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RISKS OF EQUITY- ORIENTED HEDGE FUNDS
NARAYAN Y. NAIK
LONDON BUSINESS SCHOOL
Background
Rapid growth in the hedge fund industry
Significant investment by institutional
investors including Endowments, Pension
funds, Foundations and Charities etc.
Risk-Return Characteristics
Although they trade in standard asset classes, they show low
correlation with standard asset classes.
There are many factor risk premia - Buy-and-hold type
strategies used by mutual funds provide exposure to market,
credit, interest rate, liquidity risk premia etc.
Dynamic or Option-based trading strategies used by hedge
funds provide exposure to “alternative” risk premia - bearing
stochastic volatility risk, price-jump risk etc.
STATE DEPENDENT RETURNS:
HFR GLOBAL/MACRO
7
6
5
4
3
2
MSCI-W
1
Global Macro
0
-1
-2
-3
-4
1 2 3 4 5
STATE DEPENDENT RETURNS:
TREND FOLLOWERS
8
6
4
2
0 S&P 500
-2 Trend Followers
-4
-6
-8
1 2 3 4 5
STATE DEPENDENT RETURNS:
HFR FIXED INCOME ARBITRAGE
7
6
5
4
3
2 S&P 500
1
FI Arb
0
-1
-2
-3
-4
1 2 3 4 5
STATE DEPENDENT RETURNS:
HFR FIXED INCOME ARBITRAGE
2
1.5
1
0.5 Delta(BAA-
0 10yTBond) x10
FI Arb
-0.5
-1
-1.5
-2
1 2 3 4 5
CHARACTERISING THE RISKS
Non-linear option-like exposures to standard asset
classes => traditional linear factor models need to be
augmented to capture the non-linearities
Need to select the right asset classes and need to
allow for non-linearities
WHY USE OPTIONS?
Hedge funds trade in derivatives
Take state-contingent bets
Profit sharing element of manager’s compensation
IMPLICATIONS
Returns should be broken down in two parts
Due to Location (Buy-and-Hold component)
Due to Trading Strategy (Option component)
Evidence on non-linearities
“Trend-following” strategies employed by CTAs
exhibit lookback straddle-like payoff (Fung and Hsieh
(RFS 2001))
“Event or Risk” Arbitrage strategies exhibit payoff
similar to writing an uncovered put option on the
market index (Mitchell and Pulvino (JF 2001))
An Example of Non-Linearities –
Case of Event Driven Strategy
Event Driven Index: Exposure to Russell 3000 Index
6
4
2
Event Driven Index Returns
0
-15 -10 -5 0 5 10
OLS fit
-2
-4
LOWESS
fit
Writing an at-the-
money Put -6
-8
Russell 3000 Index Returns
Behavior of Residuals without
Options
Panel A: Residuals from OLS Regression of HFR Event Driven Index against
Russell 3000 Index and Fama-French Size Factor plotted against the Russell
3000 Index
Lowess smoother, bandwidth = 0.8
4
2
Residuals
0
-2
-4
-10 -5 0 5 10
Russell 3000 Index
Behavior of Residuals with
Options
Panel B: Residuals from OLS Regression of HFR Event Driven Index against an
Out-of-the-money put option on S& P 500 Index and Fama-French Size Factor
plotted against the Russell 3000 Index
Lowess smoother, bandwidth = 0.8
4
2
Residuals
0
-2
-4
-10 -5 0 5 10
Russell 3000 Index
Our Generic Approach
Augment the traditional linear factor
model with option-based strategies
Option-based factors proxy for
Dynamic trading strategies
State-contingent bets
Key Questions
What are the systematic risk components of hedge fund returns?
Do “other” hedge fund strategies show non-linear risk-return
tradeoffs as well?
Can we passively replicate hedge fund payoffs with buy-and-hold
and option-based strategies?
What implications do non-linearities have in portfolio decisions?
How does the long-term performance of hedge funds compare to
their recent performance?
