This document is a thesis examining whether catastrophe bonds can provide efficient portfolio diversification. It begins with an introduction on the development of insurance-linked securities (ILS) markets in response to capacity issues following major natural disasters in the 1990s. The thesis then analyzes catastrophe bond markets and financial mechanisms. Through an empirical study of portfolios with and without catastrophe bonds from 2002-2015, the thesis finds that while volatility and risk levels remained similar, the portfolio diversified with catastrophe bonds saw improved returns and Sharpe ratio, suggesting potential benefits from their inclusion in portfolios.

1. 1
Majeure'15
Capital
Markets
and
International
Banking
Master
thesis
–
Neoma
BS
Rouen
Clément
Kubiak
Clement.kubiak.11@neoma-­‐bs.com
Supervisor:
Sami
Attaoui
ARE
CATASTROPHE
BONDS
EFFICIENT
DIVERSIFICATION
SECURITIES?
An
empirical
study
of
a
portfolio
diversified
with
catastrophe
bonds
from
2002
to
2015
and
of
its
correlation
with
traditional
financial
markets
Key
words:
reinsurance,
insurance-­‐linked
securities,
catastrophe
bonds,
diversification

2. 2
Abstract
The
insurance-­‐linked
securities
market
has
known
a
strong
development
for
the
past
decades.
2014
has
been
a
record
year
for
the
issuance
of
ILS
and
a
particular
type
of
this
securities,
the
catastrophe
bonds
have
started
to
attract
a
larger
range
of
institutional
investors,
and
some
asset
management
companies,
such
as
Schroder
with
its
GAIA
Cat
Bond,
are
now
efficiently
integrating
catastrophe
bonds
to
their
investment
strategy.
Furthermore,
the
previous
financial
and
banking
crisis
have
shown
the
strong
impact
of
systematic
risk
on
portfolios
and
investors
are
now
seeking
investments
offering
them
a
resilient
behaviour
in
crisis
context.
This
thesis
aims
to
highlight
the
possible
positive
impact
on
the
risk-­‐return
profile
of
a
portfolio
through
the
diversification
in
catastrophe
bonds.
Our
results
based
on
the
volatility,
returns,
Sharpe
ratio
and
Value
at
Risk
of
a
portfolio
diversified
with
catastrophe
bonds
against
a
reference
portfolio
highlight
a
positive
impact
of
the
catastrophe
bonds
on
the
Sharpe
ratio
and
the
return
over
the
studied
period,
however
the
volatility
and
the
Value
at
Risk
remains
at
similar
levels
for
both
portfolios.

3. 3
Summary
Introduction
4
Market
Evolution
Risk
management:
diversification
5
Emergence
of
alternative
risk
transfer
6
Catastrophe
bonds
Basic
of
catastrophe
bonds
7
Markets
10
Financial
mechanisms
Loss
mechanisms
13
Pricing
14
Correlation
and
sensitivity
to
traditional
markets
16
Empirical
study
Definition
of
the
studied
portfolios
18
Analysis
and
risk-­‐return
measurements
20
Conclusion
21
Appendixes
23
Bibliography
27

4. 4
I. Introduction
In
the
early
1990s,
severe
major
natural
catastrophes
such
as
the
Hurricane
Andrew
and
the
Northridge
Earthquake
created
a
lack
of
capacity
in
the
reinsurance
market,
since
then,
heavy
losses
have
become
a
source
of
concern
for
the
insurance
and
reinsurance
industries
because
the
potential
losses
from
natural
perils
seemed
to
outpace
the
(re)insurers'
capacity.
While
historically
the
government
was
providing
a
back
up
capacity
to
the
industry
in
case
of
difficulties
in
the
market
with
for
example
the
National
Flood
Insurance
Program
in
the
USA,
(re)insurers
started
to
develop
new
innovative
ways
to
hedge
their
excess
risk
and
to
finance
this
lack
of
capacity.
Geographic
diversification
was
not
an
efficient
enough,
not
all
the
regions
are
indeed
in
need
of
an
insurance
coverage
and
then
reinsurers
and
insurers
cannot
disseminate
their
risk
in
less
risky
regions
to
compensate.
Furthermore,
in
a
free-­‐market
it
is
not
possible
for
a
(re)insurance
company
to
cross-­‐
subsidize
its
business
lines.
To
face
this
issue,
insurer
and
reinsurers
innovated
in
risk
securitization
and
developed
alternative
methods
to
transfer
the
risk
emerging
from
natural
perils
to
a
third
party,
it
was
the
first
issuance
of
ILS,
the
insurance-­‐linked
securities.
Since
1996,
the
ILS
market
has
showed
a
resilient
development
worldwide.
While
the
market
was
initially
the
preserve
territory
of
insurance
and
reinsurance
companies,
the
development
of
ILS
allowed
governments
and
corporations
to
access
this
capital
market
tool
to
support
their
growth,
manage
their
capital
and
transfer
their
risk.
2014
saw
the
ILS
market
toped
new
records
with
a
total
of
$8.29bn
securities
newly
issued.
After
having
suffered
from
the
2008
crisis
with
four
years
of
contraction,
the
market
has
known
a
strong
growth
for
the
past
three
years
with
a
yearly
rate
of
growth
of
20%
to
a
record
of
$25bn
outstanding
securities
in
2015.
The
market's
demand
for
more
sophisticated
and
diversified
securities
has
supported
the
emergence
of
new
sponsors
and
new
coverage
in
the
ILS
market,
completing
the
market.
Meanwhile
on
the
traditional
markets,
the
dot-­‐com
bubble,
the
sub-­‐prime
crisis
followed
by
the
financial
crisis
and
the
euro
crisis
have
impacted
the
profits
of
investors
for
the
past
decades.
Investors
are
now
looking
for
new
ways
of
hedging
their
portfolios
from
the
market
shocks
and
for
resilient
assets
to
the
crisis.
Only
few
studies
have
been
made
on
the
use
of
ILS,
particularly
catastrophe
bonds,
to
diversify
a
portfolio.
Carayannopoulos
and
Perez
(2013)
focused
on
the
subprime
financial
crisis
to
prove
that
despite
the
peril
risk
exposure
of
catastrophe
bond
(while
a
corporate

