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# Fm10e ch06

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### Fm10e ch06

1. 1. Chapter 6 - Risk and Rates of Return  2005, Pearson Prentice Hall
2. 2. Chapter 6: Objectives <ul><li>Inflation and rates of return </li></ul><ul><li>How to measure risk </li></ul><ul><li>(variance, standard deviation, beta) </li></ul><ul><li>How to reduce risk </li></ul><ul><li>(diversification) </li></ul><ul><li>How to price risk </li></ul><ul><li>(security market line, Capital Asset Pricing Model) </li></ul>
3. 3. Inflation, Rates of Return, and the Fisher Effect Interest Rates
4. 4. Interest Rates Conceptually :
5. 5. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf
6. 6. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf =
7. 7. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k*
8. 8. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* +
9. 9. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP
10. 10. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP Mathematically :
11. 11. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP Mathematically : (1 + k rf ) = (1 + k*) (1 + IRP)
12. 12. Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP Mathematically : (1 + k rf ) = (1 + k*) (1 + IRP) This is known as the “ Fisher Effect ”
13. 13. <ul><li>Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium? </li></ul><ul><li>(1 + k rf ) = (1 + k*) (1 + IRP) </li></ul><ul><li>(1.08) = (1.03) (1 + IRP) </li></ul><ul><li>(1 + IRP) = (1.0485), so </li></ul><ul><li>IRP = 4.85% </li></ul>Interest Rates
14. 14. Term Structure of Interest Rates <ul><li>The pattern of rates of return for debt securities that differ only in the length of time to maturity. </li></ul>
15. 15. Term Structure of Interest Rates <ul><li>The pattern of rates of return for debt securities that differ only in the length of time to maturity. </li></ul>yield to maturity time to maturity (years)
16. 16. Term Structure of Interest Rates <ul><li>The pattern of rates of return for debt securities that differ only in the length of time to maturity. </li></ul>yield to maturity time to maturity (years)
17. 17. Term Structure of Interest Rates <ul><li>The yield curve may be downward sloping or “inverted” if rates are expected to fall. </li></ul>yield to maturity time to maturity (years)
18. 18. Term Structure of Interest Rates <ul><li>The yield curve may be downward sloping or “inverted” if rates are expected to fall. </li></ul>yield to maturity time to maturity (years)
19. 19. For a Treasury security, what is the required rate of return?
20. 20. For a Treasury security, what is the required rate of return? Required rate of return =
21. 21. For a Treasury security, what is the required rate of return? <ul><li>Since Treasuries are essentially free of default risk , the rate of return on a Treasury security is considered the “ risk-free ” rate of return. </li></ul>Required rate of return = Risk-free rate of return
22. 22. For a corporate stock or bond , what is the required rate of return?
23. 23. For a corporate stock or bond , what is the required rate of return? Required rate of return =
24. 24. For a corporate stock or bond , what is the required rate of return? Required rate of return = Risk-free rate of return
25. 25. For a corporate stock or bond , what is the required rate of return? <ul><li>How large of a risk premium should we require to buy a corporate security? </li></ul>Required rate of return = + Risk-free rate of return Risk premium
26. 26. Returns <ul><li>Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc. </li></ul><ul><li>Required Return - the return that an investor requires on an asset given its risk and market interest rates. </li></ul>
27. 27. Expected Return <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><li>For each firm, the expected return on the stock is just a weighted average : </li></ul>
