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- 1. Finance Lecture:Risk, Return and the Cost of Equity Brad Simon
- 2. Lecture Overview Risk and Return Measuring Returns Volatility Portfolios Diversification Risk Premium CAPM Summary2
- 3. Motivating the topic: Risk and Return3
- 4. Motivating the topic: Risk and Return The relationship between risk and return is fundamental to finance theory4
- 5. Motivating the topic: Risk and Return The relationship between risk and return is fundamental to finance theory You can invest very safely in a bank or in Treasury bills. Why would you invest in risky stocks and bonds?5
- 6. Motivating the topic: Risk and Return The relationship between risk and return is fundamental to finance theory You can invest very safely in a bank or in Treasury bills. Why would you invest in risky stocks and bonds? If you want the chance of earning higher returns, it requires that you take on higher risk investments6
- 7. Motivating the topic: Risk and Return The relationship between risk and return is fundamental to finance theory You can invest very safely in a bank or in Treasury bills. Why would you invest in risky stocks and bonds? If you want the chance of earning higher returns, it requires that you take on higher risk investments There is a positive relationship between risk and return7
- 8. Historical Returns8
- 9. Historical Returns Ending Price - Beginning Price Dividend Percentage Return Beginning Price Beginning Price9
- 10. Historical Returns Ending Price - Beginning Price Dividend Percentage Return Beginning Price Beginning Price Percentage Return Capital Gains Yield Dividend Yield10
- 11. Historical Returns Ending Price -Beginning Price Dividend Percentage Return Beginning Price Beginning Price Percentage Return Capital Gains Yield Dividend Yield Example: You held 250 shares of Hilton Hotel‟s common stock. The company‟s share price was $24.11 at the beginning of the year. During the year, the company paid a dividend of $0.16 per share, and ended the year at a price of $34.90. What is the dollar return, the percentage return, the capital gains yield, and the dividend yield for Hilton?11
- 12. Historical Returns12
- 13. Historical Returns Percent return = Capital gains yield + Dividend Yield13
- 14. Historical Returns Percent return = Capital gains yield + Dividend Yield Capital gains yield = ($34.90 - $24.11)/$24.11 = 44.75%14
- 15. Historical Returns Percent return = Capital gains yield + Dividend Yield Capital gains yield = ($34.90 - $24.11)/$24.11 = 44.75% Dividend yield = $0.16/$24.11 = 0.66%15
- 16. Historical Returns Percent return = Capital gains yield + Dividend Yield Capital gains yield = ($34.90 - $24.11)/$24.11 = 44.75% Dividend yield = $0.16/$24.11 = 0.66% Percent return = 44.75% + 0.66% = 45.42%16
- 17. Volatility17
- 18. Volatility High volatility in historical returns are an indication that future returns will be volatile18
- 19. Volatility High volatility in historical returns are an indication that future returns will be volatile One popular way of quantifying volatility is to compute the standard deviation of percentage returns19
- 20. Volatility High volatility in historical returns are an indication that future returns will be volatile One popular way of quantifying volatility is to compute the standard deviation of percentage returns Standard deviation is a measure of total risk20
- 21. Volatility High volatility in historical returns are an indication that future returns will be volatile One popular way of quantifying volatility is to compute the standard deviation of percentage returns Standard deviation is a measure of total risk A large standard deviation indicates greater return variability, or high risk21
- 22. Volatility High volatility in historical returns are an indication that future returns will be volatile One popular way of quantifying volatility is to compute the standard deviation of percentage returns Standard deviation is a measure of total risk A large standard deviation indicates greater return variability, or high risk N 2 (Return t - Average Return) t 1 Standard Deviation N -122
- 23. Volatility - Example23
- 24. Volatility - Example Example: Using the following returns, calculate the average return, the variance, and the standard deviation for Acme stock.24
- 25. Volatility - Example Example: Using the following returns, calculate the average return, the variance, and the standard deviation for Acme stock. Year Acme 1 10% 2 4 3 -8 4 13 5 525
- 26. Volatility - Example Average Return = (10 + 4 - 8 + 13 + 5 ) / 5 = 4.80%26
- 27. Volatility - Example Average Return = (10 + 4 - 8 + 13 + 5 ) / 5 = 4.80% σ2Acme = [(10 – 4.8)2 + (4 – 4.8)2 (- 8 – 4.8)2 + (13 – 4.8)2 + (5 – 4.8)2 ] / (5 - 1)27
