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# Portfolio Analysis

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### Portfolio Analysis

1. 1. Portfolio Management and Capital Market Theory- Learning Objectives <ul><li>1. Understand the basic statistical techniques for measuring risk and return </li></ul><ul><li>2. Explain how the portfolio effect works to reduce the risk of an individual security. </li></ul><ul><li>3. Discuss the concept of an efficient portfolio </li></ul><ul><li>4. Explain the importance of the capital asset pricing model. </li></ul><ul><li>5. Understand the concept of the beta coefficient </li></ul>
2. 3. Standard Deviation= 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. Standard Deviation= Investment j
3. 4. Portfolio Effect ( 2 stocks, equal weight) 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 21-3. K p = x 1 K 1 + x 2 K 2 = .5(10 %) + .5(10 %) = 10%
4. 5. Standard Deviation of a Two-Stock Portfolio ( 2 stocks, equal weight) r ij   p +1.0 4.5 p + .5 3.9 0.0 3.2 - .5 2.3 - .7 1.8 -1.0 0.0 Calculated standard deviation with differing correlation coefficients. =  3.85 +6.4 + .5 r ij 19.9 Correlation Coefficient i =  .5 2 (3.9) 2 +.5 2 (5.1) 2 +2(.5)(.5) r ij (3.9)(5.1)
5. 6. Developing and Efficient Portfolio <ul><li>Many possible portfolios (i.e., combinations of investments) </li></ul><ul><li>The investor determines his personal risk-return criteria </li></ul><ul><li>An investor should select from the most efficient portfolios (i.e., those with the maximum return for a given risk). </li></ul><ul><li>Portfolios do not exist above the &quot;efficient frontier&quot; </li></ul>
6. 7. Diagram of Risk-Return Trade-Offs (Figure 21-3) A B C D E F G H Expected return K p Portfolio standard deviation (  p ) (risk) Efficient frontier 1 2 3 4 5 6 7 8 0 11 14 13 15 12 10 9
7. 8. Diagram of Risk-Return Trade-offs A B C D E F G H Expected return K p Portfolio standard deviation (  p ) (risk) Efficient frontier 1 2 3 4 5 6 7 8 0 11 14 13 15 12 10 9 Inefficient portfolios
8. 9. Capital Asset Pricing Model <ul><li>The CAPM introduces the risk-free asset where  RF = 0. </li></ul><ul><li>Under the CAPM, inv estors combine the risk-free asset with risky portfolios on the efficient frontier. </li></ul>
9. 10. The CAPM and Indifference Curves (Fig21-8) Expected return K p R F M Portfolio standard deviatio n (  p ) Z Efficient frontier Initial: risk free point Satisfies efficient frontier Maximum attainable risk-return Risk Return line
10. 11. Capital Asset Pricing Model <ul><li>The R F MZ line represents investment opportunities that are superior to the existing efficient frontier. </li></ul><ul><li>R F MZ line is called capital market line. </li></ul><ul><li>How do investors reach points on the R F MZ line? </li></ul>
11. 12. Capital Asset Pricing Model <ul><li>To attain line R F M </li></ul><ul><ul><li>Buy a combination of R F F and M portfolio </li></ul></ul><ul><li>To attain M Z </li></ul><ul><ul><li>Buy M portfolio and borrow additional funds at the risk-free rate. </li></ul></ul>
12. 13. Capital Asset Pricing Model <ul><li>Portfolio M is an optimum “market basket of investments.” </li></ul><ul><li>M portfolio can be represented by NYSE,or S&P 500. </li></ul><ul><li>Broadly based index is better than narrowly based index. </li></ul>
13. 14. Security Market Line <ul><li>Refers to an individual stock </li></ul><ul><ul><li>Trade-off between risk & return </li></ul></ul><ul><ul><li>Analogous to Capital Market Line for market portfolios </li></ul></ul><ul><li>Formula is: </li></ul><ul><ul><li>K i = R F + b i (K M - R F ) </li></ul></ul>
14. 15. Illustration of the Capital Market Line (Figure 21-12) Risk (Beta) R F Market standard deviation O K M 1.0 Security Market Line (CML) return Expected return K p 2.0
15. 16. Sharpe Approach Measures excess return per unit of total risk. Also known as &quot;excess return to variability&quot; ratio. Higher values indicate superior performance Market data: K F = 5% Portfolio Data: k p = .12  p = 1.2  p = .14 Sharpe measure Total portfolio return - Risk-free rate Portfolio standard deviation = = = 0.50 .12 - .05 .14 Sharpe Measure
16. 17. Treynor Approach Measures excess return per unit of systematic risk. Also known as &quot;excess return to volatility&quot; ratio. Higher values indicate superior performance Market data: K F = 6% Portfolio Data: k p = 0.10  p = 0.9 Treynor measure Total portfolio return - Risk-free rate Portfolio Beta = = = 0 . 044 .10 - .06 0.9 Treynor Measure
17. 18. Jensen Approach <ul><li>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. </li></ul><ul><li>Alpha = the actual rate of return minus the rate of return predicted by the CAPM. </li></ul><ul><li>The McGraw-Hill Companies, Inc.,1999 </li></ul>
18. 19. Figure 22-2 Risk-Adjusted Portfolio Returns Portfolio Beta Excess returns (%) O Market M Z Y ML =  (EMR) EMR is &quot;excess market return&quot; Market line O .5 1.O 1.5 6 4 2 1 -1 3 -2 -3 5
19. 20. Jensen Approach <ul><li>Jensen computed the alpha value of 115 mutual funds. </li></ul><ul><li>The average alpha was a negative 1.1% and only 39 out of 115 funds had a positive alpha. </li></ul>
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