1. 5.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Chapter 5 Risk and Return

2. 5.2 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. After studying Chapter 5, you should be able to: 1. Understand the relationship (or “trade-off”) between risk and return. 2. Define risk and return and show how to measure them by calculating expected return, standard deviation, and coefficient of variation. 3. Discuss the different types of investor attitudes toward risk. 4. Explain risk and return in a portfolio context, and distinguish between individual security and portfolio risk. 5. Distinguish between avoidable (unsystematic) risk and unavoidable (systematic) risk and explain how proper diversification can eliminate one of these risks. 6. Define and explain the capital-asset pricing model (CAPM), beta, and the characteristic line. 7. Calculate a required rate of return using the capital-asset pricing model (CAPM). 8. Demonstrate how the Security Market Line (SML) can be used to describe this relationship between expected rate of return and systematic risk. 9. Explain what is meant by an “efficient financial market” and describe the three levels (or forms) of market efficiency.

3. 5.3 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Risk and Return Defining Risk and Return Using Probability Distributions to Measure Risk Attitudes Toward Risk Risk and Return in a Portfolio Context Diversification The Capital Asset Pricing Model (CAPM) Efficient Financial Markets Defining Risk and Return Using Probability Distributions to Measure Risk Attitudes Toward Risk Risk and Return in a Portfolio Context Diversification The Capital Asset Pricing Model (CAPM) Efficient Financial Markets

4. 5.4 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Defining Return u Return is defined as “the total gain or loss experienced on an investment over a given period of time”. u It is measured as follows:

5. 5.5 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Defining Return Income received change in market price beginning market price Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. (see eqn 5.1 p.98) D t P t – P t - 1 D t + (P t – P t - 1 ) P t - 1 R =

6. 5.6 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Defining Return u Where: u R = Actual, expected or required rate of return during the period t u D t = Cash flow received from the investment in the time period [t – 1 to t] u P t = Price of the asset at time t u P t-1 = Price of the asset at time t – 1

7. 5.7 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Return Example $10 $9.50 $1 dividend The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year? $10 $9.50 $1 dividend The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year? $1.00 $9.50$10.00 $1.00 + ($9.50 – $10.00 ) $10.00 R R = 5% = 5%

8. 5.8 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another Example

9. 5.9 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Defining Risk What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? Does it matter if it is a bank CD or a share of stock? What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? Does it matter if it is a bank CD or a share of stock? he variability (difference) of returns from those that are expected. Risk is defined as “the chance of financial loss”. It is the variability (difference) of returns from those that are expected.

10. 5.10 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The Risk-and-Return Trade-off u Investments must be analysed in terms of both their return potential as well as their riskiness or variability. u u Historically, its been proven that higher returns are accompanied by higher risks. u

11. 5.11 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Risk Assessment Of A Single Asset – Probability Distribution u Provides a more quantitative, yet behavioural, insight into an asset’s risk. u Probability is the chance of a particular outcome occurring. u Can be graphed as a model relating probabilities and their associated outcomes. u The expected value of a return R [the most likely return on an asset] can be calculated by:

12. 5.12 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Probability Distribution u A probability distribution is a model that relates probabilities to the associated out comes. u The simplest type of probability distribution is the bar chart, which shows only a limited number of outcome-probability coordinates.

13. 5.13 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Probability Distribution u The bar charts for Shuia Na Ltd’s assets A and B are shown in Slide 13. u Although both assets have the same most likely return, the range of return is much more dispersed for asset B than for asset A—16% versus 4%.

14. 5.14 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Probability Distribution

15. 5.15 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Probability Distribution u If we knew all the possible outcomes and associated probabilities, a continuous probability distribution could be developed. This type of distribution can be thought of as a bar chart for a very large number of outcomes. u Slide 15 shows continuous probability distributions for assets A and B. Note that although assets A and B have the same most likely return (15%), the distribution of returns for asset B has much greater dispersion than the distribution for asset A. u Clearly, asset B is more risky than asset A.

16. 5.16 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Probability Distribution

17. 5.17 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Discrete versus. Continuous Distributions Discrete Continuous

18. 5.18 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Risk Measurement – Standard Deviation u A normal probability distribution will always resemble a bell shaped curve.

