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Chapter 21

Chapter 21. A Basic Look at Portfolio Management and Capital Market Theory. Objectives. Understand the basic statistical techniques for measuring risk and return Explain how the portfolio effect works to reduce the risk of an individual security

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Chapter 21

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  1. Chapter 21 A Basic Look at Portfolio Management and Capital Market Theory

  2. Objectives • Understand the basic statistical techniques for measuring risk and return • Explain how the portfolio effect works to reduce the risk of an individual security • Discuss the concept of an efficient portfolio

  3. Objectives continued • Explain the importance of the capital asset pricing model • Understand the concept of the beta coefficient • Discuss the required rate of return on an individual stock and how it relates to its beta

  4. A Basic Look at Portfolio Management and Capital Market Theory • Formal Measurement of Risk • Portfolio Effect • Developing and Efficient Portfolio • Capital Asset Pricing Model • Return on an Individual Security • Assumptions of the Capital Asset Pricing Model

  5. A Basic Look at Portfolio Management and Capital Market Theory continued • Appendix 21A: The Correlation Coefficient • Appendix 21B: Least Squares Regression Analysis • Appendix 21 C: Derivation of the Security Market Line (SML) • Appendix 21D: Arbitrage Pricing Theory

  6. Review from Chapter 1Risk & Expected Return • Risk • uncertainty about future outcomes • The greater the dispersion of possible outcomes, the greater the risk • Most investors tend to be risk averse • all things being equal, investors prefer less risk to more risk • investors will increase risk-taking position only if premium for risk is involved • Each investor has different attitude toward risk

  7. Formal Measurement of Risk • Expected Value • Standard Deviation

  8. Formal Measurement of Risk • How to measure risk? • Design probability distribution of anticipated future outcomes • Establish • Probability distribution • Determine expected value • Calculate dispersion around expected value The greater the dispersion the greater the risk

  9. Formal Measurement of Risk Outcomes and associated probabilities are likely to be based on • Economic projections • Past experience • Subjective judgments • Many other variables

  10. Expected Value Each possible outcome Probability of occurrence Expected value x = Click

  11. Expected Value

  12. Standard Deviation σ • The commonly used measure of dispersion is the standard deviation, which is a measure of the spread of the outcomes around the expected value K = Possible outcomes    P = Probability of that outcome based on the state of the economy i = Investment i For stocks,     K = Price appreciation potential plus the dividend yield (total return) = Expected Value — K

  13. Standard Deviation σ

  14. Expected Value and Standard Deviation for Investment j

  15. Standard Deviation σ • Expected value of both investments is 10% • σi= 3.9% • σj= 5.1% • Compare investment i with j • j has a larger dispersion than i • j is riskier than i • Investment j is countercyclical • It does well during a recession • Poorly in a strong economy

  16. Portfolio Effect Expected Value for a 2-Asset Portfolio • Combine investment i andj into one portfolio • Weighted evenly (50-50) • New portfolio’s expected value = 10% • Kp = expected value of portfolio • X values represent weights assigned

  17. Portfolio Effect Expected Value for a 2-Asset Portfolio

  18. Portfolio Effect - σ for a 2-Asset Portfolio σ for combined portfolio (p ) using weighted average σof i & j Portfolio σ would be 4.5% IF • Investor i appears to lose! • Expected value remains at 10% • σ increases from 3.9 to 4.5% WHY? There is one fallacy in the analysis

  19. Portfolio Effect - σ for a 2-Asset Portfolio Standard Deviation of a portfolio is not based on simple weighted average of individual standard deviations!

  20. Investment Outcomes under Different Conditions

  21. Appropriate Standard Deviation Two-Asset Portfolio • σp =Standard deviation of portfolio • ri j = Correlation coefficient * • ri jmeasures joint movement of 2 variables • Value for ri jcan be from -1 to +1 *See Appendix 21A

  22. Correlation Analysis

  23. Xi = 0.5 σi= 3.9 ri j= -0.70 See Appendix 21A Xj = 0.5 σj = 5.1

  24. < σp=1.8 σj=5.1 σi=3.9 < Portfolio standard deviation is less than standard deviation of either investment

  25. Impact of various assumed correlation coefficients for the two investments

  26. Combine 2 investments to reduce risk • Reduced risk (less dispersion) • Expected value constant at 10%

  27. Developing an Efficient Portfolio • Consider large number of portfolios based on • Expected value • Standard deviation • Correlations between the individual securities • A portfolio of 14 to 16 stocks is fully diversified • Portfolio theory developed by Professor Harry Markowitz (1950s)

  28. Assume we have identified the following risk-return possibilities for eight different portfolios Next slide shows graph

  29. Efficient Frontier Line • 4 points out of 8 possibilities lie on the frontier • ACFH delineates the efficient set of portfolios • It is efficient because portfolios on this line dominate all other attainable portfolios ACFH line: efficient frontier because portfolios on it provide best risk-return trade-off

  30. Developing an Efficient Portfolio • Efficient frontier line gives • Maximum return for a given level of risk • Minimum risk for a given level of return • No portfolios exist above the efficient frontier • Portfolios below it are not acceptable alternatives compared to points on the line

  31. Example – Getting Maximum Return for a given Level of Risk Choose F - Same risk Higher return

  32. Example – Getting Minimum Risk for a given Level of Return Choose A - Same return Lower risk

  33. Expanded View of Efficient Frontier

  34. Risk-Return Indifference Curves • Investor’s trade-off between risk & return • Steeper slopes means more risk-averse • Investor B has a steeper slope than investor A • B requires more return (more risk premium) for each additional unit of risk • From point X to Y investor B requires approx. twice as much incremental return as A

  35. Indifference Curves for Investor A

  36. Optimum Portfolio • Match indifference curve with efficient frontier • Highest point is Con efficient frontier • Point of tangency of two curves • Same slope at point • Crepresents same risk-return characteristics C Relate risk-return indifference curves to efficient frontier to determine that point of tangency providing maximum benefits

  37. Capital Asset Pricing Model (CAPM) • Professors Sharpe et al advanced efficient portfoliosto capital asset pricing model • Assets value based on risk characteristics • CAPM takes off where efficient frontier stops • Introduce • New investment outlet • Risk-free asset (RF)

  38. Risk-free (RF) Asset • Has no risk of default • Standard deviation of zero (-0-) • Lowest/safest return • U.S. Treasury bill • U.S. Treasury bond Zero risk CAPM combines risk-free asset & efficient frontier

  39. Basic Diagram of the Capital Market Line

  40. The Capital Market Line and Indifference Curves

  41. Capital Market Line (CML) • RFMZ line capital market line (CML) • Formula for the capital market line See next slide Kp = Expected value of the portfolio σP= Portfolio standard deviation RF= Risk-free rate KM = Market rate of return σM= Market standard deviation

  42. Return on an Individual Security • Beta Coefficient • Systematic and Unsystematic Risk • Security Market Line

  43. Beta Coefficient Measures The market in general A stock’s performance Up Up Relationship Down Down

  44. Example: Total return of stock i for 5 years compared with the market return

  45. Return on an Individual Security Ki = Stock return, dependent variable, Y-axis ai (alpha) = Line intersects vertical axis bi (beta) = Slope of the line KM = Market return, independent variable, X-axis ei = Random error term ai + biKM : Straight line ei = Deviations, nonrecurring movements

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