5. 5
bond
is
exposed
to
the
credit
risk),
in
time
of
crisis
they
were
not
zero
beta
investments
and
not
immune
to
the
effect
of
the
recent
financial
crisis
but
represent
an
efficient
diversification
tool
for
investors
in
quiet
market
using
a
multivariable
GARCH
model
on
the
return
of
different
asset
classes.
However,
their
results
were
purely
quantitative
and
only
based
on
the
returns,
in
addition,
a
single
index
based
on
US
securities
was
used
to
represent
an
asset
class.
This
thesis
aims
to
study
the
behaviour
of
cat-­‐bonds
against
other
assets
by
comparing
the
return,
volatility,
value
at
risk
and
the
Sharpe
ratio
of
2
portfolios,
one
including
cat-­‐bonds
and
the
other
without
exposure
to
cat-­‐bonds.
The
time
period
studied
is
13
years,
from
January
2002
to
January
2015.
II. Market
evolution
a. Risk
management:
diversification
For
an
investor,
there
are
two
techniques
to
manage
its
risk:
hedging
its
positions
and/or
diversifying
its
portfolio
through
a
strategic
and
dynamic
capital
allocation.
Diversification
is
based
on
the
lack
of
a
tight
positive
relationship
among
the
assets'
return
and
on
the
theory
that
the
risk
of
an
asset
can
be
decomposed
in
two
parts,
each
representing
a
type
of
risk:
the
systematic
risk
and
the
specific
risk.
The
specific
risk
is
the
risk
specific
to
the
asset,
for
instance
for
a
bond
it
is
the
announcement
of
capital
loss
or
a
profit
warning
for
a
stock.
This
kind
of
risk
is
only
related
to
the
asset
itself
and
then
to
the
risk
only
supported
by
the
issuer.
Meanwhile,
the
systematic
risk
is
related
to
the
movement
of
the
market
as
a
whole,
it
is
then
the
impact
of
an
event
affecting
all
the
asset
class
because
of
for
example
a
revision
of
the
economic
forecasts
or
because
of
a
global
financial
crisis
as
seen
with
the
sub-­‐primes
in
2008
or
with
the
debt
crisis
in
Europe.
The
specific
risk
is
also
called
the
"diversifiable"
risk
since
it
is
possible
to
extremely
reduce
it
by
diversifying
its
portfolio
by
investing
in
different
securities
of
the
asset
class
or
by
varying
the
geographic
coverage
of
the
portfolio,
for
example
an
equity
portfolio
invested
in
more
than
30
different
stocks
has
a
specific
risk
considered
as
almost
zero;
whereas
the
systematic
risk
cannot
be
reduced
as
easily.

6. 6
Then,
a
question
remains
on
the
reduction
of
the
systematic
risk.
It
is
fair,
in
the
investor
point
of
view,
to
assume
that
investing
in
financials
products
reproducing
indexes
is
a
way
of
eliminating
the
specific
risk
since
indexes,
by
their
nature,
are
computed
in
a
way
of
reproducing
the
market
performance
of
a
given
industry
or
country
asset
class
while
moderating
the
impact
of
specific
risk.
Most
equity
indexes
are
for
instance
using
a
formula
to
moderate
the
impact
of
larger
capitalizations
on
the
index,
then
an
index
of
any
asset
class
can
be
considered
as
"specific
risk
free"
as
long
as
it
takes
in
consideration
more
than
20
or
30
securities.
Investors
should
then
find
a
way
of
decreasing
the
exposure
of
their
portfolios
to
the
systematic
risk.
b. Emergence
of
alternative
risk
transfer
During
the
1990s,
insurers
and
reinsurers
faced
capacity
issues
driving
them
to
look
for
new
way
to
transfer
the
risk
linked
to
their
business
to
a
third
party.
These
issues
supported
the
development
of
Alternative
Risk
Transfer,
known
as
ART.
ART
consists
in
using
alternative
ways
to
achieve
the
same
hedging
and
transfer
of
risk
from
a
(re)insurance
company
to
a
third
party,
this
enables
(re)insurers
to
receive
protection
against
some
risks
linked
to
their
(re)insurance
activities
by
transferring
it
to
the
capital
markets.
The
most
common
area
of
ART
includes
risk
securitization,
derivative
contracts
(weather
derivatives)
and
the
transformation
of
capital
market
risks
into
reinsurance
using
transformer
vehicle1
;
some
other
methods
are
captive
insurance
companies
and
life
insurance
securitization.
This
strong
growth
of
ART
is
leading
in
the
short-­‐term
to
the
convergence
of
insurance
and
financial
markets,
thus
creating
a
new
risk
market.
The
emergence
of
alternative
risk
transfer
solutions
has
supported
the
growth
of
a
new
alternative
asset
class
within
the
insurance
market:
the
Insurance
Linked
Securities.
ILS
provide
to
(re)insurers
an
innovative
way
of
financing
their
capital
by
selling
their
capital
risk
as
any
other
assets
in
order
to
funds
claims
payments
arising
from
mega-­‐catastrophes
and
other
extreme
loss
events.
ILS
products
are
typically
sponsored
by
insurers
or
reinsurers,
governments
and
companies
who
see
in
ILS
a
way
to
transfer
their
insurance
risk
(its
capital
for
a
(re)insurance
company)
to
the
capital
markets
where
a
wide
range
of
institutional
investors
such
as
pension
funds,
hedge
funds
and
banks
are
now
including
this
products
in
1
Artemis.bm
–
What
is
Alternative
Risk
Transfer
?

