Transcript Class 2

Risk Measurement and
Management
Week 11 –November 2, 2006
J. K. Dietrich - FBE 525 - Fall, 2006
Measuring Holding-Period Risk
Price
sensitivity of bonds is measured
in terms of a bond price elasticity
%price
d1 
%(1  yield )
This
elasticity is called duration
denoted d1, which is widely used by
bond traders and analysts and is often
available on quote sheets
J. K. Dietrich - FBE 525 - Fall, 2006
Example of Duration
Assume
a 10-year 8% coupon bond is
priced at 12% yield to maturity and has
value of 77.4 and duration of 6.8
If yields changed immediately from
12% to 10%, that is a 2/112 or 1.8%
change in gross yield
The bond price should change about
1.8% * 6.8 = 12.1%
J. K. Dietrich - FBE 525 - Fall, 2006
Duration as Time Measure
 In
1930’s, Macauley noted that maturity
was not relevant measure of timing of
payments of bonds and defined his own
measure, duration
 The definition of duration is (19-4):
19-4
1
1cF
2cF
McF
MF
+
+...+
+
)
duration1 = d1 = (
2
M
M
(1 + i )
(1 + i )
Po (1 + i) (1 + i )
J. K. Dietrich - FBE 525 - Fall, 2006
Duration has two interpretations
 Elasticity
of bond prices with respect to
changes in one plus the yield to maturity
 Weighted average payment date of cash
flows (coupon and interest) from bonds
 Duration measure
– Can be modified to be a yield elasticity by
dividing by (1+yield to maturity)
– can be redefined using term structure of yields
(Fisher-Weil duration noted d2)
J. K. Dietrich - FBE 525 - Fall, 2006
Duration Calculations
 Duration
can be calculated for bonds:

1 i
1 
1

d 
M
cM 
M 1 
i
pi 
(1  i)

 For
level-payment loans (e.g. mortgages):
1 i
M
d 

M
i
(1  i)  1
J. K. Dietrich - FBE 525 - Fall, 2006
Duration is an Approximation
p
i
Derivative is used in
calculating duration
Actual price
change
Change
predicted by
duration
0
J. K. Dietrich - FBE 525 - Fall, 2006
i

Yield to Maturity
Properties of Duration
 Can
be interpreted as price elasticity or
weighted average payment period
 Note when c=0 that d1= M
 When M is infinite d1= (1+i)/i
 Duration measure effect of parallel shift in
interest rates
 Other economic risks are not assessed
J. K. Dietrich - FBE 525 - Fall, 2006
Duration as Risk Measure
 Good
– Balances reinvestment yield risk against capital
gains risk
– Widely used and clear mathematical expression
assessing holding-period yield risk
 Bad
– Approximation and theoretical issues
– Convexity adjustment only approximate
improvement
J. K. Dietrich - FBE 525 - Fall, 2006
Asset Liability Management:
Definitions
 Approach
to balance sheet management
including financing and balance sheet
composition and use of off-balance sheet
instruments
 Assessment or measurement of balance
sheet risk, especially to interest rate changes
 Simulation of earnings performance of a
portfolio or balance sheet under a variety of
economic scenarios
J. K. Dietrich - FBE 525 - Fall, 2006
History of ALM
 After
World War II to mid 1960’s
– ASSET MANAGEMENT
– Interest rates stable, large post-war holdings of
government bonds, deposit markets protected
 Mid
1960’s to late 1970’s
– LIABILITY MANAGEMENT
– Interest rates rising, global financial markets
developing (e.g. Eurodollars), regulation
binding (maximum deposit interest rates)
J. K. Dietrich - FBE 525 - Fall, 2006
History of ALM (continued)
 Late
1970’s to present
– ASSET/LIABILITY MANAGEMENT
– Use balance sheet composition or off-balance
sheet instruments to management interest rate
and other economic risks
– Changing markets - increased competition from
non-banks, foreign institutions
– Goverment concerns - S&L failures,
Continental Bank and Texas banks, etc.
