Are hedgefundssimplytooriskaninvestorsperspective nilstuchschmid_050815

Are Hedge Funds Simply too Risky?
An Investor’s Perspective
Nils S. Tuchschmid
Tages Capital LLP
Global Association of Risk Professionals
May 2015

2
The views expressed in the following material are the
author’s and do not necessarily represent the views of
the Global Association of Risk Professionals (GARP),
its Membership or its Management.

Agenda

•  Asset
management
or
risk
management?

•  Why
hedge
funds?

•  Hedge
Fund
strategies
and
risks

•  Exogenous
or
endogenous
risk
?

•  Concluding
remarks

«
Hedge-‐fund
investors
and
managers
o2en
dismiss
risk
management
as

secondary
with
”alpha”
or
performance
as
the
main
objec=ve
»

Lo
A.,
Risk
Management
for
Hedge
Funds
:
IntroducFon
and
Overview,
2001,
hJp://papers.ssrn.com/
sol3/papers.cfm?abstract_id=283308

Asset
Management
or
Risk
Management?

•  Asset
management
is
somehow
hard
to
disFnguish
from

risk
management

•  ….
indeed
when
allocaFng
to
risk
assets
–and
even
more

so
when
allocaFng
to
investment
styles
or
investment

strategies,
one
needs
to
know
something
–or
hopes
to

know
something,
about
return
generaFng
processes

–  What
are
the
underlying
“risk
factors”
that
are
driven

returns?

4

Asset
Management
or
Risk
Management?

Input data Corporate Bond Treasury Bond Risk-free asset
Expected Return pa 7.38% 5.75% 5.36%
Volatility pm 1.58% 1.90%
Correlation 0.9654
Output data $19.66 -$15.66 -$3.06
Optimal Portfolio Return and Risk
Initial Equity $1
Expected Return (monthly) 3.1%
Volatility (monthly) 8.1%
Ratio of equity to SD 12.31
Source:
Risk
Management
Lessons
from
LTCM,
Jorion
P.,
EFM,
2000

5

Why
invesFng
into
Hedge
Funds
?

…
before
the
crisis

Source:
Edhec-‐Risk

0.00%$
10.00%$
20.00%$
30.00%$
40.00%$
50.00%$
60.00%$
70.00%$
For$their$
diversifica9on$
benefits$with$
bonds$
For$their$
diversifica9on$
benefits$with$
equi9es$
Hedge$funds$
offer$absolute$
returns$
BeEer$
performance$
on$average$
than$that$of$
tradi9onal$
funds$
The$vola9lity$of$
hedge$fund$
performance$is$
lower$than$
that$of$
tradi9onal$
assets$
The$poten9al$
for$maximal$
loss$is$lower$
than$for$
tradi9onal$
assets$
Other$
Why
Hedge
Funds
?

Why
invesFng
into
Hedge
Funds
?

…
a]er
the
crisis

Source:
JPMorgan
Cap.
Intro,
2014

Why
Hedge
Funds
?

8

Source:
Prequin
Investor
Interview,
July
2013

…
but
what
are
the
issues?

Why
Hedge
Funds
?

…
and
what
are
the
trends
?

E&Y, Global Hedge Fund and Investor Survey 2012
9
Why
Hedge
Funds
?

Classically,
investors
tend
to
separate
hedge
funds’
risks
into

two
broad
categories,
that
is:

–  Market
risk…
or
everything
that
could
be
related
to
markets
and

hedge
fund
strategies

–  OperaFonal
risk…
or
any
other
risks
that
would
stem
from
the

operaFonal
side
of
the
business
and
not
related
to
market-‐wide

risk

To
note
that
business
risk
should
be
part
of
what
people

deﬁned
as
operaFonal
risk.
Yet,
it
certainly
has
a
special

“ﬂavor”
when
it
comes
to
hedge
funds
(see
e.g.
Comac)

10
Hedge
Fund
Strategies
and
Risks

Market
Risk

–  SensiFvity
of
the
fund
to
market
risk
factors,
both
tradiFonal
and

alternaFve
(yield
curve,
credit
spread,
…)

–  Captured
by
risk
factor
models

Residual
Risk

–  Not
captured
by
risk
factor
models

–  Driven
by
the
hedge
fund’s
parFcular
poriolio
holdings
or
investment

style
?

Concentrated
poriolio
(area,
sector,
asset
class),
high
poriolio
turnover,
illiquid

assets,
exoFc
instruments,…

Tail
Risk

–  Stemming
from
exogenous
extreme
events
and
quite
o]en
associated

with
leverage,
concentraFon
and
liquidity
(e.g.
SNB
January

announcement)

–  PotenFal
to
signiﬁcantly
aﬀect
monthly
returns
in
parFcular
if
its

impact
has
not
been
observed
in
the
past
(e.g.
LTCM)
11
Hedge
Fund
Strategies
and
Risks

What
if
it
were
to
be
“alpha”
only…
?