7. 7
their
portfolios.
Most
known
ILS
products
are
catastrophe
bonds,
industry
loss
warranties
and
sidecars
and
usually
cover
natural
catastrophes
(windstorm,
typhoon,
earthquake),
man-­‐made
events
(aviation,
marine)
and
life
(re)insurance
(mortality,
life
insurance
policy
pools).
A
sidecar
in
the
reinsurance
industry
is
a
financial
technique
allowing
investors
to
benefit
from
the
return
of
a
defined
insurance
or
reinsurance
business
book
while
supporting
an
equivalent
or
proportional
part
of
the
risk.
Sidecars
have
been
mostly
joint-­‐
ventures
between
two
or
more
(re)insurers
but
they
are
now
becoming
an
simple
and
efficient
way
of
using
third
party
capital
in
the
underwriting
activities.
For
instance,
capital
provided
by
investors
will
be
used
to
pay
the
claims
on
the
books
and
they
receive
a
part
of
the
(re)insurance
premiums
to
take
this
risk.
Sidecars
are
fully-­‐collateralized
securities
and
the
collateral
is
totally
exposed
to
the
(re)insurance
risk
for
their
duration.
ILW,
also
known
as
Industry
loss
warranty
can
be
understood
as
a
derivative
contract
allowing
the
buyer
to
buy
a
coverage
against
a
pre-­‐defined
amount
of
losses
experienced
by
the
industry
from
a
specific
event.
ILW
are
set
up
with
a
limited
amount
the
buyer
could
receive
and
a
minimum
amount
of
industry
losses
as
a
trigger.
ILW
are
usually
written
by
reinsurers
or
hedge
funds
and
sometimes
have
specific
clauses
requesting
that
the
buyer
suffered
from
losses
to
receive
the
pay-­‐out.
III. Catastrophe
bonds
a. Basics
of
catastrophe
bonds
Cat-­‐bonds
are
the
most
used
type
of
ILS
and
probably
the
most
known
from
investors.
A
cat-­‐bond
is
a
fully
collateralized
security
paying
off
only
if
a
previously
defined
catastrophic
event
occurs
during
its
lifetime.
Although
the
cat-­‐bonds
markets
is
small
comparing
to
the
larger
non-­‐life
(re)insurance
market,
its
significant
size
within
the
property
catastrophe
market
is
expanding
for
the
last
two
decades.
The
most-­‐used
structure
used
to
securitize
cat-­‐bond
is
the
same
as
the
one
used
for
classic
ABS
transactions
that
are
executed
by
banks
for
loans,
mortgages
and
leases.
Firstly,
a
special
purpose
vehicle
(SPV,
or
SPRV)
is
created
and
located
in
a
low-­‐tax
country,
usually

8. 8
Ireland
for
Europe
or
in
Bermuda,
then
the
SPV
issues
bonds
to
investors
and
receive
cash
from
them.
The
cash
is
invested
by
the
SPV
through
a
trust
account
in
safe
and
short-­‐term
securities.
If
the
event
occurs
then
the
call
option
held
by
the
(re)insurer
on
the
proceeds
is
triggered
to
help
the
(re)insurer
to
pay
claims
from
the
event.
If
there
is
no
trigger
activated
during
the
life
of
the
bond,
the
principal
is
returned
to
investors
at
maturity.
The
use
of
a
SPV
is
beneficial
for
both
issuers
and
investors.
It
indeed
allows
the
issuers
to
have
tax
and
accounting
benefits
linked
to
traditional
reinsurance2
while
the
investors
are
isolated
from
the
operational
and
solvency
risk
of
the
(re)insurer.
The
following
schema
summarize
the
structure
of
a
"standard"
cat-­‐bonda:
However,
the
occurrence
of
a
catastrophe
is
not
enough
to
affect
the
contract.
For
every
issued
cat-­‐bond,
various
parameters
impacting
the
contract
are
defined;
the
most
obvious
are
the
geographic
area
and
the
covered
peril(s).
The
following
table
highlights
the
most
common
perils
according
to
their
geographic
coverage:
Perils:
Geographic
areas:
Storms
Northern
Europe
Florida
Hurricanes
US
–
East
Cost
Floods
Australia
Southern
Asia
Earthquake
Japan
US
–
West
Cost
Mexico
2
Cat-­‐bonds
have
lower
corporate
tax
costs
than
financing
through
equity
and
are
less
risky
in
terms
of
potential
future
degradations
of
(re)insurer
financial
ratings
and
capital
structure
than
financing
through
subordinated
debt,
Harrington
and
Niehaus
(2003)

9. 9
This
table
is
not
exhaustive,
covered
risks
and/or
perils
can
in
addition
include
volcanic
eruption,
meteorite
impact,
wildfire,
extreme
mortality
and
extreme
lottery
winnings;
there
are
indeed
numerous
perils
with
no
link
to
the
classical
mean
of
the
words
"natural
catastrophe".
Another
important
parameter
is
the
trigger
mechanism
on
which
the
investor
loss
is
based
on.
This
loss
is
indeed
not
necessarily
based
on
the
sponsor's
loss
and
there
are
many
trigger
mechanism
that
can
be
use
of
which
we
can
highlight
4
main
types.
The
simplest
one
to
understand
is
the
indemnity
for
which
the
trigger
is
the
actual
loss
of
the
issuer
due
to
the
event
defined
with
respect
to
the
parameters
of
the
bond
and
behaves
like
traditional
catastrophe
reinsurance,
for
example
if
the
bond
is
$20m
in
excess
of
$100m
and
the
claims
are
more
than
$100m,
then
the
bond
is
triggered,
the
bond
can
also
simply
be
used
to
cover
the
claims
from
the
first
claims.
This
trigger
is
advantageous
for
the
issuer
since
its
claims
payments
can
be
fully
covered
but
is
difficult
to
mitigate
and
evaluate
the
expected
losses
for
the
investor.
But
instead
of
using
the
actual
claims,
the
trigger
can
be
a
modelled
losses
threshold.
An
external
agent
run
through
a
modelling
software
the
impact
of
a
catastrophic
event
to
define
an
exposure,
then
if
the
event
occurs,
the
actual
event's
parameters
are
used
in
the
model
to
determine
if
the
modelled
losses
are
above
threshold,
in
this
case
the
(re)insurer
has
the
right
to
call
on
the
bond.
An
alternative
to
the
indemnity
trigger
is
the
parametric
trigger,
instead
of
basing
the
trigger
on
the
claims
or
on
the
losses,
an
objective
parameter,
relative
to
the
natural
catastrophe,
is
defined.
If
the
actual
value
of
the
parameter
during
the
catastrophe
is
greater
than
the
reference
parameter,
for
example
it
can
be
the
wind
speed
for
a
windstorm
covering
cat-­‐
bond,
the
bond
is
triggered.
This
trigger
insures
a
maximum
transparency
for
the
investor
and
allows
the
issuer
to
call
on
the
bond
quickly
after
the
payable
event.
A
last
common
trigger
is
the
trigger
indexed
on
the
industry
losses,
the
trigger
is
based
on
the
cumulated
losses
of
a
defined
insurers
and
reinsurers
basket.
The
trigger
can
be
the
sum
of
the
loss,
or
an
index
calculated
on
the
estimated
losses.
Because
of
the
different
(re)insurers'
losses
included,
this
type
of
trigger
is
more
transparent
that
the
indemnity
parameter
which
is
based
on
a
single
(re)insurer
claims.