19. 5.19 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Determining Expected Return (Discrete Dist.) R =  ( R i )( P i ) R is the expected return for the asset, R i is the return for the i th possibility, P i is the probability of that return occurring, n is the total number of possibilities. R =  ( R i )( P i ) R is the expected return for the asset, R i is the return for the i th possibility, P i is the probability of that return occurring, n is the total number of possibilities. n I = 1

20. 5.20 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Risk Measurement – Standard Deviation u Measures the dispersion around the expected value. u The higher the standard deviation the higher the risk.

21. 5.21 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. How to Determine the Expected Return and Standard Deviation Stock BW R i P i (R i )(P i ) -0.15 0.10 –0.015 -0.03 0.20 –0.006 0.09 0.40 0.036 0.21 0.20 0.042 0.33 0.10 0.033 0.090 Sum 1.00 0.090 Stock BW R i P i (R i )(P i ) -0.15 0.10 –0.015 -0.03 0.20 –0.006 0.09 0.40 0.036 0.21 0.20 0.042 0.33 0.10 0.033 0.090 Sum 1.00 0.090 The expected return, R, for Stock BW is.09 or 9%

22. 5.22 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Determining Standard Deviation (Risk Measure)   =  ( R i – R ) 2 ( P i ) Standard Deviation  Standard Deviation, , is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Note, this is for a discrete distribution.   =  ( R i – R ) 2 ( P i ) Standard Deviation  Standard Deviation, , is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Note, this is for a discrete distribution. n i = 1

23. 5.23 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. How to Determine the Expected Return and Standard Deviation Stock BW R i P i (R i )(P i ) (R i - R ) 2 (P i ) –0.15 0.10 –0.015 0.00576 –0.03 0.20 –0.006 0.00288 0.09 0.40 0.036 0.00000 0.21 0.20 0.042 0.00288 0.33 0.10 0.033 0.00576 0.090 0.01728 Sum 1.00 0.090 0.01728 Stock BW R i P i (R i )(P i ) (R i - R ) 2 (P i ) –0.15 0.10 –0.015 0.00576 –0.03 0.20 –0.006 0.00288 0.09 0.40 0.036 0.00000 0.21 0.20 0.042 0.00288 0.33 0.10 0.033 0.00576 0.090 0.01728 Sum 1.00 0.090 0.01728

24. 5.24 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Determining Standard Deviation (Risk Measure) n i=1   =  ( R i – R ) 2 ( P i )   =.01728  0.131513.15%  = 0.1315 or 13.15%   =  ( R i – R ) 2 ( P i )   =.01728  0.131513.15%  = 0.1315 or 13.15%

25. 5.25 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another example u Shuia Na Ltd, a tennis-equipment manufacturer, is attempting to choose the better of two alternative investments, A and B. Each requires an initial outlay of $10,000 and each has a most likely annual rate of return of 15%. To evaluate the riskiness of these assets, management has made pessimistic and optimistic estimates of the returns associated with each. u The expected values for these assets are presented in the Table on slide 18. Column 1 gives the Pri’s and column 2 gives the ri’s, n equals 3 in each case. The expected value for each asset’s return is 15%. u Slide 19 shows the standard deviations for these assets

26. 5.26 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another example – cont. u Before looking at the standard deviations, can you identify which asset is most risky?

27. 5.27 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another example – cont.

28. 5.28 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Which Asset Is Riskier?

29. 5.29 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Risk Measurement – Coefficient Of Variation u A measure of relative dispersion, useful in comparing the risk of assets with differing expected returns. u The higher the coefficient of variation, the greater the risk. u Allows comparison of assets that have different expected returns.

30. 5.30 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Coefficient of Variation standard deviation mean The ratio of the standard deviation of a distribution to the mean of that distribution. RELATIVE It is a measure of RELATIVE risk.  R CV =  /R 0.13150.09 CV of BW = 0.1315 / 0.09 = 1.46 standard deviation mean The ratio of the standard deviation of a distribution to the mean of that distribution. RELATIVE It is a measure of RELATIVE risk.  R CV =  /R 0.13150.09 CV of BW = 0.1315 / 0.09 = 1.46

31. 5.31 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Risk Preferences u Three Preferences: u Risk Averse: Require a higher rate of return to compensate for taking higher risk. u Risk Seeking: Will accept a lower return for a greater risk. u Risk Indifferent: Required return does not change in response to a change in risk.