12
Hedge
Fund
Strategies
and
Risks

Source:
Brad
Jones,
Asset
Bubbles:
Re-‐thinking
Policy
for
the
Age
of
Asset
Management,
IMF
Paper,
2015

DirecFonal
Strategies
(EH)

–  Stock
markets
risk

–  Other
risks

Sector

Size
(Small
vs.
Large
Caps)

Style
(Value
vs.
Growth
companies)

…

Event
Driven
Strategies

–  a
priori
idiosyncraFc
risks
that
risks
linked
to
speciﬁc
events

e.g.
deal
risk

–  Some
market
direcFonality,
for
example,

Corporate
M&A
acFvity
tends
to
be
higher
during
bull
markets

Default
rates
are
lower
during
bull
markets:
recovery
capitalizaFon

13
Hedge
Fund
Strategies
and
Risks

RV
Strategies

–  Liquidity
risk

Issues
of
converFble
bonds
issues
for
example,
are
on
average

small,
which
limits
the
depth
of
the
market

–  Credit
risk
and
event
risk

Corporate
and
even
“sovereign”
bonds
have
a
credit
risk

component
embedded
into
their
prices

–  NegaFve
convexity

ConverFble
bonds
and
other
hybrid
instruments
are
o]en
callable

–  Model
risk

Complex
pricing
models

–  …

14
Hedge
Fund
Strategies
and
Risks

TacFcal
Trading
Strategies

–  Leverage risk
–  Nonlinear market exposures to IR,
FX,
EquiFes,
Credit
or
Commodity

that
is
stemming from the opportunistic nature of trading strategies
–  Model risk and estimation risk
–  … and more importantly the ability of the managers (programs) to
implement well their trading ideas

Each
broad
family
of
strategies
has
been
empirically
tested

either
“boJom-‐up”
or
“top-‐down”
(see
e.g.
Mitchell
and

Pulvino
(2001),
Durate,
Longstaﬀ,
and
Yu
(2007),
Fung
and

Hsieh
(2001)…

Let’s
think
for
example
about
the
famous
poriolio
of
lookback
straddles

when
it
comes
to
explain
trend-‐followers’
risk-‐return
proﬁle

15
Hedge
Fund
Strategies
and
Risks

Hedge
Fund
Strategies
and
Risks

Yet,
the
heterogeneity
of
risks
among
strategies
and
styles

seems
to
cancel
out
when
hedge
funds
are
bundled
together

into
a
classic
mulF-‐strategy
poriolio.

Indeed,
factor
models
are
doing
quite
a
good
job
at

explaining
returns.
Stated
otherwise,
the
famous
“alpha”

component
appears
o]en
to
be
both
small
and
insigniﬁcant.

“The
empirical
literature
sounds
irrevocable.
Only
a
minority
of
hedge
fund

managers
deliver
signiﬁcant
and
posi=ve
alpha
and
it
even
seems
that
their

number
diminishes
over
=me.
The
picture
is
even
more
depressing
for
funds

of
hedge
funds.
They
appear
unable
to
produce
alpha
and
barely
relay
the

alpha,
if
any,
generated
by
the
underlying
hedge
fund
managers.”
Pirotte et al. 2014

17
Hedge
Fund
Strategies
and
Risks

18
•  Data

–  Monthly
net-‐of-‐fees
HFs’
performance
provided
by
TASS

–  Period
:
1/1994
to
8/2009

–  From
4564
FoHFs
to
1315
by
deleFng
:

•  ‘duplicated
funds’
and
non-‐USD
funds

•  funds
with
no
informaFon
on
date
added
to
database

•  funds
with
obvious
outliers

–  For
the
FDR
methodology
we
require
at
least
60
months
of
returns

à
280
funds

–  Returns
are
“unsmoothed”
using
the
Getmansky,
Lo
&
Makarov

methodology

•  PotenFal
bias

–  Survivorship
bias
:
not
a
problem
as
we
have
living
and
dead
funds

–  Backﬁlling
(instant
history)
bias
:
not
a
problem
as
we
delete
return

entries
from
incepFon
to
the
date
added
to
database

–  SelecFon
bias
:
less
of
a
concern
for
FoHFs

Hedge
Fund
Strategies
and
Risks

Source
:
Dewaele
et
al.
2013

Hedge
Fund
Strategies
and
Risks

Find
the
addi<onal
return
above
the
expected

return
(alpha)
of
a
:

PorHolio
made
of
HF
strategies
(DJCS
model)

PorHolio
of
HFs
underlying
factors
(FH
model)

Separate
the
cross
sec<on
of
alphas
into:

Skilled
funds

Unskilled
funds

Zero-‐alpha
funds

by
taking
luck
into
account…

α
extracFon

α
signiﬁcant
?

