4-1         CHAPTER 4  Risk and Return: The Basics Basic return concepts Basic risk concepts Stand-alone risk Portfoli...
4-2    What are investment returns? Investment returns measure the  financial results of an investment. Returns may be h...
4-3 What is the return on an investment   that costs $1,000 and is sold       after 1 year for $1,100? Dollar return:    ...
4-4      What is investment risk? Typically, investment returns are not  known with certainty. Investment risk pertains ...
4-5              Focus on EthicsIf It Sounds Too Good To Be True...  For many years, investors around the world   clamore...
4-6    Risk and Return Fundamentals:           Risk PreferencesEconomists use three categories to describe howinvestors re...
4-7Probability distribution                           Stock X     Stock Y                                          Rate of...
4-8              Assume the Following             Investment Alternatives Economy     Prob. T-Bill    Alta    Repo   Am F....
4-9        What is unique about         the T-bill return? The T-bill will return 8% regardless  of the state of the econ...
4 - 10Do the returns of Alta Inds. and Repo  Men move with or counter to the             economy? Alta Inds. moves with t...
4 - 11Calculate the expected rate of return        on each alternative.     ^     r = expected rate of return.         ∧  ...
4 - 12                         ^                          r  Alta                 17.4%  Market               15.0  Am. Fo...
4 - 13What is the standard deviationof returns for each alternative?      σ = Standard deviation      σ = Variance =      ...
4 - 14         n      ∧ 2                  σ = ∑  ri − r  Pi .      i =1      Alta Inds:σ = ((-22 - 17.4)20.10 + (-2...
4 - 15Prob.            T-bill              Am. F.                            Alta 0      8   13.8     17.4                ...
4 - 16 Standard deviation measures the  stand-alone risk of an investment. The larger the standard deviation,  the highe...
4 - 17    Expected Return versus Risk              ExpectedSecurity       return    Risk, σAlta Inds.     17.4%     20.0%M...
4 - 18         Return vs. Risk (Std. Dev.):         Which investment is best?         20.0%         18.0%                 ...
4 - 19            Risk of a Single Asset:            Coefficient of Variation The coefficient of variation, CV, is a meas...
4 - 20        Coefficient of Variation:CV = Standard deviation/Expected returnCVT-BILLS     = 0.0%/8.0%     = 0.0CVAlta In...
4 - 21Expected Return versus Coefficient of             Variation             Expecte     Risk:     Risk:                 ...
4 - 22            Risk of a Portfolio In real-world situations, the risk of any  single investment would not be viewed  i...
4 - 23      Portfolio Risk and ReturnAssume a two-stock portfolio with$50,000 in Alta Inds. and $50,000 inRepo Men.       ...
4 - 24        Portfolio Return, ^p                          r   ^ is a weighted average:   rp                 n           ...
4 - 25             Alternative Method                           Estimated Return  Economy      Prob.      Alta    Repo    ...
4 - 26 σ p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 +         (10.0 - 9.6)20.40 + (12.5 - 9.6)20.20         + (15.0 - 9.6)2...
4 - 27    Risk of a Portfolio: Correlation (ρ) Correlation is a statistical measure of the relationship  between any two ...
4 - 28                Figure 8.4 Correlations© 2012 Pearson Education                           8-28
4 - 29        Risk of a Portfolio: Diversification     To reduce overall risk, it is best to diversify by      combining,...
Figure 8.5      4 - 30               Diversification© 2012 Pearson Education                  8-30
4 - 31        Two-Stock Portfolios Two stocks can be combined to form  a riskless portfolio if ρ = -1.0. Risk is not red...
4 - 32      What would happen to the       risk of an average 1-stock      portfolio as more randomly     selected stocks ...
4 - 33Prob.                   Large                   2                           1 0        15                      Retur...
4 - 34σ p (%)                 Company Specific35                (Diversifiable) Risk                    Stand-Alone Risk, ...
4 - 35Stand-alone Market   Diversifiable   risk    = risk  +     risk     .Market risk is that part of a security’sstand-a...
4 - 36             Conclusions As more stocks are added, each new  stock has a smaller risk-reducing  impact on the portf...
4 - 37Can an investor holding one stock earn a return commensurate with its risk? No. Rational investors will minimize  r...
4 - 38    How is market risk measured for         individual securities? Market risk, which is relevant for stocks  held ...