Main findings
A wide range of hedge fund strategies show non-linear risk-return
payoffs similar to writing a put option on the equity index
Findings for Event Arbitrage are similar to that of Mitchell and
Pulvino (JF 2001) results – independent corroboration
Replicating portfolios explain out-of-sample variation
Findings are robust to Choice of database, Options on broader
index and alternative non-linear specifications
Significant negative tail risk underestimated by M-V framework
Recent performance appears better than the long-run performance
Sample Data
Hedge Fund Research (HFR) Database
In-sample Index Performance – Jan ’90 to Jun ’00
Out-of-sample Performance – Jul ’00 to Dec ’01 (Index) and Jul ’00
to Aug ’01 (Individual funds)
CSFB/Tremont (CSFB) Database
In-sample Index Performance – Jan ’94 to Jun ’00
Out-of-sample Performance – Jul ’00 to Dec ’01 (Index) and Jul ’00
to Aug ’01 (Individual funds)
Equity-Oriented Hedge Funds
Event Arbitrage
Restructuring
Event Driven
Relative Value Arbitrage
Convertible Arbitrage
Equity Hedge (Long-Short Equity)
Equity Non-Hedge
Short Selling (Dedicated Short-Bias)
Classification
Non-directional Strategies
Event Arbitrage
Restructuring
Event Driven
Relative Value Arbitrage
Convertible Arbitrage
Equity Hedge (Long-Short Equity)
Directional Strategies
Equity Non-Hedge
Short Selling (Dedicated Short-Bias)
Multifactor Model
HFt = C + λBH t + γOSt + et
HFt – Hedge Fund Return at time t
BHt – Buy-and-Hold Risk Factor Return at time t
OSt – Option-Based Risk Factor Return at time t
Buy-and-Hold Strategies
Market Risk Factors
Equities – U.S. and Non-U.S.
Fama-French Size and Book-to-Market Factors
Carhart’s Momentum Factor
Bonds – Government and Corporate
Currencies
Commodities
Default Risk
Change in Default Spread
High Yield Bond
Option-Based Strategies
CME-traded S&P 500 Composite index
options (European)
At-the-money options
S / PV(X) = 1.0
Out-of-the-money options
S / PV(X) = 1.0 ± 0.01
Admissible Trading Strategies
Buying Put Buying Call
Options Options
S / PV(X) S / PV(X) S / PV(X)
= 1.01 = 1.00 = 0.99
The figures in percentages have been rounded to whole numbers for illustration purpose.
Admissible Trading Strategies
S / PV(X) S / PV(X)
= 1.01 = 0.99
S / PV(X)
= 1.00
Writing Put Writing Call
Options Options
Results
Sample Period: Jan 90 - Jun 00 (HFR) and Jan 94 – Jun 00 (CSFB/Tremont
HFR CSFB/Tremont
Strategy
Adj. Adj.
c Sig. Factors c Sig. Factors
R2 R2
Event Arbitrage 0.04 -SPPo, SMB, HML 0.44
-SPPo, SMB, HML
Restructuring 0.43 0.66
LRUS, LHY, FRBI, MEM
-SPPo,RUS, SMB, -SPPo, SMB, MEM
Event Driven 0.20 0.73 0.59 0.74
HML, MEM LHY, -SBG, -DEFSPR
Relative Value -SPPo, SMB, HML,
0.38 0.52
Arbitrage -MOM, MXUS
Convertible -SPPo, LRUS, SMB,
0.24 0.41 0.59 LRUS, -SBW, LHY 0.33
Arbitrage MEM, SBG
Equity Hedge 0.99 RUS,SMB, -HML, GSCI 0.73 0.26 RUS,SMB, -HML 0.84
Equity Non-
0.56 RUS,SMB,MEM 0.92
Hedge
-SPCo ,-RUS,-SMB, -RUS, -SMB, MOM
Short Selling -0.07 0.82 0.40 0.85
HML -DEFSPR, HML
Robustness Checks
Choice of database
Sub-period Analysis
Use of lagged Russell 3000 index
Options on a broader equity index (Russell 2000)
Use of deeper out-of-the-money options
Use of American-style options on S&P 500 futures
