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Chapter 6 - Risk and Rates of Return

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**1. **Chapter 6 - Risk and Rates of Return

**2. **Chapter 6: Objectives Inflation and rates of return
How to measure risk
(variance, standard deviation, beta)
How to reduce risk
(diversification)
How to price risk
(security market line, Capital Asset Pricing Model)

**3. **Inflation, Rates of Return, and the Fisher Effect

**4. **Interest Rates

**5. **Interest Rates

**6. **Interest Rates

**7. **Interest Rates

**8. **Interest Rates

**9. **Interest Rates

**10. **Interest Rates

**11. **Interest Rates

**12. **Interest Rates

**13. **Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium?
(1 + krf) = (1 + k*) (1 + IRP)
(1.08) = (1.03) (1 + IRP)
(1 + IRP) = (1.0485), so
IRP = 4.85% Interest Rates

**14. **Term Structure of Interest Rates The pattern of rates of return for debt securities that differ only in the length of time to maturity.

**15. **Term Structure of Interest Rates The pattern of rates of return for debt securities that differ only in the length of time to maturity.

**16. **Term Structure of Interest Rates The pattern of rates of return for debt securities that differ only in the length of time to maturity.

**17. **Term Structure of Interest Rates The yield curve may be downward sloping or “inverted” if rates are expected to fall.

**18. **Term Structure of Interest Rates The yield curve may be downward sloping or “inverted” if rates are expected to fall.

**19. **For a Treasury security, what is the required rate of return?

**20. **For a Treasury security, what is the required rate of return?

**21. **For a Treasury security, what is the required rate of return? Since Treasuries are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return.

**22. **For a corporate stock or bond, what is the required rate of return?

**23. **For a corporate stock or bond, what is the required rate of return?

**24. **For a corporate stock or bond, what is the required rate of return?

**25. **For a corporate stock or bond, what is the required rate of return? How large of a risk premium should we require to buy a corporate security?

**26. **Returns Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc.
Required Return - the return that an investor requires on an asset given its risk and market interest rates.

**27. **Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession .20 4% -10%
Normal .50 10% 14%
Boom .30 14% 30%
For each firm, the expected return on the stock is just a weighted average:

**28. **State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession .20 4% -10%
Normal .50 10% 14%
Boom .30 14% 30%
For each firm, the expected return on the stock is just a weighted average:
k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn Expected Return

**29. **Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession .20 4% -10%
Normal .50 10% 14%
Boom .30 14% 30%
k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn
k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

**30. **Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession .20 4% -10%
Normal .50 10% 14%
Boom .30 14% 30%
k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn
k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%

**31. **Based only on your expected return calculations, which stock would you prefer?

**33. **What is Risk? The possibility that an actual return will differ from our expected return.
Uncertainty in the distribution of possible outcomes.

**34. **What is Risk? Uncertainty in the distribution of possible outcomes.

**35. **What is Risk? Uncertainty in the distribution of possible outcomes.

**36. **What is Risk? Uncertainty in the distribution of possible outcomes.

**37. **How do We Measure Risk? To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year.

**38. **How do We Measure Risk? A more scientific approach is to examine the stock’s standard deviation of returns.
Standard deviation is a measure of the dispersion of possible outcomes.
The greater the standard deviation, the greater the uncertainty, and, therefore, the greater the risk.

**39. **Standard Deviation = (ki - k)2 P(ki)

**40. **Orlando Utility, Inc.

**41. **Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2

**42. **Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0

**43. **Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8

**44. **Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance = 12

**45. **Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance = 12
Stand. dev. = 12 =

**46. **Orlando Utility, Inc.
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance = 12
Stand. dev. = 12 = 3.46%

**47. **Orlando Technology, Inc.

**48. **Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2

**49. **Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) = 0

**50. **Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) = 0
(30% - 14%)2 (.3) = 76.8

**51. **Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) = 0
(30% - 14%)2 (.3) = 76.8
Variance = 192

**52. **Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) = 0
(30% - 14%)2 (.3) = 76.8
Variance = 192
Stand. dev. = 192 =

**53. **Orlando Technology, Inc.
(-10% - 14%)2 (.2) = 115.2
(14% - 14%)2 (.5) = 0
(30% - 14%)2 (.3) = 76.8
Variance = 192
Stand. dev. = 192 = 13.86%

**54. **Which stock would you prefer?
How would you decide?

**55. **Which stock would you prefer?
How would you decide?

**56. **
Orlando Orlando
Utility Technology
Expected Return 10% 14%
Standard Deviation 3.46% 13.86% Summary

**57. **It depends on your tolerance for risk!
Remember, there’s a tradeoff between risk and return.

**58. **It depends on your tolerance for risk!
Remember, there’s a tradeoff between risk and return.

**59. **It depends on your tolerance for risk!
Remember, there’s a tradeoff between risk and return.

**60. **Portfolios Combining several securities in a portfolio can actually reduce overall risk.
How does this work?

**66. ** Diversification Investing in more than one security to reduce risk.
If two stocks are perfectly positively correlated, diversification has no effect on risk.
If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified.

