CONTEMPORARY CONCERNS STUDY
INDIAN INSTITUTE OF MANAGEMENT BANGALORE
Hedge Funds: Risk return analysis
Submitted to
Prof. Dinesh Kumar
Indian Institute of Management Bangalore
on
August 28, 2007
in partial fulfilment of the requirements for the course
Contemporary Concerns Study undertaken in Term IV
by
Anirban Barman Roy (0611151)
Karan Singal (0611168)
Acknowledgement
We would like to extend our sincerest gratitude to Professor Dinesh Kumar for giving us the
opportunity to work on this project. He has been our constant source of guidance throughout the
course of the project. we hope that this essay is a proper reflection of our efforts and imbibed
insights on hedge funds’ mysteries and related concerns.
We would also like to thank Vinod Bhaskaran, Analyst, Lehman Brothers, London, for allowing
us to download data of Hedge Funds from Bloomberg to be used as a good starting point for
analysing data and completing this project.
Contents
Introduction ................................................................................................................................................... 4
Previous approaches...................................................................................................................................... 8
Data and Methodology .................................................................................................................................. 9
Performance Analysis using DEA .................................................................................................... 9
I.
II.
1.
Spearman’s Rank Correlation ..................................................................................................... 11
2.
Principal Component Analysis.................................................................................................... 15
Comparison of individual funds within Strategies .......................................................................... 18
III. Hypothesis Testing .......................................................................................................................... 21
Results ........................................................................................................................................................ 22
I.
Performance Analysis using DEA .................................................................................................. 22
II.
Comparison of Individual Funds within Strategies ......................................................................... 23
III. Hypothesis Testing ......................................................................................................................... 25
Conclusion ................................................................................................................................................. 27
Appendix .................................................................................................................................................... 28
Basic definitions...................................................................................................................................... 28
Correlation between strategies of hedge funds ....................................................................................... 30
References .................................................................................................................................................. 31
Bibliography .............................................................................................................................................. 33
Hedge Fund: Risk Return Analysis
Anirban Barman Roy
Student PGP, IIM Bangalore
anirbanb06@iimb.ernet.in
Karan Singal
Student PGP, IIM Bangalore
karans06@iimb.ernet.in
U Dinesh Kumar
Professor, IIM Bangalore
dineshk@iimb.ernet.in
Abstract: This paper looks at the Hedge Funds as an alternative investment strategy. It
enumerates the various characteristics of Hedge Funds that make it different from conventional
investment strategies and also investigates into the structure of a typical Hedge Fund. The main
thrust of the paper, is however, to present a new approach to investigate into the risk return
profile of 18 different hedge fund strategies. The originality of the work lies in using DEA (Data
Envelopment Analysis) to decipher the risk return profile of these strategies using advanced
measures of risk and return like CVaR, Drawdown and Skewness. The paper also presents results
of a z-test that throws light on whether Hedge Funds were responsible for Asian Financial Crisis
of 1997. Several other z-tests are also presented in the paper that enables an investor to choose
the strategy with best risk return profile and eliminate some during market meltdowns of specific
nature. In a nutshell, the paper seeks to demystify Hedge Fund investing for an intelligent
investor using the latest mathematical and statistical tools.
Keywords: Hedge Fund, Data Envelopment Analysis, Equity, Fixed Income, Sharpe ratio
Introduction
“Hedge funds are a huge fad. You can pick any ten hedge funds and I'll bet that on average they
will underperform the S&P over the next ten years.” – Warren Buffet
Hedge funds have always been intriguing for the regular investor. With the outlandish fees that
these funds charge, it’s only natural that investors seek spectacular if not astronomic returns. The
sector's allure is its supposed ability to make positive returns whatever is happening on global
markets. The potential for absolute returns, plus the lack of correlation between hedge funds and
almost all other asset classes, is an irresistible mix for most investors, Prosser [2007]. Yet, the
“Oracle of Ohama”, Warren Buffet, has categorically ruled out any possibility of them even
outperforming the S&P. Why should then Hedge Funds even be in existence? Are they merely
the pampered darling of an investor or is there sufficient evidence to disprove one of the greatest
investors of all times?
The first known hedge fund was started by Alfred Jones in 1949. Jones used a combination of
both leverage and short selling strategies to enable investing in both rising and falling markets.
During the 1950’s and 60’s Jones’s Fund consistently outperformed the best equity mutual funds
and thus attracted more players in the Hedge Fund arena. By 1968 there were 200 hedge funds in
US. However, many funds used only one leg of Jones' Strategy – leverage while keeping short
selling at bay. This led to obliteration of many funds during the bear market of 1970’s and only
by 1984 only 68 hedge funds remained in the market. The 1980s and 90s saw a stellar growth in
hedge funds with exceptional performance by few star managers. Throughout this period hedge
funds continued attracting investment from High net worth individuals, Private Banks, insurance
companies, pension plans and Hedge fund of funds. AIMA [2004] describes how this rapid
growth took shape. However, Hedge funds have also acquired a lot of bad reputation to their
name. A speculation regarding their large carry trade positions in yen led the meltdown of the
financial markets on 27th February 2007. The case of Bayou Group hedge fund has been making
rounds in courts after the group declined to return the principal amounts of the investors who had
exited from the fund before its crash. The more publicised Amaranth Hedge Fund has been found
guilty of taking huge bets on natural gas futures. When faced with a liquidity crunch in the gas
futures market, the fund had to file bankruptcy bringing a bad repute to the whole hedge fund
industry. In spite of such jitters, the hedge fund industry has grown at a phenomenal pace over
the years. Exhibit 1 illustrates that the hedge fund industry has grown by 5.5 times from 1995 to
2005.
Exhibit 1: Growth of the hedge Fund Industry From 1990
Exhibit 2: Returns of Hedge Funds vis-à-vis Stock Market Index
Hedge Funds’ investors are concerned about two simple questions – the risk of investing in a
hedge fund and the expected returns. A look at the data regarding hedge fund performance
reveals that apprehensions about the underperformance of hedge funds relative to the stock
market are anything but valid. From the year 2001 to 2006 the hedge funds have yielded excess
returns to the tune of 30 % on an average over the Traditional investor’s return from stock
markets. Exhibit 2 compares the cumulative returns that would be earned by an investor when
investing in a Stock Market portfolio vis-à-vis Hedge Fund of Funds with an initial investment of
$1000, 000. It is seen that hedge funds have ubiquitously outperformed the Stock Market during
the period. Hence, it appears that the premonitions of the Oracle of Ohama regarding Hedge
Funds being a black sheep of the Investment products family, might as well are taken with a
pinch of salt.
