Theory of Hedge Funds I: Arbitrage Pricing

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Yale
School of Management

Hedge Funds

William N. Goetzmann

Yale School of Management

Yale
School of Management

Overview


Background


Industry Performance


Management Styles


Hedge Funds as Portfolio Assets


Manager Track Records


Yale
School of Management

History and Background


Alfred Winslow Jones


Sociologist


Fortune

Editor


Fund Manager


1949 Partnership


market
-
neutral position


high incentive fee


leverage

Yale
School of Management

Theory of Hedge Funds


“Arbitrage in
expectations”


Short position’s
exposure matches long
position’s


Short finances long


Market neutral
investment


Market Exposure
Expected Return
Long Position
Short Position
Spread
Yale
School of Management

Basis of Hedge Fund Returns


Manager skill in identifying opportunities


Not derived from passive long position


Focused on “imperfect” market sectors


Depend critically upon special skills and
knowledge

Yale
School of Management

Defining Hedge Funds


Freedom from ICA (1940) controls on:


leverage


short
-
selling


cross
-
holding


10% limits


incentive compensation


derivatives positions

Yale
School of Management

Defining Hedge Funds


Limitations on:


number of U.S. investors (99 maximum)


solicitation of U.S. investors


public advertising and disclosure


Information problems:


no public performance records


data vendors only maintain “live fund” data


Yale
School of Management

A Sample of Hedge Funds


Survivorship issues


U.S. Offshore Hedge Fund Directory


Annual returns, 1989
-

1995


Net of fees and expenses


Includes defunct funds


Brown, Goetzmann & Ibbotson,
Offshore Hedge
Funds, Survival and Performance
, 1997 Yale
Working Paper

Yale
School of Management

Offshore Funds


Based in tax havens


Invest alongside major domestic entities


Represent a substantial portion of the
industry


399 Funds with $40 Billion in 12/1995

Yale
School of Management

Manager Compensation



Fixed fee 1% to 2%


Incentive fee 10% to 30% [20% typical] of
positive return


High water mark provision


Yale
School of Management

Industry Performance

Average Hedge Fund Retur ns
full sample and survivors
Full Sample
Survivors
Extant in 95
S&P 500
1989
1990
1991
1992
1993
1994
1995
-10
-5
0
5
10
15
20
25
30
35
40
Yale
School of Management

Summary Statistics 1989
-

1995

Time-Weighted
Mean Return
For Value-
Weighted Index
Time-Weighted
Mean Return
For Equal-
Weighted Index
Time-
Weighted
Mean Return
For the S&P
500 Index
Arithmetic Mean
24
.71
13
.27
16
.47
Geometric Mean
23
.48
12
.94
15
.00
Standard Deviation
16
.72
8
.40
15
.11
Sharpe Ratio
1
.19
0
.94
0
.73
Yale
School of Management

Manager Styles


Event
-
Driven


Market Neutral


Market Trend/Timing


Opportunistic
Investing


Multi
-
Strategy



Short Sellers


Sector Funds


Global Macro


Fund of Funds


Derivatives

Yale
School of Management

Event
-
Driven


Distressed Securities


bankruptcy


reorganization


equity and debt


Risk Arbitrage


position in acquired and acquirer


trade on collars and other options


hedge with derivatives

Yale
School of Management

Market Neutral



Classic Hedge Fund


true arbitrage on convertibles & derivatives


index arbitrage


fixed income arbitrage


pairs trading


APT arbitrage in expectations

Yale
School of Management

Market Trend/Timing



Timing U.S. Markets


exploit technical analysis


Timing Global Markets


seek country opportunities


Yale
School of Management

Opportunistic Investing


Largest Category of Hedge Fund


Value


liquidation value, book value, out
-
of
-
favor


Growth


future earnings potential


Short
-
Term Hold


active trading to exploit opportunity


Yale
School of Management

Short Sellers



Seeks overvalued equities to short


may hedge market exposure or may not

Yale
School of Management

Global Macro


Soros style


Currency speculation with futures
instruments


Forecast influence of global macro trends
on liquid instruments

Yale
School of Management

Fund of Funds



Select multiple managers



Use track records for choice



Promote diversification


major issue, since good funds are closed to
small investors.