J. K. Dietrich - FBE 525 - Fall, 2006
Measurement of Risk of
Balance Sheet
Maturity
gaps are common way to
assess the sensitivity of a balance sheet
to changes in interest rates
– Assets and liabilities classified by
maturity or repricing interval
– Cumulative gap calculated
Not easy to interpret in terms of risk
J. K. Dietrich - FBE 525 - Fall, 2006
Duration of Balance Sheet
 Duration
of a number of assets is
d
 Duration
A
Aa a

d
a TA
of net worth in a portfolio is
A A L L
d  d  d
E
E
E
J. K. Dietrich - FBE 525 - Fall, 2006
Simulation
Computer
simulation can handle more
complex economic changes
Many simulations can assess
sensitivity of earnings to changes
Regulators require and consultants can
apply
J. K. Dietrich - FBE 525 - Fall, 2006
Managing Interest Rate Risk
Change
balance sheet composition
– Adjust assets and liabilities until dE
is at acceptable level
Use futures or options to adjust next
exposure
What is source of value added?
J. K. Dietrich - FBE 525 - Fall, 2006
Can Risk Management Add
Value?
 Return
to risk-free portfolio is the risk-free
rate
 Investors can manage their own interest rate
risk
 Does risk distract management or prevent
exploitation of competitive advantage?
 Pleasing regulators and better understanding
may be biggest advantage of ALM
J. K. Dietrich - FBE 525 - Fall, 2006
Risk Management
 Balance
sheet management
– ALM
– Duration and immunization
 Off balance sheet
– Futures
– Options
– Swaps
J. K. Dietrich - FBE 525 - Fall, 2006
Types of Derivative Contracts
Three
basic types of contracts
– Futures or forwards
– Options
– Swaps
Many basic underlying assets
– Commodities
– Currencies
– Fixed incomes or residual claims
J. K. Dietrich - FBE 525 - Fall, 2006
Managing Risk with Futures
 Offset
price or interest rate risk with
contract which moves in opposite direction
 “Cross diagonally in the box”
 Identify contract with price or interest rate
which moves as close as possible with the
price or interest rate exposure
 Imperfect correlation is basis risk
 Not using futures or forwards can be
speculation
J. K. Dietrich - FBE 525 - Fall, 2006
Hedging
Bank Planning
to Borrow
Time/
Situation
Have,
Will Have, or
Will Receive
Need,
Will Need, or
Will Deliver
Present or
Present Plan
Future Time
Period
LONG
LONG
SHORT
SHORT
Insurance Company
with Premiums
J. K. Dietrich - FBE 525 - Fall, 2006
Insurance
Hedge
Borrowing
Hedge
Interest-Rate Options
 Interest
rates and asset values move in
opposite directions
 Long cash means short assets
 Short cash means long (someone else’s)
asset
 Basis risk comes from spreads between
exposure and hedge instrument
 Problem with production risk
J. K. Dietrich - FBE 525 - Fall, 2006
Caps, floors, and collars
 If
a borrower has a loan commitment with a
cap (maximum rate), this is the same as a
put option on a note
 If at the same time, a borrower commits to
pay a floor or minimum rate, this is the
same as writing a call
 A collar is a cap and a floor
J. K. Dietrich - FBE 525 - Fall, 2006
Collars: Cap 6%, floor 4%
Profit
0
Loss
J. K. Dietrich - FBE 525 - Fall, 2006
9400
9500
9600
Options and Product Pricing
pricing is well established
technology
– Black-Scholes approaches
– Present value approaches
– Simulation
– In interest rates, lattice models used
which are consistent with interest rate
movements
 Can model any cash flow with
combinations of options
J. K. Dietrich - FBE 525 - Fall, 2006
“Rocket Science”
 Option
Replication Futures with Options
Profit
Profit
Long
0
Loss
J. K. Dietrich - FBE 525 - Fall, 2006
P0
0
Loss
Buy Call
P0
Write Put
Other option developments
Credit
risk options
Casualty risk options
Requirements for developing an option
– Interest
– Calculable payoffs
– Enforceable
J. K. Dietrich - FBE 525 - Fall, 2006
Swaps
 Exchange
of future cash flows based on
