Risk
Management
nd
Risk
Management
and
Financial
Institutions
–
John
C.
Hull
(2
Edition)
By
Laurens
van
der
Helm
,
Content
Chapter
1
–
Introduction
.................................................................................................................................
4
1.1
Risk
vs.
Return
for
investors
..........................................................................................................................
4
1.2
The
efficient
frontier
......................................................................................................................................
4
1.3
The
capital
asset
pricing
model
(CAPM)
........................................................................................................
4
1.5
Risk
vs.
Return
for
companies
........................................................................................................................
5
1.6
Risk
management
by
financial
institutions
....................................................................................................
5
Chapter
2
–
Banks
...........................................................................................................................................
5
2.1
Commercial
Banking
......................................................................................................................................
5
2.3
Deposit
insurance
..........................................................................................................................................
5
2.4
Investment
banking
.......................................................................................................................................
5
2.5
Securities
trading
...........................................................................................................................................
6
2.7
Today’s
large
banks
.......................................................................................................................................
6
2.8
The
risks
facing
banks
....................................................................................................................................
6
Chapter
3
–
Insurance
Companies
and
Pension
Plans
......................................................................................
6
3.1
Life
insurance
.................................................................................................................................................
7
3.2
Annuity
contracts
..........................................................................................................................................
7
3.10
The
risks
facing
insurance
companies
..........................................................................................................
7
3.12
Pension
plans
...............................................................................................................................................
7
Chapter
5
–
Financial
Instruments
...................................................................................................................
7
5.1
The
markets
...................................................................................................................................................
7
5.2
Long
and
short
positions
in
assets
.................................................................................................................
8
5.3
Derivative
markets
.........................................................................................................................................
8
5.4
Plain
vanilla
derivatives
.................................................................................................................................
8
5.5
Margins
..........................................................................................................................................................
9
Chapter
6
–
How
Traders
Manage
Their
Exposures
..........................................................................................
9
6.1
Delta
..............................................................................................................................................................
9
6.2
Gamma
........................................................................................................................................................
10
6.3
Vega
.............................................................................................................................................................
10
6.4
Theta
............................................................................................................................................................
10
6.5
Rho
...............................................................................................................................................................
10
6.8
The
realities
of
hedging
...............................................................................................................................
10
Chapter
7
–
Interest
Rate
Risk
.......................................................................................................................
11
7.1
The
management
of
net
interest
income
....................................................................................................
11
7.2
LIBOR
and
swap
rates
..................................................................................................................................
11
7.3
Duration
.......................................................................................................................................................
11
7.4
Convexity
.....................................................................................................................................................
12
7.5
Generalization
.............................................................................................................................................
12
7.6
Nonparallel
yield
curve
shifts
......................................................................................................................
12
7.7
Interest
rate
deltas
in
practice
.....................................................................................................................
12
Chapter
8
–
Value
at
Risk
(VaR)
.....................................................................................................................
12
8.1
Definition
of
VaR
..........................................................................................................................................
12
8.2
Examples
of
the
calculation
of
VaR
..............................................................................................................
13
8.3
VaR
vs.
expected
shortfall
...........................................................................................................................
13
8.4
VaR
and
capital
............................................................................................................................................
13
8.6
Choice
of
parameters
for
VaR
......................................................................................................................
13
8.7
Marginal
VaR,
incremental
VaR,
and
component
VaR
................................................................................
13
8.8
Back-‐testing
.................................................................................................................................................
14
Chapter
9
–
Volatility
....................................................................................................................................
14
9.1
Definition
of
volatility
..................................................................................................................................
14
9.2
Implied
volatilities
.......................................................................................................................................
14
9.3
Estimating
volatility
from
historical
data
.....................................................................................................
14
9.4
Are
daily
percentage
changes
in
financial
variables
normal?
......................................................................
14
2
,
9.5
Monitoring
daily
volatility
............................................................................................................................
14
9.6
The
exponentially
weighted
moving
average
model
...................................................................................
15
Chapter
10
–
Correlations
and
copulas
..........................................................................................................
15
10.1
Definition
of
correlation
............................................................................................................................
15
10.2
Monitoring
correlation
..............................................................................................................................
15
10.4
Copulas
......................................................................................................................................................