Yale
School of Management

Commodities/ Options/ Futures



Distinction from CTA’s is blurred



Speculate in commodities markets


Yale
School of Management

Performance by Style

Value Weighted Return Benchmarks:
Multi
Event
Driven
Mkt.
Neutral
Mkt.Tren
d
/Timing
U.S.
Oppty
Sector
Global
Fund of
Funds
Short
Sellers
1989
23.22%
9.80%
7.10%
24.29%
25.20%
25.30%
29.69%
16.11%
N/A
1990
-0.17%
-9.55%
4.39%
6.70%
8.91%
11.78%
26.33%
5.77%
N/A
1991
27.00%
16.44%
27.77%
19.60%
31.60%
59.44%
51.94%
19.16%
-38.12%
1992
21.23%
44.26%
13.86%
52.01%
11.87%
19.29%
52.58%
25.97%
-12.61%
1993
52.10%
39.76%
20.14%
17.53%
18.22%
23.01%
54.13%
32.44%
-9.86%
1994
-9.14%
-14.08%
3.81%
1.33%
-5.98%
-5.14%
-5.84%
-9.00%
16.68%
1995
15.12%
14.27%
-7.99%
33.06%
25.54%
46.45%
22.42%
28.19%
-11.50%
Average
18.48%
14.41%
9.87%
22.07%
16.48%
25.73%
33.04%
16.95%
-11.08%
Geometric
17.07%
12.56%
9.32%
21.10%
15.85%
24.17%
31.36%
16.13%
-12.83%
Std. Dev
19.81%
22.15%
11.80%
16.91%
12.73%
21.46%
21.85%
14.44%
19.41%
Beta
0.471
0.364
-0.035
0.413
0.644
1.092
0.285
0.464
-0.960
Alpha
0.079
0.050
0.049
0.121
0.040
0.082
0.245
0.064
-0.028
Theta
0.637
0.387
0.356
0.956
0.907
0.958
1.236
0.766
-0.767
Yale
School of Management

Risk
-
Adjusted Performance
1989
-
1995

-0.05
0
0.05
0.1
0.15
0.2
0.25
MULTI
TIMING
GLOBAL
COM/FUT
Annual Returns
Yale
School of Management

Hedge Funds as a Portfolio Asset



Low Correlation to U.S. Market


Negative Correlation to GS Commodity
Index


Positive Correlation to Fixed Income


Low Correlation Across Styles


Neutral Position Attractive to Diversified
Investor


Yale
School of Management

Net Exposure: S&P 500 Beta

-1
-0.5
0
0.5
1
1.5
MULTI
NEUTRAL
OPPTY
GLOBAL
SHORT
S&P Beta
Yale
School of Management

Hedge Fund Correlation to Bonds
and Commodities

-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
MULTI
NEUTRAL
OPPTY
GLOBAL
SHORT
LTG Correlation
Commodity Correlation
Yale
School of Management

Market Neutral in Portfolio

1989
-

1995 Data Inputs

Standard Deviation (Risk)
Expected Return
Efficient Frontier
MSCI EAFE TR
Mkt. Neutral
S&P 500 TR
U.S. LT Gvt TR
0.00
19.72
3.00
6.00
9.00
12.00
15.00
5.16
16.29
9.00
12.00
15.00
Yale
School of Management

Minimum Variance Portfolio

Position 0
S&P 500 TR (10.2%)
U.S. LT Gvt TR (53.1%)
Mkt. Neutral (36.7%)
Yale
School of Management

Manager Track Records


Does survivorship matter?


Does positive performance persist?


Is bigger better?


Do benchmarks matter?

Yale
School of Management

Fund and Manager Survival

Yale
School of Management

Survivor Bias in Track Record


Chance of surviving six years <20%


Managers survive more than funds


Bias in annual return estimates for the index
are 100 to 300 BP


May be higher for individual fund

Yale
School of Management

Do Winners Repeat?

Next Year
Winner
Next Year
Loser
This Year
Winner
171
203
This Year
Loser
202
183
Yale
School of Management

Same Results For:


Winner defined as positive alpha


Winner defined as positive information ratio


Pre
-
fee performance


Style
-
adjusted performance


Size as predictor of performance

Yale
School of Management

Conclusions



Positive risk adjusted performance


even with survival bias considered


alphas, Sharpe ratios, information ratios



Excellent portfolio asset


some styles have low correlations


ideal for institutional investors



Funds of Funds not that successful


track records are misleading


hard to identify consistent top performers