4 - 39      How are betas calculated? In addition to measuring a stock’s  contribution of risk to a portfolio,  beta also...
4 - 40Using a Regression to Estimate Beta Run a regression with returns on  the stock in question plotted on  the Y axis ...
4 - 41Use the historical stock returns to   calculate the beta for PQU.Year        Market        PQU   1         25.7%    ...
4 - 42   Calculating Beta for PQU          40%               r KWE          20%              0%                           ...
4 - 43       What is beta for PQU? The regression line, and hence  beta, can be found using a  calculator with a regressi...
4 - 44    Calculating Beta in Practice Many analysts use the S&P 500 to  find the market return. Analysts typically use ...
4 - 45        How is beta interpreted? If b = 1.0, stock has average risk. If b > 1.0, stock is riskier than average. I...
4 - 46 Finding Beta Estimates on the WebGo to www.thomsonfn.com.Enter the ticker symbol for a “Stock Quote”, such as IBM...
4 - 47 Expected Return versus Market Risk                 Expected  Security        return      Risk, b  Alta            1...
4 - 48  Use the SML to calculate each   alternative’s required return. The Security Market Line (SML) is  part of the Cap...
4 - 49        Required Rates of ReturnrAlta    = 8.0% + (7%)(1.29)         = 8.0% + 9.0%         = 17.0%.rM       = 8.0% +...
4 - 50  Expected versus Required Returns            ^            r      rAlta      17.4%   17.0% UndervaluedMarket 15.0   ...
4 - 51           ri (%) SML: ri = rRF + (RPM) bi                       ri = 8% + (7%) bi                            Alta ....
4 - 52Calculate beta for a portfolio with 50%         Alta and 50% Repo      bp = Weighted average         = 0.5(bAlta) + ...
4 - 53 What is the required rate of return   on the Alta/Repo portfolio?rp = Weighted average r   = 0.5(17%) + 0.5(2%) = 9...
4 - 54Impact of Inflation Change on SMLRequired Rateof Return r (%)                          ∆ I = 3%              New SML...
Impact of Risk Aversion Change           4 - 55                    After increaseRequired Rate      in risk aversionof Ret...
4 - 56Has the CAPM been completely confirmed   or refuted through empirical tests? No. The statistical tests have  proble...
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CH 04 - Risk & Return Basics

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CH 04 - Risk & Return Basics

  1. 1. 4-1 CHAPTER 4 Risk and Return: The Basics Basic return concepts Basic risk concepts Stand-alone risk Portfolio (market) risk Risk and return: CAPM/SML
  2. 2. 4-2 What are investment returns? Investment returns measure the financial results of an investment. Returns may be historical or prospective (anticipated). Returns can be expressed in: Dollar terms. Percentage terms.
  3. 3. 4-3 What is the return on an investment that costs $1,000 and is sold after 1 year for $1,100? Dollar return: $ Received - $ Invested $1,100 - $1,000 = $100. Percentage return: $ Return/$ Invested $100/$1,000 = 0.10 = 10%.
  4. 4. 4-4 What is investment risk? Typically, investment returns are not known with certainty. Investment risk pertains to the probability of earning a return less than that expected. The greater the chance of a return far below the expected return, the greater the risk.
  5. 5. 4-5 Focus on EthicsIf It Sounds Too Good To Be True... For many years, investors around the world clamored to invest with Bernard Madoff. Madoff generated high returns year after year, seemingly with very little risk. On December 11, 2008, the U.S. Securities and Exchange Commission (SEC) charged Madoff with securities fraud. Madoff’s hedge fund, Ascot Partners, turned out to be a giant Ponzi scheme. What are some hazards of allowing investors to pursue claims based their most recent accounts statements?
  6. 6. 4-6 Risk and Return Fundamentals: Risk PreferencesEconomists use three categories to describe howinvestors respond to risk. Risk averse is the attitude toward risk in which investors would require an increased return as compensation for an increase in risk. Risk-neutral is the attitude toward risk in which investors choose the investment with the higher return regardless of its risk. Risk-seeking is the attitude toward risk in which investors prefer investments with greater risk even if they have lower expected returns.
  7. 7. 4-7Probability distribution Stock X Stock Y Rate of -20 0 15 50 return (%)  Which stock is riskier? Why?