As the average investor might suspect, the high returns come at considerably large risks. It is a
popular belief that most hedge funds use global macro strategies and place large directional bets
on stocks, currencies, bonds, commodities and gold while using lots of leverage. The most
common measure of risk is volatility, that is, the annualised standard deviation of returns.
Surprisingly, most academic studies demonstrate that hedge funds, on average, are less volatile
than the market. For example, over the bull market period of 1994 to 2000, volatility of the S&P
500 was about 14% while volatility of the aggregated hedge funds was only about 10%. That is,
about two-thirds of the time, expected returns were within 10% of the average return. Thus
contrary to popular belief hedge fund returns come out to be considerably less volatile and more
concentrated than the market returns. As Crestmont Research [2007] points out, hedge fund
returns hardly drift into the tail regions of the frequency distribution. Exhibit 3 and Exhibit 4
illustrate that the Frequency distribution of Hedge Funds have much shorter tails (and hence
Deviation) than the S&P counterpart.
Are then all fears about the “dreaded tails” of Hedge Funds a myth? Is the Markov’s [1952]
portfolio theory incorrect? The answer to these questions might come from one of the
assumptions in the theory that the investor’s utility curves are a function of only return and
standard deviation of returns, and higher moments are ignored. The answer lies in the measures
of risk and return for Hedge Funds which do not follow a normal distribution defining its returns.
Most of the current analysis in the financial markets is based on the assumption of returns
following a normal distribution with the mean as a measure of expected return and the standard
deviation denoting the risk. Such analysis cannot be applied to hedge funds as the current studies
have ubiquitously shown that hedge fund returns have marked non-normal characteristics.
Typically hedge funds follow negatively skewed distributions characterised by positive cases but
having high possibility of extreme losses. Hence all traditional measures looked at by investors
for analysing Hedge Funds like the Sharpe Ratio (excess of return over unit standard deviation)
are rendered ineffective for portraying a proper picture of risk and return. It is due to this
wrongful assumption of normality that the volatility of hedge funds has often been stated to be
lower than market with returns being considerably higher.
Exhibit 3: Frequency distribution of S&P Index around the expected return
Exhibit 4: Frequency distribution of Hedge Fund of Fund around the expected return
This paper is organized as follows. Section 2 covers the previous approaches in studying the
risks associated with hedge funds in the recent past. Section 3 covers the methodology used in
this paper and how the data was collected. The results section 4 describes the observations made
in the research and the conclusion follows. The Appendix contain definitions of various riskreturn measures.
Previous approaches
Numerous articles have been written on the reason of a negative-skew in hedge funds.
(Goetzmann, Ingersoll, Spiegel and Welch [2002], Spurgin [2001], Mitchell and Pulvino [2001],
Goetzmann, Ingersoll and Ross [2003], Taleb [2004] and Chan, Getmansky, Haas and Lo
[2005]) Hedge funds implement dynamic option-like strategies, trade derivative securities and
have a fee structure which combined generate a non-linear payoff.
The non-normality of Hedge fund returns makes it imperative to devise new techniques of hedge
fund risk and return measurement. Since, a typical distribution of a hedge fund is negatively
skewed; measures of downside risk are more potent in describing the actual risk associated with
Hedge Funds. Specifically measures like Semi Deviation Estrada [2001], extreme value
theory(EVT) Gupta and Liang [2005], Value at Risk (VaR) Jorion[2000], CVaR (Conditional
Value at Risk) Agarwal and Naik [2004] and Alexander and Baptista [2004] etc. are more
appropriate measures of risk. For return measures, Arithmetic Excess Returns (AER), Geometric
Excess Returns (GER) and Kurtosis are suitable among others.
Liang [2006] analyzed the risk-return trade-off in hedge funds using semi-deviation, value at
risk, expected shortfall and tail risk using the deciles portfolio approach as mentioned in Fama
and French [1992]. They found that during 1995-2004 hedge funds with high ES outperform
those with low ES by an annual return difference margin of 7% after adjusting for autocorrelation and heteroskedasticity. Agarwal and Naik [2004] use empirical distributions of
returns of funds to determine expected shortfall or CVaR. Their observations clearly reveal that
that the mean-variance framework is inadequate to measure the downside risk and suggest ESoptimization technique instead. Using a normal distribution, a fat-tailed generalized error
distribution (GED), the Cornish-Fisher (CF) expansion, and the extreme value theory (EVT),
Bali and Gokcan [2004] estimate VaR for hedge fund portfolios. They use the Hedge Fund
Research indexes and find that the EVT approach and the CF expansion capture tail risk better
than the other approaches.
However, VaR is also subject to severe criticism. Lo [2001] points out that only several years of
historical data may not show the distribution of returns and questions the usefulness of VaR
based risk management. Traditionally, VaR has always suffered from these theoretical
shortcomings. It does not provide the magnitude of the possible losses below the threshold it
identifies. VaR also lacks convexity and monotonicity along with continuity (see Artzner
[1999]).
Eling [2006] describes a lot of risk and return parameters. The complete set of input and output
parameters that have been measured for each fund strategy in this paper are tabulated in Exhibit
5
Data and Methodology
I.
Performance Analysis using DEA
Collection of Data and layout of Approach
We collected data on NAVs for 4730 hedge funds from the Bloomberg Terminal for the period
spanning 14 years from 1995 to 2007. Specifically, the data collected was on monthly basis
which commenced on Jan- 1995 and continued till Apr-2007. These hedge funds were grouped
according to fund strategies. A total of 18 different strategies were found consisting of
Convertible, Corporate/Preferred, Currency, Derivative, Emerging market, Equity Directional,
Equity Market Neutral, Event Driven, Fixed income directional, Fixed income relative value,
Flexible portfolio, Geographically focused, Global Macro, Government/Corporate, Managed
Futures, Multi-Strategy, Sector Funds and Various Assets. After the grouping was done, the
NAV for each strategy was arrived at using the average NAV of all funds within the strategy
bucket. The NAV data was then normalized with the Apr-2007 NAV set to 1. Subsequently, the
monthly NAV data was used to find the returns for each period between Jan-1995 and Apr-2007
for each of the 18 strategies.