FDR

False
Discoveries
Rate
–
an
overview

Hedge
Fund
Strategies
and
Risks

20

21

If
we
consider
that
funds’
alpha
are
divided
in
3
categories
(unskilled,

zero
alpha
and
skilled),
we
get
the
following
cross-‐secFonal
distribuFon
:

StarFng
from
the
cross-‐secFon,
the
FDR
method
separates

alphas
into
these
3
categories
by
taking
luck
into
account

(by
luck
we
mean
zero-‐alpha
funds
that
will
in
a
classical
test

be
considered
as
skilled
or
unskilled)

Source
:
Barras,
Scaillet,
Wermers
(JoF
–
2010)

Steps 1-4 Step 5Step 5
Hedge
Fund
Strategies
and
Risks

22
•  Alpha

–  Regress
excess
returns
on
two
sets
of
factors
:

•  The
7+1
factors
of
Fung
&
Hsieh
(2004)

•  A
13
factors
model,
where
factors
are
constructed
as
the
excess
return
of

13
index
of
HF
strategies
provided
by
DJCS
(“unsmoothed”
using
GLM

methodology)

–  Using
a
classical
linear
regression
framework
:

•  Alpha
t-‐staFsFcs
:

–  Instead
of
alpha,
we
rely
on
t-‐staFsFcs
as
it
is
shown
that
alpha
t-‐
staFsFcs
have
beJer
staFsFcal
properFes
than
alphas

–  As
regression
residuals
present
autocorrelaFon
and
heteroskedasFcity,

we
use
a
heteroskedasFcity
and
autocorrelaFon-‐consistent
esFmator.

ri,t
= αi
+ βi
j
j=1
k
∑ Ft
j
+εi,t
Find
alpha
and
alpha
t-‐stats
(steps
1
and
2)

Hedge
Fund
Strategies
and
Risks

23
•  The
7
+
1
factos
of
Fung
and
Hsieh
are:

–  the
excess
return
on
the
S&P
500
Index

–  the
"small-‐minus-‐big"
factor
computed
as
the
diﬀerence

between
the
Russell
2000
index
monthly
total
return
and
the

S&P
500
monthly
total
return

–  the
monthly
change
in
the
diﬀerence
between
the
10-‐year

Treasury
constant
maturity
yield
and
the
1-‐month
LIBOR

–  the
change
in
the
credit
spread
of
Moody's
BAA
bond
over
the

10-‐year
Treasury
bond

–  the
excess
returns
on
a
poriolio
of
lookback
opFons
on
bonds,

currencies
and
commodiFes

–  the
excess
return
on
the
MSCI
Emerging
Markets
Index

Find
alpha
and
alpha
t-‐stats
(steps
1
and
2)

Hedge
Fund
Strategies
and
Risks

24
•  t-‐stat’s
p-‐values

–  FoHFs'
returns
are
not
normally-‐distributed
è
instead
of
relying
on
a

student-‐t
distribuFon,
we
build
the
t-‐stat
distribuFon
under
the
null

hypothesis
using
a
bootstrap
procedure
(Kosowski
et
al.
(2006)

methodology)
:

•  Adding
back
randomly-‐sampled
residuals
from
the
former
regression
(step

1)
to
the
same
regression
equaFon
omi}ng
the
alpha
constant
(1’000

Fmes
for
each
FoHF).

•  Bootstrapped
returns
are
regressed
against
the
factors,
resulFng
in
an

empirical
distribuFon
under
the
“zero-‐alpha”
hypothesis.

•  The
alpha
p-‐value
for
each
fund
is
obtained
by
comparing
the
original
t-‐
staFsFc
to
the
distribuFon
obtained
here
above.

ri,t
b
= βi
j
j=1
k
∑ Ft
j
+εi,t
b
Determine
t-‐stats’
p-‐value
(steps
3)

Hedge
Fund
Strategies
and
Risks

25
•  Percentage
of
zero-‐alpha
funds

–  If
all
funds
were
zero-‐alpha,
p-‐values
would
be
uniformly
distributed

over
the
interval
[0,1]

–  Using
this
property,
the
objecFve
is
to
choose
a
threshold
level
(λ)

above
which
funds
are
considered
as
being
zero-‐alpha
funds

–  The
opFmal
level
(λ*)
is
found
using
a
bootstrap
methodology
(Storey

(2002))

Determine
the
%
of
zero-‐alpha
funds
(steps
4)

Hedge
Fund
Strategies
and
Risks

26
•  Determine
the
percentage
of
(un)skilled
funds
:

–  Individual
bootstrapped
t-‐stats
are
aggregated
to
get
the
non-‐
parametric
cross-‐secFonal
distribuFon
under
H0.