movement of some asset or price
– Interest rates
– Exchange rates
– Commodity prices or other contingencies
 Swaps are all over-the-counter contracts
 Two contracting entities are called counterparties
 Financial institution can take both sides
J. K. Dietrich - FBE 525 - Fall, 2006
Interest Rate Swap:
Plain vanilla, [email protected]%
1/2 5% fixed
Company A
(receive floating)
$2.75mm
$2.5mm
1/2 6-month LIBOR
Notional Amount
$100 mm
J. K. Dietrich - FBE 525 - Fall, 2006
Company B
(receive fixed)
Issues in Hedging
 Micro-hedging
versus macro-hedging
– Accounting
– Regulation
 Assumptions
underlying hedging
– Market liquidity
– Covariance structure (second moments)
 Notorious
examples
– PNC, IG Metall, Bankers Trust, Orange Cy,
Long-Term Capital Mgmt (LTCM), BancOne
J. K. Dietrich - FBE 525 - Fall, 2006
Overview of Credit Risk
 Usual
interpretation of credit risk is default
on a loan or bond
 New views of credit risk are focused on the
change in the credit-worthiness of debt
instruments as well as default
 Risk changes will be reflected in the value
of a portfolio over time as write-downs or
downgrades short of default reduce value of
claims (mark-to-market view of risk)
J. K. Dietrich - FBE 525 - Fall, 2006
Default
 Private
debt (corporate and household) may
not pay cash flows as promised
– Late payments
– Nonpayment of interest or principal
 Other
default or credit events
– Violation of covenants and other creditor
interventions in operations
– Change in risk of default (e.g. highly leveraged
transactions)
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Events
 Probability
of default (PD) can change
affecting the value of default-risky
securities
 Upgrades and downgrades reflecting
changes in PD are credit events
 Recent progress has been made in
quantifying these probabilities
J. K. Dietrich - FBE 525 - Fall, 2006
Bond and Debt Ratings
 Rating
agencies
– Standard and Poor’s (AAA to D)
– Moody’s (Aaa to C)
– Fitch and Duff and Phelps
 Migration
of ratings, e.g. from BBB to BB
(investment grade to below investment
grade) represents credit risk
 For example, change from BBB to BB has
historical probability of 5.3% (S&P, 1996)
J. K. Dietrich - FBE 525 - Fall, 2006
Ratings and Defaults
Ratings
Moody/S&P
Aaa/AAA
Aa1/AA+
Aa2/AA
Aa3/AAA1/A+
A2/A
A3/ABaa1/BBB+
Baa2/BBB
Baa3/BBBBa1/BB+
Ba2/BB
Ba3/BBB1/B+
B2/B
B3/B-
Cumulative Default Rates (%)
1
2
3
4
0.00
0.00
0.00
0.07
0.00
0.00
0.00
0.31
0.00
0.00
0.09
0.29
0.09
0.15
0.27
0.42
0.00
0.04
0.49
0.79
0.00
0.04
0.21
0.57
0.00
0.20
0.37
0.52
0.06
0.39
0.79
1.17
0.06
0.26
0.35
1.07
0.45
1.06
1.80
2.87
0.85
2.68
4.46
7.03
0.73
3.37
6.47
9.43
3.12
8.09
13.49
18.55
4.50
10.90
17.33
23.44
8.75
15.18
22.10
27.95
13.49
21.86
27.84
32.08
5
0.23
0.31
0.65
0.60
1.01
0.88
0.61
1.53
1.70
3.69
9.52
12.28
23.15
29.05
31.86
36.10
Source: Carty & Lieberm an (1996) based on Moody's Investors Services
J. K. Dietrich - FBE 525 - Fall, 2006
Risk of Fixed Incomes
Maximum value=F
Future Value of Debt
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Losses
 Three
elements in credit losses
– Estimated default probability (PD)
– Loss given default (LGD)
– Exposure at default (EAD)
 Credit
losses = PD*LGD*EAD
 Investors in debt securities will be
concerned about all these elements in
managing their risks
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Risk Analysis
 Credit
risk has become a major focus of
rating agencies, regulators, and investors
– Very important to capital market development
(e.g. asset securitizations, loan syndications)
– Enron, Global Crossing, and GE exemplify
different stages of concern with these issues
 Consulting
industry in credit analysis
– RiskMetrics (formerly J.P. Morgan)
– KMV (academic based research)
– Others (KPMG, PricewaterhouseCoopers, etc.)
