Saunders Cornett Chapter 10

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					Chapter 10

    Market Risk

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   This chapter discusses the nature of market
    risk and appropriate measures
    ◦   Dollar exposure
    ◦   RiskMetrics
    ◦   Historic or back simulation
    ◦   Monte Carlo simulation
    ◦   Links between market risk and capital requirements

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Trading Risks

   Trading exposes banks to risks
    ◦ 1995 Barings Bank
    ◦ 1996 Sumitomo Corp. lost $2.6 billion in
      commodity futures trading
    ◦ 1997 market volatility in Eastern Europe and Asia
    ◦ 1998 continuation with Russian bonds
    ◦ AllFirst/ Allied Irish $691 million loss
      Partly preventable with software
      Rusnak currently serving 7 ½ year sentence for fraud
      Allfirst sold to Buffalo based M&T Bank
   LP Gas futures – 2007

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   Emphasizes importance of:

    ◦ Measurement of exposure
    ◦ Control mechanisms for direct market risk—and
      employee created risks
    ◦ Hedging mechanisms

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Market Risk
   Market risk is the uncertainty resulting
    from changes in market prices .

    ◦ Affected by other risks such as interest rate
      risk and FX risk
    ◦ It can be measured over periods as short as
      one day.
    ◦ Usually measured in terms of dollar exposure
      amount or as a relative amount against some
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Market Risk Measurement
   Important in terms of:
    ◦   Management information
    ◦   Setting limits
    ◦   Resource allocation (risk/return tradeoff)
    ◦   Performance evaluation
    ◦   Regulation
         BIS and Fed regulate market risk via capital
          requirements leading to potential for overpricing of
         Allowances for use of internal models to calculate
          capital requirements

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Calculating Market Risk Exposure

 Generally concerned with estimated
  potential loss under adverse
 Three major approaches of measurement
    ◦ JPM RiskMetrics (or variance/covariance
    ◦ Historic or Back Simulation
    ◦ Monte Carlo Simulation

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JP Morgan RiskMetrics Model
 ◦ Idea is to determine the daily earnings at risk
   = dollar value of position × price sensitivity ×
   potential adverse move in yield or,
 DEAR = Dollar market value of position ×
   Price volatility.
 ◦ Can be stated as (-MD) × adverse daily yield
   move where,
     MD = D/(1+R)
 Modified duration = MacAulay duration/(1+R)

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Confidence Intervals
 ◦ If we assume that changes in the yield are
   normally distributed, we can construct
   confidence intervals around the projected
   DEAR. (Other distributions can be
   accommodated but normal is generally
 ◦ Assuming normality, 90% of the time the
   disturbance will be within 1.65 standard
   deviations of the mean.

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      Confidence Intervals: Example
◦ Suppose that we are long in 7-year zero-coupon bonds
  and we define “bad” yield changes such that there is
  only 5% chance of the yield change being exceeded in
  either direction. Assuming normality, 90% of the time
  yield changes will be within 1.65 standard deviations of
  the mean. If the standard deviation is 10 basis points,
  this corresponds to 16.5 basis points. Concern is that
  yields will rise. Probability of yield increases greater
  than 16.5 basis points is 5%.

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Confidence Intervals: Example
Price volatility = (-MD)  (Potential
 adverse change in yield)
 = (-6.527)  (0.00165) = -1.077%
DEAR = Market value of position  (Price
     = ($1,000,000)  (.01077) = $10,770

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Confidence Intervals: Example
 To calculate the potential loss for more
  than one day:
  Market value at risk (VARN) = DEAR ×
 Example:
     For a five-day period,
     VAR5 = $10,770 × 5 = $24,082

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Foreign Exchange & Equities
 In the case of Foreign Exchange, DEAR is
  computed in the same fashion we
  employed for interest rate risk.
 For equities, if the portfolio is well
  diversified then
  DEAR = dollar value of position × stock
  market return volatility where the market
  return volatility is taken as 1.65 sM.

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      Aggregating DEAR Estimates
 Cannot simply sum up individual DEARs.
 In order to aggregate the DEARs from individual
  exposures we require the correlation matrix.
 Three-asset case:
  DEAR portfolio = [DEARa2 + DEARb2 + DEARc2 +
  2rab × DEARa × DEARb + 2rac × DEARa ×
  DEARc + 2rbc × DEARb × DEARc]1/2

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Historic or Back Simulation
     Advantages:
      ◦ Simplicity
      ◦ Does not require normal distribution of returns
        (which is a critical assumption for RiskMetrics)
      ◦ Does not need correlations or standard
        deviations of individual asset returns.

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Historic or Back Simulation
 Basic idea: Revalue portfolio based on
  actual prices (returns) on the assets that
  existed yesterday, the day before, etc.
  (usually previous 500 days).
 Then calculate 5% worst-case (25th lowest
  value of 500 days) outcomes.
 Only 5% of the outcomes were lower.