28. 28. <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><li>For each firm, the expected return on the stock is just a weighted average : </li></ul><ul><li>k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn </li></ul>Expected Return
29. 29. Expected Return <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><li>k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn </li></ul><ul><li>k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10% </li></ul>
30. 30. Expected Return <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><li>k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn </li></ul><ul><li>k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14% </li></ul>
31. 31. <ul><li>Based only on your expected return calculations, which stock would you prefer? </li></ul>
32. 32. RISK? Have you considered
33. 33. What is Risk? <ul><li>The possibility that an actual return will differ from our expected return. </li></ul><ul><li>Uncertainty in the distribution of possible outcomes. </li></ul>
34. 34. What is Risk? <ul><li>Uncertainty in the distribution of possible outcomes. </li></ul>
35. 35. What is Risk? <ul><li>Uncertainty in the distribution of possible outcomes. </li></ul>Company A return
36. 36. What is Risk? <ul><li>Uncertainty in the distribution of possible outcomes. </li></ul>return Company B Company A return
37. 37. How do We Measure Risk? <ul><li>To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year. </li></ul>52 weeks Yld Vol Net Hi Lo Sym Div % PE 100s Hi Lo Close Chg 134 80 IBM .52 .5 21 143402 98 95 95 49 -3 115 40 MSFT … 29 558918 55 52 51 94 -4 75
38. 38. How do We Measure Risk? <ul><li>A more scientific approach is to examine the stock’s standard deviation of returns. </li></ul><ul><li>Standard deviation is a measure of the dispersion of possible outcomes . </li></ul><ul><li>The greater the standard deviation, the greater the uncertainty, and, therefore, the greater the risk. </li></ul>
39. 39. Standard Deviation <ul><li>= (k i - k) 2 P(k i ) </li></ul> n i =1 
40. 40. <ul><li>Orlando Utility, Inc. </li></ul>= (k i - k) 2 P(k i )  n i =1 
41. 41. <ul><li>Orlando Utility, Inc. </li></ul><ul><li>( 4% - 10%) 2 (.2) = 7.2 </li></ul>= (k i - k) 2 P(k i )  n i =1 
42. 42. <ul><li>Orlando Utility, Inc. </li></ul><ul><li>( 4% - 10%) 2 (.2) = 7.2 </li></ul><ul><li>(10% - 10%) 2 (.5) = 0 </li></ul>= (k i - k) 2 P(k i )  n i =1 
43. 43. <ul><li>Orlando Utility, Inc. </li></ul><ul><li>( 4% - 10%) 2 (.2) = 7.2 </li></ul><ul><li>(10% - 10%) 2 (.5) = 0 </li></ul><ul><li>(14% - 10%) 2 (.3) = 4.8 </li></ul>= (k i - k) 2 P(k i )  n i =1 
44. 44. <ul><li>Orlando Utility, Inc. </li></ul><ul><li>( 4% - 10%) 2 (.2) = 7.2 </li></ul><ul><li>(10% - 10%) 2 (.5) = 0 </li></ul><ul><li>(14% - 10%) 2 (.3) = 4.8 </li></ul><ul><li>Variance = 12 </li></ul>= (k i - k) 2 P(k i )  n i =1 
45. 45. <ul><li>Orlando Utility, Inc. </li></ul><ul><li>( 4% - 10%) 2 (.2) = 7.2 </li></ul><ul><li>(10% - 10%) 2 (.5) = 0 </li></ul><ul><li>(14% - 10%) 2 (.3) = 4.8 </li></ul><ul><li>Variance = 12 </li></ul><ul><li>Stand. dev. = 12 = </li></ul>= (k i - k) 2 P(k i )  n i =1 
46. 46. <ul><li>Orlando Utility, Inc. </li></ul><ul><li>( 4% - 10%) 2 (.2) = 7.2 </li></ul><ul><li>(10% - 10%) 2 (.5) = 0 </li></ul><ul><li>(14% - 10%) 2 (.3) = 4.8 </li></ul><ul><li>Variance = 12 </li></ul><ul><li>Stand. dev. = 12 = 3.46% </li></ul>= (k i - k) 2 P(k i )  n i =1 
47. 47. <ul><li>Orlando Technology, Inc. </li></ul>= (k i - k) 2 P(k i )  n i =1 
48. 48. <ul><li>Orlando Technology, Inc. </li></ul><ul><li>(-10% - 14%) 2 (.2) = 115.2 </li></ul>= (k i - k) 2 P(k i )  n i =1 
49. 49. <ul><li>Orlando Technology, Inc. </li></ul><ul><li>(-10% - 14%) 2 (.2) = 115.2 </li></ul><ul><li>(14% - 14%) 2 (.5) = 0 </li></ul>= (k i - k) 2 P(k i )  n i =1 