Alternative non-linear specifications
Out-of-sample Index Performance
H FR Event D riven In de x HF R Re structuring In dex
8 .0 0 6 .0 0
5 .0 0
6 .0 0
4 .0 0
4 .0 0
3 .0 0
2 .0 0 2 .0 0
Retur n
Retur n
EDRP RESTRP
ED REST
0 .0 0 1 .0 0
Jul- Aug- Sep- Oct- N ov- Dec- Jan- Feb- Ma r- Ap r- M Jun- Ju l- Au g- Se p- Oct- Nov- Dec-
0 0 00 00 00 00 00 01 01 01 01 ay- 01 01 0 1 0 1 01 01 01 0 .0 0
-2 .0 0 01 Jul- Aug - Sep - Oct- Nov- Dec- Ja n- Feb- Mar- Apr- M Jun- Ju l- Aug- Se p- Oct- No v- D ec-
-1 .0 0 0 0 0 0 0 0 00 0 0 00 01 01 01 01 ay- 01 01 01 01 01 01 01
01
-4 .0 0
-2 .0 0
-6 .0 0 -3 .0 0
Month Month
HF R Eq uity N on -He dge In dex H FR Sh ort Selling Ind ex
15.00 20.00
15.00
10.00
10.00
5.00
5.00
Retur n
SHORTRP
Return
ENH RP
0.00
ENH SHORT
Ju l- Aug- Sep- Oct- No v- De c- Jan- Feb- Ma r- Ap r- M Jun- Jul - A ug- Sep- Oc t- Nov- Dec-
0.00
00 00 00 0 0 00 00 01 01 01 01 ay - 01 01 01 01 01 01 01
Jul- A S Oct- Nov- D Jan- Feb- Ma r- Apr- M Jun- Jul - A S Oc t- Nov- D
01
-5.00 00 u g- e p- 00 00 ec- 01 01 01 01 a y- 01 01 ug- ep- 01 01 ec -
-5.00 00 00 00 01 01 01 01
-10.00 -10.00
-15.00 -15.00
Month Month
Out-of-sample Performance of
Individual Funds
HFR: Out-of-sample R-squares using Replicating Portfolios HFR: Out-of-sample R-squares using Indexes
30% Mean R2 = 26.71% 30% Mean R2 = 30.87%
Median R2 =22.50% Median R2 =27.44%
25% 25%
Percentage of funds
Percentage of funds
20% 20%
15% 15%
10% 10%
5% 5%
0% 0%
Less -10- 10- 30- 50- 70- 90- Less -10- 10- 30- 50- 70- 90-
than - 0% 20% 40% 60% 80% 100% than - 0% 20% 40% 60% 80% 100%
20% 20%
Range of R-squares Range of R-squares
CSFB/Tremont: Out-of-sample R-squares using Replicating CSFB/Tremont: Out-of-sample R-squares using Indexes
Portfolios
Mean R2 = 27.17% 18% Mean R2 = 23.01%
18% Median R2 =22.64% 16% Median R2 = 13.76%
Percentage of funds
16% 14%
Percentage of funds
14% 12%
12% 10%
10%
8%
8%
6%
6%
4% 4%
2% 2%
0% 0%
Less -10- 10- 30- 50- 70- 90- Less -10- 10- 30- 50- 70- 90-
than - 0% 20% 40% 60% 80% 100% than - 0% 20% 40% 60% 80% 100%
20% 20%
Range of R-squares Range of R-squares
Long/Short Strategies used by
HMC
Domestic Equity Portfolio
Convertible
Long: Solectron zero-convertible convertible
Short: Solectron common
Merger
Long: Associates First
Short: Citigroup
Balance Sheet
Long: Petrie Stores
Short: Toys “R” Us (major component of Petrie’s
balancesheet)
Long/Short Strategies used by
HMC (contd.)
Foreign Equity Portfolio
Dual Listing
Long:Allied Zurich (UK)
Zurich Allied (Swiss)
Voting/non-voting
Long: Telecom Italia Moblie savings shares (non-voting)
Short: Telecom Italia Moblie ordinary shares (voting)
Holding Company
Long: Investor
Short: Ericsson; Altas Copco; S-E Banken; Astra/Zeneca;
ABB Stora; OMX Index futures
Closed-end Fund
Long: India Investment Fund
Short: MSCI India Index Swap
Long/Short Strategies used by
HMC (contd.)
Fixed-Income
Synthetic Treasury
Long: US Treasury 10.75% 10 yr; US Treasury 0% 10 yr
Short: US Treasury 6.25% 10 yr
Relative Value
Long: Brazil Discount due 2024 (including Brady collateral)
Short: Brazil 10.125 due 2027; Brazil 11.625 due 2004; US
Treasuries due 2030
Futures/swaps
Long: Japanese Govt. Bond futures
Short: Interest rate swap
Long/Short Strategies used by
HMC (contd.)