15
Chapter
11
–
Regulation,
Basel
II,
and
Solvency
II
..........................................................................................
16
11.1
Reasons
for
regulating
banks
.....................................................................................................................
16
11.2
Bank
regulation
pre-‐1988
..........................................................................................................................
16
11.3
The
1988
Basel
accord
...............................................................................................................................
16
11.4
The
G-‐30
policy
recommendations
............................................................................................................
16
11.5
Netting
.......................................................................................................................................................
17
11.6
The
1996
amendment
...............................................................................................................................
17
11.7
Basel
II
........................................................................................................................................................
17
11.8
Credit
risk
capital
under
Basel
II
................................................................................................................
17
11.9
Operational
risk
capital
under
Basel
II
.......................................................................................................
18
11.10
Pillar
2:
supervisory
review
......................................................................................................................
19
11.12
Revisions
to
Basel
II
.................................................................................................................................
19
11.13
Solvency
II
................................................................................................................................................
19
Chapter
12
–
Market
Risk
VaR:
Historical
Simulation
Approach
.....................................................................
19
12.1
The
methodology
.......................................................................................................................................
19
12.2
Accuracy
....................................................................................................................................................
19
12.3
Extensions
..................................................................................................................................................
19
Chapter
13
–
Market
Risk
VaR:
Model-‐Building
Approach
.............................................................................
20
13.1
The
basic
methodology
..............................................................................................................................
20
13.3
Correlation
and
covariance
matrices
.........................................................................................................
20
13.8
Monte
Carlo
simulation
.............................................................................................................................
20
13.10
Model
building
vs.
historical
simulation
..................................................................................................
20
Chapter
14
–
Credit
Risk:
Estimating
Default
Probabilities
.............................................................................
21
14.1
Credit
ratings
.............................................................................................................................................
21
14.2
Historical
default
probabilities
..................................................................................................................
21
14.3
Recovery
dates
..........................................................................................................................................
21
14.4
Credit
default
swaps
..................................................................................................................................
21
14.5
Credit
spreads
............................................................................................................................................
21
14.6
Estimating
default
probabilities
from
credit
spreads
................................................................................
22
14.7
Comparison
of
default
probability
estimates
............................................................................................
22
14.8
Using
equity
prices
to
estimate
default
probabilities
................................................................................
22
Chapter
15
–
Credit
Risk
Losses
And
Credit
VaR
.............................................................................................
23
Chapter
16
–
ABSs,
CDOs,
and
the
Credit
Crunch
of
2007
...............................................................................
23
Chapter
19
–
Liquidity
risk
.............................................................................................................................
23
19.1
Liquidity
trading
risk
..................................................................................................................................
23
19.2
Liquidity
funding
risk
.................................................................................................................................
24
19.3
Liquidity
black
holes
..................................................................................................................................
24
Chapter
20
–
Model
Risk
...............................................................................................................................
24
20.1
Marking
to
market
.....................................................................................................................................
25
Appendix
A
–
Compounding
Frequencies
and
Interest
Rates
.........................................................................
25
Appendix
C
–
Valuing
Forward
and
Futures
Contracts
...................................................................................
25
Appendix
E
–
Valuing
European
Options
.......................................................................................................
25
Without
dividend
yield
......................................................................................................................................
25
With
dividend
yield
............................................................................................................................................
26
3
,
Chapter
1
–
Introduction
The
primary
responsibility
of
the
risk
management
function
is
to
understand
the
portfolio
of
risks
that
the
company
is
currently
taking
and
the
risks
it
plans
to
take
in
the
future.
1.1
Risk
vs.
Return
for
investors
In
risk
management
it
is
about
the
trade-‐off
between
risk
and
expected
return.
Most
investors
are
risk-‐
averse,
meaning
that
investors
want
to
increase
expected
return
while
reducing
the
standard
deviation
of
return.
The
expected
return
of
a
single
stock
is
a
weighted
average
of
the
possible
returns,
where
the
weight
applied
to
a
particular
return
equals
the
probability
of
occurrence.
The
risk
of
a
single
stock
can
be
quantified
by
the
standard
deviation:
! = E(R 2 ) ![E(R)]2
[E(R)]2 = # (probability " return)2
E(R 2 ) = # probability " return 2
In
a
portfolio
consisting
of
two
types
of
investments,
the
expected
return
is
the
weighted
average
of
the
weights
applied
to
a
particular
investment
and
the
expected
investment
returns.