**67. **If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified?
YES!
Would you have eliminated all of your risk?
NO! Common stock portfolios still have risk.

**68. **Some risk can be diversified away and some cannot. Market risk (systematic risk) is nondiversifiable. This type of risk cannot be diversified away.
Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification.

**69. **Market Risk Unexpected changes in interest rates.
Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.

**70. **Company-unique Risk A company’s labor force goes on strike.
A company’s top management dies in a plane crash.
A huge oil tank bursts and floods a company’s production area.

**71. **As you add stocks to your portfolio, company-unique risk is reduced.

**72. **As you add stocks to your portfolio, company-unique risk is reduced.

**73. **As you add stocks to your portfolio, company-unique risk is reduced.

**74. **As you add stocks to your portfolio, company-unique risk is reduced.

**75. **Do some firms have more market risk than others? Yes. For example:
Interest rate changes affect all firms, but which would be more affected:
a) Retail food chain
b) Commercial bank

**76. **Yes. For example:
Interest rate changes affect all firms, but which would be more affected:
a) Retail food chain
b) Commercial bank Do some firms have more market risk than others?

**77. **Note
As we know, the market compensates investors for accepting risk - but only for market risk. Company-unique risk can and should be diversified away.
So - we need to be able to measure market risk.

**78. **This is why we have Beta. Beta: a measure of market risk.
Specifically, beta is a measure of how an individual stock’s returns vary with market returns.
It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market.

**79. **A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market. The market’s beta is 1

**80. **A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market.
(ex: technology firms) The market’s beta is 1

**81. **A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market.
(ex: technology firms)
A firm with a beta < 1 is less volatile than the market. The market’s beta is 1

**82. **A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
A firm with a beta > 1 is more volatile than the market.
(ex: technology firms)
A firm with a beta < 1 is less volatile than the market.
(ex: utilities) The market’s beta is 1

**83. **Calculating Beta

**84. **Calculating Beta

**85. **Calculating Beta

**86. **Calculating Beta

**87. **Calculating Beta

**88. **Summary: We know how to measure risk, using standard deviation for overall risk and beta for market risk.
We know how to reduce overall risk to only market risk through diversification.
We need to know how to price risk so we will know how much extra return we should require for accepting extra risk.

**89. **What is the Required Rate of Return? The return on an investment required by an investor given market interest rates and the investment’s risk.

**96. **Required
rate of
return

**97. **Required
rate of
return

**98. **Required
rate of
return

**99. **This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM).

**100. **Required
rate of
return

**101. **Required
rate of
return

**102. **Required
rate of
return

**103. **Required
rate of
return

**104. **Required
rate of
return

**105. **Required
rate of
return

**106. **Required
rate of
return

**107. **The CAPM equation:

**108. **kj = krf + j (km - krf )
The CAPM equation:

**109. **kj = krf + j (km - krf )
where:
kj = the required return on security j,
krf = the risk-free rate of interest,
j = the beta of security j, and
km = the return on the market index. The CAPM equation:

**110. **Example: 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.
According to the CAPM, what should be the required rate of return on Disney stock?

**111. **kj = krf + (km - krf ) kj = .06 + 1.2 (.12 - .06)
kj = .132 = 13.2%
According to the CAPM, Disney stock should be priced to give a 13.2% return.

**112. **Required
rate of
return

**113. **Required
rate of
return

**114. **Required
rate of
return

**115. **Required
rate of
return

**116. **Required
rate of
return

**117. **Simple Return Calculations

**118. **Simple Return Calculations

**119. **Simple Return Calculations

**120. **Simple Return Calculations

**137. **Calculator solution using HP 10B: Enter monthly return on 10B calculator, followed by sigma key (top right corner).
Shift 7 gives you the expected return.
Shift 8 gives you the standard deviation.