32. 5.32 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Certainty Equivalent CE Certainty Equivalent (CE) is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Risk Attitudes

33. 5.33 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Risk Averse Most individuals are Risk Averse. Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Risk Averse Most individuals are Risk Averse. Risk Attitudes

34. 5.34 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. You have the choice between (1) a guaranteed dollar reward or (2) a coin-flip gamble of $100,000 (50% chance) or $0 (50% chance). The expected value of the gamble is $50,000. Mary requires a guaranteed $25,000, or more, to call off the gamble. Raleigh is just as happy to take $50,000 or take the risky gamble. Shannon requires at least $52,000 to call off the gamble. Risk Attitude Example

35. 5.35 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. What are the Risk Attitude tendencies of each? Risk Attitude Example “risk aversion”. Mary shows “risk aversion” because her “certainty equivalent” < the expected value of the gamble. “risk indifference”. Raleigh exhibits “risk indifference” because her “certainty equivalent” equals the expected value of the gamble. “risk preference”. Shannon reveals a “risk preference” because her “certainty equivalent” > the expected value of the gamble. “risk aversion”. Mary shows “risk aversion” because her “certainty equivalent” < the expected value of the gamble. “risk indifference”. Raleigh exhibits “risk indifference” because her “certainty equivalent” equals the expected value of the gamble. “risk preference”. Shannon reveals a “risk preference” because her “certainty equivalent” > the expected value of the gamble.

36. 5.36 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Portfolios u A portfolio is a collection of assets. u An efficient portfolio is: u One that maximises the return for a given level of risk. u OR u One that minimises risk for a given level of return.

37. 5.37 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Portfolio Return u Is calculated as a weighted average of returns on the individual assets from which it is formed. u Is calculated by (Eqn 5.6): u u Where: u r p = Return on a portfolio u w j = Proportion of the portfolio’s total dollar value u represented by asset j u r j = Return on asset j

38. 5.38 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. R P =  ( W j )( R j ) R P is the expected return for the portfolio, W j is the weight (investment proportion) for the j th asset in the portfolio, R j is the expected return of the j th asset, m is the total number of assets in the portfolio. R P =  ( W j )( R j ) R P is the expected return for the portfolio, W j is the weight (investment proportion) for the j th asset in the portfolio, R j is the expected return of the j th asset, m is the total number of assets in the portfolio. Determining Portfolio Expected Return m J = 1

39. 5.39 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Determining Portfolio Standard Deviation m J=1 m K=1  P  P =  W j W k  jk W j is the weight (investment proportion) for the j th asset in the portfolio, W k is the weight (investment proportion) for the k th asset in the portfolio,  jk is the covariance between returns for the j th and k th assets in the portfolio.  P  P =  W j W k  jk W j is the weight (investment proportion) for the j th asset in the portfolio, W k is the weight (investment proportion) for the k th asset in the portfolio,  jk is the covariance between returns for the j th and k th assets in the portfolio.

40. 5.40 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. What is Covariance? u Covariance is a statistical measure of the degree to which two variables (eg, securities‘ returns) move together. u Positive covariance shows that the two variables move together. u Negative covariance suggests that the two variables move in opposite diiections. u Zero covariance means that the two variables show no tendency to vary together in either a positive or negative linear fashion. u Covariance between security returns complicates the calculation of portfolio standard deviation. u Covariance between securities provides for the possibility of eliminating some risk without reducing potential return.

41. 5.41 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Covariance  r  jk =  j  k r  jk  j is the standard deviation of the j th asset in the portfolio,  k is the standard deviation of the k th asset in the portfolio, r jk is the correlation coefficient between the j th and k th assets in the portfolio.

42. 5.42 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Correlation u A statistical measure of the relationship, if any, between a series of numbers representing data of any kind. u Three types: u Positive Correlation: Two series move in the same direction. u Uncorrelated: No relationship between the two series. u Negative Correlation: Two series move in opposite directions.

