Fixed Income Arbitrage Versus Long-Only Bond Fund (12/98-12/00)
5
7.5
10
12.5
15
0 1 2 3 4 5 6 7 8 9 10
Directional Risk
Fixed Income Arb Index
Active US Bond FoF
Benchmarks: 3-Mon. LIBOR and Salomon BIG IndexQuarterly Exposures: 12/98-12/00
10-YearRate
HighYldSpread
Int.RateVolatility
EquityVolatility
10-YearRate
Direct'lRisk
FourFacotrs
(b.p.) (b.p.) (10 b.p.) (10 b.p.)Fixed Inc. Arb. Coef. 0.18 -0.21 -0.24 0.14 0.08 0.30 0.58 T-Stat 2.28 -2.21 -2.04 3.96Long-Only Fund Coef. 0.04 -0.05 -0.33 0.09 0.01 0.16 0.42 T-Stat 0.56 -0.51 -2.76 2.41
Average Statistics R-Square
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portfolios (ranging from 18% to 41% during the period). This is substantially higher than
the 8% achieved if only the changes in interest rate levels (10-year rates) is used21.
Adding volatility risk factors, average explanatory power increases to 58% for the
arbitrage index. As for the long-only bond fund, directional risk explains 16% of active
return variance and volatility risk factors add another 26%.
During this period, hedge funds as well as the long-only fund generally maintained their
directional risk but decreased exposures to volatility risk. Mimicking Portfolio/Strategy Approach to Risk Analysis
Recently, several researchers have taken a more direct approach to analyze hedge fund�s
systematic risk beyond market returns. We call this the mimicking portfolio/strategy
approach since it attempts to replicate either the payoff pattern or explicit trading
strategies of hedge fund activities22. Fung and Hsieh (1997) apply principal component
analysis to extract benchmarks for various trading strategies as implied in hedge fund
return series. When combined with conventional asset class factors, it can effectively
capture the essence of hedge funds' extreme outcomes.
Following the contingent claim concept of performance measurement advocated by
Glosten and Jagannathan (1994), several studies use a series of financial options to
directly replicate the option-like pattern which existed in hedge fund data23. Other
methods involve constructing naive trading strategies actually employed by hedge funds
21 As a reference, if one follows the conventional approach of using a bond market index as the risk factor (e.g., Lehman Aggregate Index), the R-square is only 3%. 22 Broadly speaking, style analysis approach using market/factor portfolios or risk factors can be considered a mimicking portfolio/strategy method for analyzing a fund�s risk and return. 23 Fung and Hsieh (2000b) construct five trend-following mimicking benchmarks that produce straddle option payoffs commonly observed in hedge fund returns. R-squares were about 48% versus average 7% with standard asset return factors. Agarwal and Naik (2001) also employ a similar methodology to studying Event Driven and Relative Value Arbitrage funds. Lo (2000) uses a trading strategy of selling out-of-the-money puts on equity index to demonstrate the illusion of a hypothetical hedge fund�s super �risk�-adjusted performance.
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and thus, provide a more direct and realistic evaluation framework24. Tang (1999)
extends the framework by simulating hypothetical investment opportunities available to
hedge fund managers, rather than replicating hedge funds� trading strategies and
instruments used. The approach attempts to address a difficult task in hedge fund
research: hedge funds (especially arbitrageurs) generally employ multiple investment
strategies within a fund that are seemingly uncorrelated and hard to replicate by trading
unified instruments25.
In all these studies, they found that return patterns from these simulated passive trading
strategies resemble those of actual hedge funds or CTAs. Risk attributes detected from
these time series are generally consistent with what we would expect from specific
trading strategies employed by hedge funds. Return series obtained from this analytical
approach can be used to:
• Evaluate and extract various systematic risks not observed by return series of
conventional asset classes. In the spirit of Sharpe�s style analysis framework,
mimicking portfolios can be viewed as alternative or additional asset/benchmark style
factors.