10. 10
Below
are
two
examples
of
recently
issued
cat-­‐bonds
with
different
covered
perils
and
trigger
types:
Everglades
Re
II
Ltd.
Serie
2015-­‐1,
source
Artemis.bm
deal
directory
Issuer
/
SPV:
Everglades
Re
II
Ltd.
(Series
2015-­‐1)
Cedent
/
Sponsor:
Citizens
Property
Insurance
Placement
/
structuring
agent/s:
Citigroup
is
sole
structuring
agent
and
bookrunner.
BofA
Merrill
Lynch
is
joint
bookrunner.
Risk
modelling
/
calculation
agents
etc:
AIR
Worldwide
Risks
/
Perils
covered:
Florida
named
storms
Size:
$300m
Trigger
type:
Indemnity
Ratings:
S&P:
Class
A
-­‐
'BB(sf)'
Date
of
issue:
May
2015
Atlas
IX
Capital
Limited
Series
2015-­‐1,
source
Artemis.bm
deal
directory
Issuer
/
SPV:
Atlas
IX
Capital
Limited
(Series
2015-­‐1)
Cedent
/
Sponsor:
SCOR
Global
P&C
SE
Placement
/
structuring
agent/s:
Aon
Benfield
Securities
is
sole
structuring
agent
and
bookrunner
Risk
modelling
/
calculation
agents
etc:
AIR
Worldwide
Risks
/
Perils
covered:
U.S.
named
storm,
U.S.
and
Canada
earthquake
Size:
$150m
Trigger
type:
Industry
loss
index
Ratings:
-­‐
Date
of
issue:
Feb
2015
b. Markets
Cat-­‐bonds
are
less
known
by
investors
than
traditional
asset
classes
and
even
if
some
institutional
investors
have
started
to
use
them
either
like
any
other
traditional
securities
or
by
creating
dedicated
funds,
providing
investors
and
portfolio
managers
with
a
better
understanding
of
these
products,
the
market
is
not
as
developed
as
for
traditional
assets.
The
cat-­‐bonds
market
is
indeed
relatively
small
comparing
to
the
traditional
ones,
for
instance
at
the
end
of
July
2014,
the
cat-­‐bonds
markets
was
representing
only
$25bn
of

11. 11
outstanding
securities
while
the
US
High
Yield
and
US
Bank
loan
combined
were
at
the
same
time
corresponding
to
roughly
$12,000bn
of
outstanding
securities3
.
The
cat-­‐bond
primary
market
shares
some
characteristics
with
the
corporate
bond
primary
market.
The
main
difference
is
that
at
the
issuance
of
a
new
catastrophe
bond,
the
goal
is
for
the
sponsor
to
get
capital
to
cover
its
possible
claims
payments
instead
of
strengthening
its
capital
to
support
its
business
or
fulfil
with
regulatory
obligations.
The
coupon
is
typically
floating
and
obtained
by
adding
a
spread
corresponding
to
the
risk
premium
to
a
reference
rate
such
as
the
LIBOR.
The
pricing
depends
on
various
variables
and
is
not
part
of
the
aim
of
this
study,
then
we
will
only
lightly
aboard
it
later
in
this
paper
as
for
the
loss
mechanism.
Overall,
a
catastrophe
bond
is
issued
with
the
following
specifics4
:
Maturity:
typically
between
3
and
4
years
Type
of
security:
floating
rate
Rating:
usually
B
or
BB
rated
by
one
of
the
largest
worldwide
rating
agency
such
as
S&P
Loss
calculation:
computed
by
a
independent
firm
at
the
issuance
of
the
bond
While
various
perils
and
risks
are
covered,
the
market
can
be
split
in
three
main
types
of
perils;
10%
are
covering
earthquakes
in
California
only
and
25%
of
issued
cat-­‐bonds
cover
US
Hurricane/Wind,
then
40%
are
multi-­‐peril
and
the
remaining
25%
cover
European
3
Dan
Singleman
for
BNP
Paribas
IP
FFTW,
"Cat
bonds:
why
they
are
not
a
catastrophe
for
your
portfolio",
09/2014
4
Source:
Swiss
Re,
2011

12. 12
windstorms,
earthquakes
outside
the
US
(Mexico,
Japan)
and
extreme
mortality.
After
issuance,
the
cat-­‐bonds
secondary
market
is
quite
similar
to
the
corporate
bonds
secondary
market.
Most
cat-­‐bonds
are
publicly
listed,
usually
at
the
Bermuda
Stock
Exchange
or
at
the
Cayman
Islands
Stock
Exchange,
but
most
of
the
transactions
are
over
the
counter
between
the
issuance
and
the
maturity.
The
price
of
a
cat-­‐bond
on
the
secondary
market
is
then
variable
and
comparable
to
the
one
of
a
traditional
coupon-­‐bearing
corporate
bond
with
the
difference
that
the
risk
is
a
catastrophe
risk
and
not
a
credit
risk.
The
price
is,
in
addition
of
the
demand/supply
law,
impacted
by
other
factors
such
as
the
period
of
the
year
and
the
occurrence
of
catastrophic
event
since
the
issuance.
Hurricanes
seasons
in
the
Atlantic
Ocean
are
indeed
known
to
be
most
likely
to
happen
between
August
and
October5
,
then
the
knowledge
of
a
benign
hurricanes
season
at
the
end
of
September
should
be
implicitly
included
in
the
price
of
the
bond
since
at
this
date,
the
occurrence
of
a
hurricane
triggering
the
bond
is
now
less
likely.
This
is
the
same
reasoning
for
the
potential
loss
of
principal
resulting
from
a
triggering
event
since
there
is
usually
a
delay
between
an
event
and
the
moment
when
the
trigger
is
activated
(this
is
due
to
the
various
trigger
and
the
need
to
sometimes
collect
numerous
data
before
deciding
to
call
on
the
bond).
Investors
when
valuing
the
bond
must
consider
these
characteristics,
specific
to
catastrophe
bonds.
The
liquidity
on
the
cat-­‐bonds
secondary
market
is
cyclical,
due
to
the
seasonal
activity
for
certain
perils
such
as
hurricanes,
windstorms
and
typhoons.
While
this
type
of
security
is
not
available
for
retail
investors,
institutional
ones
can
easily
found
liquidity
to
exit
their
positions
or
reduce
their
risks
exposure,
for
instance
the
secondary
trading
volume
at
Swiss
Re
Capital
Markets
was
above
$1bn
in
2010
and
growing,
insuring
a
relatively
liquid
market.
5
"Analysis
and
Optimization
of
a
Portfolio
of
Catastrophe
Bonds",
Fredrik
Giertz,
KTH
40%
25%
10%
25%
Perils
repar77on
-­‐
Source:
Swiss
Re,
2011
Mulo-­‐perils
US
Hurricanes/Winds
California
Earthquakes
Others

