Value at Risk

Value at Risk - Risk Management Value at Risk Copyright...

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Copyright © 1996-2006 Investment Analytics Slide: 1 Value at Risk Risk Management Value at Risk Copyright © 1996-2006 Investment Analytics
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Copyright © 1996-2006 Investment Analytics Slide: 2 Value at Risk Agenda ¾ Statistical Distributions ¾ Value at Risk ¾ Factors affecting VAR ¾ VAR & Derivatives ¾ The Delta-Normal Model ¾ Model testing ¾ Other VAR models
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Copyright © 1996-2006 Investment Analytics Slide: 3 Value at Risk Confidence Intervals ¾ You can use normal probability tables to find: 9 The probability of achieving a given minimum return ¾ Confidence Intervals 9 Turn this idea round 9 Given a specified probability, what’s the minimum return? ¾ Example: 90% confidence interval What minimum rate of return can I expect to achieve 9 times out of 10?
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Copyright © 1996-2006 Investment Analytics Slide: 4 Value at Risk Confidence Intervals 10% 90% of returns lie above this value Probability
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Copyright © 1996-2006 Investment Analytics Slide: 5 Value at Risk Confidence Factor 90% of returns lie above this value Probability CF = 1.28 90%
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Copyright © 1996-2006 Investment Analytics Slide: 6 Value at Risk Value at Risk ¾ Measures the maximum expected loss For a given holding period For a given confidence level 9 chosen by the portfolio manager ¾ Example Portfolio with daily VAR of $1MM with 99% confidence 9 There is a 1% chance that the portfolio will lose more than $1MM in the next 24 hours
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Copyright © 1996-2006 Investment Analytics Slide: 7 Value at Risk Value at Risk Market Value Probability VAR = $1MM 99%
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Copyright © 1996-2006 Investment Analytics Slide: 8 Value at Risk Using VAR for Simple Risk Comparisons ¾ VAR gives a simple yardstick: Portfolio A: VAR $30MM over 30 days, 99% conf. Portfolio B: VAR $10MM over 30 days, 99% conf. If both A & B have same value, which is riskier?
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Copyright © 1996-2006 Investment Analytics Slide: 9 Value at Risk VAR Question ¾ A VAR of $1MM, with 87% conf means: Portfolio is expected to return at least 13%? Portfolio manager is 87% sure he will earn less than $1MM? Portfolio manager is 87% sure he will not lose more than $1MM? There is a 13% chance that the portfolio will earn more than $1MM?
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Copyright © 1996-2006 Investment Analytics Slide: 10 Value at Risk Calculating VAR ¾ Portfolio VAR VAR = Market Value x Confidence Factor x Volatility ¾ Example: Portfolio value $10MM Daily volatility 5% Confidence level = 88% 9 CF = 1.17 DAILY VAR = $10MM x 1.17 x 0.05 = $585,000 9 Interpretation: there is a 12% chance the portfolio will lose more than $585,000 in a day
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Copyright © 1996-2006 Investment Analytics Slide: 11 Value at Risk Portfolio Volatility & VAR ¾ Use historical correlations to estimate portfolio volatility RiskMetrics (JP Morgan) 9 provides estimates of volatilities and correlations of returns (daily, monthly) using 75 day data ] [ 2 2 J I IJ J IJ I I I i p σ ρ ω ∑∑ + =
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Copyright © 1996-2006 Investment Analytics Slide: 12 Value at Risk Factors Affecting VAR ¾ VAR reflects 3 key aspects of Risk Mgt.
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Value at Risk - Risk Management Value at Risk Copyright...

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