Most modern approaches use variance as the measure of risk and mean return as the measure of
return from a portfolio. However, variance does not separate the upside risk (which investors
seek) from the downside (the detrimental one). Hence, classic measures of performance like the
Sharpe Ratio has been modified to incorporate alternative risk measures like drawdown, lower
partial moments and Modified Value at Risk (MVaR) leading to the formulation of new
measures like the Sortino Ratio, Omega or Calmar Ratio. However, as researchers point out
[Eling, 2006] all such ratios, whether classical or modern, allow the integration of only one
dimension of risk and return. Consequently, one single measure that reports performance of a
hedge fund comprehensively is still wanting. It is here that use of DEA can be made to
incorporate the numerous ‘risk and return’ measures for a hedge fund and then arrive at an
efficiency score denoting the performance. Thus, use of this non-parametric linear programming
technique helps in multi dimensional performance analysis as opposed to existing measures.
DEA is now being used extensively to gauge individual hedge fund performance. This paper
tries to extend the technique to the different strategies in hedge fund management. Thus for each
strategy, several input and output measures are calculated using the returns data and finally a
performance score is arrived at for each strategy. It is understood that funds within the same
strategy may have low correlations Kat [2006] and precludes the possibility of absolute
uniformity of funds within the same strategy. However, it is easily seen that the correlations
between funds within the same strategy is markedly higher than between strategies. (See
Appendix Correlation between hedge fund strategies) Thus, it is reasonable to assume that funds
within a strategy have relatively more similarity and can be grouped to provide a rough measure
of the overlying strategy.
While computing the performance scores for each strategy using DEA, risk measures were taken
as inputs and return measure as output. An exhaustive list of the input and output parameters is
given below:
Risk Measures - Input
Return Measures - Output
Standard Deviation
Arithmetic Excess Return (AER)
LPM0
Geometric Excess Return (GER)
LPM1
HPM0
LPM2
HPM1
LPM3
HPM2
Maximum Drawdown (MD)
HPM3
Average Drawdown (AD)
Skewness
Standard Deviation of Drawdown (SDD)
Value at Risk (VaR)
Conditional Value at Risk (CVaR)
Modified Value at Risk (MVaR)
Exhibit 5: Risk returns measures
The definitions of these eleven input and seven output parameters have been detailed in the
Appendix on Basic definitions.
Selection of Input and Output measures
Once the input and output parameters have been identified, it remains to select the appropriate
ones for DEA. As suggested by Eling, two different approaches are used to arrive at the final list
of inputs and outputs. The first is the Spearman’s Rank Correlation and second is Principal
Component Analysis.
1. Spearman’s Rank Correlation
Spearman’s Rank correlation involves the selection of parameters that are least correlated with
each other. This is done by first computing all the risk and return measures for the hedge fund
strategies, ranking them and then finding the correlation between the rankings. Those measures
with the smallest Rank Correlations are used as inputs and outputs.
Before using the Spearman’s Rank Correlation for isolation of input and output variables, we
compute all the risk and return measures for each of the 18 strategies. The risk free rate has been
computed to be 0.42% per month, which corresponds to the average yield of 10 year US
Treasury bonds from 1995 to 2007. For all the measures involving lower Partial moments, the
Minimum Acceptable Rate (MAR) is used as 0.42%. For Average Drawdown and Standard
Deviation of Drawdown eight largest values have been considered (K=8).
The following table gives the SPSS output of Spearman’s Rank Correlation among all the input parameters
SD
LPM0
LPM1
LPM2
LPM3
MD
AD
SD
LPM0
LPM1
LPM2
LPM3
MD
AD
SDD
VAR
CVAR
MVAR
Correlation
Coefficient
Sig.
(2tailed)
N
1.000
-0.476
0.626
0.725
0.740
0.614
0.641
0.137
-0.465
-0.620
-0.224
.
0.046
0.005
0.001
0.000
0.007
0.004
0.587
0.052
0.006
0.372
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
-0.476
1.000
-0.154
-0.215
-0.254
-0.432
-0.403
0.029
0.160
0.386
0.108
0.046
.
0.542
0.392
0.309
0.074
0.098
0.909
0.526
0.113
0.668
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
0.626
-0.154
1.000
0.868
0.794
0.721
0.740
0.075
-0.934
-0.544
-0.129
0.005
0.542
.
0.000
0.000
0.001
0.000
0.766
0.000
0.020
0.610
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
0.725
-0.215
0.868
1.000
0.981
0.825
0.822
0.379
-0.738
-0.765
-0.030
0.001
0.392
0.000
.
0.000
0.000
0.000
0.121
0.000
0.000
0.906
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
0.740
-0.254
0.794
0.981
1.000
0.847
0.837
0.414
-0.662
-0.825
-0.022
0.000
0.309
0.000
0.000
.
0.000
0.000
0.088
0.003
0.000
0.932
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
0.614
-0.432
0.721
0.825
0.847
1.000
0.992
0.164
-0.695
-0.882
0.094
0.007
0.074
0.001
0.000
0.000
.
0.000
0.515
0.001
0.000
0.711
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
0.641
-0.403
0.740
0.822
0.837
0.992
1.000
0.096
-0.699
-0.862
0.063
Sig.
tailed)
N
SDD
VAR
CVAR
MVAR
(2-
0.004
0.098
0.000
0.000
0.000
0.000
.
0.705
0.001
0.000
0.804
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
0.137
0.029
0.075
0.379
0.414
0.164
0.096
1.000
0.018
-0.273
0.139
0.587
0.909
0.766
0.121
0.088
0.515
0.705
.
0.945
0.272
0.581
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
-0.465
0.160
-0.934
-0.738
-0.662
-0.695
-0.699
0.018
1.000
0.457
0.036
0.052
0.526
0.000
0.000
0.003
0.001
0.001
0.945
.
0.056
0.887
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
-0.620
0.386
-0.544
-0.765
-0.825
-0.882
-0.862
-0.273
0.457
1.000
0.028
0.006
0.113
0.020
0.000
0.000
0.000
0.000
0.272
0.056
.
0.913
18
18
18
18
18
18
18
18
18
18
18
Correlation
Coefficient
Sig.
(2tailed)
N
-0.224
0.108
-0.129
-0.030
-0.022
0.094
0.063
0.139
0.036
0.028
1.000
0.372
0.668
0.610
0.906
0.932
0.711
0.804
0.581
0.887
0.913
.