43. 5.43 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. A standardized statistical measure of the linear relationship between two variables. –1.0 0 +1.0 Its range is from –1.0 (perfect negative correlation), through 0 (no correlation), to +1.0 (perfect positive correlation). A standardized statistical measure of the linear relationship between two variables. –1.0 0 +1.0 Its range is from –1.0 (perfect negative correlation), through 0 (no correlation), to +1.0 (perfect positive correlation). Correlation Coefficient

44. 5.44 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Correlation u The degree of correlation is measured by the correlation coefficient.

45. 5.45 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Diversification u Combining assets with low or negative correlation can reduce the overall risk of the portfolio. u Combining uncorrelated risks can reduce overall portfolio risk. u Combining two perfectly positively correlated assets cannot reduce the risk below the risk of the least risky asset. u Combining two assets with less than perfectly positive correlations can reduce the total risk to a level below that of either asset.

46. 5.46 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Diversification

47. 5.47 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Correlation, Diversification, Risk & Return u The lower the correlation between asset returns, the greater the potential diversification of risk.

48. 5.48 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Stock D Stock BW $2,000 Stock BW $3,000Stock D Stock BW 9%13.15% Stock D 8%10.65%correlation coefficient 0.75 You are creating a portfolio of Stock D and Stock BW (from earlier). You are investing $2,000 in Stock BW and $3,000 in Stock D. Remember that the expected return and standard deviation of Stock BW is 9% and 13.15% respectively. The expected return and standard deviation of Stock D is 8% and 10.65% respectively. The correlation coefficient between BW and D is 0.75. What is the expected return and standard deviation of the portfolio? Stock D Stock BW $2,000 Stock BW $3,000Stock D Stock BW 9%13.15% Stock D 8%10.65%correlation coefficient 0.75 You are creating a portfolio of Stock D and Stock BW (from earlier). You are investing $2,000 in Stock BW and $3,000 in Stock D. Remember that the expected return and standard deviation of Stock BW is 9% and 13.15% respectively. The expected return and standard deviation of Stock D is 8% and 10.65% respectively. The correlation coefficient between BW and D is 0.75. What is the expected return and standard deviation of the portfolio? Portfolio Risk and Expected Return Example

49. 5.49 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. W BW = $2,000/$5,000 = 0.4 W D 0.6 W D = $3,000/$5,000 = 0.6 W D R D R P = ( W BW )(R BW ) + ( W D )(R D ) 0.68% R P = (0.4)(9%) + (0.6)(8%) 4.8%8.4% R P = (3.6%) + (4.8%) = 8.4% W BW = $2,000/$5,000 = 0.4 W D 0.6 W D = $3,000/$5,000 = 0.6 W D R D R P = ( W BW )(R BW ) + ( W D )(R D ) 0.68% R P = (0.4)(9%) + (0.6)(8%) 4.8%8.4% R P = (3.6%) + (4.8%) = 8.4% Determining Portfolio Expected Return

50. 5.50 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.  P = 0.0028 + (2)(0.0025) + 0.0041  P = SQRT(0.0119)  P = 0.1091 or 10.91% You will not be asked to do this calculation.  P = 0.0028 + (2)(0.0025) + 0.0041  P = SQRT(0.0119)  P = 0.1091 or 10.91% You will not be asked to do this calculation. Determining Portfolio Standard Deviation

51. 5.51 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The WRONG way to calculate is a weighted average like:  P = 0.4 (13.15%) + 0.6(10.65%)  P = 5.26 + 6.39 = 11.65% 10.91% = 11.65% This is INCORRECT. The WRONG way to calculate is a weighted average like:  P = 0.4 (13.15%) + 0.6(10.65%)  P = 5.26 + 6.39 = 11.65% 10.91% = 11.65% This is INCORRECT. Determining Portfolio Standard Deviation

52. 5.52 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Stock C Stock D Portfolio Return Return 9.00% 8.00% 8.64%Stand. Dev. Dev.13.15% 10.65% 10.91% CV CV 1.46 1.33 1.26 The portfolio has the LOWEST coefficient of variation due to diversification. Stock C Stock D Portfolio Return Return 9.00% 8.00% 8.64%Stand. Dev. Dev.13.15% 10.65% 10.91% CV CV 1.46 1.33 1.26 The portfolio has the LOWEST coefficient of variation due to diversification. Summary of the Portfolio Return and Risk Calculation

