Practical Problems with Building Fixed-Income VAR Models

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Practical Problems with Building Fixed-Income VAR
Models
Rick KlotzManaging Director Global Head of
Market Risk ManagementGreenwich NatWest
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Value At Risk Definition

• The value at risk (VAR) of a portfolio is the
  loss in value in the portfolio that can be
  expected over a given period of time (e.g.,
  1-Day) with a probability not exceeding a given
  number (e.g., 5).
• Probability (Portfolio Loss lt - VAR) K
• K Given Probability

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Visualizing VAR An Example

• A one day VAR of 10mm using a probability of 5
  means that there is a 5 chance that the
  portfolio could lose more than 10mm in the next
  trading day.

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VAR and Capital Requirements For Banks

• Regulatory Capital Market Risk Capital
  Specific Risk Capital Counterparty Risk
  Capital
• Market Risk Capital Max Ave. of 10-Day 99
  VAR x Multiplier, yesterdays
  10-Day 99 VAR

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Back-Testing A VAR Model

• Calculate 1-Day 95 VAR for a (changing)
  portfolio each day for some substantial period of
  time (e.g., 100 Days)
• Compare the P/L on the succeeding trading day
  with the previous close of business days VAR
• Count the number of times the loss exceeds the
  VAR

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The Need For VAR Model Accuracy

• If the VAR is systematically too low, the model
  is underestimating the risk and you tend to have
  too many occasions where the loss in the
  portfolio exceeds the VAR. This can lead to an
  increase in the multiplier for the capital
  calculation.
• If the VAR is systematically too high, the
  model is over estimating the risk and your
  regulatory capital charge will be too high

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Building A VAR Model Estimating the Change in
the Value of the Portfolio

• Estimate the change in the value of the portfolio
  P, as a function of the change in the value
  of risk factors , . . ., (e.g.,
  , may be the change in 1-year U.S. interest
  rates, may be the change in 2-year U.S.
  interest rates, etc.).
• Example

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Building A VAR Model Basic Methodologies

• 1) Variance/Covariance Method - Use historical
  variances and covariances
  
  
  
  of risk factors, , to estimate
  how large 1.645 (for 5) is for the
  
  
  
  distribution of .
  

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Building A VAR Model Basic Methodologies

• 2) Historical Simulation Method - Take an
  historical period, say the last 501 trading days,
  and calculate
• Order from highest to lowest and take
  the 475th as the VAR

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Building A VAR Model Basic Methodologies

• 3) Monte Carlo Simulation Method - Simulate a set
  of 500 (for example) by choosing
  for risk factors ( can be historical or
  implied from options, are usually
  historical). Order the from highest
  to lowest and take the 475th as the VAR.

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Model Specific Issues
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General Challenges for VAR Models

• Obtaining Good Historical Data
• Finding a complete set of risk factors - fixed
  income VAR models generally miss bond specific
  information (e.g., issuer specific risk)
• How to weight historical data to accurately
  determine a 1-day VAR.

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Obtaining Good Historical Data

• Poor Data
• Even actively traded markets can have noisy
  historical data
• Less actively traded markets can pose a
  significant challenge to
  
  
  
  finding clean historical data
• Historical data can be misleading if a market is
  maturing over that
  
  
  
  period
• Missing Data
• It may be difficult to find historical data in
  relatively new (e.g., U.K. Asset
  
  
  
  Backeds) or inactive markets (e.g.,
  inverse I.O.s)
• Asynchronous Data
• The data for risk factors that are traded
  against each other (e.g., Mortgages and
  
  
  
  Treasuries, Futures and Cash
  Securities, etc.) must reflect simultaneous
  closes.

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Finding a Complete Set of Risk Factors

• Fixed Income VAR models generally miss bond (even
  market) specific information
• Coupon to coupon trades
• Basis trades
• Issuer specific risk
• Some market specific risks (e.g., U.K. Asset
  Backeds)
• Some risk factors are mapped to risk factors that
  have adequate historical data but may not be good
  proxies

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How Should Historical Data Be Weighted To
Calculate a 1-Day VAR?

• Regulators require that you use at least one year
  of historical data
• An option trader buying or selling a 1-Day option
  would give very little weight to old data