50. 50. <ul><li>Orlando Technology, Inc. </li></ul><ul><li>(-10% - 14%) 2 (.2) = 115.2 </li></ul><ul><li>(14% - 14%) 2 (.5) = 0 </li></ul><ul><li>(30% - 14%) 2 (.3) = 76.8 </li></ul>= (k i - k) 2 P(k i )  n i =1 
51. 51. <ul><li>Orlando Technology, Inc. </li></ul><ul><li>(-10% - 14%) 2 (.2) = 115.2 </li></ul><ul><li>(14% - 14%) 2 (.5) = 0 </li></ul><ul><li>(30% - 14%) 2 (.3) = 76.8 </li></ul><ul><li>Variance = 192 </li></ul>= (k i - k) 2 P(k i )  n i =1 
52. 52. <ul><li>Orlando Technology, Inc. </li></ul><ul><li>(-10% - 14%) 2 (.2) = 115.2 </li></ul><ul><li>(14% - 14%) 2 (.5) = 0 </li></ul><ul><li>(30% - 14%) 2 (.3) = 76.8 </li></ul><ul><li>Variance = 192 </li></ul><ul><li>Stand. dev. = 192 = </li></ul>= (k i - k) 2 P(k i )  n i =1 
53. 53. <ul><li>Orlando Technology, Inc. </li></ul><ul><li>(-10% - 14%) 2 (.2) = 115.2 </li></ul><ul><li>(14% - 14%) 2 (.5) = 0 </li></ul><ul><li>(30% - 14%) 2 (.3) = 76.8 </li></ul><ul><li>Variance = 192 </li></ul><ul><li>Stand. dev. = 192 = 13.86% </li></ul>= (k i - k) 2 P(k i )  n i =1 
54. 54. <ul><li>Which stock would you prefer? </li></ul><ul><li>How would you decide? </li></ul>
55. 55. <ul><li>Which stock would you prefer? </li></ul><ul><li>How would you decide? </li></ul>
56. 56. <ul><li>Orlando Orlando </li></ul><ul><li> Utility Technology </li></ul><ul><li>Expected Return 10% 14% </li></ul><ul><li>Standard Deviation 3.46% 13.86% </li></ul>Summary
57. 57. <ul><li>It depends on your tolerance for risk! </li></ul><ul><li>Remember, there’s a tradeoff between risk and return. </li></ul>
58. 58. <ul><li>It depends on your tolerance for risk! </li></ul><ul><li>Remember, there’s a tradeoff between risk and return. </li></ul>Return Risk
59. 59. <ul><li>It depends on your tolerance for risk! </li></ul><ul><li>Remember, there’s a tradeoff between risk and return. </li></ul>Return Risk
60. 60. Portfolios <ul><li>Combining several securities in a portfolio can actually reduce overall risk . </li></ul><ul><li>How does this work? </li></ul>
61. 61. Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time
62. 62. Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time k A
63. 63. Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time k A k B
64. 64. What has happened to the variability of returns for the portfolio? rate of return time k A k B
65. 65. What has happened to the variability of returns for the portfolio? rate of return time k p k A k B
66. 66. Diversification <ul><li>Investing in more than one security to reduce risk . </li></ul><ul><li>If two stocks are perfectly positively correlated , diversification has no effect on risk. </li></ul><ul><li>If two stocks are perfectly negatively correlated , the portfolio is perfectly diversified. </li></ul>
67. 67. <ul><li>If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified? </li></ul><ul><li>YES! </li></ul><ul><li>Would you have eliminated all of your risk? </li></ul><ul><li>NO! Common stock portfolios still have risk. </li></ul>
68. 68. Some risk can be diversified away and some cannot. <ul><li>Market risk ( systematic risk) is nondiversifiable. This type of risk cannot be diversified away. </li></ul><ul><li>Company-unique risk (unsystematic risk) is diversifiable . This type of risk can be reduced through diversification. </li></ul>
69. 69. Market Risk <ul><li>Unexpected changes in interest rates. </li></ul><ul><li>Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle. </li></ul>
70. 70. Company-unique Risk <ul><li>A company’s labor force goes on strike. </li></ul><ul><li>A company’s top management dies in a plane crash. </li></ul><ul><li>A huge oil tank bursts and floods a company’s production area. </li></ul>
71. 71. <ul><li>As you add stocks to your portfolio, company-unique risk is reduced. </li></ul>
72. 72. <ul><li>As you add stocks to your portfolio, company-unique risk is reduced. </li></ul>portfolio risk number of stocks