Portfolio
risk
can
be
measured
by
the
including
the
correlation
between
the
investments:
! p = w12! 12 + w22! 22 + 2(w1w2! 1! 2 "12 )
cov12
"12 =
! 1! 2
1.2
The
efficient
frontier
In
the
case
more
investments
are
added
to
a
portfolio,
the
efficient
frontier
represents
the
limits
of
the
risk-‐return
trade-‐off.
There
are
no
investments
possible
that
will
dominate
the
investment
combinations
of
the
efficient
frontier
given
a
certain
risk-‐return
trade-‐off.
When
a
risk-‐free
investment
is
considered,
the
efficient
frontier
must
be
a
straight
line
since
there
should
be
a
linear
trade-‐off
between
the
expected
return
and
the
standard
deviation
of
returns.
Hereby,
all
investors
should
choose
the
same
portfolio
of
risky
assets:
the
market
portfolio.
1.3
The
capital
asset
pricing
model
(CAPM)
The
expected
return
required
on
an
investment
should
reflect
the
extend
to
which
the
investment
contributes
to
the
risks
of
the
market
portfolio.
There
are
two
components
to
the
risk
in
the
investment’s
return.
Both
are
captured
in
the
CAPM: E(R) = ! + RF + " [E(RM ) ! RF ] .
• Systematic
risk:
the
market
risk
that
cannot
be
diversified
by
an
investor.
• Unsystematic
risk:
the
risk
that
is
unrelated
to
the
return
from
the
market
portfolio.
The
!
represents
the
superior
the
difference
between
the
actual
return
and
the
expected
return
on
a
portfolio.
An
alpha
can
be
created
by
trying
to
pick
stocks
that
outperform
the
market
or
by
anticipating
on
market
movements
(‘market
timing’).
The
higher
the
! ,
the
greater
the
systematic
risk
being
taken
and
the
greater
the
extend
to
which
returns
are
dependent
on
the
performance
of
the
market.
4
Management
nd
Risk
Management
and
Financial
Institutions
–
John
C.
Hull
(2
Edition)
By
Laurens
van
der
Helm
,
Content
Chapter
1
–
Introduction
.................................................................................................................................
4
1.1
Risk
vs.
Return
for
investors
..........................................................................................................................
4
1.2
The
efficient
frontier
......................................................................................................................................
4
1.3
The
capital
asset
pricing
model
(CAPM)
........................................................................................................
4
1.5
Risk
vs.
Return
for
companies
........................................................................................................................
5
1.6
Risk
management
by
financial
institutions
....................................................................................................
5
Chapter
2
–
Banks
...........................................................................................................................................
5
2.1
Commercial
Banking
......................................................................................................................................
5
2.3
Deposit
insurance
..........................................................................................................................................
5
2.4
Investment
banking
.......................................................................................................................................
5
2.5
Securities
trading
...........................................................................................................................................
6
2.7
Today’s
large
banks
.......................................................................................................................................
6
2.8
The
risks
facing
banks
....................................................................................................................................
6
Chapter
3
–
Insurance
Companies
and
Pension
Plans
......................................................................................
6
3.1
Life
insurance
.................................................................................................................................................
7
3.2
Annuity
contracts
..........................................................................................................................................
7
3.10
The
risks
facing
insurance
companies
..........................................................................................................
7
3.12
Pension
plans
...............................................................................................................................................
7
Chapter
5
–
Financial
Instruments
...................................................................................................................
7
5.1
The
markets
...................................................................................................................................................
7
5.2
Long
and
short
positions
in
assets
.................................................................................................................
8
5.3
Derivative
markets
.........................................................................................................................................
8
5.4
Plain
vanilla
derivatives
.................................................................................................................................
8
5.5
Margins
..........................................................................................................................................................
9
Chapter
6
–
How
Traders
Manage
Their
Exposures
..........................................................................................
9
6.1
Delta
..............................................................................................................................................................
9
6.2
Gamma
........................................................................................................................................................
10
6.3
Vega
.............................................................................................................................................................
10
6.4
Theta
............................................................................................................................................................