18
18
18
18
18
18
18
18
18
18
18
Similarly, the table below gives the Rank Correlation between all the output parameters.
Spearman's rho
AER
GER
AER
GER
HPM0
HPM1
HPM2
HPM3
Skewness
Correlation
Coefficient
Sig. (2-tailed)
1.000
0.891
0.623
0.614
0.787
0.802
0.822
.
0.000
0.006
0.007
0.000
0.000
0.000
N
18
18
18
18
18
18
18
Correlation
Coefficient
Sig. (2-tailed)
0.891
1.000
0.674
0.418
0.573
0.598
0.631
0.000
.
0.002
0.084
0.013
0.009
0.005
N
18
18
18
18
18
18
18
HPM0
HPM1
HPM2
HPM3
Skewness
Correlation
Coefficient
Sig. (2-tailed)
0.623
0.674
1.000
0.467
0.482
0.472
0.307
0.006
0.002
.
0.051
0.043
0.048
0.216
N
18
18
18
18
18
18
18
Correlation
Coefficient
Sig. (2-tailed)
0.614
0.418
0.467
1.000
0.853
0.812
0.591
0.007
0.084
0.051
.
0.000
0.000
0.010
N
18
18
18
18
18
18
18
Correlation
Coefficient
Sig. (2-tailed)
0.787
0.573
0.482
0.853
1.000
0.992
0.856
0.000
0.013
0.043
0.000
.
0.000
0.000
N
18
18
18
18
18
18
18
Correlation
Coefficient
Sig. (2-tailed)
0.802
0.598
0.472
0.812
0.992
1.000
0.897
0.000
0.009
0.048
0.000
0.000
.
0.000
N
18
18
18
18
18
18
18
Correlation
Coefficient
Sig. (2-tailed)
0.822
0.631
0.307
0.591
0.856
0.897
1.000
0.000
0.005
0.216
0.010
0.000
0.000
.
N
18
18
18
18
18
18
18
It is seen from the above tables that the risk ad return measures identified from the Spearman’s Rank Correlation Coefficient are
Risk Measures - Inputs
1. Standard Deviation of Drawdown (SDD)
2. Value At Risk (VAR)
Return Measures- Outputs
1. Higher Partial Moment of order 0 (HPM0)
2. Skewness
Now using these measures as the inputs and outputs, the following data table was constructed for
Data Envelopment Analysis.
INPUTS
Convertible
Corporate/Preferred
Currency
Derivative
Emerging Market
Equity Directional
Equity Market Neutral
Event Driven
Fixed Income Directional
Fixed Income Relative Value
Flexible Portfolio
Geographically Focused
Global Macro
Government/Corporate
Managed Futures
Multi-Strategy
Sector Funds
Various Assets
SDD
0.030163701
0.026188886
0.007894643
0.017775788
0.006818085
0.003447805
0.107381629
0.008050702
0.010129653
0.037941993
0.004288358
0.016330112
0.007797424
0.005968036
0.005611176
0.004920136
0.007390233
0.02133803
OUTPUTS
VAR
-0.031880746
-0.035590332
-0.010555947
-0.075344446
-0.068450064
-0.026569062
-0.022121135
-0.036646385
-0.035724338
-0.02847733
-0.01706434
-0.010019875
-0.029100049
-0.001661175
-0.047447801
-0.049610237
-0.01346531
-0.016801682
HPM0
0.619047619
0.551020408
0.457142857
0.461538462
0.56462585
0.585034014
0.523809524
0.673469388
0.503401361
0.523809524
0.5
0.445544554
0.462585034
0.761904762
0.448979592
0.571428571
0.253012048
0.5625
Skewness
-0.464167287
-0.065164724
-0.21817855
-0.245196918
-2.128659422
2.112549166
10.31052686
10.44591062
-1.436205692
6.024246406
3.886533576
0.451091032
5.74046094
7.075467894
8.869269506
8.944211243
-4.375743718
2.658813393
The results of the DEA output are discussed in the Results Section.
2. Principal Component Analysis
Principal Component Analysis (PCA) is a data reduction technique. In PCA the total variance in
the data is considered. PCA is used to determine the minimum number of components that
accounts for the maximum variance in the data. A principal component is by definition a linear
combination of optimally weighted variables. Typically a factor is defined as below
Where,
= Estimate of the ith factor
= Weight or Factor Score Coefficient
k = Number of Variables
The four principal components for the Input parameters as identified by SPSS are shown below:
Component
SD
LPM0
LPM1
LPM2
LPM3
MD
AD
SDD
VAR
CVAR
MVAR
1
0.848
-0.368
0.581
0.940
0.807
0.953
0.944
0.173
-0.543
-0.896
-0.006
2
0.335
-0.417
-0.754
0.129
0.413
-0.060
-0.082
0.242
0.798
-0.081
0.181
3
0.158
0.254
0.152
-0.001
0.028
-0.021
-0.080
0.473
-0.124
0.222
0.831
4
0.039
0.234
0.057
-0.040
-0.185
0.041
-0.047
0.798
0.112
-0.147
-0.485
Similarly, for the output parameters, two components were identified as below:
Component
AER
GER
HPM0
HPM1
HPM2
HPM3
Skewness
1
0.961
0.701
0.714
0.828
0.838
0.764
0.852
2
0.188
0.661
0.471
-0.155
-0.525
-0.575
0.032
On the inputs side, it is seen that Maximum Drawdown (MD), Value at Risk (VAR),Modified
Value at Risk (MVAR) and Standard Deviation of Drawdown(SDD) have maximum impact on
the Components 1, 2, 3 and 4 respectively. As seen from the appendix, the four components
together explain 86.777% of the total variance. On the outputs side, Arithmetic Excess Return
(AER) and Geometric Excess Return (GER) have highest impact in component 1 and 2
respectively. The complete results in the Appendix show that the two components explain
84.975% of the total variance.
Using the weights given by SPSS results, the components were constructed for each of the 18
strategies and then used as inputs and outputs for the same. The table below shows the data set
that was used to carry out DEA and arrive at performance scores based on selection through
Principal Component Analysis.
