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Understanding Risk Aversion in Portfolio Management: Key Concepts and Theories

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This chapter delves into the principles of risk aversion in portfolio management, focusing on the decision-making processes investors undergo when considering stock purchases. Learn about the Markowitz Portfolio Theory, which emphasizes diversification and the variance of returns, illustrating how investors maximize expected utility and assess risk. Discover alternative risk measures including standard deviation and covariance, along with the concepts of correlation and the efficient frontier. This comprehensive overview equips you with the tools to analyze and optimize investment portfolios effectively.

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Understanding Risk Aversion in Portfolio Management: Key Concepts and Theories

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  1. CHAPTER 7 PortfolioManagement

  2. Whatarewegoingtolearn in thischapter?

  3. Risk Aversion • Youhavetwostocksyouconsiderforpurchase; whichone do youpick? Why? • 50 TL certain – 100/0 coinflipexample • Risk averse • Risk neutral • Risk seeking • Mainassumptionabout risk aversion

  4. MarkowitzPortfolioTheory • Variance of returnsanddiversification • The Markowitz model isbased on several assumptions regarding investor behavior: 1. Investors consider each investment alternative as being represented by a probability distributionof expected returns over some holding period. 2. Investors maximize one-period expected utility, and their utility curves demonstrate diminishingmarginalutility of wealth. 3. Investors estimate the risk of the portfolio on the basis of the variability of expectedreturns. 4. Investors base decisions solely on expected return and risk. 5. For a given risk level, investors prefer higher returns to lower returns. Similarly, for agiven level of expected return, investors prefer less risk to more risk.

  5. Alternative Risk Measures • Variance & standard deviation of expectedreturns • Range of returns • Semivariance

  6. ExpectedRates of Return • The expected rate of return for an individual investment • What is theexpectedreturnfor Tortu?

  7. ExpectedRates of Return • The expected rate of return for a portfolio of riskyassets • What is theexpectedreturnfor a portfolio of Sütaş, Arçelik, Merko, Penguan Gıda?

  8. Risk • Standard deviation of returns for an individualinvestment • What is thestandarddeviationfor Tortu?

  9. Risk • Standard deviation of returns for a portfolio of riskyassets • Covariance • Correlation

  10. Covariance • What is Covariance? • Prices vs. returns? • A positivecovariance means ……. • A negative covariance indicates …… • The magnitude of the covariance depends on ……

  11. Covariance • Tukaş & Ünye Çimento: E(R)=?

  12. Covariance

  13. Covariance

  14. Covariance • Although the rates of return for the two stocks moved together duringsome months, in other months they moved in opposite directions. The covariance statistic providesan absolute measure of how they moved together over time. • Formulation • Formulationfor 12 monthlyreturns of 2 assets • Whenwouldcovariation be positive/negative?

  15. Covariance • Tukaş & Ünye Çimento: Covariance?

  16. Covariance & Correlation • Whatdoesthecovariancefiguremean? • Standardization • Correlation • Correlationboundariesandtheinterpretation

  17. Correlation • Tukaş & Ünye Çimento: Correlation?

  18. Standard Deviation of a Portfolio • Whatdoesthestandarddeviation of a portfolioindicate? • Formalformulation

  19. Standard Deviation of a Portfolio • EXAMPLE: E(Ra) = 0.20 Stn. Dev. = 0.10 Wa = 0.50 E(Rb) = 0.20 Stn. Dev. = 0.10 Wb = 0.50 Correlation = 0.10 Risk = ? • Thelessonlearnt?

  20. Standard Deviation of a Portfolio • EXAMPLE: E(Ra) = 0.20 Stn. Dev. = 0.10 Wa = 0.50 E(Rb) = 0.20 Stn. Dev. = 0.10 Wb = 0.50 Correlation = 0.05 Risk = ? • Thelessonlearnt?

  21. Standard Deviation of a Portfolio • EXAMPLE: E(Ra) = 0.20 Stn. Dev. = 0.10 Wa = 0.50 E(Rb) = 0.20 Stn. Dev. = 0.10 Wb = 0.50 • IfCorrelation = 0.00 Stn. Dev. ? • IfCorrelation = -0.50 Stn. Dev. ? • IfCorrelation = 0.00 Stn. Dev. ?

  22. Standard Deviation of a Portfolio • EXAMPLE: IfCorrelation is 1.00; what is the risk of theportfolio?

  23. Standard Deviation of a Portfolio • Whatifthecorrelationswere: +0.50 0.00 -0.50 -1.00

  24. ThreeAssetPortfolio • Correlations: r S,B = 0.25 r S,C = -0.08 r B,C = 0.15 Expectedreturn = ? Standard deviation = ?

  25. TheEfficientFrontier • If we examined different two-asset combinations and derived the curves assuming all the possibleweights, we would have a graph like:

  26. TheEfficientFrontier

  27. TheEfficientFrontier • Efficient frontier • Comparisons of portfolios A, B and C • As an investor, you will target a point along the efficient frontier based on your utility functionand your attitude toward risk. • No portfolio on the efficient frontier can dominate any otherportfolio on the efficient frontier. All of these portfolios have different return and risk measures,with expected rates of return that increase with higher risk.

  28. TheEfficientFrontier

  29. EfficientFrontier & InvestorUtility • Slope of the efficient frontier • An individual investor’s utility curves • Two investors will choose the same portfolio from the efficient set only if their utility curvesareidentical. • The optimal portfolio

  30. EfficientFrontier & InvestorUtility

  31. END OF CHAPTER

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