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Chapter 20 Value at Risk part 1

Chapter 20 Value at Risk part 1. 資管所 陳竑廷. Agenda. 20.1 The VaR measure 20.2 Historical simulation 20.3 Model-building approach 20.4 Linear model. 20.1 The VaR measure. Value at Risk Provide a single number summarizing the total risk in a portfolio of financial assets.

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Chapter 20 Value at Risk part 1

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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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