- 28. Volatility - Example Average Return = (10 + 4 - 8 + 13 + 5 ) / 5 = 4.80% σ2Acme = [(10 – 4.8)2 + (4 – 4.8)2 (- 8 – 4.8)2 + (13 – 4.8)2 + (5 – 4.8)2 ] / (5 - 1) σ2Acme = 258.8 / 4 = 64.7028
- 29. Volatility - Example Average Return = (10 + 4 - 8 + 13 + 5 ) / 5 = 4.80% σ2Acme = [(10 – 4.8)2 + (4 – 4.8)2 (- 8 – 4.8)2 + (13 – 4.8)2 + (5 – 4.8)2 ] / (5 - 1) σ2Acme = 258.8 / 4 = 64.70 σAcme = (64.70)1/2 = 8.04%29
- 30. Volatility - Application30
- 31. Volatility - Application31
- 32. Volatility - Application The volatility of stocks is much higher than the volatility of bonds and T-bills32
- 33. Volatility - Application The volatility of stocks is much higher than the volatility of bonds and T-bills Different periods had differing levels of volatility for the same asset class33
- 34. Diversifying risk: Portfolios34
- 35. Diversifying risk: Portfolios In the beginning of the lecture we saw that higher risks must come with (the potential for) higher returns.35
- 36. Diversifying risk: Portfolios In the beginning of the lecture we saw that higher risks must come with (the potential for) higher returns. More volatile stocks should have, on average, higher returns.36
- 37. Diversifying risk: Portfolios In the beginning of the lecture we saw that higher risks must come with (the potential for) higher returns. More volatile stocks should have, on average, higher returns. We can reduce volatility for a given level of return by grouping assets into portfolios37
- 38. Diversifying risk: Portfolios In the beginning of the lecture we saw that higher risks must come with (the potential for) higher returns. More volatile stocks should have, on average, higher returns. We can reduce volatility for a given level of return by grouping assets into portfolios This is known as “diversifying risk”38
- 39. Diversifying risk: Example39
- 40. Diversifying risk: Example In a given year a particular pharmaceutical company may fail in getting approval of a new drug, thus causing its stock price to drop.40
- 41. Diversifying risk: Example In a given year a particular pharmaceutical company may fail in getting approval of a new drug, thus causing its stock price to drop. But it is unlikely that every pharmaceutical company will fail major drug trials in the same year.41
- 42. Diversifying risk: Example In a given year a particular pharmaceutical company may fail in getting approval of a new drug, thus causing its stock price to drop. But it is unlikely that every pharmaceutical company will fail major drug trials in the same year. On average, some are likely to be successful while others will fail.42
- 43. Diversifying risk: Example In a given year a particular pharmaceutical company may fail in getting approval of a new drug, thus causing its stock price to drop. But it is unlikely that every pharmaceutical company will fail major drug trials in the same year. On average, some are likely to be successful while others will fail. Therefore, the returns for a portfolio comprised of all drug companies will have much less volatility than that of a single drug company.43
- 44. Diversifying risk: Example (cont‟d)44
- 45. Diversifying risk: Example (cont‟d) By holding stock in the entire sector of pharmaceuticals we have eliminated quite a bit of risk as just described.45
- 46. Diversifying risk: Example (cont‟d) By holding stock in the entire sector of pharmaceuticals we have eliminated quite a bit of risk as just described. But it‟s possible there is sector-level risk that may impact all drug companies.46
- 47. Diversifying risk: Example (cont‟d) By holding stock in the entire sector of pharmaceuticals we have eliminated quite a bit of risk as just described. But it‟s possible there is sector-level risk that may impact all drug companies. For example, if the FDA changes its drug- approval policy and requires all new drugs to go through more strict testing we would expect the entire sector – and our portfolio comprised of all pharmaceutical companies – to suffer.47
- 48. Diversifying risk: Example (cont‟d) By holding stock in the entire sector of pharmaceuticals we have eliminated quite a bit of risk as just described. But it‟s possible there is sector-level risk that may impact all drug companies. For example, if the FDA changes its drug- approval policy and requires all new drugs to go through more strict testing we would expect the entire sector – and our portfolio comprised of all pharmaceutical companies – to suffer. But what if we held a portfolio of not just pharmaceuticals but also of computer companies,48 manufacturing companies, service companies
- 49. Diversifying risk: Example (cont‟d)49
- 50. Diversifying risk: Example (cont‟d) We would expect this expanded portfolio to be even less risky than a portfolio comprised of just one sector.50