Strategies
Convertible
Corporate/Preferre
d
Currency
Derivative
Emerging Market
Equity Directional
Equity
Market
Neutral
Event Driven
Fixed
Income
Directional
Fixed
Income
Relative Value
Flexible Portfolio
Geographically
Focused
Global Macro
Government/Corpor
ate
Managed Futures
Multi-Strategy
Sector Funds
Various Assets
Inputs
Outputs
Component
1 (I1)
0.34929
0.35014
Component
2 (I2)
-0.20878
-0.24419
Component
3 (I3)
0.04051
0.02915
Component
4 (I4)
0.14790
0.17757
Component 1
(O1)
0.06386
0.35453
Component 2
(O2)
0.27853
0.25786
-0.07668
0.14402
1.32266
0.39314
0.69663
-0.24194
-0.31272
-0.32318
-0.23851
-0.18812
0.11552
0.09369
0.00305
0.00697
0.19165
0.14794
0.16789
0.13552
0.14605
0.18653
0.14338
0.12521
-1.40236
2.23055
9.20886
0.20793
0.20306
0.19439
0.34344
0.55769
1.52815
0.39804
-0.16924
-0.26986
0.10500
0.06290
0.05667
0.15167
9.51311
-0.86151
0.57637
0.18984
0.99283
-0.32520
-0.28886
0.37622
5.52980
0.42901
-0.02827
-0.00362
-0.23753
-0.25277
0.06571
0.09153
0.15645
0.17440
3.67183
0.70492
0.35816
0.22345
0.23415
-0.01077
-0.28951
-0.10136
-0.03678
-0.00772
0.23202
0.10805
5.23025
6.59901
0.39749
0.58807
0.34262
1.08277
-0.04925
0.17284
-0.28938
-0.28604
-0.33005
-0.22243
0.05511
-0.04739
0.18913
-0.01344
0.18290
0.17540
0.17921
0.19711
7.90250
8.06401
-3.55115
2.67708
0.48621
0.54445
-0.02225
0.34909
The results of the DEA are discussed in the next Section.
II.
Comparison of individual funds within Strategies
Once the best performing Strategies are identified using performance scores through DEA, we try to find out whether the strategy
alone is the deciding factor for performance of a particular fund. For this purpose, all the hedge fund strategies having more than 15
funds are considered. In the current case, nine such Hedge Fund Strategies are identified. From each strategy bucket, the five top
performing funds are chosen. Next, all the input/output measures and principal components as described earlier are computed for each
of these five funds in nine strategies. These values are then used for two DEA applications, which rank the individual funds (now the
DMUs) according to efficiency scores. A discussion on the results obtained can be found in the Results Section. The Table below
gives a detailed listing of all the identified hedge funds, the value of the variables and Principal Components considered for DEA.
Inputs
Strategy
DMU
Emerging Market
PRQPOWR
Equity
RUFEDFM
Equity
PRQSUBF
Equity
PROSCBI
Equity
KALTCHA
Equity
Equity Directional
Equity
market
PSPAVCL
Equity
POLPEUT
Equity
HARBOUR
Equity
CAMBFUN
Equity
PARKPLD
Equity
OKUOPPA
Outputs
Output Components
Input Components
Skewn
ess
1.29
Comp1
Comp2
Comp1
Comp2
Comp3
Comp4
1.7633
0.4073
0.7515
-0.3015
-0.5283
0.4702
SDD
VAR
KY
0.06
-0.08
HP
M0
0.73
BH
0.03
-0.11
0.64
1.29
1.7468
0.3582
0.7069
-0.3799
-0.5797
0.5027
KY
0.04
-0.07
0.72
0.39
1.0064
0.3719
0.4480
-0.2993
-0.5034
0.4460
KY
0.03
-0.12
0.63
1.00
1.4303
0.3365
0.8030
-0.4032
-0.5392
0.4820
VI
0.03
-0.16
0.61
-0.41
0.1685
0.2763
1.7899
-0.4736
-0.4297
0.3911
BZ
0.09
-0.11
0.63
2.99
3.1251
0.3945
1.0367
-0.4215
-0.7132
0.6515
VI
0.00
-0.13
0.54
2.17
2.3613
0.3258
1.2575
-0.4747
-0.5888
0.5042
BH
0.02
-0.10
0.62
0.50
0.9408
0.3134
0.5475
-0.3717
-0.4714
0.4345
VI
0.05
-0.08
0.63
0.81
1.1917
0.3299
0.5722
-0.3559
-0.5205
0.4942
BH
0.01
-0.11
0.54
2.92
3.0580
0.3426
1.2856
-0.5032
-0.8981
0.7005
VI
0.14
-0.12
0.60
1.37
1.7157
0.3247
1.1070
-0.3970
-0.6082
0.6711
Equity
GSIACGU
Equity
LLOYACE
Equity
PARKPLB
Equity
PRMUSEI
Equity
Neutral
Event Driven
Fixed
Directional
Income
Fixed
income
Relative Value
BH
0.03
-0.09
0.62
0.68
1.0707
0.3174
0.8531
-0.3602
-0.3873
0.3839
BZ
0.03
-0.07
0.64
0.04
0.5732
0.3175
0.2933
-0.3085
-0.3714
0.3791
BH
0.01
-0.04
0.56
0.06
0.4632
0.2673
0.2127
-0.3142
-0.2823
0.3408
VI
0.02
-0.06
0.62
-0.67
-0.1203
0.2708
0.6335
-0.3054
-0.2092
0.2733
RABSPSF
Equity
BAYHPTN
Equity
LIOFNDI
Equity
GAMARBI
Equity
AETOSAI
Equity
KY
0.03
-0.09
0.69
1.40
1.9254
0.3913
0.5631
-0.3098
-0.4960
0.4499
KY
0.02
-0.03
0.67
-0.11
0.3899
0.3141
0.5082
-0.2717
-0.3283
0.3266
KY
0.03
-0.03
0.68
-1.93
-1.1641
0.2622
0.2173
-0.2045
-0.1381
0.2287
VI
0.04
-0.01
0.69
0.02
0.5310
0.3304
0.1003
-0.2280
-0.3581
0.3656
VI
0.00
-0.01
0.61
0.69
1.0091
0.3112
-0.0496
-0.2472
-0.2589
0.3017
JGPFHDG
Equity
PRMFIAI
Equity
MILENTG
Equity
BSABSOV
Equity
GIRHFOA
Equity
BZ
0.00
0.00
0.92
1.34
1.7887
0.4866
0.0009
-0.1559
-0.5706
0.3670
VI
0.04
-0.03
0.68
-1.52
-0.7894
0.2734
0.3577
-0.2419
-0.2495
0.3058
BH
0.01
-0.02
0.74
0.87
1.3303
0.3844
0.1316
-0.2441
-0.4770
0.3852
KY
0.01
0.00
0.96
5.49
5.3198
0.6343
0.0496
-0.1018
-0.4626
0.2982
KY
0.03
-0.08
0.55
-0.04
0.4164
0.2588
0.5898
-0.3890
-0.4107
0.4371
KY
0.02
-0.08
0.62
-0.06
0.4345
0.2935
0.5573
-0.3427
-0.3641
0.3693
KY
0.03
-0.03
0.71
-0.30
0.2796
0.3292
0.2806
-0.2587
-0.4115
0.3792
KY
0.06
-0.02
0.73
-3.84
-2.7596
0.2244
0.4843
-0.1293
0.1286
0.0833
KY
0.01
-0.01
0.76
2.33
2.5499
0.4396
0.0069
-0.2062
-0.4148
0.3387
HAMTON1
Equity
ARGCCAA
Equity
IIIGLOB
Equity
CQSCQSF
Equity
IIIFNDI
Equity
Global Macro