–  Fix
thresholds
on
each
side
of
the
distribuFon
based
on
various
levels

of
signiﬁcance
to
be
tested
(10%,…,50%)
for
unskilled/skilled
funds.

–  Count
the
number
of
funds'
t-‐staFsFcs
superior/inferior
to
these

thresholds
and
correct
these
proporFons
for
false
discoveries

(computed
using
zero-‐alpha
proporFon)
to
get
proporFons
of
skilled

and
unskilled
managers.

Determine
the
%
of
(un)skilled
funds
(steps
5)

Hedge
Fund
Strategies
and
Risks

27
•  FH
regression

–  A
limited
set
of
“risk
factors”
seems
to
capture
well
the
return

generaFng
process
of
FoFs

•  DJCS
regression

–  A
majority
of
FoFs
does
not
add
“unexplained
returns”
or
omiJed
risk

factors
that
would
not
have
been
captured
at
the
HFs’
level

–  A]er
management
and
incenFve
fees,
only
3.57%
of
FoHFs
managed
to

provide
a]er-‐fees
alpha,
and
46.43%
delivered
negaFve
alpha.

Hedge
Fund
Strategies
and
Risks

If
factor
models
can
explain
a
signiﬁcant
porFon
of
returns
of

poriolios
of
hedge
funds,
then
one
should
be
able
to
use
the

same
models
to
replicate
what
hedge
funds
are
doing.

Let’s
indeed
take
a
simplisFc
view
and
create
a
trading

strategy
based
on
the
following
model:

…
using
a
limited
set
of
factors

28
Hedge
Fund
Strategies
and
Risks

rt
=β1
ft
1
++β5
ft
5
+εt
s.t. βi
i=1
5
∑ =1

The
factors
are
:

CBOE
S&P
500
BuyWrite
Index

Russell
2000
Index

MSCI
EAFE
Index

Barclays
Capital
U.S.
Aggregate
Corporate
AA
Bond

Index

S&P-‐GS
Commodity
Index

Using
a
24
month
rolling-‐window
to
esFmate
weights
with

one-‐month
lag

Out-‐of-‐Sample
period:
Feb-‐1992
to
Dec-‐2008

Sample
is
taken
from
HFRs
database
of
FoF

29
Hedge
Fund
Strategies
and
Risks

30
Hedge
Fund
Strategies
and
Risks

Mean
SD
Sharpe

All
fund
of
funds
Funds
0.072
0.051
1.42

Clones
0.062
0.073
0.84

ConservaFve
Funds
0.059
0.033
1.82

Clones
0.043
0.047
0.93

Diversiﬁed
Funds
0.072
0.052
1.40

Clones
0.065
0.074
0.88

Market
Defensive
Funds
0.087
0.048
1.81

Clones
0.068
0.081
0.84

Strategic
Funds
0.088
0.081
1.09

Clones
0.084
0.118
0.71

Performance of eq.-weighted portfolios. Feb-1992 to Dec-2008.
Source:
Wallerstein,
Tuchschmid,
and
Zaker
(2009a)

Performance
of
all
(eq.-‐weigthed)
clones
(solid
thick),
FoF
(solid),
HFRI
FoF

(dashed),
and
Composite
–US
Bond
/S&P500
(doted).

Sample
period:
Feb
1992
to
Dec
2008.

Source:
Wallerstein,
Tuchschmid,
and
Zaker
(2009a)

Hedge
Fund
Strategies
and
Risks

31

Hedge
Fund
Strategies
and
Risks

Source:
Tuchschmid
et
al.
(2012)
;
sample
period
:
January
2007
–
October
2010

32

When
investors
think
about
other
“market
risk”
and
hedge

funds,
they
tend
to
refer
to:

–  Lack
of
transparency

–  Leverage

–  Liquidity
risk
and
liquidity
shocks

–  …
and
contagion
effect
(?)

that
make
these
investment
vehicles
prone
to
“blow-‐ups”.

Famous
examples
could
be
LTCM,
Amaranth,
Peloton,

Endeavour,
Everest,
….

