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Derivatives

This lecture explores the principles of portfolio diversification, emphasizing the importance of correlation in managing risk across multiple assets. It provides an example illustrating how to calculate the portfolio's standard deviation when combining stocks, focusing on ABC Corp and Big Corp to demonstrate weighted averages versus real standard deviation. Additionally, the session introduces Value at Risk (VaR) as a metric for assessing potential losses in portfolio investments, detailing calculations for IBM and AT&T stocks over a specified time frame with a 99% confidence level.

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Derivatives

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  1. Derivatives Lecture 24

  2. Diversification

  3. Portfolio Diversification Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp 28 60% 15% Big Corp 42 40% 21% Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Additive Standard Deviation (common sense): = 28 (60%) + 42 (40%) = 33.6 WRONG Real Standard Deviation: = (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4) = 28.1 CORRECT

  4. Value at Risk (VaR) Value at Risk = VaR Newer term Attempts to measure risk Risk defined as potential loss Limited use to risk managers Factors Asset value Daily Volatility Days Confidence interval

  5. Value at Risk (VaR) Standard Measurements 10 days 99% confidence interval VaR

  6. Value at Risk (VaR) Example You own a $10 mil portfolio of IBM stock. IBM has a daily volatility of 2%. Calculate the VaR over a 10 day time period at a 99% confidence level.

  7. Value at Risk (VaR) Example You also own $5 mil of AT&T, with a daily volatility of 1%. AT&T and IBM have a .7 correlation coefficient. What is the VaR of AT&T and the combined portfolio?

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