Managed Futures
Multi Strategy
KY
0.04
-0.02
0.71
-2.96
-2.0182
0.2429
0.1873
-0.1540
0.0006
0.1476
VI
0.04
-0.04
0.63
2.30
2.4758
0.3775
0.4022
-0.2652
-0.3466
0.4019
VI
0.02
-0.03
0.68
0.55
0.9968
0.3442
0.1079
-0.2749
-0.4720
0.4240
KY
0.02
-0.07
0.65
0.28
0.7653
0.3205
0.5858
-0.3301
-0.3760
0.3621
NT
0.02
-0.06
0.65
-0.60
-0.0312
0.2904
0.5565
-0.2910
-0.2556
0.2849
KY
0.03
-0.04
0.56
0.20
0.5893
0.2727
0.2153
-0.3354
-0.4380
0.4593
VI
0.10
-0.02
0.76
11.49
-4319.4558
0.4002
-0.0201
0.5420
-0.1149
FP
0.04
-0.19
0.61
0.21
5762.55
52
0.7513
0.2974
1.2676
-0.5008
-0.5723
0.5024
VI
0.03
-0.11
0.63
-0.15
0.3908
0.2993
0.6529
-0.3362
-0.2663
0.3189
CN
0.05
-0.16
0.47
0.67
0.9830
0.2347
1.5405
-0.4827
-0.2426
0.3682
ID
0.02
-0.05
0.55
0.75
1.0242
0.2843
0.2912
-0.3497
-0.3922
0.4194
GAPMLTP
Equity
BZ
0.00
0.00
0.90
8.89
1016512
8.0387
0.0519
-2.2804
-10.2419
6.0118
GMSFDII
Equity
IM
0.01
-0.01
0.71
-0.95
5779352
.1477
0.1631
-5.6652
-25.2681
14.8551
HDGGFVD
Equity
FOXGRFD
Equity
ATICOLV
Equity
BZ
0.01
-0.01
0.87
9.04
8.5004
7649072.40
66
4348016.63
89
0.7157
0.1073
-0.0610
-0.0922
0.1258
BM
0.03
-0.07
0.62
0.17
0.6405
0.3051
0.4042
-0.3271
-0.3891
0.4009
BZ
0.04
-0.01
0.88
5.76
5.6629
0.6127
0.3835
-0.2352
-0.8234
0.5678
SIBCAPI
Equity
GAMMUTI
Equity
LLGASPI
Equity
FIREGLI
Equity
ODYEDMI
Equity
K1INVES
Equity
SLFPUIK
Equity
AIMSPHG
Equity
FRIEDDIV
Equity
EDFDGLI
Equity
III.
Hypothesis Testing
First hypothesis
Apart from the risk return measures, tests of few hypotheses were also carried out to determine
from an investors viewpoint the best strategies pursued by Hedge Funds. The first hypothesis
was formulated as follows
“Hedge Fund Strategy i is better than Strategy j in terms of mean returns
(where i, j = 1(1)18, and i≠j )”
The data was prepared as follows:
1. The monthly returns were calculated for each strategy during the complete time horizon.
2. Next, the pair-wise difference between the monthly returns of the strategies was
calculated.
3. The mean difference over the entire period was calculated by taking an arithmetic mean.
4. A standard z-test for difference of mean returns at 95% confidence interval was done by
taking the standard deviation as the observed standard deviation.
Second hypothesis
Another main area that interests investors is the performance of funds during times of financial
turmoil. Hedge funds and more specifically George Soros have been blamed for the Asian
economic crisis of 1997. However, the working paper by Brown, Goetzman and Park [1998]
asserts that there is no empirical evidence to support the hypothesis that George Soros or any
other hedge fund manager was responsible for the crisis. During such economic predicament, the
investor is concerned about Hedge Fund strategies that outperform its peers. A comparative
study of the various strategies during the Asian crisis of 1997 was carried out. For this purpose
the mean return of each hedge fund strategy was computed from 1995 to 1999 (1997 ± 2 years)
A strategy was deemed better than another, if the mean return was better than the other. With a
95% confidence interval, a z-test for the second hypothsis was carried out
“Hedge Fund Strategy i yielded more returns than strategy j during the Asian economic crisis of
1997 crisis (where i , j = 1(1)18, and i≠j)”
Third hypothesis
A similar hypothesis was tested for the year 2000, which saw a meltdown in global markets in
wake of the 9/11 tragedy, yielded following results in the 95% confidence interval. Data for the
analysis was considered from 1998 to 2002 (2000 ± 2 years)
“Hedge Fund Strategy i yielded more returns than strategy j during the US stock market bust of
2000 (where i , j = 1(1)18, and i≠j )”
Results
I. Performance Analysis using DEA
The results of the DEA carried out for both sets of Input and output measures (as given by
Spearman’s Rank Correlation and Principal Component Analysis) are enumerated in the table
below. The rable also contains the ranking of the various strategies using the classical measure of
Sharpe Ratio
The results of DEA using inputs and outputs as determined by the Spearman Rank Correlation
show that six strategies viz. Equity Directional, Equity Market Neutral, Event Driven, Flexible
portfolio, Multi-Strategy and Government/Corporate are the most efficient. When inputs and
outputs are selected from the Principal Component Analysis, 13 strategies emerge to be the most
efficient. The results obtained from DEA are quite contradictory with the results given by Sharpe
Ratio. In fact, Convertible which ranked 18th in both DEA applications, was the second best
strategy according the Sharpe Ratio. Mathematically, the correlation between the Rankings given
by Sharpe Ratio and DEA-Rank Correlation was found to be only 5.4%. On the other hand, the
Correlation between the rankings arrived at through DEA-Rank Correlation and DEA-Principal
Component was found to be 58.37%. From an investor’s viewpoint, the rankings arrived at using
DEA are more meaningful since more than one measure of risk and return are taken into account.