13. 13
IV. Financial
characteristics
a. Loss
mechanisms
The
pricing
of
a
cat-­‐bond,
either
at
issuance
or
on
the
secondary
market
is,
like
any
other
bond
based
on
its
underlying
risk.
However,
an
investor
must
not
analyse
default
risk
of
the
sponsor
but
the
risk
exposure
including
the
expected
loss
estimates
and
the
probability
of
various
loss
scenarios,
meaning
a
precise
evaluation
of
the
underlying
natural
catastrophe
risk
covered
by
the
bond.
This
evaluation
is
made
by
a
specialized
independent
risk-­‐consulting
firm,
the
most
known
are
AIR
Worldwide
Corporation,
EQECAT.
Inc.
or
Risk
Management
Solutions.
An
investor
with
an
actuarial
or
scientific
background
might
be
able
to
estimate
these
probabilities
but
it
will
face
the
same
difficulties
that
the
third-­‐party
consulting-­‐risk
companies.
The
frequency
of
significant
catastrophic
events
is
usually
between
decades
and
centuries6
(the
loss
scenario
for
insurers
and
reinsurers
is
indeed
based
on
a
one
over
200
years
significant
event
under
Solvency
2
rules
for
example)
and
there
is
typically
no
track
record
of
representative
claims
for
a
given
portfolio
of
catastrophe
risks.
In
addition,
the
quality
of
the
insured
objects
and
the
geographical
distribution
add
difficulties
to
properly
evaluate
the
risks.
However
it
is
possible
to
estimate
the
risk
relative
to
a
natural
catastrophe:
a
portfolio
of
risk
is
used
to
simulate
"an
artificial
loss
experience" 7
by
applying
a
representative
set
of
natural
perils
that
could
affect
the
given
portfolio.
With
this
model,
it
is
possible
to
estimate
the
expected
loss
for
cat-­‐bonds.
It
includes
four
elements:
-­‐ Hazard:
this
is
the
expected
frequency
of
events
within
a
particular
region
and
is
based
on
a
historical
track
record
of
past
events
and
on
scientific
data.
Models
may
be
as
well
consider
timing
since
for
example
atmospheric
perils
are
more
likely
to
happen
due
to
climate
changes.
-­‐ Vulnerability
of
the
insured
properties:
this
is
the
degree
of
destruction
sustained
by
the
insured
object.
The
quantification
of
such
parameter
is
based
on
past
perils
losses.
6
"The
fundamentals
of
insurance-­‐linked
securities",
Swiss
Re
7
"The
fundamentals
of
insurance-­‐linked
securities",
Swiss
Re

14. 14
-­‐ Distribution
of
the
insured
values:
insured
values
are
distributed
with
respect
to
geographical
zones
and
risk
specifications
to
assess
which
insured
value
might
be
impacted
by
a
given
peril.
-­‐ Insurance
conditions:
these
are
the
conditions
relative
to
the
insurance
contract
such
as
for
examples
claims
limits
or
deductibles
(if
the
losses
are
less
than
the
applicable
deductible
the
insurance
payments
would
be
significantly
reduced).
Some
other
factors
can
affect
the
loss
estimates
such
as
the
trigger,
the
cost
of
building
that
might
rise
following
the
event.
Overall
the
set
up
of
such
simulation
model
needs
a
large
variety
of
parameters
and
is
complex.
The
result
of
the
simulation
is
defined
as
a
loss
frequency
or
as
an
exceedance
probability
curve
as
displayed
above.
b. Pricing
As
mentioned
before,
cat-­‐bonds
are
floating
rate
securities;
the
sponsor
is
then
as
for
traditional
bonds
paying
a
spread
over
a
reference
rate
to
its
investors.
In
theory,
the
sources
of
default
are
totally
independent
for
a
corporate
and
a
catastrophe
bond
of
equivalent
rating
since
the
securitization
structure
through
a
SPV
and
the
collateral
account
insure
that
investors
in
cat-­‐bonds
are
not
impacted
in
case
of
default
from
the
(re)insurer.
Investors
should
then
be
willing
to
pay
a
premium
to
benefit
the
diversification
of
their
risk
and
the
expected
return
should
be
lower
than
for
corporate
bonds
(at
equivalent
ratings).

15. 15
However
the
following
graph8
shows
that
the
average
yield
of
BB-­‐rated
corporate
bonds
is
largely
lower
than
the
one
of
catastrophe
bonds.
This
market
behaviour
can
be
explained
by
three
factors:
(a)
catastrophe
bonds
are
not
known
enough
and
most
investors
remain
unfamiliar
with
their
characteristics
and
theirs
dynamics;
(b)
the
larger
managers
focused
on
the
sector
rather
invest
in
other
ILS
because
of
the
smaller
size
of
the
cat-­‐bonds
market
and
(c)
cat-­‐bonds
are
non-­‐proportional
reinsurance
securities
(once
the
bond
is
triggered,
the
entire
notional
will
quickly
be
lost)
The
pricing
of
catastrophe
bonds
is
still
subject
to
theories,
some
value
them
for
example
using
a
traditional
risk
securitization
approach
by
considering
the
cat-­‐bond
as
a
CDS
while
others
rather
consider
an
"index"
approach
and
each
payment
as
a
caplet
to
value
the
bond.
Jarrow
(2010)
provides
a
formula
consistent
with
any
arbitrage-­‐free
model
for
the
evolution
of
the
LIBOR
term
structure
of
interest
rates.
This
formula
is
based
on
the
probability
of
the
occurrence
of
the
covered
catastrophic
peril
and
the
expected
loss
rate
in
case
of
occurrence.
According
to
Jarrow,
the
value
of
a
cat
bond
is
equal
to
(a)
the
value
of
the
next
coupon
payment
times
the
probability
of
no
event,
(b)
added
to
the
recovery
on
the
LIBOR
floating
rate
note
times
the
probability
of
the
loss
happening
before
the
next
coupon
payment,
(c)
plus
the
value
of
a
LIBOR
floating
rate
note
received
at
the
next
payment
date
times
the
probability
of
no
events,
(d)
less
the
expected
loss
after
the
next
coupon
payment,
multiplied
by
the
probability
of
the
loss
occurring
after
the
next
payment
finally
added
to
the
(e)
expected
fixed
payments
after
the
next
coupon
payment
times
the
probability
that
it
is
8
Source:
Swiss
Re
Capital
Markets,
"The
fundamentals
of
insurance-­‐linked
securities"