High Yield
Long Credit
Long: Grand Union 11.5 Senior Debt
Short: Grand Union 12.5 Subordinated Debt
Commodities
Cash and carry
Spot heating oil (plus financing, storage & ins.)
Heating oil delivery contract 8 months forward
Absolute Return component of
HMC
HMC’s uses the following as a Benchmark for
absolute return portfolio
60% Salomon’s Global Equity Index, plus
20% Morgan Stanley Global Bonds index, plus
20% LIBOR plus 5%
What kind of benchmark would you set?
Implications of non-linearities
Underestimation of expected loss using M-V analysis
Fung and Hsieh (1999)
Mean-Variance Analysis – Limited applicability
Alternative framework for portfolio optimization and
asset allocation
Mean-Value-at-Risk approach
Conditional Value-at-Risk
Conditional Drawdown Risk
Smoothed Value-at-Risk
Implications of non-linearities
(contd.)
Value-at-Risk (VaR)
Does not satisfy sub-additivity property, i.e. VaR of portfolio can be
larger than the sum of VaR of securities in the portfolio
VaR function – non-convex and non-differentiable
Alternative – Conditional VaR
VaR measures the maximum loss for a given confidence level over
a given period of time, while
CVaR is the expected loss conditional on the losses being greater
than or equal to VaR
VaR and Conditional VaR
Tail Risk (M-V versus M-CVaR)
90% confidence level 95% confidence level 99% confidence level
σ CVaR CVaR Ratio CVaR CVaR Ratio CVaR CVaR Ratio
(M-V) (M-CVaR) (M-V) (M-CVaR) (M-V) (M-CVaR)
0.73 0.42 0.33 1.25 0.88 0.51 1.75 2.41 0.88 2.73
0.85 0.33 0.28 1.17 0.84 0.60 1.40 2.84 1.49 1.91
1.21 0.61 0.55 1.11 1.20 1.04 1.15 2.83 2.36 1.20
1.78 1.38 1.31 1.05 2.16 2.04 1.06 4.31 4.07 1.06
2.59 2.61 2.51 1.04 3.67 3.51 1.05 7.41 7.13 1.04
AVG 1.12 1.25 1.54
Ratio of CVaRs
(M-V versus M-CVaR)
Ratio of CVaR(MV) and CVaR(M-CVaR)
3.25
2.75
Ratio of CVaRs
2.25
Ratio at 90.0%
Ratio at 95.0%
Ratio at 99.0%
1.75
1.25
0.75
0.00 0.50 1.00 1.50 2.00 2.50
Sigma
Long-Run Performance of Hedge
Funds
Limited return history of hedge fund index returns
(since 1990 for HFR and 1994 for CSFB/Tremont)
Long return history of buy-and-hold risk factors such
as Market, Size, Value and Momentum factors (since
1927)
Market data for options since 1982; Black-Scholes
prices can be computed since 1927
Allows us to determine the long-run performance of
hedge fund indexes (pre-1990)
HFR: Recent Vs Long-Run
Performance
Panel A: Recent Performance (Jan 90 to Jun 00)
Hedge fund strategy Mean SD Median Min. Max. CVaR (90%) CVaR (95%) CVaR (99%)
Non-Directional
Event Arbitrage 1.00 0.88 1.18 -3.31 2.40 -1.00 -1.86 -3.31
Restructuring 1.26 1.49 1.53 -5.30 4.88 -1.83 -3.10 -5.30
Event Driven 1.08 1.61 1.50 -6.66 4.40 -2.25 -3.54 -6.66
Relative Value Arbitrage 0.82 0.89 0.94 -3.22 3.03 -0.91 -1.62 -3.22
Convertible Arbitrage 0.83 0.65 0.91 -1.90 1.99 -0.46 -0.95 -1.90
Equity Hedge 0.81 2.24 0.89 -8.54 7.82 -3.16 -4.46 -8.54
Directional
Equity Non-Hedge 1.17 3.90 1.61 -16.11 10.08 -6.22 -8.37 -16.11
Short Selling 0.15 5.81 0.10 -18.54 20.95 -9.95 -12.78 -18.54
Panel B: Long-Run Performance (Jan 27 to Dec 89)
i.