73. 73. <ul><li>As you add stocks to your portfolio, company-unique risk is reduced. </li></ul>portfolio risk number of stocks Market risk
74. 74. <ul><li>As you add stocks to your portfolio, company-unique risk is reduced. </li></ul>portfolio risk number of stocks Market risk company- unique risk
75. 75. Do some firms have more market risk than others? <ul><li>Yes . For example: </li></ul><ul><li>Interest rate changes affect all firms, but which would be more affected: </li></ul><ul><li>a) Retail food chain </li></ul><ul><li>b) Commercial bank </li></ul>
76. 76. <ul><li>Yes . For example: </li></ul><ul><li>Interest rate changes affect all firms, but which would be more affected: </li></ul><ul><li>a) Retail food chain </li></ul><ul><li>b) Commercial bank </li></ul>Do some firms have more market risk than others?
77. 77. <ul><li>Note </li></ul><ul><li>As we know, the market compensates investors for accepting risk - but only for market risk . Company-unique risk can and should be diversified away. </li></ul><ul><li>So - we need to be able to measure market risk. </li></ul>
78. 78. This is why we have Beta. <ul><li>Beta: a measure of market risk. </li></ul><ul><li>Specifically, beta is a measure of how an individual stock’s returns vary with market returns. </li></ul><ul><li>It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market. </li></ul>
79. 79. <ul><li>A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market. </li></ul><ul><li>A firm with a beta > 1 is more volatile than the market. </li></ul>The market’s beta is 1
80. 80. <ul><li>A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market. </li></ul><ul><li>A firm with a beta > 1 is more volatile than the market. </li></ul><ul><ul><li>(ex: technology firms) </li></ul></ul>The market’s beta is 1
81. 81. <ul><li>A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market. </li></ul><ul><li>A firm with a beta > 1 is more volatile than the market. </li></ul><ul><ul><li>(ex: technology firms) </li></ul></ul><ul><li>A firm with a beta < 1 is less volatile than the market. </li></ul>The market’s beta is 1
82. 82. <ul><li>A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market. </li></ul><ul><li>A firm with a beta > 1 is more volatile than the market. </li></ul><ul><ul><li>(ex: technology firms) </li></ul></ul><ul><li>A firm with a beta < 1 is less volatile than the market. </li></ul><ul><ul><li>(ex: utilities) </li></ul></ul>The market’s beta is 1
83. 83. Calculating Beta
84. 84. Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns
85. 85. Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86. 86. Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87. 87. Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beta = slope = 1.20
88. 88. Summary: <ul><li>We know how to measure risk, using standard deviation for overall risk and beta for market risk. </li></ul><ul><li>We know how to reduce overall risk to only market risk through diversification . </li></ul><ul><li>We need to know how to price risk so we will know how much extra return we should require for accepting extra risk. </li></ul>
89. 89. What is the Required Rate of Return? <ul><li>The return on an investment required by an investor given market interest rates and the investment’s risk . </li></ul>
90. 90. Required rate of return =
91. 91. Required rate of return = + Risk-free rate of return
92. 92. Required rate of return = + Risk-free rate of return Risk premium
93. 93. market risk Required rate of return = + Risk-free rate of return Risk premium
94. 94. market risk company- unique risk Required rate of return = + Risk-free rate of return Risk premium
95. 95. market risk company- unique risk can be diversified away Required rate of return = + Risk-free rate of return Risk premium
96. 96. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>Beta Let’s try to graph this relationship!