53. 5.53 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Combining securities that are not perfectly, positively correlated reduces risk. INVESTMENT RETURN TIME SECURITY E SECURITY F Combination E and F Diversification and the Correlation Coefficient

54. 5.54 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Systematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. It cannot be avoided Unsystematic Risk Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Systematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. It cannot be avoided Unsystematic Risk Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Total Risk SystematicRisk UnsystematicRisk Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Systematic Risk + Unsystematic Risk

55. 5.55 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Systematic Risk and Unsystematic Risk u Other names for these terms are: u Systematic risk u Unavoidable risk u Nondiversifiable risk u Unsystematic risk u Avoidable risk u Diversifiable risk

56. 5.56 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. TotalRisk Unsystematic (diversifiable) risk Systematic (nondiversifiable) risk STD DEV OF PORTFOLIO RETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors such as changes in the nation’s economy, tax reform by the Congress, or a change in the world situation. Total Risk = Systematic Risk + Unsystematic Risk

57. 5.57 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. TotalRisk Unsystematic risk Systematic risk STD DEV OF PORTFOLIO RETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors unique to a particular company or industry. For example, the death of a key executive or loss of a governmental defense contract. Total Risk = Systematic Risk + Unsystematic Risk

58. 5.58 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. CAPM is a model that describes the relationship between risk and expected (required) return. risk-free rate a premium systematic risk In this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security. CAPM is a model that describes the relationship between risk and expected (required) return. risk-free rate a premium systematic risk In this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security. Capital Asset Pricing Model (CAPM)

59. 5.59 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 1.Capital markets are efficient. 2.Homogeneous investor expectations over a given period. Risk-free 3.Risk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy). systematic risk 4.Market portfolio contains only systematic risk (use S&P 500 Index or similar as a proxy). 1.Capital markets are efficient. 2.Homogeneous investor expectations over a given period. Risk-free 3.Risk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy). systematic risk 4.Market portfolio contains only systematic risk (use S&P 500 Index or similar as a proxy). CAPM Assumptions

60. 5.60 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. EXCESS RETURN ON STOCK EXCESS RETURN ON MARKET PORTFOLIO Beta Beta = RiseRun Narrower spread is higher correlation Characteristic Line

61. 5.61 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Time Pd.MarketMy Stock 19.6%12% 2–15.4%–5% 326.7%19% 4–0.2%3% 520.9%13% 628.3%14% 7–5.9%–9% 83.3%–1% 912.2%12% 1010.5%10% The Market and My Stock returns are “excess returns” and have the riskless rate already subtracted. Calculating “Beta” on Your Calculator

62. 5.62 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Assume that the previous continuous distribution problem represents the “excess returns” of the market portfolio (it may still be in your calculator data worksheet – 2 nd Data ). Enter the excess market returns as “X” observations of: 9.6%, –15.4%, 26.7%, –0.2%, 20.9%, 28.3%, –5.9%, 3.3%, 12.2%, and 10.5%. Enter the excess stock returns as “Y” observations of: 12%, –5%, 19%, 3%, 13%, 14%, –9%, –1%, 12%, and 10%. Calculating “Beta” on Your Calculator

63. 5.63 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Let us examine again the statistical results (Press 2 nd and then Stat ) The market expected return and standard deviation is 9% and 13.32%. Your stock expected return and standard deviation is 6.8% and 8.76%. The regression equation is Y= a + bX. Thus, our characteristic line is Y = 1.4448 + 0.595 X and indicates that our stock has a beta of 0.595. Calculating “Beta” on Your Calculator

64. 5.64 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. systematic risk An index of systematic risk. It is the measure of market (non-diversifiable) risk, and measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The beta for the market portfolio is 1.0 beta The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. systematic risk An index of systematic risk. It is the measure of market (non-diversifiable) risk, and measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The beta for the market portfolio is 1.0 beta The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. What is Beta?