“The
received
wisdom
is
that
risk
increases
in
recessions
and
falls
in
booms.
In

contrast,
it
may
be
more
helpful
to
think
of
risk
as
increasing
during
upswings,
as

financial
imbalances
build
up,
and
materialising
in
recessions
”

CrockeJ
A.,
Marrying
the
micro-‐
and
macro-‐prudenFal
dimensions
of
financial
stability,
BIS
2000

33
Exogenous
or
endogenous
risk

Quite
o]en,
one
sees
external
or
exogenous
shocks
as
the

only
underlying
drivers
behind
these
blow-‐ups.
They
are

unexpected
events
that
suddenly
force
managers
to

deleverage
and
to
realize
their
losses.

In
some
cases,
events
can
be
clearly
idenFﬁed:

–  LTCM
(1998)
:
Russian
default

–  Everest
or
Comac
(2015)
:
SNB’s
announcement

…
but
the
laJer
is
not
always
true
(e.g.
Amaranth
or

Endeavour
and
the
widening
of
spreads)

34
Exogenous
or
endogenous
risk

“For
the
10-‐year
old
ﬁrm,
founded
by
Colm
O'Shea,
the

currency
move
crystallized
problems
that
were
already

moun=ng,
another
source
who
knows
the
fund
said.

Impa=ent
with
years
of
poor
returns,
investors
had
asked
for

their
money
back
for
some
=me,
the
person
said,
no=ng
that

the
fund
had
managed
roughly
$4.5
billion
in
late
2012
and

that
redemp=on
requests
had
mounted
recently.

O'Shea,
who
had
once
worked
for
George
Soros
the
famed

global-‐macro
investor,
gained
aRen=on
with
a
31
percent

return
in
2008,
when
most
funds
lost
money.
More
recent

returns
weren't
as
good.
In
2012,
the
fund
lost
9.0
percent

and
returns
for
2013
and
2014
were
essen=ally
ﬂat,
the

person
said”.

35
Exogenous
or
endogenous
risk

Source:
uk.reuters.com/arFcle/2015/01/20/hedgefunds-‐comac-‐idUKL6N0UZ4SW20150120

“Comac
Capital,
the
$1.2
billion
hedge
fund
ﬁrm
run
by
Colm

O’Shea,
is
returning
money
to
clients
a2er
losses
incurred
last

week
when
the
Swiss
Na=onal
Bank
abandoned
the
franc’s

cap
against
the
euro,
according
to
a
person
with
knowledge

of
the
situa=on.

Comac,
based
in
London,
lost
8
percent
as
the
franc
surged
as

much
as
41
percent
versus
the
euro
on
Jan.
15.
The
declines

bring
its
loss
this
month
to
10
percent,
said
the
person,
who

asked
not
to
be
iden=ﬁed
because
the
informa=on
is
private.

Comac
will
con=nue
to
trade
with
internal
money,
the
person

said”.

36
Exogenous
or
endogenous
risk

Source:
www.bloomberg.com/news/arFcles/2015-‐01-‐20/o-‐shea-‐s-‐comac-‐capital-‐to-‐return-‐investor-‐money-‐from-‐fund

Exogenous
or
endogenous
risk

Source:
Bloomberg

Exogenous
or
endogenous
risk

Input data Corporate Bond Treasury Bond Risk-free asset
Expected Return pa 7.38% 5.75% 5.36%
Volatility pm 1.58% 1.90%
Correlation 0.9654
Output data $19.66 -$15.66 -$3.06
Optimal Portfolio Return and Risk
Initial Equity $1
Expected Return (monthly) 3.1%
Volatility (monthly) 8.1%
Ratio of equity to SD 12.31
seems very safe !
a « 12 times volatitly
move » is needed for
equity to be wiped out!
However …
Source:
Risk
Management
Lessons
from
LTCM,
Jorion
P.,
EFM,
2000

38

Exogenous
or
endogenous
risk

Monthly Probability of Ruin
Rho SD Safety Factor Normal Student-6 Student-4
0.9999 1.56% 64.10 0.00000% 0.00000% 0.00002%
0.990 4.55% 21.98 0.00000% 0.00003% 0.00127%
0.970 7.58% 13.19 0.00000% 0.00059% 0.00954%
... ... ... ... ... ...
0.850 16.68% 6.00 0.00000% 0.04843% 0.19470%
0.800 19.24% 5.20 0.00001% 0.10099% 0.32637%
... ... ... ... ... ...
0.600 27.17% 3.68 0.01164% 0.51621% 1.05970%
Source:
Risk
Management
Lessons
from
LTCM,
Jorion
P.,
EFM,
2000

39

Liquidity
risk
has
been
spoJed
as
a
main
source
of
hedge

fund
performance
(e.g.
Sadka
2011
or
Gibson
and
Wang

2010)
…
and
interesFngly
enough,
correlaFon
of
“liquidity

risk
factor(s)”
appears
to
be
low
with
the
commonly
used

market
factors.