  8. 8. 4-8 Assume the Following Investment Alternatives Economy Prob. T-Bill Alta Repo Am F. MPRecession 0.10 8.0% -22.0% 28.0% 10.0% -13.0%Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0Average 0.40 8.0 20.0 0.0 7.0 15.0Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0Boom 0.10 8.0 50.0 -20.0 30.0 43.0 1.00
  9. 9. 4-9 What is unique about the T-bill return? The T-bill will return 8% regardless of the state of the economy. Is the T-bill riskless? Explain.
  10. 10. 4 - 10Do the returns of Alta Inds. and Repo Men move with or counter to the economy? Alta Inds. moves with the economy, so it is positively correlated with the economy. This is the typical situation. Repo Men moves counter to the economy. Such negative correlation is unusual.
  11. 11. 4 - 11Calculate the expected rate of return on each alternative. ^ r = expected rate of return. ∧ n r = ∑ rP . i=1 i i ^ = 0.10(-22%) + 0.20(-2%) rAlta + 0.40(20%) + 0.20(35%) + 0.10(50%) = 17.4%.
  12. 12. 4 - 12 ^ r Alta 17.4% Market 15.0 Am. Foam 13.8 T-bill 8.0 Repo Men 1.7 Alta has the highest rate of return. Does that make it best?
  13. 13. 4 - 13What is the standard deviationof returns for each alternative? σ = Standard deviation σ = Variance = σ 2 n ∧ 2   = ∑  ri − r  Pi . i =1  
  14. 14. 4 - 14 n ∧ 2   σ = ∑  ri − r  Pi . i =1  Alta Inds:σ = ((-22 - 17.4)20.10 + (-2 - 17.4)20.20 + (20 - 17.4)20.40 + (35 - 17.4)20.20 + (50 - 17.4)20.10)1/2 = 20.0%.σ T-bills = 0.0%. σ Repo = 13.4%. σ Alta = 20.0%. σ Am Foam = 18.8%. σ Market = 15.3%.
  15. 15. 4 - 15Prob. T-bill Am. F. Alta 0 8 13.8 17.4 Rate of Return (%)
  16. 16. 4 - 16 Standard deviation measures the stand-alone risk of an investment. The larger the standard deviation, the higher the probability that returns will be far below the expected return. Coefficient of variation is an alternative measure of stand-alone risk.
  17. 17. 4 - 17 Expected Return versus Risk ExpectedSecurity return Risk, σAlta Inds. 17.4% 20.0%Market 15.0 15.3Am. Foam 13.8 18.8T-bills 8.0 0.0Repo Men 1.7 13.4
  18. 18. 4 - 18 Return vs. Risk (Std. Dev.): Which investment is best? 20.0% 18.0% Alta 16.0% Mkt 14.0% USRReturn 12.0% 10.0% 8.0% T-bills 6.0% 4.0% 2.0% Coll. 0.0% 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% Risk (Std. Dev.)
  19. 19. 4 - 19 Risk of a Single Asset: Coefficient of Variation The coefficient of variation, CV, is a measure of relative dispersion. CV is a better measure for evaluating risk in situations where investments have substantially different expected returns. A higher coefficient of variation means that an investment has more volatility relative to its expected return.
  20. 20. 4 - 20 Coefficient of Variation:CV = Standard deviation/Expected returnCVT-BILLS = 0.0%/8.0% = 0.0CVAlta Inds = 20.0%/17.4% = 1.1.CVRepo Men = 13.4%/1.7% = 7.9.CVAm. Foam = 18.8%/13.8% = 1.4.CVM = 15.3%/15.0% = 1.0.
  21. 21. 4 - 21Expected Return versus Coefficient of Variation Expecte Risk: Risk: dSecurity return σ CVAlta Inds 17.4% 20.0% 1.1Market 15.0 15.3 1.0Am. Foam 13.8 18.8 1.4T-bills 8.0 0.0 0.0Repo Men 1.7 13.4 7.9
  22. 22. 4 - 22 Risk of a Portfolio In real-world situations, the risk of any single investment would not be viewed independently of other assets. New investments must be considered in light of their impact on the risk and return of an investor’s portfolio of assets. The financial manager’s goal is to create an efficient portfolio, a portfolio that maximum return for a given level of risk.
