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
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
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
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?
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
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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## This document was uploaded on 11/04/2011 for the course ECON 421 at CUNY York.

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

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