• Directly model hedge fund's asymmetric return distributions.
• Examine how hedge funds manage their risk exposures in extreme market conditions.
• Serve as a �true� hedge fund benchmark26. Performance in excess of these
benchmark portfolios is considered a better indication of the manager's skill.
24 See Gatev et al (1999) on paired trading (a convergence strategy used to explore relative pricing of close substitutes of financial instruments), Mitchell and Pulvino (2000) on risk arbitrage strategy and Richards (1999) on relative value trades, and Liew (1999) on equity long and short of equity risk factors. Return indices (e.g., Mount Lucas Management Index) based on naive trading strategies in active commodity and financial futures is used in analyzing CTA investment risks (see Schneeweis and Spurgin, 1998; Spurgin, 1999). 25 Under this approach composite relative value indices for capital market segments in which hedge funds operate are constructed. Each relative value index combines factors related to rich/cheap valuation and technical indicators for the market at a given point of time. For example, for yield curve trades, it calculates relative value opportunities available to carry, butterfly and basis trades. As for technical factors, it uses measures such as spreads versus their historical averages popular among practitioners. 26 In fact, recently a few hedge funds replicating index or naïve trading strategies are being publicized as passive alternatives to active hedge fund investing.
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• Avoid biases found in most hedge fund databases as discussed previously.
The replication approach to studying hedge fund performance is expected to extend to
other types of trading strategies. This should shed light on the myth surrounding hedge
fund activities.
Investment Style and Performance Evaluation
Both risk style factors and mimicking portfolios can be useful in understanding hedge
fund risk. They serve as better yardsticks for measuring hedge funds� performance and
their true active skill beyond naïve trading strategies. However, the hedge fund
investment community should keep in mind the experience of improving methods of
measuring long-only portfolio performance in recent years. Style analysis was originally
designed to facilitate the evaluation of a money manager�s active skill in view of their
exposures to some systematic risks. Style indices created from this analytical framework
are not intended to be a primary tool for managing money managers. Investors and
consultants tend to put too much emphasis on the performance tracking error versus a
style benchmark or a customized benchmark based on a set of systematic risk factors.
By doing so, they �delegate� the responsibility of understanding managers� investment
process and what truly drives active performance to a classification scheme based on
singular factor measures. The end result is the danger of further restricting (implicitly or
explicitly) an investment manager in expressing his/her true convictions. This would be
especially troublesome for hedge funds whose active returns rely on multiple, complex
and dynamic trading strategies that may not be easily classified into one particular style
box.
Conclusion The option-like return pattern of hedge funds presents a challenge for investors in
analyzing risk exposures. Singular measures of risk and return can be misleading
especially in analyzing hedge fund risk. Investors should carefully examine the return
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patterns under various market conditions and other systematic risk factor exposures. Due
to the investor�s ability of transferring alpha to a desired asset class, it is more appropriate
to evaluate hedge funds and long-only portfolios by comparing them against respective
benchmarks. Hedge funds, especially equity market neutral strategies, seem to provide
more consistent alpha than long-only portfolios for different asset classes under various
market environments. The qualitative assessments of possible explanations are reviewed
here.
Factors derived from asset prices in financial markets are timely and useful for hedge
fund risk analysis. These risk factors depict exposures to market direction, volatility and
valuation that are most relevant to hedge fund�s risk profiles. This article shows that how
a hedge fund manages its exposures to implied volatilities at extreme market conditions
can be the key to consistent performance. The results highlight the importance of
strategy diversification between funds as well as within a fund in achieving consistent
performance.
An analytical framework incorporating multiple risk factors gives investors a more
complete picture of hedge fund risk taking. In the spirit of equity style analysis popular
among practitioners, this article presents an approach of risk style analysis to evaluate
common risk factors driving the performance of hedge funds and long-only portfolios.
Various financial market risk indicators can be categorized into directional and volatility
risk dimensions to provide a more concise assessment of risk exposures over time.