10
6.5
Rho
...............................................................................................................................................................
10
6.8
The
realities
of
hedging
...............................................................................................................................
10
Chapter
7
–
Interest
Rate
Risk
.......................................................................................................................
11
7.1
The
management
of
net
interest
income
....................................................................................................
11
7.2
LIBOR
and
swap
rates
..................................................................................................................................
11
7.3
Duration
.......................................................................................................................................................
11
7.4
Convexity
.....................................................................................................................................................
12
7.5
Generalization
.............................................................................................................................................
12
7.6
Nonparallel
yield
curve
shifts
......................................................................................................................
12
7.7
Interest
rate
deltas
in
practice
.....................................................................................................................
12
Chapter
8
–
Value
at
Risk
(VaR)
.....................................................................................................................
12
8.1
Definition
of
VaR
..........................................................................................................................................
12
8.2
Examples
of
the
calculation
of
VaR
..............................................................................................................
13
8.3
VaR
vs.
expected
shortfall
...........................................................................................................................
13
8.4
VaR
and
capital
............................................................................................................................................
13
8.6
Choice
of
parameters
for
VaR
......................................................................................................................
13
8.7
Marginal
VaR,
incremental
VaR,
and
component
VaR
................................................................................
13
8.8
Back-‐testing
.................................................................................................................................................
14
Chapter
9
–
Volatility
....................................................................................................................................
14
9.1
Definition
of
volatility
..................................................................................................................................
14
9.2
Implied
volatilities
.......................................................................................................................................
14
9.3
Estimating
volatility
from
historical
data
.....................................................................................................
14
9.4
Are
daily
percentage
changes
in
financial
variables
normal?
......................................................................
14
2
,
9.5
Monitoring
daily
volatility
............................................................................................................................
14
9.6
The
exponentially
weighted
moving
average
model
...................................................................................
15
Chapter
10
–
Correlations
and
copulas
..........................................................................................................
15
10.1
Definition
of
correlation
............................................................................................................................
15
10.2
Monitoring
correlation
..............................................................................................................................
15
10.4
Copulas
......................................................................................................................................................
15
Chapter
11
–
Regulation,
Basel
II,
and
Solvency
II
..........................................................................................
16
11.1
Reasons
for
regulating
banks
.....................................................................................................................
16
11.2
Bank
regulation
pre-‐1988
..........................................................................................................................
16
11.3
The
1988
Basel
accord
...............................................................................................................................
16
11.4
The
G-‐30
policy
recommendations
............................................................................................................
16
11.5
Netting
.......................................................................................................................................................
17
11.6
The
1996
amendment
...............................................................................................................................
17
11.7
Basel
II
........................................................................................................................................................
17
11.8
Credit
risk
capital
under
Basel
II
................................................................................................................
17
11.9
Operational
risk
capital
under
Basel
II
.......................................................................................................
18
11.10
Pillar
2:
supervisory
review
......................................................................................................................
19
11.12
Revisions
to
Basel
II
.................................................................................................................................
19
11.13
Solvency
II
................................................................................................................................................
19
Chapter
12
–
Market
Risk
VaR:
Historical
Simulation
Approach
.....................................................................
19
12.1
The
methodology
.......................................................................................................................................
19
12.2
Accuracy
....................................................................................................................................................
19
12.3
Extensions
..................................................................................................................................................
19
Chapter
13
–
Market
Risk
VaR:
Model-‐Building
Approach
.............................................................................
20
13.1
The
basic
methodology
..............................................................................................................................
20
13.3
Correlation
and
covariance
matrices
.........................................................................................................
20
13.8
Monte
Carlo
simulation
.............................................................................................................................
20
13.10
Model
building
vs.
historical
simulation
..................................................................................................
20
Chapter
14
–
Credit
Risk:
Estimating
Default
Probabilities
.............................................................................
21
14.1
Credit
ratings
.............................................................................................................................................
21
14.2
Historical
default
probabilities
..................................................................................................................
21
14.3
Recovery
dates
..........................................................................................................................................
21
14.4
Credit
default
swaps
..................................................................................................................................
21
14.5
Credit
spreads
............................................................................................................................................
21
14.6
Estimating
default
probabilities
from
credit
spreads
................................................................................