- 51. Diversifying risk: Example (cont‟d) We would expect this expanded portfolio to be even less risky than a portfolio comprised of just one sector. In fact, we can imagine a market-level portfolio comprised of all assets.51
- 52. Diversifying risk: Example (cont‟d) We would expect this expanded portfolio to be even less risky than a portfolio comprised of just one sector. In fact, we can imagine a market-level portfolio comprised of all assets. Such a market portfolio would still have uncertainty and risk but it would be greatly reduced compared to just one asset or even a group of related assets52
- 53. Diversifying risk: Example (cont‟d) We would expect this expanded portfolio to be even less risky than a portfolio comprised of just one sector. In fact, we can imagine a market-level portfolio comprised of all assets. Such a market portfolio would still have uncertainty and risk but it would be greatly reduced compared to just one asset or even a group of related assets We can then think of risk as having two53 components:
- 54. Diversifying risk: Example (cont‟d) We would expect this expanded portfolio to be even less risky than a portfolio comprised of just one sector. In fact, we can imagine a market-level portfolio comprised of all assets. Such a market portfolio would still have uncertainty and risk but it would be greatly reduced compared to just one asset or even a group of related assets We can then think of risk as having two54 components: Firm-specific risk (or asset-specific risk)
- 55. Diversifying risk: Example (cont‟d) We would expect this expanded portfolio to be even less risky than a portfolio comprised of just one sector. In fact, we can imagine a market-level portfolio comprised of all assets. Such a market portfolio would still have uncertainty and risk but it would be greatly reduced compared to just one asset or even a group of related assets We can then think of risk as having two55 components: Firm-specific risk (or asset-specific risk)
- 56. Diversifying risk: Example (cont‟d)56
- 57. Diversifying risk: Example (cont‟d) Firm-specific risk can be diversified away57
- 58. Diversifying risk: Example (cont‟d) Firm-specific risk can be diversified away Market-level risk cannot be eliminated58
- 59. Diversifying risk: Naming59
- 60. Diversifying risk: Naming Firm-specific risk is also called: Asset-specific risk Diversifiable risk Idiosyncratic risk Unsystematic risk60
- 61. Diversifying risk: Naming Firm-specific risk is also called: Asset-specific risk Diversifiable risk Idiosyncratic risk Unsystematic risk Market-level risk is also called: Systematic Risk Market risk Non-diversifiable risk61
- 62. Diversifying risk: Graph62
- 63. Diversifying risk: Graph63
- 64. Diversifying risk: Conclusions64
- 65. Diversifying risk: Conclusions Investors are only compensated for risks their bear.65
- 66. Diversifying risk: Conclusions Investors are only compensated for risks their bear. Any risks which can be diversified away will not be compensated.66
- 67. Diversifying risk: Conclusions Investors are only compensated for risks their bear. Any risks which can be diversified away will not be compensated. We want to understand how to create portfolios which produce the maximum risk diversification.67
- 68. Diversifying risk: Conclusions Investors are only compensated for risks their bear. Any risks which can be diversified away will not be compensated. We want to understand how to create portfolios which produce the maximum risk diversification. We call such portfolios, “optimal portfolios”68
- 69. Optimal Portfolios69
- 70. Optimal Portfolios A portfolio is a collection of assets (stocks, bonds, real estate, etc.)70
- 71. Optimal Portfolios A portfolio is a collection of assets (stocks, bonds, real estate, etc.) Holding different combinations of assets results in different risk and return characteristics.71
- 72. Optimal Portfolios A portfolio is a collection of assets (stocks, bonds, real estate, etc.) Holding different combinations of assets results in different risk and return characteristics. We can construct portfolios with “optimal” levels of return for a given level of risk.72
- 73. Optimal Portfolios A portfolio is a collection of assets (stocks, bonds, real estate, etc.) Holding different combinations of assets results in different risk and return characteristics. We can construct portfolios with “optimal” levels of return for a given level of risk. We call such portfolios, “efficient portfolios”73
- 74. Optimal Portfolios74
- 75. Optimal Portfolios75
- 76. Optimal Portfolios The curve drawn through all the efficient portfolios is known as the “Efficiency Frontier”76
- 77. Optimal Portfolios The curve drawn through all the efficient portfolios is known as the “Efficiency Frontier” We will come back to this later.77
- 78. How does diversification work?78