Another approach to analyze hedge fund risk is to directly replicate the hedge fund�s
option payoff profile, trading strategies employed or arbitrage opportunities available.
Return series derived from this mimicking approach is particular useful in studying risk
factors and performance attributes underlying hedge fund investing. It also provides a
promising direction for future research of hedge fund asset pricing.
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References Ackermann, Carl, R. McEnally and D. Ravenscraft. 1999. �The Performance of Hedge
Funds: Risk, Return, and Incentives.� Journal of Finance, 54:833-874. Ackermann, Carl. 2000. �Essays on Hedge Funds.� Ph.D. Dissertation, University of
North Carolina, Chapel Hill. Agarwal, Vikas and Narayan Naik. 1999. �On Taking the �Alternative� Route: Risks,
Rewards Style and Performance Persistence of Hedge Funds.� Working paper, London Business School.
__________. 2000. �Multi-Period Performance Persistence Analysis of Hedge Funds.�
Journal of Financial and Quantitative Analysis, 35:327-342. __________. 2001. �Characterizing Hedge Fund Risks with Buy-and-Hold and Option-
Based Strategies.� Working paper, London Business School. Alexander, Gordon. 2000. �On Back-Testing �Zero Investment� Strategies.� Journal of
Business, vol. 73, no. 2:255-278. Asness, Clifford, Robert Krail and John Liew. 2000. �Do Hedge Funds Hedge?�
Working paper, AQR Capital Management. Brealey, Richard and Evi Kaplanis. 2001. �Changes in the Factor Exposures of Hedge
Funds.� Working paper, London Business School. Brown, Stephen and William Goetzmann. 1997. �Mutual Fund Styles.� Journal of
Financial Economics, 43:373-399. __________. 2001. �Hedge Funds with Style.� Working paper 00-29, Yale University. Brown, Stephen, William Goetzmann and Roger Ibbotson. 1999. �Offshore Hedge
Funds: Survival and Performance1989-1995.� Journal of Business, 72:91-118. Brown, Stephen, William Goetzmann, Roger Ibbotson and Stephen Ross. 1992.
�Survivorship Bias in Performance Studies.� Review of Financial Studies, 5:553-580.
Capital Market Risk Advisors, Inc. 2001. �NAV/Fair Value Practices Survey Results.�
July 9. Carhart, Mark. 1997. �Mutual Fund Survivorship.� Working paper, University of
Southern California. Carpenter, Jennifer. 2000. �Does Option Compensation Increase Managerial Risk
Appetite?� Journal of Finance, 55:2311-2331
Oct-01 Version
10/16/01 4:17 PM - 36 -
Financial Times. 2001. �More Scrutiny for Hedge Fund and Mutual Fund Managers.�
March 27. Fung, William and David Hsieh. 1997. �Empirical Characteristics of Dynamic Trading
Strategies: The Case of Hedge Funds.� Review of Financial Studies, 10:275-302. __________. 1999. �A Primer for Hedge Funds.� Journal of Empirical Finance, __________. 2000a. �Performance Characteristics of Hedge Funds and CTA Funds:
Natural versus Spurious Biases.� Journal of Quantitative and Financial Analysis. __________. 2000b. �The Risk in Hedge Fund Strategies: Theory and Evidence from
Trend Followers.� Review of Financial Studies, . __________. 2001. �Benchmarks for Hedge Fund Performance: Information Content
and Measurement Biases.� Financial Analysts Journal, Forthcoming. Gatev, Evan, William Goetzmann and Geert Rouweinhorst. 1999. �Pairs Trading:
Performance of a Relative Value Arbitrage Rule.� Working paper 7032, National Bureau of Economic Research.