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Risk Assessment
 Default
occurs when value of assets less
than value of liabilities (insolvency)
 Example of analysis used by KMV uses
simplified estimates of variables
 Must calculate market value of assets
(market value of debt and equity) and
variability of market value
 Identify book value of liabilities
J. K. Dietrich - FBE 525 - Fall, 2006
Motorola: Debt and Equity
Motorola Total Market Values 1991-1 to 2001-2
140000
120000
100000
Total Market Value
80000
60000
40000
20000
0
91
92
93
94
95
MVE
TMV
J. K. Dietrich - FBE 525 - Fall, 2006
96
97
98
LTDANDCL
CL
99
00
Distance to Default: Example
 Motorola
2001-II (billions)
Value of long-term debt
= $ 7.3
Book value of current liabilities = 12.9
Total value of liabilities
= $20.2
Market value of assets
= $56.6
Standard deviation of
change in market value
= 16.4%
 Market value  standard deviation of percent
change = $9.3 billion
J. K. Dietrich - FBE 525 - Fall, 2006
Reduced Probability of Default?
 Estimated
default point in example is
midway between book value of current
liabilities and long-term debt
 Theory is that long-term debt does not
require immediate payment, short-term
liabilities may allow some flexibility
 KMV uses historical data to fine-tune this
estimate
J. K. Dietrich - FBE 525 - Fall, 2006
Estimated Distance to Default
$56.6  $16.6
Di stance to de fau l t
 4.3
$9.3
Market value to default point = $40.0
$12.9
$20.2
$56.6
CL
CL+LTD
TMV
Default point (estimated as midpoint) = $16.6
J. K. Dietrich - FBE 525 - Fall, 2006
Distance to Default: 12-31-01
 Total
Value of Assets (from “Capital
Structure” and Financial Statements):
E + LTD + CL = TA
$33.9 + $ 8.1 + $9.7 = $ 51.7
 Book value of LTD and CL $8.4 and $9.7
Midpoint estimate of default point = $13.9
Std Dev = 16.4% * $51.7 = $8.48
$51.7  $13.9
Di stance to de fau l t
 4.5
$8.48
J. K. Dietrich - FBE 525 - Fall, 2006
Probability of Default
 KMV
has used historical data to relate
distance from default to probability of
default
 That measure is proprietary (not available)
 As example, Motorola is rated A3 by
Standard and Poors, historically associated
with a default rate of about .82% over next
five years (.61% in Moody’s experience)
J. K. Dietrich - FBE 525 - Fall, 2006
Private Firm Default Risk
 KMV
estimates non-traded firm risk by
using market-traded comparables
 Data base on 35,000 traded firms globally
 Valuations of private firms and risk
estimated by using EBITDA/Assets ratios
 KMV estimates default probabilities for
private firms based on data on 300,000
firms in 30 countries
 Estimates depend on EBITDA0
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Risk in Portfolios
 Individual
assets have probability of default
and risk and discussed last week
 Loans in portfolios will have an
interdependent risk structure due to
correlations in defaults
 Credit risk within portfolio context is a
major advance in credit risk management
 Search for a summary measure of portfolio
risk led to the concept of value at risk
J. K. Dietrich - FBE 525 - Fall, 2006
Value at Risk (VAR)
at risk (VAR) looks at risk of
portfolio accounting for covariance of