16. 16
received
with
the
probabilities
being
summed
across
all
times.
Overall,
the
probability
of
the
occurrence
of
the
natural
peril
and
the
expected
losses
are
the
key
factors
when
valuing
a
cat-­‐bond.
c. Correlation
and
sensitivity
to
traditional
markets
In
theory
cat-­‐bonds
represent
for
investors
a
way
of
gaining
a
return
uncorrelated
to
macroeconomic
data,
political
environment
and
business
activity
that
are
usually
risk
factors
for
traditional
corporate
bonds.
The
below
graph
show
the
strong
resilience
of
the
cat-­‐bonds
market
during
both
the
subprime
crisis
and
later
the
Eurozone
debt
crisis
against
equities,
sovereign
bonds
and
corporate
bonds.
However
it
is
wrong
to
consider
cat-­‐bonds
as
totally
uncorrelated
from
the
traditional
economy
and
financial
assets.
As
we
said
before,
for
an
equivalent
rating,
a
corporate
bond
and
a
catastrophe
bond
should
have
independent
return
and
should
be
uncorrelated.
While
our
computed
correlation
coefficient
for
the
past
13
years
between
cat
bonds
and
corporate
bonds
returns
is
relatively
low
with
a
value
of
0.16
for
the
Dow
Jones
Corporate
Bond
Total
Return
index
relative
to
the
Swiss
Re
BB
Rated
Cat
Bond
Total
Return
index;
the
graph
below
shows
that
the
moving
correlation
coefficient
based
on
the
weekly
return
of
the
last
6
50
100
150
200
250
300
Swiss
Re
Global
Cat
Bond
Total
Return
S&P
Total
Return
Euro
STOXX
600
Merrill
Lynch
10-­‐year
U.S.
Treasury
Futures
Total
Return
S&P
Eurozone
Sovereign
Bond
Index
Total
Return
Barclays
global
corp
total
return
hedged
USD
Dow
Jones
Corporate
Bond
Total
Return

17. 17
months
can
go
up
to
more
than
0.50.
Furthermore,
we
can
highlight
that
the
correlation
was
particularly
high
during
the
2008
financial
crisis.
This
result
is
in
line
with
the
previous
study
of
Carayannopoulos
and
Perez
(2013)
that
stated
that
catastrophe
bonds
are
low
beta
securities
only
in
non-­‐crisis
period9
.
This
correlation
can
be
explained
by
the
structure
itself
of
the
bond,
notably
because
of
the
trust
account
and
of
the
assets
used
as
a
collateral
in
this
account.
A
simple
way
to
approach
this
correlation
is
to
remember
that
cat-­‐bonds
are
competing
with
corporate
bonds,
thus
their
floating
rate
is
based
on
the
same
reference
rate,
this
and
the
collateral
assets
make
two
direct
links
or
correlation
factors
to
the
other
class
of
assets.
Furthermore,
the
investors
must
know
that
the
duration
of
a
cat-­‐bond
is
larger
than
the
duration
of
a
similar
straight
bond10
,
creating
a
positive
correlation
from
the
common
sensitivity
to
interest
rates
changes
for
catastrophe
and
corporate
bonds.
9
"Diversification
through
Catastrophe
Bonds:
Lessons
from
the
Subprime
Financial
Crisis,
2013,
Carayannopoulos
and
Perez
10
"Using
Catastrophe-­‐Linked
Securities
to
Diversify
Insurance
Risk:
A
Financial
Analysis
of
Cat
Bonds",
1999,
Loubergé,
Kellizi
&
Gilli
-­‐0.60
-­‐0.40
-­‐0.20
-­‐
0.20
0.40
0.60
0.80
CoefWicient
of
correlation
between
Dow
Jones
Corporate
Bonds
Total
Return
and
Swiss
Re
BB
Rated
Cat
Bonds
Total
Return

18. 18
V. Empirical
study
In
this
study,
we
neglect
the
specific
risk.
Indexes
are
used
to
highlight
the
systematic
risk
of
each
asset
class
defined
here
as
equities,
sovereign
bonds,
corporate
bonds
and
catastrophe
bonds
and
cover
a
wide
range
of
geographic
areas,
industries,
ratings,
nominated
currencies,
catastrophic
events.
However
it
is
important
to
notice
that
all
of
these
indexes
are
said
to
be
"total
return",
then
they
include
all
the
potential
gains
for
the
investors
including
dividends
and
coupons
payments
in
addition
to
the
price
evolution
of
the
security.
The
catastrophe
bonds
market
is
small
relatively
to
more
classic
and
better-­‐known
assets
and
there
are
only
five
indexes
tracking
the
performance
of
these
financial
products.
The
indexes
used
in
this
thesis
are
all
designed
and
computed
by
Swiss
Re
Capital
Markets,
the
company
launched
the
Swiss
Re
Cat
Bond
Indices
suite
in
2007
as
the
first
total
return
indexes
provided
to
the
industry
of
reinsurance.
Furthermore,
Swiss
Re
Capital
Markets
has
retroactively
computed
the
indexes
until
2002,
leaving
a
covered
period
of
more
than
13
years
from
January
2002
to
today.
For
each
of
these
cat-­‐bonds
indexes,
it
tracks
the
coupon
return,
representing
the
accrued
spread
plus
collateral
return
and
the
price
return
measuring
the
movement
of
secondary
bid
as
provided
by
Swiss
Re
Capital
Markets
on
a
weekly-­‐basis.11
This
study
focuses
on
a
13
years
time
period,
from
the
first
Friday
of
January
2002
to
the
second
Friday
of
January
2015
(catastrophe
bonds
indices
provided
by
Swiss
Re
are
computed
on
a
weekly
basis).
This
time
interval
allows
us
to
study
the
behaviour
of
catastrophe
bonds
during
economic
stability,
global
crisis
and
recovery
times.
The
number
of
observed
values
for
each
index
is
679,
providing
678
observations
of
weekly
returns.
The
aim
of
this
study
is
to
provide
empirical
results
and
conclusions
on
the
possible
efficiency
of
cat-­‐
bonds
as
a
diversification
tool,
thus
all
the
results
that
will
be
discussed
below
are
based
on
historical
data
only
and
no
modelled
or
forecasted
data
have
been
used.
11
Swiss
Re
Capital
Markets
Methodology
for
more
detailed
information,
please
refer
to
the
appendixes