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         Estimation of VAR: Example

 Convert today’s FX positions into dollar
  equivalents at today’s FX rates.
 Measure sensitivity of each position
    ◦ Calculate its delta.
   Measure risk
    ◦ Actual percentage changes in FX rates for each of past
      500 days.
   Rank days by risk from worst to best.

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 Disadvantage: 500 observations is not
  very many from statistical standpoint.
 Increasing number of observations by
  going back further in time is not
 Could weight recent observations more
  heavily and go further back.

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Monte Carlo Simulation
   To overcome problem of limited number
    of observations, synthesize additional
    ◦ Perhaps 10,000 real and synthetic
   Employ historic covariance matrix and
    random number generator to synthesize
    ◦ Objective is to replicate the distribution of
      observed outcomes with synthetic data.

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        Regulatory Models
   BIS (including Federal Reserve) approach:
    ◦ Market risk may be calculated using standard BIS
      Specific risk charge.
      General market risk charge.
      Offsets.
    ◦ Subject to regulatory permission, large banks may
      be allowed to use their internal models as the basis
      for determining capital requirements.

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BIS Model
 ◦ Specific risk charge:
   Risk weights × absolute dollar values of long and
    short positions
 ◦ General market risk charge:
   reflect modified durations  expected interest rate
    shocks for each maturity
 ◦ Vertical offsets:
   Adjust for basis risk
 ◦ Horizontal offsets within/between time zones

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Web Resources
 For information on the BIS framework,
Bank for International Settlement
Federal Reserve Bank

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Large Banks: BIS versus RiskMetrics
 ◦ In calculating DEAR, adverse change in rates defined
   as 99th percentile (rather than 95th under
 ◦ Minimum holding period is 10 days (means that
   RiskMetrics’ daily DEAR multiplied by 10)*.
 ◦ Capital charge will be higher of:
   Previous day’s VAR (or DEAR  10)
   Average Daily VAR over previous 60 days times a
    multiplication factor  3.

  *Proposal to change to minimum period of 5 days under Basel
    II, end of 2006.
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Pertinent Websites
American Banker
Bank of America
Bank for International Settlements
Federal Reserve

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Chapter 11

   Credit Risk, Individual Loan Risk

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   This chapter discusses types of loans, and the
    analysis and measurement of credit risk on
    individual loans. This is important for purposes
    ◦ Pricing loans and bonds
    ◦ Setting limits on credit risk exposure

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     Credit Quality Problems
  Problems with junk bonds, LDC loans,
  residential and farm mortgage loans.
 More recently, credit card and auto loans.
 Crises in Asian countries such as Korea,
  Indonesia, Thailand, and Malaysia.
 Default of one major borrower can have
  significant impact on value and reputation of
  many FIs
 Emphasizes importance of managing credit risk

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Web Resources
   For further information on credit ratings
    Standard & Poors

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Credit Quality Problems
   Over the early to mid 1990s, improvements in
    NPLs for large banks and overall credit quality.
   Late 1990s concern over growth in low quality
    auto loans and credit cards, decline in quality of
    lending standards.
   Exposure to Enron.
   Late 1990s and early 2000s: telecom companies,
    tech companies, Argentina, Brazil, Russia, South
   New types of credit risk related to loan
    guarantees and off-balance-sheet activities.
   Increased emphasis on credit risk evaluation.

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         Types of Loans:
   C&I loans: secured and unsecured
    ◦ Syndication
    ◦ Spot loans, Loan commitments
    ◦ Decline in C&I loans originated by commercial banks
      and growth in commercial paper market.
    ◦ Downgrades of Ford, General Motors and Tyco
   RE loans: primarily mortgages
    ◦ Fixed-rate, ARM
    ◦ Mortgages can be subject to default risk when loan-to-
      value declines.

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        Consumer loans
   Individual (consumer) loans: personal, auto,
    credit card.
    ◦ Nonrevolving loans
      Automobile, mobile home, personal loans
    ◦ Growth in credit card debt
      Visa, MasterCard
      Proprietary cards such as Sears, AT&T
    ◦ Risks affected by competitive conditions and usury

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Other loans
   Other loans include:
    ◦   Farm loans
    ◦   Other banks
    ◦   Nonbank FIs
    ◦   Broker margin loans
    ◦   Foreign banks and sovereign governments
    ◦   State and local governments

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Return on a Loan:
 Factors: interest payments, fees, credit risk
  premium, collateral, other requirements
  such as compensating balances and
  reserve requirements.
 Return = inflow/outflow
     k = (f + (L + M ))/(1-[b(1-R)])
 Expected return: E(r) = p(1+k)-1 where p
  equals probability of repayment
 Note that realized and expected return may
  not be equal.
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Lending Rates and Rationing
   At retail: Usually a simple accept/reject
    decision rather than adjustments to the
    ◦ Credit rationing.
    ◦ If accepted, customers sorted by loan
    ◦ For mortgages, discrimination via loan to
      value rather than adjusting rates
   At wholesale:
    ◦ Use both quantity and pricing adjustments.