assets
Risk is defined in terms of likelihood
of losses
Value at Risk
Probability
Value
Maximum value=F
J. K. Dietrich - FBE 525 - Fall, 2006
Future Value of Portfolio
VAR and Capital
Probability
B
Value at Risk
Maximum value=F
Capital
J. K. Dietrich - FBE 525 - Fall, 2006
Future Value of Portfolio
Portfolio Credit Risk
 Credit
risk different than usual portfolio risk
analysis
– Returns are not symmetric
– Concentrations of exposure complicate losses
 Major
issue is correlation of defaults and
losses given default
– We will discuss approach followed by
CreditMetrics
– Other approaches exist (including KMV)
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Risk as Rating Changes
 Increased
 Same
 Less
credit risk
credit risk (BBB)
credit risk
J. K. Dietrich - FBE 525 - Fall, 2006
Default
CCC
B
BB
BBB
A
AA
AAA
Rating Migrations (BBB rating)
Year-End Rating Probability (%)
AAA
0.02
AA
0.33
A
5.95
BBB
86.93
BB
5.30
B
1.17
CCC
0.12
Default
0.18
Source: Standard & Poors
J. K. Dietrich - FBE 525 - Fall, 2006
Two Bond Rating Migrations
Obligor #1 (BBB)
AAA
0.02
AA
0.33
A
5.95
BBB
86.93
BB
5.30
B
1.17
CCC
0.12
Default
0.18
AAA
0.09
0.00
0.00
0.02
0.07
0.00
0.00
0.00
0.00
J. K. Dietrich - FBE 525 - Fall, 2006
AA
2.27
0.00
0.04
0.39
1.81
0.02
0.00
0.00
0.00
Obligor # 2 (Single-A)
A
BBB
BB
91.05
5.52
0.74
0.02
0.00
0.00
0.29
0.00
0.00
5.44
0.08
0.01
79.69
4.55
0.57
4.47
0.64
0.11
0.92
0.18
0.04
0.09
0.02
0.00
0.13
0.04
0.01
B
0.26
0.00
0.00
0.00
0.19
0.04
0.02
0.00
0.00
C
Default
0.01
0.06
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.04
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.00
Probability of Default: Two Firms
Probability = 1/2%
Default Point B
Probability = 1/10%
Probability = 1/100%
Default Point A
J. K. Dietrich - FBE 525 - Fall, 2006
Value of Firm A
Loss Given Default
Seniority Class
Senior Secured
Senior Unsecured
Senior Subordinated
Subordinated
Junior Subordinated
Mean (%)
53.8
51.13
38.52
32.74
17.09
Standard Deviation (%)
26.86
25.45
23.81
20.81
10.9
Source: Carty & Lieberman [96a] -- Moody's Investors Service
J. K. Dietrich - FBE 525 - Fall, 2006
Simplified “Road Map”
Compute
exposure profile
Of each asset
Compute the volatility
Of value caused by
Up (down)grades and defaults
Portfolio value-at-risk due to credit
Source: Introduction to CreditMetrics (1997)
J. K. Dietrich - FBE 525 - Fall, 2006
Compute
correlations
Required Resources
 Default
probabilities (or ratings)
 Migration probabilities
– Historical data requirements
– Approaches to estimating correlations
 Complete
data on types of credits and
estimations of losses given defaults
 Exposures to classes of risks
 Models and simulations of value changes
given credit events
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Portfolio Risk
One Asset
Many Assets
0
0
Return
J. K. Dietrich - FBE 525 - Fall, 2006
Return
Incremental Risk
 Introduction
to CreditMetrics provides good
examples (in Section 5)
 Importance portfolio risk is the marginal
risk
 Marginal risk

High risk
and large
considers portfolio
size
risk implications
$ 10mm
J. K. Dietrich - FBE 525 - Fall, 2006
$ Credit Exposure
Example Portfolio
Asset
