McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 21 A Basic Look at Portfolio Management and Capital Market Theory Theory

21-2 Objectives Understand the basic statistical techniques for measuring risk and return Understand the basic statistical techniques for measuring risk and return Explain how the portfolio effect works to reduce the risk of an individual security Explain how the portfolio effect works to reduce the risk of an individual security Discuss the concept of an efficient portfolio Discuss the concept of an efficient portfolio

21-3 Objectives continued Explain the importance of the capital asset pricing model Explain the importance of the capital asset pricing model Understand the concept of the beta coefficient Understand the concept of the beta coefficient Discuss the required rate of return on an individual stock and how it relates to its beta Discuss the required rate of return on an individual stock and how it relates to its beta

21-4 A Basic Look at Portfolio Management and Capital Market Theory Formal Measurement of Risk Formal Measurement of Risk Portfolio Effect Portfolio Effect Developing and Efficient Portfolio Developing and Efficient Portfolio Capital Asset Pricing Model Capital Asset Pricing Model Return on an Individual Security Return on an Individual Security Assumptions of the Capital Asset Pricing Model Assumptions of the Capital Asset Pricing Model

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

21-6 Review from Chapter 1 Risk & Expected Return Risk Risk uncertainty about future outcomesuncertainty about future outcomes The greater the dispersion of possible outcomes, the greater the riskThe greater the dispersion of possible outcomes, the greater the risk Most investors tend to be risk averse Most investors tend to be risk averse all things being equal, investors prefer less risk to more riskall things being equal, investors prefer less risk to more risk investors will increase risk-taking position only if premium for risk is involvedinvestors will increase risk-taking position only if premium for risk is involved Each investor has different attitude toward riskEach investor has different attitude toward risk

21-7 Formal Measurement of Risk Expected Value Expected Value Standard Deviation Standard Deviation

21-8 Formal Measurement of Risk How to measure risk? How to measure risk? Design probability distribution of anticipated future outcomes Design probability distribution of anticipated future outcomes Establish Establish Probability distributionProbability distribution Determine expected valueDetermine expected value Calculate dispersion around expected valueCalculate dispersion around expected value The greater the dispersion the greater the risk

21-9 Formal Measurement of Risk Outcomes and associated probabilities are likely to be based on Economic projections Economic projections Past experience Past experience Subjective judgments Subjective judgments Many other variables Many other variables

21-10 Expected Value Expected Value Expectedvalue = Eachpossibleoutcome x Probability of occurrence Click

21-11 Expected Value Expected Value

21-12 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 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 K = Possible outcomes P = Probability of that outcome based on the state of the economy i = Investment i i = Investment i For stocks, For stocks, K = Price appreciation potential plus the dividend yield (total return) —K = Expected Value

21-13 Standard Deviation σ Standard Deviation σ

21-14 Expected Value and Standard Deviation for Investment j

21-15 Standard Deviation σ Expected value of both investments is 10% Expected value of both investments is 10% σ i = 3.9% σ i = 3.9% σ j = 5.1% σ j = 5.1% Compare investment i with j Compare investment i with j j has a larger dispersion than i j has a larger dispersion than i j is riskier than i j is riskier than i Investment j is countercyclical Investment j is countercyclical It does well during a recessionIt does well during a recession Poorly in a strong economyPoorly in a strong economy

21-16 Portfolio Effect Expected Value for a 2-Asset Portfolio Combine investment i and j into one portfolio Combine investment i and j into one portfolio Weighted evenly (50-50) Weighted evenly (50-50) New portfolio’s expected value = 10% New portfolio’s expected value = 10% K p = expected value of portfolio K p = expected value of portfolio X values represent weights assigned X values represent weights assigned

21-17 Portfolio Effect Expected Value for a 2-Asset Portfolio

21-18 Portfolio Effect - σ for a 2-Asset Portfolio σ for combined portfolio (p ) using weighted average σ of i & j using weighted average σ of i & j Portfolio σ would be 4.5% Portfolio σ would be 4.5%  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 IF

21-19 Standard Deviation of a portfolio is not based on simple weighted average of individual standard deviations! Portfolio Effect - σ for a 2-Asset Portfolio

21-20 Investment Outcomes under Different Conditions

21-21 Appropriate Standard Deviation Two-Asset Portfolio  σ p = Standard deviation of portfolio  r i j = Correlation coefficient *  r i j measures joint movement of 2 variables  Value for r i j can be from -1 to +1 * See Appendix 21A

21-22 Correlation Analysis

21-23 X i = 0.5 σ i = 3.9 X j = 0.5 σ j = 5.1 r i j = See Appendix 21A

21-24 σ p =1.8 < < σ j σ j = 5.1 σ i 3.9 σ i = 3.9 Portfolio standard deviation is less than standard deviation of either investment

21-25 Impact of various assumed correlation coefficients for the two investments

21-26 Investment Range of Outcomes i alone 5 to 15% j alone 6 to 20% ( i, j ) 7.5 to 12.5% Combine 2 investments to reduce risk  Reduced risk (less dispersion)  Expected value constant at 10%

21-27 Panel A Panel B Panel C Perfectly positive correlationreturns Perfect negative correlation returns Uncorrelated returns r i j = +1 r i j = -1 r i j = 0 As i increases in value, so does j in exact proportion to i As i increases, j decreases in exact proportion to i No correlation

21-28 Developing an Efficient Portfolio Consider large number of portfolios based on Consider large number of portfolios based on Expected valueExpected value Standard deviationStandard deviation Correlations between the individual securitiesCorrelations between the individual securities A portfolio of 14 to 16 stocks is fully diversified A portfolio of 14 to 16 stocks is fully diversified Portfolio theory developed by Professor Harry Markowitz (1950s) Portfolio theory developed by Professor Harry Markowitz (1950s)