65. 5.65 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Capital Asset Pricing Model (CAPM) – Portfolio Betas u Are interpreted exactly the same way as individual asset betas. u Can calculated by: u u Where: u w j = The proportion of the portfolio’s dollar value represented by asset j u β j = The beta of asset j

66. 5.66 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. EXCESS RETURN ON STOCK EXCESS RETURN ON MARKET PORTFOLIO Beta < 1 (defensive) Beta = 1 Beta > 1 (aggressive) characteristic Each characteristic line line has a different slope. Characteristic Lines and Different Betas

67. 5.67 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. R j R j is the required rate of return for stock j, R f R f is the risk-free rate of return,  j  j is the beta of stock j (measures systematic risk of stock j), R M R M is the expected return for the market portfolio. This is also known as the CAPM formula R j R j is the required rate of return for stock j, R f R f is the risk-free rate of return,  j  j is the beta of stock j (measures systematic risk of stock j), R M R M is the expected return for the market portfolio. This is also known as the CAPM formula R j = R f +  j (R M – R f ) Security Market Line

68. 5.68 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. R j = R f +  j (R M – R f )  M 1.0  M = 1.0 Systematic Risk (Beta) RfRfRfRf RMRMRMRM Required Return RiskPremium Risk-freeReturn Security Market Line

69. 5.69 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Capital Asset Pricing Model (CAPM) – Beta Coefficient

70. 5.70 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Obtaining Betas Can use historical data if past best represents the expectations of the future Can also utilize services like Value Line, Ibbotson Associates, etc. Adjusted Beta Betas have a tendency to revert to the mean of 1.0 Can utilize combination of recent beta and mean 2.22 (0.7) + 1.00 (0.3) = 1.554 + 0.300 = 1.854 estimate Obtaining Betas Can use historical data if past best represents the expectations of the future Can also utilize services like Value Line, Ibbotson Associates, etc. Adjusted Beta Betas have a tendency to revert to the mean of 1.0 Can utilize combination of recent beta and mean 2.22 (0.7) + 1.00 (0.3) = 1.554 + 0.300 = 1.854 estimate Security Market Line

71. 5.71 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. 6% R f market expected rate of return 10% beta1.2 required rate of return Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a 6% R f and a long-term market expected rate of return of 10%. A stock analyst following the firm has calculated that the firm beta is 1.2. What is the required rate of return on the stock of Basket Wonders? Determination of the Required Rate of Return

72. 5.72 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. R BW R f  R M R f R BW = R f +  j (R M – R f ) R BW 6%1.210%6% R BW = 6% + 1.2(10% – 6%) R BW 10.8% R BW = 10.8% The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0). R BW R f  R M R f R BW = R f +  j (R M – R f ) R BW 6%1.210%6% R BW = 6% + 1.2(10% – 6%) R BW 10.8% R BW = 10.8% The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0). BWs Required Rate of Return

73. 5.73 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. intrinsic value dividend next period $0.50grow 5.8% Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15. intrinsic value overunderpriced What is the intrinsic value of the stock? Is the stock over or underpriced? intrinsic value dividend next period $0.50grow 5.8% Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15. intrinsic value overunderpriced What is the intrinsic value of the stock? Is the stock over or underpriced? Determination of the Intrinsic Value of BW

74. 5.74 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. u Remember, from Chapter 4, the value of a share of stock is calculated by: u V = D 1 /(k e – g) u So the intrinsic value of BW is:

75. 5.75 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. intrinsic value $10 The stock is OVERVALUED as the market price ($15) exceeds the intrinsic value ($10). $0.50 10.8%5.8% 10.8% – 5.8% IntrinsicValue = = $10 Determination of the Intrinsic Value of BW

76. 5.76 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Systematic Risk (Beta) RfRfRfRf Required Return Direction of Movement Direction of Movement Stock Y Stock Y (Overpriced) Stock X (Underpriced) Security Market Line

77. 5.77 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Small-firm Effect Price/Earnings Effect January Effect These anomalies have presented serious challenges to the CAPM theory. Small-firm Effect Price/Earnings Effect January Effect These anomalies have presented serious challenges to the CAPM theory. Determination of the Required Rate of Return