Glosten, Lawrence and Ravi Jagannathan. 1994. �A Contingent Claim Approach to
Performance Evaluation.� Journal of Empirical Finance, 1:133-160. Grinold, Richard and Ronald Kahn. 2000. �Efficiency Gains of Long-Short Investing.�
Financial Analysts Journal, November/December:40-53. HedgeWorld. 2001. �Rivalry Gets Uglier: Hedge Funds vs. Mutual Funds.� The
Alternative Edge Newsletter, June 4. Lhabitant, Francois-Serge. 2001. �Assessing Market Risk for Hedge Funds and Hedge
Funds Portfolios.� Research Paper No. 24, International Center for Financial Asset Management and Engineering.
Liew, Jimmy Kyung-Soo. 1999. �Essays in Investment Strategies.� Ph.D. Dissertation,
Columbia University. Lo, Andew. 2001. �Risk Management for Hedge Funds: Introduction and Overview.�
Working paper, presented at the PricewaterhouseCoopers Risk Institute 2000 Conference.
Kao, Duen-Li. 2000a. �Analyzing Investment Styles of Fixed Income Managers.�
Journal of Investment Consulting, December. __________. 2000b. �Estimating and Pricing Credit Risk: An Overview.� Financial
Analysts Journal, 56 (July/August): 50-66.
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Kon, Stanley. 1999. �Mortgage Portfolio Performance Attribution.� Working paper,
Smith Breeden Associates. Martin, George. 2001. �Making Sense of Hedge Fund Returns: What Matters and What
Doesn�t.� Derivative Strategy. Mezrich, Jpseph, Qi Zeng and Matthew Rothman. 2000. �The Return of Stock Picker�.
Quantitative Strategies, Morgan Stanley Dean Witter, December. Michaud, Richard. 1998. �Is Value Multidimensional? Implications for Style
Management and Global Stock Selection.� The Journal of Investing, Spring:61-65.
Mitchell, Mark and Todd Pulvino. 2000. �Characteristics of Risk and Return in Risk
Arbitrage.� Working paper, Harvard University. Norland, Erik, Jose Maio Quintana and Sykes Wilford. 2000. �Leverage: A Very
Misleading Way to Measure Risk.� Derivatives Quarterly, Fall:3-15. The President�s Working Group on Financial Markets. 1999. Hedge Funds, Leverage
and the Lessons of Long-Term Capital Management. Report of the President�s Working Group on Financial Markets, April 28.
Richards, Anthony. 1999. �Idiosyncratic Risk: An Empirical Analysis, with
Implications for the Risk of Relative-Value Trading Strategies.� Working paper 99-148, International Monetary Funds.
Santini, Laura. 2001. �Trading�s Hidden Costs Hedge Funds, Technophobia and
Benchmarking Games Eat Into the Performance of Mutual Funds.� The Investment Dealers� Digest, August 14.
Schneeweis, Thomas and Richard Spurgin. 1998. �Multifactor Analysis of Hedge Fund,
Managed Futures, and Mutual Fund Return and Risk Characteristics.� Journal of Alternative Investments, 1 (Fall):1-24.
Sharpe, William. 1988. �Determining a Fund�s Effective Asset Mix.� Investment
Management Review, December:59-69. Sharpe, William. 1992. �Asset Allocation: Management Style and Performance
Measurement.� Journal of Portfolio Management, Winter:7-19. Spear Sheena and Steve Wiltshire. 2000. �The Long and the Short of Market Neutral
Investing.� Russell Research Commentary. Suprgin, Richard. 1999. �A Benchmark for Commodity Trading Advisor Performance.�
Journal of Alternative Investments, 2 (Summer):11-21.
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Sound Practices for Hedge Fund Managers. 200027. Tang, Eric. 1999. AlphaTrack. Working paper, Portfolio Management Technology. TASS. 2000. The TASS Asset Flows Report: Fourth Quarter 2000. Tremont. 2000. �Convertible Arbitrage: Opportunity & Risk.� White paper, September.
27 An excellent report on risk disclosure and management of hedge funds that was jointly developed by several well-known large hedge funds. The report can be accessed at www.hfinsoundpractices.com