II. Comparison of Individual Funds within Strategies
The results of the two DEA applications based on Spearman’s Rank Correlation and Principal Component
Analysis are as shown below:
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
DMU (Ticker)
PRQPOWR KY Equity
RUFEDFM BH Equity
PRQSUBF KY Equity
PROSCBI KY Equity
KALTCHA VI Equity
PSPAVCL BZ Equity
POLPEUT VI Equity
HARBOUR BH Equity
CAMBFUN VI Equity
PARKPLD BH Equity
OKUOPPA VI Equity
GSIACGU BH Equity
LLOYACE BZ Equity
PARKPLB BH Equity
PRMUSEI VI Equity
RABSPSF KY Equity
BAYHPTN KY Equity
LIOFNDI KY Equity
GAMARBI VI Equity
AETOSAI VI Equity
JGPFHDG BZ Equity
PRMFIAI VI Equity
MILENTG BH Equity
BSABSOV KY Equity
GIRHFOA KY Equity
HAMTON1 KY Equity
ARGCCAA KY Equity
IIIGLOB KY Equity
CQSCQSF KY Equity
IIIFNDI KY Equity
Spearman's Rank Correlation
Principal Component
Score
0.232520635
0.339858327
0.078757998
0.359693349
1.87E-02
0.493844597
1
0.138351198
0.150147042
0.684735414
0.290397753
0.148154375
8.15E-03
1.14E-02
3.48E-03
0.278547442
3.15E-03
2.02E-03
2.56E-03
1
1
2.12E-03
0.157708567
1
4.33E-03
4.66E-03
2.89E-03
1.35E-03
0.370134384
0.00158757
Score
-0.503399388
-0.466330526
-0.130914234
-0.355730432
1
-0.578690893
-1.033170308
-0.278950173
6.50E-05
1
1
-0.857834735
-0.347704053
-0.774742893
-0.682762393
-0.954289013
-0.739891021
5.70E-03
1.91E-02
-1.625145756
1
9.24E-03
-0.316573378
1
4.48E-03
-0.338312525
-0.252507786
1
-1.196673972
0.049808611
Rank
19
15
26
14
30
10
1
23
21
9
16
22
32
31
37
17
38
43
41
1
1
42
20
1
35
34
39
45
13
44
Rank
31
30
22
29
1
32
42
25
20
1
1
40
28
38
35
41
37
17
14
44
1
15
26
1
19
27
23
1
43
13
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
SIBCAPI VI Equity
GAMMUTI VI Equity
LLGASPI KY Equity
FIREGLI NT Equity
ODYEDMI KY Equity
K1INVES VI Equity
SLFPUIK FP Equity
AIMSPHG VI Equity
FRIEDDIV CN Equity
EDFDGLI ID Equity
GAPMLTP BZ Equity
GMSFDII IM Equity
HDGGFVD BZ Equity
FOXGRFD BM Equity
ATICOLV BZ Equity
0.257426537
7.89E-02
6.18E-02
3.63E-03
3.06E-02
1
1
7.24E-03
0.414462902
0.125646341
1
0.00259436
1
3.59E-02
0.467912589
18
25
27
36
29
1
1
33
12
24
1
40
1
28
11
-1.692815959
-8.72E-02
-0.721343256
-0.60079711
4.60E-03
1
7.79E-03
-0.793771315
1
-0.625185477
1
1
1
-0.253948991
1
45
21
36
33
18
1
16
39
1
34
1
1
1
24
1
In the rankings, as evident from the DEA based on Spearman’s Rank Correlation, the best funds
are POLPEUT VI (Equity Directional), AETOSAI VI (Event Driven), JGPFHDG BZ (Fixed
Income Directional), BSABSOV KY (Fixed Income Directional) , K1INVES VI (Managed
Futures), SLFPUIK FP (Managed Futures), GAPMLTP BZ (Multi-Strategy) and HDGGFVD BZ
(Multi-Strategy). In the previous DEA results, that ranked the strategies, the top performing ones
were Equity Directional, Equity Market Neutral, Event Driven, Flexible portfolio, Multi-Strategy
and Government/Corporate. It is seen that no funds belonging to Equity Market Neutral,
Flexible portfolio and Government/Corporate are classified as the best performing ones when
funds are ranked individually based on performance scores. Also, two funds from Managed
Futures rank in the most efficient ones though the strategy itself is not ranked as a top
performing one.
In the second DEA based on Principal Component Analysis, KALTCHA VI (Emerging market)
,PARKPLD BH( Equity Directional), OKUOPPA VI (Equity Market Neutral) ,JGPFHDG BZ
(Fixed Income Directional), BSABSOV KY((Fixed Income Directional) ,IIIGLOB KY(Fixed
Income Relative Value) ,K1INVES VI( Managed Futures) ,FRIEDDIV CN (Managed Futures),
GAPMLTP BZ (Multi-Strategy) , GMSFDII IM(Multi-Strategy)
, HDGGFVD BZ(MultiStrategy) and ATICOLV BZ (Multi-Strategy) emerge to be the most efficient ones. Here too,
two funds of Fixed Income Directional are observed to be efficient in spite of the strategy not
being included in the list of 13 efficient strategies thrown up by the same analysis at the strategy
level.
Hence, the results suggest, that the performance of hedge funds is not dictated solely by the
management strategy. Funds belonging to relatively inefficient strategies may achieve stellar
performances due to various other factors. Thus, at the surface, it seems that the fund managers
play the pivotal role in generating above average returns and hence there is some justification to
the high performance fees that Hedge Funds charge.
III.
