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:  Understand the meaning of risk, return and risk preferences.  Measure the risk and return of a single asset.  Measure the risk and return of a portfolio of assets.  Explain beta and the CAPM model.  Analyse shifts in the securities market line.

3. 5.3 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Corporate Value & Risk

4. 5.4 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Defining Return Return is defined as “the total gain or loss experienced on an investment over a given period of time”. Income received change in market pricebeginning 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)  It is measured as follows: D t P t – P t - 1 D t + (P t – P t - 1 ) P t - 1 R =

5. 5.5 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Defining Return  Where:  R = Actual, expected or required rate of return during the period t  D t = Cash flow received from the investment in the time period [t – 1 to t]  P t = Price of the asset at time t  P t-1 = Price of the asset at time t – 1

6. 5.6 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? $1.00 $9.50$10.00 $1.00 + ($9.50 – $10.00 ) $10.00 R R = 5% = 5%

7. 5.7 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another Example

8. 5.8 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 deposit 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 deposit 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.

9. 5.9 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. The Risk-Return Trade-off  Investments must be analysed in terms of both their return potential and their riskiness or variability.   Historically, its been shown that higher returns are accompanied by higher risks. 

10. 5.10 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Probability Distribution  A probability distribution is a model that relates probabilities to the associated outcomes.

11. 5.11 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. n I = 1

12. 5.12 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. How to Determine the Expected Return 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%

13. 5.13 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Probability Distribution  The bar charts for Shuia Na Ltd’s assets A and B are shown in Slide 13.  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  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.  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.  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. Risk Measurement – Standard Deviation  A normal probability distribution will always resemble a bell shaped curve.

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  Measures the dispersion around the expected value.  The higher the standard deviation the higher the risk.

19. 5.19 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. Using Slide 12 data, the std dev is:   =  ( 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. Using Slide 12 data, the std dev is: n i = 1

20. 5.20 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%

21. 5.21 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another example  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 (worse case) and optimistic (best case) estimates of the returns associated with each.  The expected values for these assets are presented in the Table on slide 22. The expected value for each asset’s return is 15%.  Slide 23 shows the standard deviations for these assets

22. 5.22 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another example – cont.  Before looking at the standard deviations, can you identify which asset is most risky?

23. 5.23 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Another example – cont.

24. 5.24 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Which Asset Is Riskier?

25. 5.25 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Risk Measurement – Coefficient Of Variation  A measure of relative dispersion, useful in comparing the risk of assets that have different expected returns.  The higher the coefficient of variation, the greater the risk.  Allows comparison of assets that have different expected returns.

26. 5.26 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Coefficient of Variation standard deviation mean (average) The ratio of the standard deviation of a distribution to the mean (average) 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

27. 5.27 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 that person indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Risk Attitudes

28. 5.28 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. Risk Attitudes

29. 5.29 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

30. 5.30 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.

31. 5.31 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Portfolios  A portfolio is a collection of assets.  An efficient portfolio is:  One that maximises the return for a given level of risk.  OR  One that minimises risk for a given level of return.

32. 5.32 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Portfolio Return  Is calculated as a weighted average of returns on the individual assets from which it is formed.  Is calculated by (Eqn 5.6): 

33. 5.33 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. Determining Portfolio Expected Return m J = 1

34. 5.34 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. A standardised 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

35. 5.35 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Correlation  The degree of correlation is measured by the correlation coefficient.

36. 5.36 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Diversification  Combining assets with low or negative correlation can reduce the overall risk of the portfolio.  Combining uncorrelated risks can reduce overall portfolio risk.  Combining two perfectly positively correlated assets cannot reduce the risk below the risk of the least risky asset.  Combining two assets with less than perfectly positive correlations can reduce the total risk to a level below that of either asset.

37. 5.37 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Diversification

38. 5.38 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Correlation, Diversification, Risk & Return  The lower the correlation between asset returns, the greater the potential diversification of risk.

39. 5.39 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Stock D Stock BW $2,000Stock BW $3,000Stock DStock BW’s 9% 13.15%Stock D’s8% 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 Stock BW’s expected return is 9% and its standard deviation is13.15%. Stock D’s expected return is 8% and its standard deviation is 10.65%. 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

40. 5.40 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% Determining Portfolio Expected Return

41. 5.41 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. Determining Portfolio Standard Deviation

42. 5.42 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% 8.4%Stand. Dev. Dev.13.15% 10.65% 10.91% CV CV 1.46 1.33 1.30 The portfolio has the LOWEST coefficient of variation due to diversification. Summary of the Portfolio Return and Risk Calculation

43. 5.43 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

44. 5.44 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. Total Risk SystematicRisk UnsystematicRisk Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Systematic Risk + Unsystematic Risk

45. 5.45 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Systematic Risk and Unsystematic Risk  Other names for these terms are:  Systematic risk  Unavoidable risk  Nondiversifiable risk  Unsystematic risk  Avoidable risk  Diversifiable risk

46. 5.46 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

47. 5.47 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

48. 5.48 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. Capital Asset Pricing Model (CAPM)

49. 5.49 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 – i.e all investors have similar expectations 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 Indexor similar as a proxy). CAPM Assumptions

50. 5.50 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. Characteristic Line  This is a line that describes the relationship between an individual security’s returns and returns on the market portfolio.  The slope of this line is called Beta

51. 5.51 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

52. 5.52 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. What is Beta?

53. 5.53 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

54. 5.54 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 f +  j (R M – R f ) Security Market Line

55. 5.55 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

56. 5.56 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

57. 5.57 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  Are interpreted exactly the same way as individual asset betas.  Can calculated by:   Where:  w j = The proportion of the portfolio’s dollar value represented by asset j  β j = The beta of asset j

58. 5.58 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

59. 5.59 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). BWs Required Rate of Return

60. 5.60 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer. intrinsic value dividend next period $0.50 grow5.8% 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

61. 5.61 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.  Remember, from Chapter 4, the value of a share of stock is calculated by:  V = D 1 /(k e – g)  So the intrinsic value of BW is:

62. 5.62 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

63. 5.63 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