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Credit
Rating
AAA
AA
A
BBB
BB
B
CCC
A
BB
A
A
A
B
B
B
B
BBB
BBB
BBB
AA
Portfolio Assets
Standard Deviations
Principal
Market
Stand-alone
Marginal
Amount
Maturity
Value
Absolute ($) Percent Absolute ($) Percent
7,000,000
3
7,821,049
4,905
0.06
239
0.00
1,000,000
4
1,177,268
2,007
0.17
114
0.01
1,000,000
3
1,120,831
17,523
1.56
693
0.06
1,000,000
4
1,189,432
40,043
3.37
2,934
0.25
1,000,000
3
1,154,641
99,607
8.63
16,046
1.39
1,000,000
4
1,263,523
162,251
12.84
37,664
2.98
1,000,000
2
1,127,628
255,680
22.67
73,079
6.48
10,000,000
8 14,229,071
197,152
1.39
35,104
0.25
5,000,000
2
5,386,603
380,141
7.06
105,949
1.97
3,000,000
2
3,181,246
63,207
1.99
5,068
0.16
1,000,000
4
1,181,246
15,360
1.30
1,232
0.10
2,000,000
5
2,483,322
43,085
1.73
4,531
0.18
600,000
3
705,409
107,314
15.21
25,684
3.64
1,000,000
2
1,087,841
167,511
15.40
44,827
4.12
3,000,000
2
3,263,523
610,900
18.72
270,000
8.27
2,000,000
4
2,427,046
322,720
12.77
89,120
3.53
1,000,000
6
1,315,720
28,051
2.13
2,775
0.21
8,000,000
5 10,020,611
306,892
3.06
69,624
0.69
1,000,000
3
1,118,178
1,837
0.16
120
0.01
5,000,000
5
6,181,784
9,916
0.16
389
0.01
Source: Creditmetrics Technical Document (April 2, 1997)
J. K. Dietrich - FBE 525 - Fall, 2006
Credit Risk Management
 Derivatives:
Single-name v. multi-name
 Types of credit derivatives
–
–
–
–
–
–
Total return swap
Credit risk swap
Credit risk option
Credit inter-mediation swap
Credit spread derivative
Default substitution swap
 Over
$400 billion notional amount 2000-IV
J. K. Dietrich - FBE 525 - Fall, 2006
Hedging Credit Risk
Change in Portfolio Value
Hedging Instrument Payoff
0
J. K. Dietrich - FBE 525 - Fall, 2006
Risky Outcomes
Example of Total Return Swap
 3-year
8% coupon bond
Probability
Price
YTM
0.9
849.12
14.56%
0.8
794.32
17.36%
0.7
739.52
20.45%
 If default probability increases from 10 to 20%,
bond return is 8% - 6.4537% = 1.5463% (coupon
minus loss due to downgrade)
J. K. Dietrich - FBE 525 - Fall, 2006
Total Return Swap
(8-6.5437)%
Company A
(pay total return) $750,000
$154,626
7.5%
Notional Amount
$10 mm
J. K. Dietrich - FBE 525 - Fall, 2006
Company B
(pay fixed)
Total Return Swap
 Difference
between payments and receipts
by total return receiver is compensation for
risk
 Total return payer receives cash in case of
downgrade as in example, subsidizing loss
realized on balance sheet
 Can have other swap types, as in default
swap
J. K. Dietrich - FBE 525 - Fall, 2006
Limitations of Derivatives
 Market
limited to single name and portfolio
instruments
– Typically individual corporate borrowers
– Some portfolio of commercial loans
 Market
not developed for consumer credit
– Growth of consumer market but most riskmanagement consists of sales of loans
– Global market ready for consumer-risk
derivatives
J. K. Dietrich - FBE 525 - Fall, 2006
For Next Classes
 Prepare
First American Bank: Credit
Default Risk case for November 9
 Read Chapters 23 and 24 for discussion in
class on November 9 and November 16
 Read KMV paper and Creditmetrics paper
before November 16 class
 Teams should schedule appointments with
me
J. K. Dietrich - FBE 525 - Fall, 2006