- 79. How does diversification work? Diversification comes when stocks are subject to different kinds of events such that their returns differ over time, i.e. the stock‟s returns are not perfectly correlated. Their price movements often counteract each other79
- 80. How does diversification work? Diversification comes when stocks are subject to different kinds of events such that their returns differ over time, i.e. the stock‟s returns are not perfectly correlated. Their price movements often counteract each other By contrast, if two stocks are perfectly positively correlated, diversification has no effect on risk.80
- 81. Risk Premium81
- 82. Risk Premium We have previously said that the higher the risk an investment is, the higher the return it needs to offer.82
- 83. Risk Premium We have previously said that the higher the risk an investment is, the higher the return it needs to offer. We can re-state this concept in the following way:83
- 84. Risk Premium We have previously said that the higher the risk an investment is, the higher the return it needs to offer. We can re-state this concept in the following way: An investment in a risk-free US Treasury bill offers a low return with no risk84
- 85. Risk Premium We have previously said that the higher the risk an investment is, the higher the return it needs to offer. We can re-state this concept in the following way: An investment in a risk-free US Treasury bill offers a low return with no risk Investors who take on risk expect a higher return compared to this risk-free opportunity, therefore:85
- 86. Risk Premium We have previously said that the higher the risk an investment is, the higher the return it needs to offer. We can re-state this concept in the following way: An investment in a risk-free US Treasury bill offers a low return with no risk Investors who take on risk expect a higher return compared to this risk-free opportunity, therefore: Required Return = Risk-free Rate + Risk Premium86
- 87. Risk Premium We have previously said that the higher the risk an investment is, the higher the return it needs to offer. We can re-state this concept in the following way: An investment in a risk-free US Treasury bill offers a low return with no risk Investors who take on risk expect a higher return compared to this risk-free opportunity, therefore: Required Return = Risk-free Rate + Risk Premium87 The risk-free rate equals the real interest rate and expected
- 88. Risk Premium We have previously said that the higher the risk an investment is, the higher the return it needs to offer. We can re-state this concept in the following way: An investment in a risk-free US Treasury bill offers a low return with no risk Investors who take on risk expect a higher return compared to this risk-free opportunity, therefore: Required Return = Risk-free Rate + Risk Premium The risk-free rate equals the real interest rate and expected inflation88 Typically considered the return on U.S. government
- 89. Risk Premium89
- 90. Risk Premium The risk premium is the reward investors require for taking risk90
- 91. Risk Premium The risk premium is the reward investors require for taking risk But the market doesn‟t reward all risks91
- 92. Risk Premium The risk premium is the reward investors require for taking risk But the market doesn‟t reward all risks Since the firm-specific portion of risk can be diversified away, an efficient market will not reward investors for taking this risk92
- 93. Risk Premium The risk premium is the reward investors require for taking risk But the market doesn‟t reward all risks Since the firm-specific portion of risk can be diversified away, an efficient market will not reward investors for taking this risk The market rewards only the remaining risk after the firm-specific risk is diversified away: the market risk93
- 94. Risk Premium - Examples94
- 95. Risk Premium - Examples Below are historical market-level risk premia over different historical time periods:95
- 96. CAPM96
- 97. CAPM We can combine our concepts of optimal portfolios, the efficiency frontier and risk premium to create a theory seeking to relate an asset‟s risk characteristics to its required risk premium (i.e. it‟s return)97
- 98. CAPM We can combine our concepts of optimal portfolios, the efficiency frontier and risk premium to create a theory seeking to relate an asset‟s risk characteristics to its required risk premium (i.e. it‟s return) Such a theory is called an “asset pricing theory”98
- 99. CAPM We can combine our concepts of optimal portfolios, the efficiency frontier and risk premium to create a theory seeking to relate an asset‟s risk characteristics to its required risk premium (i.e. it‟s return) Such a theory is called an “asset pricing theory” The most famous asset pricing theory is the Capital Asset Pricing Model (or CAPM)99