Hypothesis Testing
First hypothesis
A test of the hypothesis using the standard z-test for difference of mean returns showed that at
95% confidence interval,
1. Convertible Strategy is better than Currency, Emerging Market , Fixed Income
Directional , Geographically focused and Sector Funds
2. Corporate/Preferred strategy is better than Sector Funds
3. Currency is better than fixed income Directional and Sector Funds
4. Emerging market is better than Currency ,Derivative, Flexible, Geographically focused
and sector funds
5. Equity directional is better than fixed income directional
6. Fixed Income directional is better than Sector Funds
7. Fixed Income Relative Value is better than Sector Funds
8. Flexible portfolio is better than Global Macro and Sector Funds
9. Geographically focused is better than sector funds
10. Government/Corporate is better than currency, Fixed income directional, fixed income
relative value, Flexible portfolio, geographically focused, Global Macro, Multi Strategy
and Sector Funds
Second hypothesis
The results of the 1997 crisis hypothesis testing showed that
1. Convertible was better than Emerging market, Flexible portfolio and geographically
focused
2. Corporate/Preferred is better than Emerging Market and Flexible portfolio
3. Currency is better than Geographically focused and fixed income directional
4. Emerging market is better than geographically focused
5. Equity directional is better than Currency, Geographically focused, emerging market and
Fixed income directional
6. Equity market neutral is better than Geographically focused, Emerging market and Fixed
income directional
7. Event driven is better than emerging market
8. Fixed income directional is better than emerging market
9. Flexible portfolio is better than Fixed income directional
10. Global Macro is better than Emerging market
11. Managed futures is better than Emerging Market and Flexible portfolio
12. Multi-Strategy is better than Emerging Market and Flexible portfolio
A close look at the results reveals that nine strategies performed distinctly better than
Emerging Market strategy during the Asian Finacial Crisis. The Asian Financial crisis started
in July 1997 in Thailand and South Korea with the financial collapse of Kia, and affected
currencies, stock markets, and other asset prices in Asian countries, many considered Four
Asian Tigers. Indonesia, South Korea and Thailand were the countries most affected by the
crisis. Hong Kong, Malaysia, Laos and the Philippines were also hit by the slump. China,
India, Taiwan, Singapore and Vietnam were relatively unaffected. Japan was not affected
much by this crisis but was going through its own long-term economic difficulties. However,
all nations mentioned above saw their currencies dip significantly relative to the US dollar,
though the harder hit nations saw extended currency losses. Out of all the countries affected,
South Korea was hit hardest. Thus it is not hard to see that the Hedge funds investing in
Emerging Markets of Asia were liable to be more adversely affected than most other
strategies. The results of the z-test substantiate this finding with a 95% confidence level. The
results of the test are also shown in Exhibit 6
Third hypothesis
The results of the 2000 technology bubble bust time mean return testing showed that
1. Convertible is better than Emerging Market, Fixed Income Directional and
Geographically Focused
2. Corporate/Preferred is better than Sector Funds
3. Currency is better than Sector Funds and fixed income directional
4. Emerging market is better than Sector Funds
5. Fixed income directional is better than Sector Funds
6. Fixed Income Relative Value is better than Sector Funds
7. Multi Strategy is better than emerging market, Fixed income directional and Fixed
income relative value
8. Various Assets are better than Global Macro and Sector Funds
Exhibit 6: z-test certainty level of fund in Column better than fund in Row during 1997 crisis
Conclusion
The paper shows that traditional measures of performance like mean-deviation ratio are not
sufficient to capture the complete risk return profile of hedge funds. Various risk return measures
are considered and then principal component analysis and spearman rank correlation techniques
are used to select the parameters to compare the hedge funds both at the strategy level and the
fund level. DEA is used as the tool for comparison by computing performance scores for each
strategy.
The paper serves as a comprehensive guide to an investor looking for alternative investments in
hedge funds. The first question of which strategies are most efficient is answered using Sharpe’s
ratio (with two-dimensional risk return analysis) and then the DEA-Principal Components and
DEA-Rank Correlation (with multi-dimensional risk return analysis). The next natural question
whether this research is relevant in the changing environment is answered using the research on
the 1997 Asian financial crisis and the 2000 asset bubble burst periods. These are similar to what
is currently looming in the form of yen carry trade and sub-prime mortgage crisis. The time
window used is 5 years and is ample to observe all the shock generated in these crunch
situations. After having decided which strategies to look at, the investor will need to select the
funds. The research on top performing funds across the strategies provides additional
information to do the last part and find the right funds for the investor.
Appendix
Basic definitions
Under the condition of non-normality few of the measures that have been used to describe the
risk and return are defined below:
Value at Risk: Value at Risk (VaR) is the prediction of the worst loss that can happen within a
given period with a certain level of confidence.
Expected Shortfall: Expected Shortfall (ES) is the expected loss, greater or equal to the VaR.
Semi Deviation: Semi deviation unlike the standard deviation considers deviation from the mean
only when it is negative. The formal expression for semi-deviation is
Where,
is the average return.
Tail Risk: Tail risk is a measure of deviation of losses of larger than the VaR. It can be
compared to the Expected Shortfall (ES) which is a measure of the mean of the losses larger than
VaR.
Skewness: Skewness is defined as the third standardized moment. It is expressed as
Where
is the third moment about the mean and σ is the standard deviation.
Lower Partial Moments:
Higher Partial Moments:
n = Order of partial moment
= minimum acceptable return
Average Drawdown (AD):
,
Where, K = number of drawdowns
= drawdown of Fund i
Standard Deviation of Drawdown (SDD)
Value at Risk (VaR)
Conditional Value at Risk (CVaR):
Modified Value at Risk (MVaR)
Average Excess Return: AER =
Geometric Excess Return: GER =
= discrete return of fund i in month t
= (constant) risk free interest rate
T = number of months
Modified Value at Risk (MVaR):
, with
as the value at Risk
Correlation between strategies of hedge funds
Merger
Arbitrage
Distressed
Securities
Equity
Market
Neutral
Convertible
Arbitrage
Global
Macro
Long/Short
Equity
Emerging
Markets
MA
0.45
DS
0.30
EMN
-.04
CA
0.18
GM
0.07
L/S
0.24
EM
0.29
.30
.39
.18
.28
.15
.32
.14
-.04
.18
.23
.09
0.03
-0.02
0.05
0.18
0.28
0.09
0.28
0.09
0.23
0.08
0.07
0.15
0.03
0.09
0.26
0.09
0.10
0.24
0.32
-.02
0.23
0.09
0.24
0.27
0.29
0.14
0.05
0.08
0.10
0.27
0.52
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