This
suggests
that
…
hedge-‐fund
returns
can
be
characterized
as

selling
out-‐of-‐the
money
put
op=on
on
market
liquidity
events,

collec=ng
fees
during
normal,
non-‐crisis
periods
and
paying
out

during
crisis
periods.

Sadka,
Hedge
Fund
Performance
and
Liquidity
Risk,
Journal
of
Investment
Management
2011

Examples
of
“liquidity
shocks”
are
numerous.
Recently
we

could
think
about

the
“Treasury
ﬂash
crash”
of
October
15,
a

move
of
40
bps,
that
is,
seven
standard
deviaFons
away
from

its
intraday
norm

40
Exogenous
or
endogenous
risk

Exogenous
or
endogenous
risk

Source
:
Sadka,
Hedge
Fund
Performance
and
Liquidity
Risk,
Journal
of
Investment
Management
2011

Exogenous
or
endogenous
risk

The
majority
of
hedge
fund
strategies
can
be
also
analyzed
in

terms
of
risk
limits
or
risk
constraints

–  Equity
L/S
:
sizing,
net
exposure,
gross
exposure,
…

–  CTAs
:
volaFlity
target,
margin
to
equity
raFo,
…

–  Global
Macro
:
VaR,
…

–  FI
arbitrageurs
:
leverage
(10y
equivalent),
VaR,
…

–  Credit
L/S
:
gross
exposure,
spread
widening,
beta,
…

–  Event
Driven,
spread
widening,
…

…
associated
quite
o]en
with
stop-‐loss
policies

All
risk
limits
or
risk
constraints
set
a
predetermined
trading

behavior
or
degree
of
risk
appeFte.

43

Exogenous
or
endogenous
risk

Let’s
take
the
simple
case
of
a
M-‐V
investor
with
two
risky

securiFes
(with
respecFve
holding
a1
and
a2)
and
cash
(c).
By

deﬁniFon,
one
should
have*
:

a1
+
a2
+
c
=
e

where
“e”
stands
for
capital
or
equity.
We
thus
simply
have:

*
Source:
Risk
and
Liquidity,
Shin,
Oxford
University
Press,
2010

U = E r −!
1
2τ
Var r !
= cr! + a!!! + a!!! !−!
1
2τ
Var cr! + a!r! + a!r! !
= er! + a! !! − r! + a! !! − r! !!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!−!
1
2τ
a!
!
σ!
!
+ a!
!
σ!
!
+ 2a!a!σ!" !
44

Exogenous
or
endogenous
risk

…
and
classically,
we
obtain:

“τ”,
the
investor’s
risk
tolerance,
is
obviously
here
a
key
parameter…

Let’s
for
instance
assume
that
e
=
1
and
τ
=
0.25.
With
µ1
=

0.1,
µ2
=
0.05,
r0
=
0.02,
σ1
=
σ2
=
0.2
and
ρ
=
0.925,
one
gets:

*
Source:
Risk
and
Liquidity,
Shin,
Oxford
University
Press,
2010

a!
a!
= !τ
σ!
!
σ!"
σ!" σ!
!
!!
!! − r!
!! − r!
!
a!
a!
=!
2.2619
−1.9047
!!⟹ ! =!
!""#$"
!"#$%&
=
2.26 + 0.64
1
= 2.9!
45

Exogenous
or
endogenous
risk

Let’s
now
take
the
case
of
a
(risk
neutral)
hedge
fund

manager*.
Of
course,
we
sFll
have
that
:

a1
+
a2
+
c
=
e

Here,
the
manager
aims
at
maximizing
returns
for
a
given

VaR
constraint,
such
that

If
we
set
VaR
=
ασr,
we
thus
have:

and
we
end
up
with
the
following
problem
to
solve

*
Source:
Risk
and
Liquidity,
Shin,
Oxford
University
Press,
2010

Max!E r !subject!to!VaR! ≤ e!
ασ!! ≤ e!or!equivatenly!σ!
!
≤
e
α
!
!
ℒ = !E r − !λ !!
!
−
!
!
!
!
46

Exogenous
or
endogenous
risk

Hence
we
get:

since

We
obtain
ﬁnally:

*
Source:
Risk
and
Liquidity,
Shin,
Oxford
University
Press,
2010

a!
a!
=!
1
2!
σ!
!
σ!"
σ!" σ!
!
!!
!!
!!
=
1
2!
Σ!!
!!
!!
!
σ!
!
= a!
Σa =!
1
4λ!
!!
Σ!!
! ⇒!
1
4λ!
!!
Σ!!
! =
e
α
!
!
a!
a!
=!
e
!
×
1
!′Σ!!!
σ!
!
σ!"
σ!" σ!
!
!!
!!
!!
!
47

Exogenous
or
endogenous
risk

We
can
note
that
the
investor’s
risk
tolerance
“τ”
is
here

replaced
by:

which
somehow
can
be
seen
as
the
manager’s
degree
of

“risk
appeFte”
–e.g.
favorable
market
outcome
leads
to

greater
holdings
of
risk
assets
and
vice
versa.