- 100. CAPM We can combine our concepts of optimal portfolios, the efficiency frontier and risk premium to create a theory seeking to relate an asset‟s risk characteristics to its required risk premium (i.e. it‟s return) Such a theory is called an “asset pricing theory” The most famous asset pricing theory is the Capital Asset Pricing Model (or CAPM)100
- 101. CAPM101
- 102. CAPM We saw how we can construct an efficiency frontier comprised of „efficient portfolios.‟102
- 103. CAPM We saw how we can construct an efficiency frontier comprised of „efficient portfolios.‟ Each portfolio combines a group of assets in such a way that they provide the highest expected return for a given level of risk.103
- 104. CAPM We saw how we can construct an efficiency frontier comprised of „efficient portfolios.‟ Each portfolio combines a group of assets in such a way that they provide the highest expected return for a given level of risk.104
- 105. CAPM105
- 106. CAPM The horizontal axis in this example starts at 10% risk (the standard deviation or volatility)106
- 107. CAPM The horizontal axis in this example starts at 10% risk (the standard deviation or volatility) But we could modify this graph – and our portfolio – by including some amount of the risk-free asset.107
- 108. CAPM108
- 109. CAPM109
- 110. CAPM The top graph is simply the Efficiency frontier from the prior slide.110
- 111. CAPM The top graph is simply the Efficiency frontier from the prior slide. The bottom graph now includes the risk- free asset and the efficiency frontier.111
- 112. CAPM The top graph is simply the Efficiency frontier from the prior slide. The bottom graph now includes the risk- free asset and the efficiency frontier. We can imagine a line being drawn that starts at the risk-free asset and running tangent to the112 efficiency frontier
- 113. CAPM The top graph is simply the Efficiency frontier from the prior slide. The bottom graph now includes the risk-free asset and the efficiency frontier. We can imagine a line being drawn that starts at the risk-free asset and running tangent to the efficiency frontier Such a line is known as the Capital Market Line (CML).113
- 114. CAPM114
- 115. CAPM115
- 116. CAPM By using holding some combination of the risk-free asset and an optimal portfolio we can maximize our expected return.116
- 117. CAPM By using holding some combination of the risk-free asset and an optimal portfolio we can maximize our expected return. Such returns reside on the Capital Market Line.117
- 118. CAPM By using holding some combination of the risk-free asset and an optimal portfolio we can maximize our expected return. Such returns reside on the Capital Market Line. The CML demonstrates that an investor will hold the market portfolio. Since such an investor will be fully diversified, the only relevant risk is market risk.118
- 119. CAPM119
- 120. CAPM Since the investor has only market risk, it would be desirable to have a measure of risk that measured only market risk120
- 121. CAPM Since the investor has only market risk, it would be desirable to have a measure of risk that measured only market risk Such as measure is called beta (β):121
- 122. CAPM Since the investor has only market risk, it would be desirable to have a measure of risk that measured only market risk Such as measure is called beta (β): Required Return = Rf + β(Risk PremuimMarket)122
- 123. CAPM Since the investor has only market risk, it would be desirable to have a measure of risk that measured only market risk Such as measure is called beta (β): Required Return = Rf + β(Risk PremuimMarket) Required Return = Rf + β(RM – Rf)123
- 124. CAPM124
- 125. CAPM Beta measures the co-movement between a stock and the market portfolio125
- 126. CAPM Beta measures the co-movement between a stock and the market portfolio The beta of the overall market is 1126
- 127. CAPM Beta measures the co-movement between a stock and the market portfolio The beta of the overall market is 1 Stocks with betas greater than 1 are considered riskier than the market portfolio and are called aggressive stocks127
- 128. CAPM Beta measures the co-movement between a stock and the market portfolio The beta of the overall market is 1 Stocks with betas greater than 1 are considered riskier than the market portfolio and are called aggressive stocks Stocks with betas less than 1 are less risky than the market portfolio and are called defensive stocks128
- 129. CAPM129
- 130. CAPM130
- 131. CAPM The CAPM equation allows us to estimate any stock‟s required return once we have determined the stock‟s beta, risk-free rate and market-risk premium.131