22
14.7
Comparison
of
default
probability
estimates
............................................................................................
22
14.8
Using
equity
prices
to
estimate
default
probabilities
................................................................................
22
Chapter
15
–
Credit
Risk
Losses
And
Credit
VaR
.............................................................................................
23
Chapter
16
–
ABSs,
CDOs,
and
the
Credit
Crunch
of
2007
...............................................................................
23
Chapter
19
–
Liquidity
risk
.............................................................................................................................
23
19.1
Liquidity
trading
risk
..................................................................................................................................
23
19.2
Liquidity
funding
risk
.................................................................................................................................
24
19.3
Liquidity
black
holes
..................................................................................................................................
24
Chapter
20
–
Model
Risk
...............................................................................................................................
24
20.1
Marking
to
market
.....................................................................................................................................
25
Appendix
A
–
Compounding
Frequencies
and
Interest
Rates
.........................................................................
25
Appendix
C
–
Valuing
Forward
and
Futures
Contracts
...................................................................................
25
Appendix
E
–
Valuing
European
Options
.......................................................................................................
25
Without
dividend
yield
......................................................................................................................................
25
With
dividend
yield
............................................................................................................................................
26
3
,
Chapter
1
–
Introduction
The
primary
responsibility
of
the
risk
management
function
is
to
understand
the
portfolio
of
risks
that
the
company
is
currently
taking
and
the
risks
it
plans
to
take
in
the
future.
1.1
Risk
vs.
Return
for
investors
In
risk
management
it
is
about
the
trade-‐off
between
risk
and
expected
return.
Most
investors
are
risk-‐
averse,
meaning
that
investors
want
to
increase
expected
return
while
reducing
the
standard
deviation
of
return.
The
expected
return
of
a
single
stock
is
a
weighted
average
of
the
possible
returns,
where
the
weight
applied
to
a
particular
return
equals
the
probability
of
occurrence.
The
risk
of
a
single
stock
can
be
quantified
by
the
standard
deviation:
! = E(R 2 ) ![E(R)]2
[E(R)]2 = # (probability " return)2
E(R 2 ) = # probability " return 2
In
a
portfolio
consisting
of
two
types
of
investments,
the
expected
return
is
the
weighted
average
of
the
weights
applied
to
a
particular
investment
and
the
expected
investment
returns.
Portfolio
risk
can
be
measured
by
the
including
the
correlation
between
the
investments:
! p = w12! 12 + w22! 22 + 2(w1w2! 1! 2 "12 )
cov12
"12 =
! 1! 2
1.2
The
efficient
frontier
In
the
case
more
investments
are
added
to
a
portfolio,
the
efficient
frontier
represents
the
limits
of
the
risk-‐return
trade-‐off.
There
are
no
investments
possible
that
will
dominate
the
investment
combinations
of
the
efficient
frontier
given
a
certain
risk-‐return
trade-‐off.
When
a
risk-‐free
investment
is
considered,
the
efficient
frontier
must
be
a
straight
line
since
there
should
be
a
linear
trade-‐off
between
the
expected
return
and
the
standard
deviation
of
returns.
Hereby,
all
investors
should
choose
the
same
portfolio
of
risky
assets:
the
market
portfolio.
1.3
The
capital
asset
pricing
model
(CAPM)
The
expected
return
required
on
an
investment
should
reflect
the
extend
to
which
the
investment
contributes
to
the
risks
of
the
market
portfolio.
There
are
two
components
to
the
risk
in
the
investment’s
return.
Both
are
captured
in
the
CAPM: E(R) = ! + RF + " [E(RM ) ! RF ] .
• Systematic
risk:
the
market
risk
that
cannot
be
diversified
by
an
investor.
• Unsystematic
risk:
the
risk
that
is
unrelated
to
the
return
from
the
market
portfolio.
The
!
represents
the
superior
the
difference
between
the
actual
return
and
the
expected
return
on
a
portfolio.
An
alpha
can
be
created
by
trying
to
pick
stocks
that
outperform
the
market
or
by
anticipating
on
market
movements
(‘market
timing’).
The
higher
the
! ,
the
greater
the
systematic
risk
being
taken
and
the
greater
the
extend
to
which
returns
are
dependent
on
the
performance
of
the
market.
4
