Bradyn BreonDrish breonhaas'berkeley'edu

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MFE 230HSection 2

• Bradyn Breon-Drishbreon_at_haas.berkeley.edu
• Aug. 21, 2007

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Administrative details

• Sections
• Tue. 400-530, MFE lab?
• Fri. choices
• Morning (1000-1130)
• Midday (1130-100)
• Early Afternoon (100-230)

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Orange County Case

• VAR using yield volatility
• Computing probabilities
• Parametric
• Empirical (nonparametric)
• Conditional volatility
• Hedging

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Simplified example

• 1bil portfolio
• D5
• Leverage1.5
• 10-year T-note yields (1/62-12/06)

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Portfolio VAR

• Delta-normal method
• Compute volatility of yield changes
• Use normal distribution along with duration
  approximation
• Historical-simulation method
• Find empirical 0.05 percentile
• Use empirical returns along with duration
  approximation

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Computing probabilities

• In March 1994, yields increased by 62bps
• What is the probability of an increaese this
  large or larger?
• NORMDIST(0.0062,mean,volatility,1) gives the
  cumulative probability of change lt 0.0062

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Conditional volatility

• RiskMetrics general formula
• Vardy(t)kVardy(t-1) (1-k)dy(t-1)2
• K0.97 for monthly data
• Use unconditional variance for t0

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Exceptions test

• Compute normal distribution VAR(dy) each month
  using the conditional volatilities
• Count number of exceptions (x)
• To test, can use

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Hedging

• Can use
• T-bond futures
• Interest rate swaps
• Interest rate caps and/or floors
• Describe positions qualitatively (long vs. short)
• Compute number of futures contracts

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Hedging with futures

• Dollar duration of our portfolio
• 1bil 2 1.5 3bil
• Effective duration of N futures contracts
• N futures price duration

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Questions?