McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 1 1 Portfolio Management and Capital Market Theory- Learning Objectives 1. Understand the basic statistical techniques for measuring risk and return 2. Explain how the portfolio effect works to reduce the risk of an individual security. 3. Discuss the concept of an efficient portfolio 4. Explain the importance of the capital asset pricing model. 5. Understand the concept of the beta coefficient

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 2 2

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 3 3 Standard Deviation= Investment j Investment i Note that the average is the same for each investment but that the standard deviation is different. Also note that this model assumes no correlation between i and j.

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 4 4 Portfolio Return k Assume stocks x 1 and x 2 with parameters: x 1 =.5 K 1 = 10%  1 = 3.9 x 2 =.5 K 2 = 10%  2 = 5.1 Definition of portfolio expected return according to equation K p = x 1 K 1 + x 2 K 2 =.5(10 %) +.5(10 %) = 10% Portfolio Effect ( 2 stocks, equal weight)

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 5 5 Standard Deviation of a Two-Stock Portfolio ( 2 stocks, equal weight) i r ij   p p Calculated standard deviation with differing correlation coefficients. = .5 2 (3.9) (5.1) 2 +2(.5)(.5) r ij (3.9)(5.1) =  r ij 19.9 Correlation Coefficient

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 6 6 Developing and Efficient Portfolio  Many possible portfolios (i.e., combinations of investments)  The investor determines his personal risk- return criteria  An investor should select from the most efficient portfolios (i.e., those with the maximum return for a given risk).  Portfolios do not exist above the "efficient frontier"

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 7 7 (Figure 21-3) A B C D E F G H Expected return K p Portfolio standard deviation (  p ) (risk) Efficient frontier Diagram of Risk-Return Trade-Offs

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block A B C D E F G H Expected return K p Portfolio standard deviation (  p ) (risk) Efficient frontier Inefficient portfolios Diagram of Risk-Return Trade-offs

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 9 9 Capital Asset Pricing Model  The CAPM introduces the risk-free asset where  RF = 0.  Under the CAPM, inv estors combine the risk-free asset with risky portfolios on the efficient frontier.

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 10 (Fig21-8) Expected return K p RFRF M Portfolio standard deviatio n (  p ) Z Efficient frontier Initial: risk free point Satisfies efficient frontier Maximum attainable risk- return Risk Return line The CAPM and Indifference Curves

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 11 The R F MZ line represents investment opportunities that are superior to the existing efficient frontier. R F MZ line is called capital market line. How do investors reach points on the R F MZ line? Capital Asset Pricing Model

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 12 Capital Asset Pricing Model  To attain line R F M Buy a combination of R F F and M portfolio  To attain M Z Buy M portfolio and borrow additional funds at the risk-free rate.

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 13 Capital Asset Pricing Model  Portfolio M is an optimum “market basket of investments.”  M portfolio can be represented by NYSE,or S&P 500.  Broadly based index is better than narrowly based index.

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 14 Security Market Line  Refers to an individual stock Trade-off between risk & return Analogous to Capital Market Line for market portfolios  Formula is: K i = R F + b i (K M - R F )

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 15 (Figure 21-12) Risk (Beta) RFRF Market standard deviation O KMKM 1.0 Security Market Line (CML) return Expected return K p Illustration of the Capital Market Line 2.0

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 16 Measures excess return per unit of total risk. Also known as "excess return to variability" ratio. Higher values indicate superior performance Sharpe Approach Sharpe measure Total portfolio return - Risk-free rate Portfolio standard deviation = Market data: K F = 5% Portfolio Data: k p =.12  p = 1.2  p =.14 = = Sharpe Measure

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 17 Measures excess return per unit of systematic risk. Also known as "excess return to volatility" ratio. Higher values indicate superior performance Treynor Approach Treynor measure Total portfolio return - Risk-free rate Portfolio Beta = Market data: K F = 6% Portfolio Data: k p = 0.10  p = 0.9 = = Treynor Measure

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 18 © The McGraw-Hill Companies, Inc.,1999 Jensen Approach  Alpha (average differential) return indicates the difference between a) the return on the fund and b) a point on the market line that corresponds to a beta equal that of the fund.  Alpha = the actual rate of return minus the rate of return predicted by the CAPM.

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 19 Portfolio Beta Excess returns (%) O Market line O.51.O Market M Z Y Figure 22-2 Risk-Adjusted Portfolio Returns ML =  (EMR) EMR is "excess market return"

McGraw-Hill/Irwin Fundamentals of Investment Management Hirt Block 20 Jensen Approach  Jensen computed the alpha value of 115 mutual funds.  The average alpha was a negative 1.1% and only 39 out of 115 funds had a positive alpha.