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Money is better than poverty, if only for
financial reasons,

• Woody Allen

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Market Risk

• The impact of unanticipated changes in market
  conditions (interest rates, exchange rates,
  securities prices) on the market value and
  earnings of the FI.
• Widespread adoption of Value at Risk (VaR)
  methodologies.
• VaR is the minimum losses incurred under adverse
  market conditions. That is, if tomorrow is a
  bad day measured statistically such that only
  1 of all days have even worse conditions.
• First commercially available VaR model was
  RiskMetrics.

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The Concept of VAR

• Example of VAR applied to market risk.
• Market price of equity 80 with estimated daily
  standard deviation 10.
• If tomorrow is a bad day (1 in 100 worst) then
  what is the value at risk?
• If normally distributed, then the cutoff is 2.33?
  below the mean 80 2.33(10) 56.70. 99
  VAR 23.30 Figure 6.1.

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Appendix 1.1A Brief Overview of Key VAR Concepts

• Banks hold capital as a cushion against losses.
  What is the acceptable level of risk?
• Losses change in the assets value over a fixed
  credit horizon period (1 year) due to credit
  events.
• Figure 1.1- normal loss distribution. Figure 1.2
  skewed loss distribution. Mean of distribution
  expected losses (reserves).
• Unexpected Losses (UL) tile VAR. Losses
  exceed UL with probability .
• Definition of credit event
• Default Mode only default
• Mark-to-market all credit upgrades, downgrades
  default.

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FIGURE 1.1
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RiskMetrics

• Daily Earnings at Risk (DEAR)
  (Dollar MV of position) x (Price sensitivity of
  position) x (Potential adverse move)
  (Dollar MV of position) x (Price volatility)
• DEAR calculated for each source of market
  volatility interest rates, security prices,
  exchange rates. RiskMetrics uses a 95th
  percentile VAR. BIS uses a 99th percentile for
  capital requirements.
• The VaR is calculated over an N-day period VAR
  DEAR x ?N
• Finally, aggregate VAR over the entire portfolio
  using correlation coefficients.

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DEAR for Interest Rate Risk

• Use duration model
• DEAR -MD(?R)/(1R)
• FI has a 10m long position in a bond with
  MD12.5 yrs. Exposed to interest rate increases.
  Only a 1 chance that rates will increase more
  than 10 bp per day.
• DEAR -12.5(10m)(.0010) -125,000
• 5 day VaR 125,000 x ?5 279,508

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DEAR for Exchange Rate Risk

• US FI has 100m short position in euros. Exposed
  to increases in euro/ FX rate.
• There is only a 1 chance that the euro will go
  up more than 50 bp per day.
• DEAR (100m) x (.0050) 500,000
• 5 day VaR 500,000 x ?5 1,118,034

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Portfolio DEAR

• For the 2 risk example
• DEAR DEAR2intrate DEAR2FXrate
  2?int,FXDEARintrateDEARFXrate0.5
• Correlation coeff. ?int,FX -.05
• DEAR 125,0002 500,0002
  2(-.05)(125,000)(500,000)0.5 509,289
• Portfolio DEAR is NOT the sum of the individual
  DEARs if correlations are lt 1.
• 5 day Portfolio VAR 509,289 x ?5 1,138,804

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Backtesting Using the Historic Approach

• Actual security distributions are not normal.
  Exhibit skewness and fat tails.
• Use current positions.
• Apply to observed market fluctuations over the
  past 500 days.
• For a 1 VAR, the 5th worst day out of 500. For
  a 5 VAR, the 25th worst day of 500.

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Example of Back Simulation Using a Bond Portfolio

• 50 million bond portfolio with MD4.5 yrs
• 20 days of actual rate changes
• DEAR50m x MD x ?R
• The 5th worst day is day 3 for a
• Loss of 900,000. If this were
• 500 observations, then the
• 1 VaR900,000

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Advantages Disadvantages of Back Simulation

• Non-parametric.
• Uses available data. But insufficient no. of
  observations.
• But, past data may not be indicative of the
  future.
• Monte Carlo simulation generates additional
  observations that conform with historical
  distribution by multiplying the var/covariance
  matrix by a random number generator. Typically
  constructs from 10,000 to 100,000 observations.

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The BIS Standardized Market Risk Framework

• Can use the standardized framework or internal
  models.
• Capital Charge 99th -DEAR x 3 x ?10
• If use internal models, must be approved and
  back-tested. Traffic light system
• If underestimates risk lt 4 days out of 250, then
  green light and multiplier3
• If between 4-9 days of underestimates of risk,
  then yellow light and multiplier gt 3.
• If 10 days or more underestimated risk, then red
  light and multiplier is set at 4.

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BIS Standardized Model for Fixed Income Securities

• Specific Risk Charge measures risk of liquidity
  or credit event. Multiply risk weight x position
  amount.
• Risk weights 0 (US Treasuries), .25-1.6 for
  investment grade (qual) corporate of varying
  maturities, 4-8 for junk (non qual) corporate
  of varying maturities.
• General Market Risk Charge MD x interest rate
  shock expected for each maturity
• Vertical Offsets disallowance factors limiting
  hedging of long and short positions in the same
  maturity bucket. 10 disallowance.
• Horizontal Offsets within Time Zones Zone 1 (1
  mo-12mos) 40 disallowance, Zone 2 (gt1yr-4yrs)
  30 disallowance, Zone 3 (gt4yrs) 30
  disallowance.
• Horizontal Offsets between Time Zones Zone 12
  40 disall., Nonadjacent Zone 1 3 150
  disallowance.

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BIS Standardized Model for Equities

• For each stock the long positions are totalled
  (ex 200m) and the short positions are totalled
  (ex 125m).
• X Factor 4 of sum of long and short positions
  .04 x 325 13 million
• Y Factor 8 of net of long and short positions
  .08 x 75 6 million
• Total Capital Required x factor y factor
• 13 6 19 million for one stock.

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BIS Standardized Model of Foreign Exchange

• Long Currency Positions Totalled
• Short Currency Positions Totalled
• Capital Charge 8 of the higher of the longs or
  the shorts.
• If Long 125m yen 500m euros 625m and
  Short 75m British pound 100m Canadian dollar
  -175m then capital charge .08 x 625m 50
  million.