*
Source:
Risk
and
Liquidity,
Shin,
Oxford
University
Press,
2010

e
!
×
1
!′Σ!!!
!
48

Exogenous
or
endogenous
risk

Let’s
assume
that
σ2 =
1,
µ1=
0.1, µ2=
0.05
and
α=
2.33

For
posiFve
correlaFon
and
greater
than
0.50,
leverage
is

then
equal
to
(see
Shin,
op.
cit.)

*
Source:
Risk
and
Liquidity,
Shin,
Oxford
University
Press,
2010

L = 1 −!
a!
e
= 1 +
1
ασ
×
ρ!! −!!!
1 − ρ! !!
!
− 2ρ!!!! + !!
! !
0"
20"
40"
60"
80"
100"
120"
140"
160"
0.5" 0.55" 0.6" 0.65" 0.7" 0.75" 0.8" 0.85" 0.9" 0.95"
Leverage'and'VaR'constraint''
ρ

49

Exogenous
or
endogenous
risk

Endogenous
risk
is
intrinsically
linked
to
responses
originated

by
market
parFcipants,
responses
that
in
turn
amplify
price

moves
through
a
feedback
loop
(see
the
previous
example).

If
increased
demand
for
the
risky
security
puts
large
upward
pressure
on

the
price
of
the
risky
security,
then
the
feedback
eﬀect
will
be
strong…
the

ampliﬁca=on
of
ini=al
shocks
to
prices
…
is
a
key
channel
through
which

risk
becomes
endogenous

Danielsson
et
al.
2010

Think
about
the
downgrading
of
Ford
and
GM
in
May
2005

or
more
recently
market
reacFon
to
Bernanke's
tapering

comments
in
May
2013

50

Exogenous
or
endogenous
risk

Market
parFcipants’
responses
to
liquidity
shock
and
more

precisely
funding
liquidity
shock
creates
what
Boyson
et
al.

(2010)
describe
as
“liquidity
spirals”…
that,
in
turn
“aﬀect
all

assets
held
by
speculators
that
face
funding
liquidity

constraints,
leading
to
commonality
in
the
performance
of

these
assets”.

Boyson
et
al.
2010

Variables
used
are

–  measure of stock market liquidity,
–  measure of credit spreads
–  TED spread
–  returns to banks and prime brokers
–  changes in repo volume
–  flows to hedge funds

51

Exogenous
or
endogenous
risk

According
to
Boyson
et
al
(JF
2010),
their
results
show
that

–  “liquidity
shocks
to
a
number
of
contagion
channel
variables
help

explain
…
hedge
fund
contagion”.

–  There
is
yet
liJle
evidence
that
“liquidity
itself
could
be
a
risk

factor
…
that
could
explain
the
existence
of
hedge
fund

contagion”.

–  Stated
otherwise,
“while
small
changes
to
liquidity
are
not

associated
with
hedge
fund
contagion,
large
shocks
to
liquidity
are

associated
with
it.
Further,
hedge
funds
appear
to
share
a

common
exposure
to
large
liquidity
shocks,
and
exis=ng
models

used
to
explain
hedge
fund
returns
do
not
capture
this
exposure”.

52

Concluding
remarks

ü  Factor
models
can
do
quite
a
good
job
at
explaining
the

risk
characterisFcs
of
hedge
funds
poriolios
…
under

normal
market
condiFons,
leading
to
:

–  replicaFon
soluFons

–  decomposiFon
between
tradiFonal
risk
premia
and
alternaFve

risk
premia

ü  If
liquidity
risk
factors
seem
to
embedded
into
hedge
fund

returns…

ü  they
are
not
suﬃcient
to
understand
hedge
fund

contagion

53

Source : DJCS index
1996 1997 1998 1999
GM(30,7% EM(34,5% GM(37,1% MF(20,6% ELS(47,2% CA(25,6%
2000 2001 2002 2003 20041995
DST(26,1% GM(25,6% EM(26,6% ELS(17,2% EM(44,8% DS(15,8% GM(18,4%
DST(20,0% MF(18,3% EM(28,8% DST(15,6%
ELS(23,0% DST(25,5% HF(25,9% EMN(13,3% HF(23,4% EMN(15,0% CA(14,6% GM(14,7%
DS(18,1% DST(25,1% ED(14,5%
ED(20,0% EM(12,5%
HF(21,7% ED(23,1% ELS(21,5% MS(7,7% ED(22,3%
HF(9,6%ED(18,3% HF(22,2% DST(20,7% RA(5,6% DST(22,2% GM(11,7%
RA(14,7% ED(11,5% EMN(7,4% GM(18,0% ELS(11,6%
HF(15,4% GM(8,5%CA(16,6% CA(17,9% ED(20,0% HF(;0,4% CA(16,0% MS(11,2% FIA(8,0%
EMN(9,3% EM(7,4% ELS(17,3%
MS(15,0% MS(7,5%FIA(12,5% ELS(17,1% MS(18,3% DST(;1,7% EMN(15,3% ED(7,3% EM(5,8% FIA(5,8%
MS(6,3%
EMN(16,6%EMN(14,8% GM(;3,6% RA(13,2%
MS(11,9% FIA(15,9% CA(14,5% CA(;4,4% FIA(12,1% HF(4,8%
FIA(6,3% RA(5,7% CA(4,0% MF(14,1% FIA(6,9%RA(11,9%
EMN(11,0% MS(14,1% RA(9,8% ED(;4,9% MS(9,4% MF(4,2% HF(4,4%
MS(5,5% HF(3,0% CA(12,9% EMN(6,5%
MF(;7,1% RA(13,8% FIA(9,3% DS(;6,0% GM(5,8% ELS(2,1% MF(1,9% DST(;0,7%
ED(0,2% RA(9,0% MF(6,0%
FIA(8,0% RA(5,5%
DS(;7,4% MF(12,0% MF(3,1% FIA(;8,2% MF(;4,7%
EM(;16,9% DS(;5,5% DS(0,4% EM(;37,7% DS(;14,2% EM(;5,5% ELS(;3,7%
DST(1,9% DS(;3,6% ELS(;1,6% EMN(7,1% CA(2,0%
RA(;3,5% DS(;32,6% DS(;7,7%
2012 2013 20142006 2007 2008 2009 2010 20112005
ELS.17,7% MF.18,4%EM.20,3% MF.18,3% CA.47,3% GM.13,5% GM.6,4% DST.11,8%EM.17,4% EM.20,5%
MS.6,1%DS.14,9% EM.30,0% ED.12,6% FIA.4,7% MS.11,2% DST.16,0%DS.17,0% ED.15,7% GM.17,4%
EMN.4,5% FIA.11,0% ED.15,5% ELS.5,5%DST.11,7% DST.15,6% ELS.13,7% RA.;3,3%
ELS.9,7%
FIA.27,4% FIA.12,5%
GM.9,2% ELS.14,4%
ED.10,6% MS.11,2% FIA.4,4%MS.14,5% ED.13,2% GM.;4,6% MS.24,6% MF.12,2% DS.3,8%
ED.9,0% CA.14,3% MS.10,1%
HF.9,7% HF.4,1%HF.12,6% ED.;17,7% DST.20,9% EM.11,3% MS.1,8% EM.10,3%
DST.2,5%HF.7,6% HF.13,9% EMN.9,3% ELS.;19,8%
GM.3,1%HF.;19,1% ED.20,4% CA.11,0% CA.1,1% ELS.8,2% EMN.9,3%
ELS.19,5% HF.10,9% RA.0,8% CA.7,8% EM.8,8%
HF.7,7% CA.6,0% ED.1,6%GM.13,5% RA.8,8% DST.;20,5% HF.18,6% DST.10,3% HF.;2,5%MS.7,5%
RA.4,9% EM.1,5%DST.8,4% MS.;23,6% RA.12,0% MS.9,3% MF.;4,2% GM.4,6%EMN.6,1% EMN.11,2%
EMN.;1,2%FIA.;28,8% GM.11,6% ELS.9,3% DST.;4,2% RA.2,8% GM.4,3%RA.3,1% FIA.8,7% DS.6,0%
EMN.0,9% FIA.3,8% RA.;1,3%FIA.0,6% RA.8,1% MF.6,0% EM.;30,4% EMN.4,1% RA.3,2% EM.;6,7%
MF.;2,9% MF.;2,6% CA.;1,7%MF.8,1% CA.5,2% CA.;31,6% MF.;6,6% EMN.;0,8% ELS.;7,3%MF.;0,1%
DS.;5,6%EMN.;40,3%DS.;25,0% DS.;22,5% ED.;9,1% DS.;20,4% DS.;24,9%CA.;2,5% DS.;6,6% FIA.3,8%
HF is the Global HF index. DST stands for « distressed » and DS is for « Dedicated Short »
54

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N.,
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Hedge
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SFI,
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R.,
Hedge
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H.,
Risk
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Oxford
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