97. 97. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Risk-free rate of return (6%) Beta 12% 1
98. 98. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Risk-free rate of return (6%) Beta 12% 1 security market line (SML)
99. 99. <ul><li>This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM). </li></ul>
100. 100. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Risk-free rate of return (6%) Beta 12% 1 SML 0
101. 101. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Risk-free rate of return (6%) Beta 12% 1 SML 0 Is there a riskless (zero beta) security?
102. 102. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>Beta . 12% 1 SML 0 Is there a riskless (zero beta) security? Treasury securities are as close to riskless as possible. Risk-free rate of return (6%)
103. 103. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML Where does the S&P 500 fall on the SML? Risk-free rate of return (6%) 0
104. 104. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML Where does the S&P 500 fall on the SML? The S&P 500 is a good approximation for the market Risk-free rate of return (6%) 0
105. 105. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML Utility Stocks Risk-free rate of return (6%) 0
106. 106. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML High-tech stocks Risk-free rate of return (6%) 0
107. 107. The CAPM equation:
108. 108. <ul><li>k j = k rf + j (k m - k rf ) </li></ul>The CAPM equation: 
109. 109. <ul><li>k j = k rf + j (k m - k rf ) </li></ul><ul><li>where: </li></ul><ul><li>k j = the required return on security j, </li></ul><ul><li>k rf = the risk-free rate of interest, </li></ul><ul><li>j = the beta of security j, and </li></ul><ul><li>k m = the return on the market index. </li></ul>The CAPM equation:  
110. 110. Example: <ul><li>Suppose the Treasury bond rate is 6% , the average return on the S&P 500 index is 12% , and Walt Disney has a beta of 1.2 . </li></ul><ul><li>According to the CAPM , what should be the required rate of return on Disney stock? </li></ul>
111. 111. k j = k rf + (k m - k rf ) <ul><li>k j = .06 + 1.2 (.12 - .06) </li></ul><ul><li>k j = .132 = 13.2% </li></ul><ul><li>According to the CAPM, Disney stock should be priced to give a 13.2% return. </li></ul>
112. 112. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML 0 Risk-free rate of return (6%)
113. 113. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML 0 Theoretically, every security should lie on the SML Risk-free rate of return (6%)
114. 114. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML 0 Theoretically, every security should lie on the SML If every stock is on the SML, investors are being fully compensated for risk. Risk-free rate of return (6%)
115. 115. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML 0 If a security is above the SML, it is underpriced. Risk-free rate of return (6%)
116. 116. <ul><li>Required </li></ul><ul><li>rate of </li></ul><ul><li>return </li></ul>. Beta 12% 1 SML 0 If a security is above the SML, it is underpriced. If a security is below the SML, it is overpriced. Risk-free rate of return (6%)
117. 117. Simple Return Calculations
118. 118. Simple Return Calculations t t+1 \$50 \$60
119. 119. Simple Return Calculations = = 20% P t+1 - P t 60 - 50 P t 50 t t+1 \$50 \$60
120. 120. Simple Return Calculations P t+1 60 P t 50 - 1 = -1 = 20% = = 20% P t+1 - P t 60 - 50 P t 50 t t+1 \$50 \$60
121. 121. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 Feb \$63.80 Mar \$59.00 Apr \$62.00 May \$64.50 Jun \$69.00 Jul \$69.00 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