Hedge fund strategy Mean SD Median Min. Max. CVaR (90%) CVaR (95%) CVaR (99%)
Non-Directional
Event Arbitrage 0.72 1.45 0.95 -7.76 7.81 -2.45 -3.47 -5.71
Restructuring 0.97 2.40 1.25 -11.11 18.78 -3.99 -5.56 -8.53
Event Driven 0.85 2.64 1.16 -11.73 19.94 -4.38 -5.96 -9.18
Relative Value Arbitrage 0.61 1.46 0.70 -6.37 10.16 -2.23 -3.12 -5.12
Convertible Arbitrage 0.57 0.97 0.66 -3.97 6.57 -1.41 -1.97 -3.05
Equity Hedge 0.60 2.69 0.66 -11.70 19.32 -4.26 -5.71 -9.30
Directional
Equity Non-Hedge 0.96 5.53 1.20 -23.43 39.87 -8.95 -11.77 -18.82
Short Selling 0.00 6.27 0.05 -39.72 26.94 -11.08 -14.76 -25.94
CSFB/Tremont: Recent Vs
Long-Run Performance
Panel A: Recent Performance (Jan 94 to Jun 00)
Hedge fund strategy Mean SD Median Min. Max. CVaR CVaR CVaR
(90%) (95%) (99%)
Non-Directional
Event Driven 1.26 1.56 1.56 -6.29 4.16 -1.85 -2.98 -6.29
Convertible Arbitrage 0.91 0.68 1.04 -1.57 1.84 -0.49 -0.97 -1.57
Equity Hedge 1.16 3.38 1.01 -11.61 10.86 -5.05 -7.00 -11.61
Directional
Short Selling -0.55 4.88 -0.83 -9.73 21.60 -7.28 -8.26 -9.73
i.
Panel B: Long-Run Performance (Jan 27 to Dec 93)
Hedge fund strategy Mean SD Median Min. Max. CVaR CVaR CVaR
(90%) (95%) (99%)
Non-Directional
Event Driven 0.83 2.27 1.17 -10.83 15.60 -3.92 -5.44 -8.65
Convertible Arbitrage 0.59 1.00 0.70 -4.31 5.50 -1.45 -2.13 -3.36
Equity Hedge 0.62 3.23 0.77 -15.35 18.52 -5.38 -7.12 -12.02
Directional
Short Selling -0.18 6.65 -0.41 -55.01 29.85 -11.64 -16.08 -33.86
Long-Run Performance of Hedge
Funds: Findings
Mean long-run returns are smaller
By 23 bp per month (2.76% per year) for HFR
By 22 bp per month (2.64% per year) for CSFB/Tremont
Median long-run returns are smaller
By 25 bp per month (3.00% per year) for HFR
By 55 bp per month (6.60% per year) for CSFB/Tremont
Volatility of long-run returns is bigger
Significant in 7 out of 8 HFR strategies
Significant in 3 out of 4 CSFB/Tremont strategies
CVaRs of long-run returns are bigger
By 100%, 60% and 40% (at 90%, 95% and 99% levels)
By 90%, 70% and 100% (at 90%, 95% and 99% levels)
Concluding Remarks
Option-based strategies capture non-
linear risks
Number of hedge fund strategies
writing deep out-of-the-money options
(similar to selling portfolio insurance
or catastrophic insurance)
Concluding Remarks (contd.)
Hedge funds exhibit significant left-tail
risk underestimated by Mean-
Variance framework
Long-run performance of hedge funds
is inferior to recent performance in
terms of lower mean and median
returns, higher volatility and CVaR
Concluding Remarks (contd.)
Potentially useful in
Asset allocation
Construction of fund of hedge funds
Risk management
Design of benchmark and managerial
compensation contract
Research Paper URLs
http://papers.ssrn.com/paper.taf?Abstract_id=153088
http://papers.ssrn.com/paper.taf?Abstract_id=190389
http://papers.ssrn.com/paper.taf?Abstract_id=238708
Or
http://www.hedgeworld.com/research/reports/top_dl.cgi
Most requested research reports number 2, 7 and 8.
Or
http://www.gsu.edu/~fncvaa/research.htm
Or
http://www.london.edu/faculty_research/working_papers/working_papers
.html (Search under author “Naik NY”)
IFA working paper numbers 289, 298, 300 and 305
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