19. 19
The
aim
of
this
thesis
is
to
highlight
the
potential
benefits
for
the
investor
of
adding
cat-­‐
bonds
to
its
portfolio,
thus
the
chosen
indexes
to
represent
the
different
asset
classes
are
strictly
the
same
for
the
two
studied
portfolio,
only
the
allocation
is
varying.
The
descriptive
statistics
of
the
two
cat
bonds
indexes
can
be
found
in
the
appendixes.
a. Definition
of
the
two
portfolios
Both
portfolios
have
the
same
initial
amount
of
capital,
which
for
simplification
reason,
is
assumed
to
be
equal
to
1
or
100%.
Each
portfolio
has
its
capital
allocated
between
listed
stocks,
sovereign
bonds,
corporate
bonds
and
cat-­‐bonds.
The
allocated
proportions
for
equity
and
government
bonds
are
the
same
for
both
portfolios
and
since
the
asset
that
has
the
most
of
common
characteristics
with
a
cat-­‐bond
is
a
corporate
bond,
the
only
two
differences
between
the
two
studied
portfolios
are
the
proportions
of
capital
allocated
to
the
corporate
bonds
and
to
the
catastrophe
bonds.
The
indexes
used
in
this
thesis
are
the
following
-­‐ Equity:
o CAC
40
o FOOTSIE
100
o DAX
o S&P
Total
Return
o NASDAQ
100
o EURO
STOXX
600
-­‐ Sovereign
bonds:
o Merrill
Lynch
10-­‐y
US
Treasury
Futures
Total
Return
o JP
Morgan
Global
Government
Bond
Index
Hedged
in
USD
Ex
US
1-­‐y
to
10-­‐y
Maturity
o S&P
Eurozone
Sovereign
Bond
Index
Total
Return
o Barclays
EuroAgg
Treasury
Total
Return
Index
Value
Unhedged
EUR
-­‐ Corporate
bonds:
o The
BofA
Merrill
Lynch
1-­‐y
to
5-­‐y
US
Corporate
Index
o Dow
Jones
Corporate
Bond
Total
Return
Index
o Barclays
Global
Corp
Total
Return
Hedged
USD
-­‐ Catastrophe
bonds:

20. 20
o Swiss
Re
BB
Rated
Cat
Bond
Total
Return
o Swiss
Re
Global
Cat
Bond
Total
Return
All
values
have
been
downloaded
from
Bloomberg
databases
being
already
provided
as
USD
denominated
to
avoid
potential
interpretation
issues
arising
from
the
currency
price
variations
between
EUR
and
USD.
Since
the
investment
scenario
in
this
study
is
based
on
a
diversification
strategy,
the
capital
is
firstly
allocated
between
equities,
government
bonds
and
non-­‐government
bonds,
and
then
the
sub-­‐allocation
is
made
between
corporate
bonds
and
catastrophe
bonds
within
the
allocated
capital
for
non-­‐government
bonds.
The
allocation
is
capped
at
40%
and
floored
at
30%
to
remain
within
the
diversification
strategy
principle.
For
the
reference
portfolio,
the
sub-­‐allocation
is
always
100%
for
corporate
bonds
(between
30%
and
40%
of
the
total
allocated
capital)
and
variable
between
corporate
and
catastrophe
bonds
for
the
test
portfolio.
For
the
different
allocation,
we
highlight
the
following
parameters
described
below.
We
then
simulate
the
two
portfolios
for
the
different
possible
allocation
combinations.
b. Analysis
and
risk-­‐return
measurements
To
highlight
the
potential
benefit
of
a
portfolio
diversification
through
the
investment
in
catastrophe
bonds,
we
will
study
returns
and
risk
indicators
for
the
studied
period:
-­‐ The
historical
average
return
based
on
the
last
3
months
calculated
adding
the
last
13
weekly
return
values
without
any
weight
and
dividing
the
sum
by
13.
-­‐ The
historical
average
volatility
based
on
the
last
3
months.
The
volatility
is
computed
using
the
traditional
mean-­‐centred
formula
over
a
3
months
time
period
representing
an
interval
of
13
observations
as
below:
𝜎 =
1
13
(𝑟! − 𝑟 )
!"
!!!
Where
𝑟
is
the
mean
return
of
the
portfolio
over
the
last
13
weeks
and
𝑟!
the
weekly
return
for
the
week
ending
i.
The
historical
average
is
calculated
adding
the
13
volatility
values
without
any
weight
and
dividing
the
sum
by
13.

21. 21
-­‐ The
historical
Value
at
Risk
(VaR)
within
a
99%
confidence
interval.
The
VaR
in
this
study
is
calculated
by
taking
the
second
worst
price
variation
on
a
100
previous
days
time
interval.
-­‐ The
yearly
Sharpe
ratio
calculated
on
the
yearly
performance
of
the
portfolio,
using
the
following
formula:
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 𝑓𝑜𝑟 𝑦𝑒𝑎𝑟 𝑒𝑛𝑑𝑖𝑛𝑔 𝑖 =
𝑟!"#$%"&'"
!
− 𝑟!"#$!!"##
!
𝜎!"#$%"&'"
!
Where
the
risk-­‐free
return
is
the
yearly
return
of
the
sovereign
bond
index
chosen
in
the
two
portfolios.
This
is
not
the
traditional
definition
of
a
risk-­‐free
return
but
the
aim
of
this
study
is
to
determine
the
delivered
potential
excess
return
thanks
to
the
investment
in
cat-­‐bonds
and
the
weights
of
governments
bonds
being
the
same
for
the
two
portfolio
we
can
assume
than
the
risk
free
return
is
the
return
of
the
chosen
sovereign
bonds
index.
VI. Conclusion
The
results
of
the
analysis
of
the
two
portfolios
are
conclusive.
Overall
the
portfolio
diversified
with
catastrophe
bonds
performed
better
by
more
than
10%
than
the
one
without
cat-­‐bonds
on
the
13
years
period,
representing
an
outperformance
of
0.45%
on
a
mean
yearly
basis.
However,
investing
in
cat-­‐bonds
does
not
provide
an
efficient
way
to
avoid
volatility,
there
is
indeed
no
difference
between
the
two
portfolios
on
a
mean
yearly
basis.
The
average
Sharpe
ratio
for
the
total
studied
period
is
always
higher
for
the
portfolio
including
cat-­‐bonds
of
0.55.
Diversification
through
catastrophe
bonds
is
then
not
reducing
the
risk
but
is
nevertheless
more
remunerating
the
investor
for
this
risk.
The
investor
is
indeed
receiving
a
higher
return
for
an
equivalent
risk.
The
value
at
risk
at
100
days
at
99%
confidence
interval
is
slightly
reduced
thanks
to
the
cat-­‐bonds
but
not
in
term
of
level
of
losses;
both
portfolios
experienced
equivalent
levels
of
VaR(99%,
100
days),
but
the
portfolio
including
cat-­‐bonds
came
back
to
lower
level
in
a
shorter
time
than
the
reference
portfolio.
Furthermore,
during
the
banking
and
financial
crisis
the
volatility
of
the
portfolio
containing
cat-­‐bonds
was
more
resilient
to
the
market
shocks,
highlighting
a
average
3-­‐months
volatility
around
1%
lower
than
the
reference
portfolio.
In
addition,
the
geographic
diversification
within
the
traditional
asset
classes
has
an
additional
positive
impact
on
the
Sharpe
ratio,
for