122. 122. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 Mar \$59.00 Apr \$62.00 May \$64.50 Jun \$69.00 Jul \$69.00 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
123. 123. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 Apr \$62.00 May \$64.50 Jun \$69.00 Jul \$69.00 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
124. 124. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 May \$64.50 Jun \$69.00 Jul \$69.00 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
125. 125. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 Jun \$69.00 Jul \$69.00 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
126. 126. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 Jul \$69.00 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
127. 127. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 0.070 Jul \$69.00 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
128. 128. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 0.070 Jul \$69.00 0.000 Aug \$75.00 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
129. 129. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 0.070 Jul \$69.00 0.000 Aug \$75.00 0.087 Sep \$82.50 Oct \$73.00 Nov \$80.00 Dec \$86.00
130. 130. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 0.070 Jul \$69.00 0.000 Aug \$75.00 0.087 Sep \$82.50 0.100 Oct \$73.00 Nov \$80.00 Dec \$86.00
131. 131. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 0.070 Jul \$69.00 0.000 Aug \$75.00 0.087 Sep \$82.50 0.100 Oct \$73.00 -0.115 Nov \$80.00 Dec \$86.00
132. 132. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 0.070 Jul \$69.00 0.000 Aug \$75.00 0.087 Sep \$82.50 0.100 Oct \$73.00 -0.115 Nov \$80.00 0.096 Dec \$86.00
133. 133. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 Feb \$63.80 0.100 Mar \$59.00 -0.075 Apr \$62.00 0.051 May \$64.50 0.040 Jun \$69.00 0.070 Jul \$69.00 0.000 Aug \$75.00 0.087 Sep \$82.50 0.100 Oct \$73.00 -0.115 Nov \$80.00 0.096 Dec \$86.00 0.075
134. 134. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 0.049 Feb \$63.80 0.100 0.049 Mar \$59.00 -0.075 0.049 Apr \$62.00 0.051 0.049 May \$64.50 0.040 0.049 Jun \$69.00 0.070 0.049 Jul \$69.00 0.000 0.049 Aug \$75.00 0.087 0.049 Sep \$82.50 0.100 0.049 Oct \$73.00 -0.115 0.049 Nov \$80.00 0.096 0.049 Dec \$86.00 0.075 0.049
135. 135. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 0.049 0.012321 Feb \$63.80 0.100 0.049 0.002601 Mar \$59.00 -0.075 0.049 0.015376 Apr \$62.00 0.051 0.049 0.000004 May \$64.50 0.040 0.049 0.000081 Jun \$69.00 0.070 0.049 0.000441 Jul \$69.00 0.000 0.049 0.002401 Aug \$75.00 0.087 0.049 0.001444 Sep \$82.50 0.100 0.049 0.002601 Oct \$73.00 -0.115 0.049 0.028960 Nov \$80.00 0.096 0.049 0.002090 Dec \$86.00 0.075 0.049 0.000676
136. 136. (a) (b) monthly expected month price return return (a - b) 2 Dec \$50.00 Jan \$58.00 0.160 0.049 0.012321 Feb \$63.80 0.100 0.049 0.002601 Mar \$59.00 -0.075 0.049 0.015376 Apr \$62.00 0.051 0.049 0.000004 May \$64.50 0.040 0.049 0.000081 Jun \$69.00 0.070 0.049 0.000441 Jul \$69.00 0.000 0.049 0.002401 Aug \$75.00 0.087 0.049 0.001444 Sep \$82.50 0.100 0.049 0.002601 Oct \$73.00 -0.115 0.049 0.028960 Nov \$80.00 0.096 0.049 0.002090 Dec \$86.00 0.075 0.049 0.000676 0.0781 St. Dev: sum, divide by (n-1), and take sq root:
137. 137. Calculator solution using HP 10B: <ul><li>Enter monthly return on 10B calculator, followed by sigma key (top right corner). </li></ul><ul><li>Shift 7 gives you the expected return. </li></ul><ul><li>Shift 8 gives you the standard deviation. </li></ul>