Risk Measurement and Management

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
  1.8 6.8 12.1

4
Duration as Time Measure

• In 1930s, 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)

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 (1yield 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)

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Duration is an Approximation
Derivative is used in calculating duration
Price (Par1.0)
Actual price change
Change predicted by duration
0
Yield to Maturity
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Properties of Duration

• Can be interpreted as price elasticity or
  weighted average payment period
• Note when c0 that d1 M
• When M is infinite d1 (1i)/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 ManagementDefinitions

• 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

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History of ALM

• After World War II to mid 1960s
• ASSET MANAGEMENT
• Interest rates stable, large post-war holdings of
  government bonds, deposit markets protected
• Mid 1960s to late 1970s
• LIABILITY MANAGEMENT
• Interest rates rising, global financial markets
  developing (e.g. Eurodollars), regulation binding
  (maximum deposit interest rates)

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History of ALM (continued)

• Late 1970s 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 - SL failures, Continental
  Bank and Texas banks, etc.

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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

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Duration of Balance Sheet

• Duration of a number of assets is
• Duration of net worth in a portfolio is

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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?

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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

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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

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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 Hedge
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 elses) 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

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Collars Cap 6, floor 4

• Profit

0
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
0
0
P0
P0
Loss
Loss
Write Put
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Other option developments

• Credit risk options
• Casualty risk options
• Requirements for developing an option
• Interest
• Calculable payoffs
• Enforceable

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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

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Interest Rate SwapPlain vanilla, LIBOR_at_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
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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

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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)

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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)

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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

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Bond and Debt Ratings

• Rating agencies
• Standard and Poors (AAA to D)
• Moodys (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 (SP, 1996)

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Ratings and Defaults
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Risk of Fixed Incomes
Probability
Maximum valueF
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 PDLGDEAD
• Investors in debt securities will be concerned
  about all these elements in managing their risks

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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.)

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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
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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

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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

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Estimated Distance to Default
Market value to default point 40.0
56.6
20.2
12.9
TMV
CLLTD
CL
Default point (estimated as midpoint) 16.6
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Distance to Default 12-31-01

• Total Value of Assets (from Capital Structure
  and Financial Statements) E LTD CL
  TA33.9 8.1 9.7 51.7
• Book value of LTD and CL 8.4 and 9.7Midpoint
  estimate of default point 13.9Std Dev 16.4
  51.7 8.48

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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
  Moodys experience)

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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

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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

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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)

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Credit Risk as Rating Changes

• Increased credit risk Default
  CCC B BB
• Same credit risk (BBB) BBB
• A AA
• AAA
• Less credit risk

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Rating Migrations (BBB rating)
Source Standard Poors
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Two Bond Rating Migrations
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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
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Loss Given Default
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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)
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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

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Credit Portfolio Risk
One Asset
Many Assets
Frequency
Frequency
0
0
Return
Return
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Incremental Risk

• Introduction to CreditMetrics provides good
  examples (in Section 5)
• Importance portfolio risk is the marginal risk
• Marginal risk considers portfoliorisk
  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

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Hedging Credit Risk
Hedging Instrument Payoff
Change in Portfolio Value
0
Risky Outcomes
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Example of Total Return Swap

• 3-year 8 coupon bond
• If default probability increases from 10 to 20,
  bond return is 8 - 6.4537 1.5463 (coupon
  minus loss due to downgrade)

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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
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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

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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