Market Risk

1
Chapter 10

• Market Risk

2
Overview

• 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

3
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 MT Bank
• LP Gas futures 2007

4
Implications

• Emphasizes importance of
• Measurement of exposure
• Control mechanisms for direct market riskand
  employee created risks
• Hedging mechanisms

5
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
  benchmark.

6
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 risks
• Allowances for use of internal models to
  calculate capital requirements

7
Calculating Market Risk Exposure

• Generally concerned with estimated potential loss
  under adverse circumstances.
• Three major approaches of measurement
• JPM RiskMetrics (or variance/covariance approach)
• Historic or Back Simulation
• Monte Carlo Simulation

8
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/(1R)
• Modified duration MacAulay duration/(1R)

9
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 sufficient).
• Assuming normality, 90 of the time the
  disturbance will be within 1.65 standard
  deviations of the mean.

10
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.

11
Confidence Intervals Example

• Price volatility (-MD) ? (Potential adverse
  change in yield)
• (-6.527) ? (0.00165) -1.077
• DEAR Market value of position ? (Price
  volatility)
• (1,000,000) ? (.01077) 10,770

12
Confidence Intervals Example

• To calculate the potential loss for more than one
  day
• Market value at risk (VARN) DEAR ?N
• Example
• For a five-day period,
• VAR5 10,770 ?5 24,082

13
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.

14
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 DEARc1/2

15
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.

16
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.

17
Estimation of VAR Example

• Convert todays FX positions into dollar
  equivalents at todays 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.

18
Weaknesses

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

19
Monte Carlo Simulation

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

20
Regulatory Models

• BIS (including Federal Reserve) approach
• Market risk may be calculated using standard BIS
  model.
• 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.

21
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

22
Web Resources

• For information on the BIS framework, visit
• Bank for International Settlement www.bis.org
• Federal Reserve Bank www.federalreserve.gov

23
Large Banks BIS versus RiskMetrics

• In calculating DEAR, adverse change in rates
  defined as 99th percentile (rather than 95th
  under RiskMetrics)
• Minimum holding period is 10 days (means that
  RiskMetrics daily DEAR multiplied by ?10).
• Capital charge will be higher of
• Previous days 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.

24
Pertinent Websites

• American Banker www.americanbanker.com
• Bank of America www.bankofamerica.com
• Bank for International Settlements
  www.bis.org
• Federal Reserve www.federalreserve.gov
• J.P.Morgan/Chase www.jpmorganchase.com
• RiskMetrics www.riskmetrics.com

25
Chapter 11

• Credit Risk, Individual Loan Risk

26
Overview

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

27
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

28
Web Resources

• For further information on credit ratings visit
• Moodys www.moodys.com
• Standard Poors www.standardandpoors.com

29
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
  Korea
• New types of credit risk related to loan
  guarantees and off-balance-sheet activities.
• Increased emphasis on credit risk evaluation.

30
Types of Loans

• CI loans secured and unsecured
• Syndication
• Spot loans, Loan commitments
• Decline in CI 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.

31
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, ATT
• Risks affected by competitive conditions and
  usury ceilings

32
Other loans

• Other loans include
• Farm loans
• Other banks
• Nonbank FIs
• Broker margin loans
• Foreign banks and sovereign governments
• State and local governments

33
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(1k)-1 where p equals
  probability of repayment
• Note that realized and expected return may not be
  equal.

34
Lending Rates and Rationing

• At retail Usually a simple accept/reject
  decision rather than adjustments to the rate.
• Credit rationing.
• If accepted, customers sorted by loan quantity.
• For mortgages, discrimination via loan to value
  rather than adjusting rates
• At wholesale
• Use both quantity and pricing adjustments.

35
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 collateral.
• Market specific factors include business cycle
  and interest rate levels.

36
Credit Scoring Models

• Linear probability models
• Zi
• Statistically unsound since the Zs obtained are
  not probabilities at all.
• Since superior statistical techniques are
  readily available, little justification for
  employing linear probability models.

37
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 interval.
• 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

38
Altmans Linear Discriminant Model

• Z1.2X1 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 debt.
• X5 Sales/total assets.

39
Linear Discriminant Model

• Problems
• Only considers two extreme cases (default/no
  default).
• 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.

40
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 rates.
• The loan can be assessed using the inferred
  probabilities from comparable quality bonds.

41
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

42
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/(1R)) where DR is an
  estimate of the worst change in credit risk
  premiums for the loan class over the past year.
• RAROC one-year income on loan/DLN

43
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 widely.

44
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)lnN(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

45
CreditMetrics

• 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 borrowers credit rating (ii) Rating
  transition matrix (iii) Recovery rates on
  defaulted loans (iv) Yield spreads.

46
Credit Risk

• Developed by Credit Suisse Financial Products.
• Based on insurance literature
• Losses reflect frequency of event and severity of
  loss.
• Loan default is random.
• Loan default probabilities are independent.
• Appropriate for large portfolios of small loans.
• Modeled by a Poisson distribution.

47
Pertinent Websites

• Federal Reserve Bank www.federalreserve.gov
• OCC www.occ.treas.gov
• KMV www.kmv.com
• Card Source One www.cardsourceone.com
• FDIC www.fdic.gov
• Robert Morris Assoc. www.rmahq.org

48
Pertinent Websites

• Fed. Reserve Bank St. Louis www.stls.frb.org
• Federal Housing Finance Board www.fhfb.gov
• Moodys www.moodys.com
• Standard Poors www.standardandpoors.com