21-29 Assume we have identified the following risk- return possibilities for eight different portfolios Next slide shows graph

21-30

21-31 Efficient Frontier Line 4 points out of 8 possibilities lie on the frontier 4 points out of 8 possibilities lie on the frontier ACFH delineates the efficient set of portfolios ACFH delineates the efficient set of portfolios It is efficient because portfolios on this line dominate all other attainable 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

21-32 Developing an Efficient Portfolio Efficient frontier line gives Efficient frontier line gives Maximum return for a given level of riskMaximum return for a given level of risk Minimum risk for a given level of returnMinimum risk for a given level of return No portfolios exist above the efficient frontier No portfolios exist above the efficient frontier Portfolios below it are not acceptable alternatives compared to points on the line Portfolios below it are not acceptable alternatives compared to points on the line

21-33 Example – Getting Maximum Return for a given Level of Risk PortfolioReturnRisk F14%5% E13%5% Choose F - Same risk Higher return Higher return

21-34 Example – Getting Minimum Risk for a given Level of Return PortfolioReturnRisk A10%1.8% B10%2.1% Choose A - Same return Lower risk

21-35 Expanded View of Efficient Frontier

21-36

21-37 Risk-Return Indifference Curves Investor’s trade-off between risk & return Investor’s trade-off between risk & return Steeper slopes means more risk-averse Steeper slopes means more risk-averse Investor B has a steeper slope than investor A Investor B has a steeper slope than investor A B requires more return (more risk premium) for each additional unit of risk 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 From point X to Y investor B requires approx. twice as much incremental return as A

21-38 Indifference Curves for Investor A

21-39

21-40 Optimum Portfolio Match indifference curve with Match indifference curve with efficient frontier efficient frontier Highest point is C on efficient frontier Highest point is C on efficient frontier Point of tangency of two curves Point of tangency of two curves Same slope at point Same slope at point C represents same risk-return characteristics C represents same risk-return characteristics Relate risk-return indifference curves to efficient frontier to determine that point of tangency providing maximum benefits C

21-41 Capital Asset Pricing Model (CAPM) Professors Sharpe et al advanced Professors Sharpe et al advanced efficient portfolios to efficient portfolios to capital asset pricing model capital asset pricing model Assets value based on risk characteristics Assets value based on risk characteristics CAPM takes off where efficient frontier stops CAPM takes off where efficient frontier stops Introduce Introduce New investment outletNew investment outlet Risk-free asset (R F )Risk-free asset (R F )

21-42 Risk-free (RF) Asset Has no risk of default Has no risk of default Standard deviation of zero (-0-) Standard deviation of zero (-0-) Lowest/safest return Lowest/safest return U.S. Treasury billU.S. Treasury bill U.S. Treasury bondU.S. Treasury bond Zero risk CAPM combines risk-free asset & efficient frontier

21-43 Basic Diagram of the Capital Market Line

21-44 The Capital Market Line and Indifference Curves

21-45 Capital Market Line (CML) R F MZ line capital market line (CML) R F MZ line capital market line (CML) Formula for the capital market line Formula for the capital market line K p = Expected value of the portfolio σ P = Portfolio standard deviation R F = Risk-free rate K M = Market rate of return σ M = Market standard deviation See next slide

21-46

21-47 Return on an Individual Security Beta Coefficient Beta Coefficient Systematic and Unsystematic Risk Systematic and Unsystematic Risk Security Market Line Security Market Line

21-48 Beta Coefficient Measures A stock’s performance Relationship The market in general Up Down

21-49 Example: Total return of stock i for 5 years compared with the market return

21-50 Return on an Individual Security K i = Stock return, dependent variable, Y-axis a i (alpha) = Line intersects vertical axis b i (beta) = Slope of the line K M = Market return, independent variable, X-axis e i = Random error term a i + b i K M : Straight line e i = Deviations, nonrecurring movements

21-51 Beta Draw line of best fit - see Figure 21–11 or Draw line of best fit - see Figure 21–11 or Least squares regression analysis Appendix 21B Least squares regression analysis Appendix 21B Beta Stock’s volatility & risk explanation % more volatile – riskier than market 1 Average volatility – moves with market <1 Less risk than the market

21-52 Relationship of Individual Stock to the Market

21-53 SystematicUnsystematic Change entirely due to market movement Change in value not associated with market If market goes up stock goes up Not correlated with market If market goes down stock goes down Peculiar to an individual security or industry Beta risk The error term e i Risk

21-54 In a diversified portfolio unsystematic risk approaches 0 unsystematic risk approaches 0 Company specificMarket movement

21-55 Security Market Line (SML) SML shows risk-return trade-off for a stock SML shows risk-return trade-off for a stock CML shows risk-return trade-off for a portfolio CML shows risk-return trade-off for a portfolio K i = Expected return on stock i R F = Risk-free rate of return b i = Beta risk, systematic risk K M = Market rate of return

21-56

21-57 Assumptions of the Capital Asset Pricing Model All investors 1.Can borrow/lend unlimited funds at risk-free rate 2.Have the same one-period time horizon 3.Maximize expected utility, evaluate investments by standard deviations of portfolio returns

21-58 Assumptions of the Capital Asset Pricing Model continued All investors 4.Have the same expectations 5.All assets are perfectly divisible 6.There are no taxes or transactions costs 7.The market is efficient and in equilibrium

21-59 Test of the Security Market Line