  23. 23. 4 - 23 Portfolio Risk and ReturnAssume a two-stock portfolio with$50,000 in Alta Inds. and $50,000 inRepo Men. ^ and σ . Calculate rp p
  24. 24. 4 - 24 Portfolio Return, ^p r ^ is a weighted average: rp n ^ ^ rp = Σ wiri. i=1^rp = 0.5(17.4%) + 0.5(1.7%) = 9.6%. ^ ^ ^ rp is between rAlta and rRepo.
  25. 25. 4 - 25 Alternative Method Estimated Return Economy Prob. Alta Repo Port.Recession 0.10 -22.0% 28.0% 3.0%Below avg. 0.20 -2.0 14.7 6.4Average 0.40 20.0 0.0 10.0Above avg. 0.20 35.0 -10.0 12.5Boom 0.10 50.0 -20.0 15.0 ^ = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 rp + (12.5%)0.20 + (15.0%)0.10 = 9.6%. (More...)
  26. 26. 4 - 26 σ p = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 + (10.0 - 9.6)20.40 + (12.5 - 9.6)20.20 + (15.0 - 9.6)20.10)1/2 = 3.3%. σ p is much lower than: either stock (20% and 13.4%). average of Alta and Repo (16.7%). The portfolio provides average return but much lower risk. The key here is negative correlation.
  27. 27. 4 - 27 Risk of a Portfolio: Correlation (ρ) Correlation is a statistical measure of the relationship between any two series of numbers.  Positively correlated describes two series that move in the same direction.  Negatively correlated describes two series that move in opposite directions. The correlation coefficient is a measure of the degree of correlation between two series.  Perfectly positively correlated describes two positively correlated series that have a correlation coefficient of +1.  Perfectly negatively correlated describes two negatively correlated series that have a correlation coefficient of –1.ρ
  28. 28. 4 - 28 Figure 8.4 Correlations© 2012 Pearson Education 8-28
  29. 29. 4 - 29 Risk of a Portfolio: Diversification  To reduce overall risk, it is best to diversify by combining, or adding to the portfolio, assets that have the lowest possible correlation.  Combining assets that have a low correlation with each other can reduce the overall variability of a portfolio’s returns.  Uncorrelated describes two series that lack any interaction and therefore have a correlation coefficient close to zero.© 2012 Pearson Education 8-29
  30. 30. Figure 8.5 4 - 30 Diversification© 2012 Pearson Education 8-30
  31. 31. 4 - 31 Two-Stock Portfolios Two stocks can be combined to form a riskless portfolio if ρ = -1.0. Risk is not reduced at all if the two stocks have ρ = +1.0. In general, stocks in US markets have ρ ≈ 0.65, so risk is lowered but not eliminated. Investors typically hold many stocks. What happens when ρ = 0?
  32. 32. 4 - 32 What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added? σ p would decrease because the added stocks would not be perfectly correlated, but rp would remain relatively constant. ^ In the real world, it is impossible to form a completely riskless stock portfolio.
  33. 33. 4 - 33Prob. Large 2 1 0 15 Return σ 1 ≈ 35% ; σ Large ≈ 20%.
  34. 34. 4 - 34σ p (%) Company Specific35 (Diversifiable) Risk Stand-Alone Risk, σ p20 Market Risk0 10 20 30 40 2,000+ # Stocks in Portfolio
  35. 35. 4 - 35Stand-alone Market Diversifiable risk = risk + risk .Market risk is that part of a security’sstand-alone risk that cannot beeliminated by diversification.Firm-specific, or diversifiable, risk isthat part of a security’s stand-alonerisk that can be eliminated bydiversification.
  36. 36. 4 - 36 Conclusions As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio. σ p falls very slowly after about 40 stocks are included. The lower limit for σ p is about 20% = σ M . By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stock.
  37. 37. 4 - 37Can an investor holding one stock earn a return commensurate with its risk? No. Rational investors will minimize risk by holding portfolios. They bear only market risk, so prices and returns reflect this lower risk. The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk.
  38. 38. 4 - 38 How is market risk measured for individual securities? Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio. It is measured by a stock’s beta coefficient. For stock i, its beta is: bi = (ρ iM σ i) / σ M
  39. 39. 4 - 39 How are betas calculated? In addition to measuring a stock’s contribution of risk to a portfolio, beta also which measures the stock’s volatility relative to the market.
  40. 40. 4 - 40Using a Regression to Estimate Beta Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis. The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.