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Measuring Credit Risk
   Availability, quality and cost of information
    are critical factors in credit risk assessment
    ◦ Facilitated by technology and information
 Qualitative models: borrower specific factors
  are considered as well as market or
  systematic factors.
 Specific factors include: reputation, leverage,
  volatility of earnings, covenants and
 Market specific factors include: business
  cycle and interest rate levels.

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          Credit Scoring Models
   Linear probability models:
    Zi =   j X i, j  error
            j 1

    ◦ Statistically unsound since the Z’s obtained are not
      probabilities at all.
    ◦ *Since superior statistical techniques are readily
      available, little justification for employing linear
      probability models.

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Other Credit Scoring Models
 Logit models: overcome weakness of the
  linear probability models using a
  transformation (logistic function) that
  restricts the probabilities to the zero-one
 Other alternatives include Probit and other
  variants with nonlinear indicator functions.
 Quality of credit scoring models has
  improved providing positive impact on
  controlling write-offs and default

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Altman’s Linear Discriminant Model:

          Z=1.2X1+ 1.4X2 +3.3X3 + 0.6X4 + 1.0X5
           Critical value of Z = 1.81.
           ◦ X1 = Working capital/total assets.
           ◦ X2 = Retained earnings/total assets.
           ◦ X3 = EBIT/total assets.
           ◦ X4 = Market value equity/ book value LT
           ◦ X5 = Sales/total assets.

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Linear Discriminant Model
   Problems:
    ◦ Only considers two extreme cases (default/no
    ◦ Weights need not be stationary over time.
    ◦ Ignores hard to quantify factors including
      business cycle effects.
    ◦ Database of defaulted loans is not available to
      benchmark the model.

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Term Structure Based Methods
 ◦ If we know the risk premium we can infer the
   probability of default. Expected return equals
   risk free rate after accounting for probability
   of default.
      p (1+ k) = 1+ i
 ◦ May be generalized to loans with any maturity
   or to adjust for varying default recovery
 ◦ The loan can be assessed using the inferred
   probabilities from comparable quality bonds.

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Mortality Rate Models
 ◦ Similar to the process employed by insurance
   companies to price policies. The probability of
   default is estimated from past data on defaults.
 ◦ Marginal Mortality Rates:
   MMR1 = (Value Grade B default in year 1)
       (Value Grade B outstanding yr.1)
 MMR2 = (Value Grade B default in year 2)
   (Value Grade B outstanding yr.2)
 ◦ Many of the problems associated with credit
   scoring models such as sensitivity to the period
   chosen to calculate the MMRs

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RAROC Models
 ◦ Risk adjusted return on capital. This is one of
   the more widely used models.
 ◦ Incorporates duration approach to estimate
   worst case loss in value of the loan:
 ◦ DLN = -DLN x LN x (DR/(1+R)) where DR is
   an estimate of the worst change in credit risk
   premiums for the loan class over the past
 ◦ RAROC = one-year income on loan/DLN

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Option Models:
 ◦ Employ option pricing methods to evaluate
   the option to default.
 ◦ Used by many of the largest banks to monitor
   credit risk.
 ◦ KMV Corporation markets this model quite

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Applying Option Valuation Model
 Merton showed value of a risky loan
  F(t) = Be-it[(1/d)N(h1) +N(h2)]
 Written as a yield spread
  k(t) - i = (-1/t)ln[N(h2) +(1/d)N(h1)]
where k(t) = Required yield on risky debt
ln = Natural logarithm
i = Risk-free rate on debt of equivalent maturity.
t  remaining time to maturity

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 “If next year is a bad year, how much will I
  lose on my loans and loan portfolio?”
      VAR = P × 1.65 × s
 Neither P, nor s observed.
Calculated using:
    ◦ (i)Data on borrower’s credit rating; (ii) Rating
      transition matrix; (iii) Recovery rates on
      defaulted loans; (iv) Yield spreads.

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* Credit Risk+
   Developed by Credit Suisse Financial
    ◦ Based on insurance literature:
      Losses reflect frequency of event and severity of
    ◦ Loan default is random.
    ◦ Loan default probabilities are independent.
 Appropriate for large portfolios of small
 Modeled by a Poisson distribution.

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Pertinent Websites
Federal Reserve Bank
Card Source One
Robert Morris Assoc.

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Pertinent Websites
Fed. Reserve Bank St. Louis
Federal Housing Finance Board
Standard & Poors

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