1. Risk Measurement and Management
Week 11 –November 2, 2006

2. Measuring Holding-Period Risk
Price sensitivity of bonds is measured in terms of a bond price elasticity
This elasticity is called duration denoted d1, which is widely used by bond traders and analysts and is often available on quote sheets

3. 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 % * 6.8 = 12.1%

4. 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

5. 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)

6. Duration Calculations
Duration can be calculated for bonds:
For level-payment loans (e.g. mortgages):

7. Duration is an Approximation
Derivative is used in calculating duration
Price (Par=1.0)
Actual price change
Change predicted by duration
Yield to Maturity

8. 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

9. 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

10. 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

11. 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)

12. 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.

13. 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

14. Duration of Balance Sheet
Duration of a number of assets is
Duration of net worth in a portfolio is

15. Simulation
Computer simulation can handle more complex economic changes
Many simulations can assess sensitivity of earnings to changes
Regulators require and consultants can apply

16. 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?

17. 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

18. Risk Management Balance sheet management ALM Duration and immunization
Off balance sheet
Futures
Options
Swaps

19. 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

20. 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

21. Hedging Bank Planning to Borrow Insurance Hedge Borrowing
Insurance Company
with Premiums

22. 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

23. 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

24. Collars: Cap 6%, floor 4%
Profit
9400
9500
9600
Loss

25. Options and Product Pricing
Option 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
“Rocket Science”

26. Replication Futures with Options
Profit
Profit
Buy Call
Long P0 P0
Loss
Loss
Write Put 25

27. Other option developments
Credit risk options
Casualty risk options
Requirements for developing an option
Interest
Calculable payoffs
Enforceable

28. 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 counter-parties
Financial institution can take both sides

29. Interest Rate Swap: Plain vanilla, LIBOR@5.5%
1/2 5% fixed
Company A
(receive floating)
Company B
(receive fixed)
$2.5mm
$2.75mm
1/2 6-month LIBOR
Notional Amount
$100 mm

30. 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

31. 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)

32. 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)

33. 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

34. 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)

35. Ratings and Defaults

36. Risk of Fixed Incomes
Probability
Maximum value=F
Future Value of Debt

37. 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

38. 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.)

39. 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

40. Motorola: Debt and Equity
Total Market Value

41. Distance to Default: Example
Motorola 2001-II (billions) Value of long-term debt = $ Book value of current liabilities = Total value of liabilities = $ 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

42. 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

43. Estimated Distance to Default
Market value to default point = $40.0
$20.2
$56.6
$12.9 CL
CL+LTD
TMV
Default point (estimated as midpoint) = $16.6

44. Distance to Default: 12-31-01
Total Value of Assets (from “Capital Structure” and Financial Statements): E LTD + CL = TA $ $ $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

45. 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)

46. 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

47. 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

48. Value at Risk (VAR)
Value at risk (VAR) looks at risk of portfolio accounting for covariance of assets
Risk is defined in terms of likelihood of losses

49. VAR and Capital B
Capital

50. 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)

51. Credit Risk as Rating Changes
Increased credit risk Default CCC B BB
Same credit risk (BBB) BBB
A AA
AAA
Less credit risk

52. Rating Migrations (BBB rating)
Source: Standard & Poors

53. Two Bond Rating Migrations

54. Probability of Default: Two Firms
Value of Firm B
Probability = 1/2%
Probability = 1/10%
Probability = 1/100%
Default Point B
Value of Firm A
Default Point A

55. Loss Given Default

56. Simplified “Road Map” Compute exposure profile Of each asset
Compute the volatility
Of value caused by
Up (down)grades and defaults
Compute
correlations
Portfolio value-at-risk due to credit
Source: Introduction to CreditMetrics (1997)

57. 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

58. Credit Portfolio Risk One Asset Many Assets Frequency Frequency Return
Return
Return

59. Incremental Risk
Introduction to CreditMetrics provides good examples (in Section 5)
Importance portfolio risk is the marginal risk
Marginal risk considers portfolio risk implications
10% 
High risk and large size
$ 10mm
$ Credit Exposure

60. Example Portfolio
Source: Creditmetrics Technical Document (April 2, 1997)

61. 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

62. Hedging Credit Risk Hedging Instrument Payoff
Change in Portfolio Value
Risky Outcomes

63. Example of Total Return Swap
3-year 8% coupon bond
If default probability increases from 10 to 20%, bond return is 8% % = % (coupon minus loss due to downgrade)

64. Total Return Swap (8-6.5437)% Company A (pay total return) Company B
(pay fixed)
$154,626
$750,000
7.5%
Notional Amount
$10 mm

65. 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

66. 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 risk-management consists of sales of loans
Global market ready for consumer-risk derivatives

67. 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 13