  41. 41. 4 - 41Use the historical stock returns to calculate the beta for PQU.Year Market PQU 1 25.7% 40.0% 2 8.0% -15.0% 3 -11.0% -15.0% 4 15.0% 35.0% 5 32.5% 10.0% 6 13.7% 30.0% 7 40.0% 42.0% 8 10.0% -10.0% 9 -10.8% -25.0% 10 -13.1% 25.0%
  42. 42. 4 - 42 Calculating Beta for PQU 40% r KWE 20% 0% r M-40% -20% 0% 20% 40% -20% r PQU = 0.83r M + 0.03 -40% 2 R = 0.36
  43. 43. 4 - 43 What is beta for PQU? The regression line, and hence beta, can be found using a calculator with a regression function or a spreadsheet program. In this example, b = 0.83.
  44. 44. 4 - 44 Calculating Beta in Practice Many analysts use the S&P 500 to find the market return. Analysts typically use four or five years’ of monthly returns to establish the regression line. Some analysts use 52 weeks of weekly returns.
  45. 45. 4 - 45 How is beta interpreted? If b = 1.0, stock has average risk. If b > 1.0, stock is riskier than average. If b < 1.0, stock is less risky than average. Most stocks have betas in the range of 0.5 to 1.5. Can a stock have a negative beta?
  46. 46. 4 - 46 Finding Beta Estimates on the WebGo to www.thomsonfn.com.Enter the ticker symbol for a “Stock Quote”, such as IBM or Dell, then click GO.When the quote comes up, select Company Earnings, then GO.
  47. 47. 4 - 47 Expected Return versus Market Risk Expected Security return Risk, b Alta 17.4% 1.29 Market 15.0 1.00 Am. Foam 13.8 0.68 T-bills 8.0 0.00 Repo Men 1.7 -0.86 Which of the alternatives is best?
  48. 48. 4 - 48 Use the SML to calculate each alternative’s required return. The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM).SML: ri = rRF + (RPM)bi . ^ Assume rRF = 8%; rM = rM = 15%. RPM = (rM - rRF) = 15% - 8% = 7%.
  49. 49. 4 - 49 Required Rates of ReturnrAlta = 8.0% + (7%)(1.29) = 8.0% + 9.0% = 17.0%.rM = 8.0% + (7%)(1.00) = 15.0%.rAm. F. = 8.0% + (7%)(0.68) = 12.8%.rT-bill = 8.0% + (7%)(0.00) = 8.0%.rRepo = 8.0% + (7%)(-0.86) = 2.0%.
  50. 50. 4 - 50 Expected versus Required Returns ^ r rAlta 17.4% 17.0% UndervaluedMarket 15.0 15.0 Fairly valuedAm. F. 13.8 12.8 UndervaluedT-bills 8.0 8.0 Fairly valuedRepo 1.7 2.0 Overvalued
  51. 51. 4 - 51 ri (%) SML: ri = rRF + (RPM) bi ri = 8% + (7%) bi Alta . Market rM = 15 . . rRF = 8 . T-bills Am. FoamRepo . Risk, bi-1 0 1 2 SML and Investment Alternatives
  52. 52. 4 - 52Calculate beta for a portfolio with 50% Alta and 50% Repo bp = Weighted average = 0.5(bAlta) + 0.5(bRepo) = 0.5(1.29) + 0.5(-0.86) = 0.22.
  53. 53. 4 - 53 What is the required rate of return on the Alta/Repo portfolio?rp = Weighted average r = 0.5(17%) + 0.5(2%) = 9.5%.Or use SML:rp = rRF + (RPM) bp = 8.0% + 7%(0.22) = 9.5%.
  54. 54. 4 - 54Impact of Inflation Change on SMLRequired Rateof Return r (%) ∆ I = 3% New SML SML2 18 SML1 15 11 Original situation 8 0 0.5 1.0 1.5 2.0
  55. 55. Impact of Risk Aversion Change 4 - 55 After increaseRequired Rate in risk aversionof Return (%) SML2 rM = 18% rM = 15% 18 SML1 15 ∆ RPM = 3% 8 Original situation Risk, bi 1.0
  56. 56. 4 - 56Has the CAPM been completely confirmed or refuted through empirical tests? No. The statistical tests have problems that make empirical verification or rejection virtually impossible. Investors’ required returns are based on future risk, but betas are calculated with historical data. Investors may be concerned about both stand-alone and market risk.

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