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Understanding Value at Risk (VaR): Measure, Historical Simulation, Model-Building Approach, Linear Model

Learn about the concept of Value at Risk (VaR) in financial asset portfolios, including calculation methods like Historical Simulation and the Linear Model. Explore confidence intervals, time horizons, and advantages of VaR in risk assessment.

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Understanding Value at Risk (VaR): Measure, Historical Simulation, Model-Building Approach, Linear Model

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  1. Chapter 20Value at Riskpart 1 資管所 陳竑廷

  2. Agenda 20.1 The VaR measure 20.2 Historical simulation 20.3 Model-building approach 20.4 Linear model

  3. 20.1 The VaR measure Value at Risk • Provide a single number summarizing the total risk in a portfolio of financial assets. • We are X percent certain that we will not lose more than V dollars in the next N days.

  4. Example When N = 5 , and X = 97, VaR is the third percentile of the distribution of change in the value of the portfolio over the next 5 days. VaR ( 100-X ) %

  5. Advantages of VaR • It captures an important aspect of risk in a single number • It is easy to understand • It asks the simple question: “How bad can things get?”

  6. Parameters • We are X percent certain that we will not lose more than V dollars in the next N days. • X • The confidence interval • N • The time horizon measured in days

  7. Time Horizon • In practice , set N =1, because there’s not enough data. • The usual assumption:

  8. Example • Instead of calculating the 10-day, 99% VaR directly analysts usually calculate a 1-day 99% VaR and assume

  9. 20.2 Historical Simulation • One of the popular way of estimate VaR • Use past data in a vary direct way

  10. When N = 1 , X = 99 • Step1 • Identify the market variables affecting the portfolio • Step2 • Collect data on the movements in these market variables over the most recent 500 days • Provide 500 alternative scenarios for what can happen between today and tomorrow

  11. The fifth-worst daily change is the first percentile of the distribution

  12. 20.3 The Model-Building Approach • Daily Volatilities • In option pricing we measure volatility “per year” • In VaR calculations we measure volatility “per day”

  13. Single Asset • Portfolio A consisting of $10 million in Microsoft • Standard deviation of the return is 2% (daily) • N = 10 , X = 99 • N(-2.33) = 0.01 • 1-day 99%： 2.33 x ( 10,000,000 x 2% ) = $ 466,000 • 10-day 99%：

  14. Two Asset • Portfolio B consisting of $10 million in Microsoft and $5 million in AT&T 1-day 99%： 10-day 99% ：

  15. 20.4 The Linear Model We assume • The daily change in the value of a portfolio is linearly related to the daily returns from market variables • The returns from the market variables are normally distributed

  16. Linear Model and Options define define

  17. As an approximation • Similarly when there are many underlying market variables where di is the delta of the portfolio with respect to the ith asset

  18. Example • Consider an investment in options on Microsoft and AT&T. Suppose that SMS = 120 , SAT&T = 30 , dMS = 1000 , and dAT&T = 1000

  19. Thank you.

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