22. 22
instance,
the
simulation
using
the
CAC40
index
provided
significant
lower
Sharpe
ratio
than
the
EURO
STOXX
600.
Catastrophe
bonds
market
has
been
growing
for
decades,
while
it
is
still
not
available
for
retail
or
individual
investors,
it
keeps
on
attracting
more
and
more
institutional
investment
companies.
The
market
is
relatively
liquid
and
lightly
correlated
to
traditional
markets
in
"normal"
times,
this,
linked
to
the
convergence
of
financial
markets
with
reinsurance
industry
supports
the
expansion
of
the
catastrophe
bonds
market.
In
addition,
the
strong
diversification
bought
by
cat-­‐bonds
thanks
to
both
their
various
geographic
and
perils
coverage
make
them
an
efficient
diversification
tools
for
investors,
however
the
lack
of
consensus
on
a
valuation
formula
and
the
complexity
of
estimated
losses
probability
are
still
barriers
to
a
larger
use
of
this
ILS.

23. 23
Appendixes
Swiss
Re
Global
Cat
Bonds
Indice,
99%
confidence
interval
Nombre
678
Coefficient
de
dissymétrie
-­‐1.2930
Moyenne
0.0016
Erreur
type
sur
le
coefficient
de
dissymétrie
0.0937
Moyenne
LCL
0.0012
Coefficient
d'aplatissement
41.4148
Moyenne
UCL
0.0019
Erreur
type
de
l'aplatissement
0.1866
Variance
0.0000
Dissymétrie
alternative
(de
Fisher)
-­‐1.2959
Déviation
standard
0.0037
Aplatissement
alternatif
(de
Fisher)
38.7085
Erreur
type
(de
la
moyenne)
0.0001
Coefficient
de
variation
2.3819
Minimum
-­‐
0.0319
Déviation
moyenne
0.0017
Maximum
0.0402
Moment
d'ordre
2
0.0000
Intervalle
0.0721
Moment
d'ordre
3
0.0000
Somme
1.0594
Moment
d'ordre
4
0.0000
Somme
des
erreurs
types
0.0969
Médiane
0.0015
Total
des
sommes
des
carrés
0.0110
Erreur
médiane
0.0000
Somme
des
carrés
ajustée
0.0094
Centile
25%
(Q1)
0.0009
Moyenne
géométrique
0.0034
Centile
75%
(Q2)
0.0026
Moyenne
harmonique
0.0015
IQR
0.0018
Mode
#N/A
MAD
0.0008
0
50
100
150
200
-­‐0.0324
-­‐0.03
-­‐0.0276
-­‐0.0252
-­‐0.0228
-­‐0.0204
-­‐0.018
-­‐0.0156
-­‐0.0132
-­‐0.0108
-­‐0.0084
-­‐0.006
-­‐0.0036
-­‐0.0012
0.0012
0.0036
0.006
0.0084
0.0108
0.0132
0.0156
0.018
0.0204
0.0228
0.0252
0.0276
0.03
0.0324
0.0348
0.0372
0.0396
Nb.
d'obs.
Valeur

24. 24
Swiss
Re
BB
Rated
Cat
Bonds
Indice,
99%
confidence
interval
Nombre
678
Coefficient
de
dissymétrie
-­‐2.2956
Moyenne
0.0013
Erreur
type
sur
le
coefficient
de
dissymétrie
0.0937
Moyenne
LCL
0.0009
Coefficient
d'aplatissement
47.0138
Moyenne
UCL
0.0017
Erreur
type
de
l'aplatissement
0.1866
Variance
0.0000
Dissymétrie
alternative
(de
Fisher)
-­‐2.3007
Déviation
standard
0.0042
Aplatissement
alternatif
(de
Fisher)
44.3490
Erreur
type
(de
la
moyenne)
0.0002
Coefficient
de
variation
3.2010
Minimum
-­‐
0.0400
Déviation
moyenne
0.0017
Maximum
0.0439
Moment
d'ordre
2
0.0000
Intervalle
0.0839
Moment
d'ordre
3
0.0000
Somme
0.8925
Moment
d'ordre
4
0.0000
Somme
des
erreurs
types
0.1097
Médiane
0.0014
Total
des
sommes
des
carrés
0.0132
Erreur
médiane
0.0000
Somme
des
carrés
ajustée
0.0120
Centile
25%
(Q1)
0.0008
Moyenne
géométrique
0.0031
Centile
75%
(Q2)
0.0024
Moyenne
harmonique
0.0015
IQR
0.0016
Mode
#N/A
MAD
0.0008
0
50
100
150
200
250
-­‐0.0406
-­‐0.0386
-­‐0.0366
-­‐0.0346
-­‐0.0326
-­‐0.0306
-­‐0.0286
-­‐0.0266
-­‐0.0246
-­‐0.0226
-­‐0.0206
-­‐0.0186
-­‐0.0166
-­‐0.0146
-­‐0.0126
-­‐0.0106
-­‐0.0086
-­‐0.0066
-­‐0.0046
-­‐0.0026
-­‐0.0006
0.0014
0.0034
0.0054
0.0074
0.0094
0.0114
0.0134
0.0154
0.0174
0.0194
0.0214
0.0234
0.0254
0.0274
0.0294
0.0314
0.0334
0.0354
0.0374
0.0394
0.0414
0.0434
Nb.
d'obs.
Valeur
Histogramme
pour
0.00111340206185

25. 25
Intermediary
results
for
a
30%
equity
allocation
a
non-­‐government
bonds
allocation
varying
between
30%
and
40%
for
a
step
of
5%
on
the
catastrophe
bonds
allocation.

26. 26
3
months
volatility
evolution

27. 27
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