- 132. CAPM The CAPM equation allows us to estimate any stock‟s required return once we have determined the stock‟s beta, risk-free rate and market-risk premium. CAPM Equation is: Required Return = Rf + β(RM – Rf)132
- 133. CAPM The CAPM equation allows us to estimate any stock‟s required return once we have determined the stock‟s beta, risk-free rate and market-risk premium. CAPM Equation is: Required Return = Rf + β(RM – Rf) Example:133
- 134. CAPM The CAPM equation allows us to estimate any stock‟s required return once we have determined the stock‟s beta, risk-free rate and market-risk premium. CAPM Equation is: Required Return = Rf + β(RM – Rf) Example: Let‟s say we expect the market portfolio to earn 12%, and T-bill yields are 5%. Home Depot has a beta of 1.08. Calculate Home Depot‟s required return134
- 135. CAPM The CAPM equation allows us to estimate any stock‟s required return once we have determined the stock‟s beta, risk-free rate and market-risk premium. CAPM Equation is: Required Return = Rf + β(RM – Rf) Example: Let‟s say we expect the market portfolio to earn 12%, and T-bill yields are 5%. Home Depot has a beta of 1.08. Calculate Home Depot‟s required return Required Return = 5% + 1.08(12% - 5%) = 12.56%135
- 136. CAPM136
- 137. CAPM Finding Beta137
- 138. CAPM Finding Beta The easiest way to find betas is to look them up. Many companies provide betas:138
- 139. CAPM Finding Beta The easiest way to find betas is to look them up. Many companies provide betas: Value Line Investment Survey Hoovers MSN Money Yahoo! Finance Zacks139
- 140. CAPM Finding Beta The easiest way to find betas is to look them up. Many companies provide betas: Value Line Investment Survey Hoovers MSN Money Yahoo! Finance Zacks You can also calculate beta for yourself140
- 141. Caveats141
- 142. Caveats Measures of betas for a given asset can vary depending on how it is calculated142
- 143. Caveats Measures of betas for a given asset can vary depending on how it is calculated The “risk / return” relationship rests on the assumption that the stock (or asset) is priced “correctly”143
- 144. Caveats Measures of betas for a given asset can vary depending on how it is calculated The “risk / return” relationship rests on the assumption that the stock (or asset) is priced “correctly” This in turn, requires that asset markets price assets correctly144
- 145. Caveats Measures of betas for a given asset can vary depending on how it is calculated The “risk / return” relationship rests on the assumption that the stock (or asset) is priced “correctly” This in turn, requires that asset markets price assets correctly Given historical events and other evidence, there are reasons to question how “efficient” markets are at pricing an asset at its true price145
- 146. Summary146
- 147. Summary We need the expectation of extra reward for taking on more risk147
- 148. Summary We need the expectation of extra reward for taking on more risk An asset‟s risk premium is the additional compensation required above the risk-free rate for holding that asset148
- 149. Summary We need the expectation of extra reward for taking on more risk An asset‟s risk premium is the additional compensation required above the risk-free rate for holding that asset At the market level, the market risk premium is the additional return above the risk-free rate to hold the market portfolio149
- 150. Summary We need the expectation of extra reward for taking on more risk An asset‟s risk premium is the additional compensation required above the risk-free rate for holding that asset At the market level, the market risk premium is the additional return above the risk-free rate to hold the market portfolio For a given asset, the CAPM will tell us how much return we will require for holding that asset relative to the risk free rate and market portfolio150
- 151. Summary We need the expectation of extra reward for taking on more risk An asset‟s risk premium is the additional compensation required above the risk-free rate for holding that asset At the market level, the market risk premium is the additional return above the risk-free rate to hold the market portfolio For a given asset, the CAPM will tell us how much return we will require for holding that asset relative to the risk free rate and market portfolio Required Return = Rf + β(RM – Rf)151
- 152. Summary We need the expectation of extra reward for taking on more risk An asset‟s risk premium is the additional compensation required above the risk-free rate for holding that asset At the market level, the market risk premium is the additional return above the risk-free rate to hold the market portfolio For a given asset, the CAPM will tell us how much return we will require for holding that asset relative to the risk free rate and market portfolio Required Return = Rf + β(RM – Rf)152

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