1. Risk and Rates of Return

2. RISK How to measure risk (variance, standard deviation, beta)
How to reduce risk
(diversification)
How to price risk
(security market line (SML), CAPM)

3. For a Treasury security, what is the required rate of return?=

4. For a Treasury security, what is the required rate of return?=
Risk-free
Since Treasury’s are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return.

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

6. For a corporate stock or bond, what is the required rate of return?
Risk-free
rate of
return =

7. For a corporate stock or bond, what is the required rate of return?=
Risk-free +
Risk
Premium
How large of a risk premium should we require to buy a corporate security?

8. 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.

9. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
For each firm, the expected return on the stock is just a weighted average:

10. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
For each firm, the expected return on the stock is just a weighted average:
R = P(1)*R1 + P(2)*R P(n)*Rn

11. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
R = P(1)*R1 + P(2)*R P(n)*Rn
R (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%

12. Expected Return State of Probability Return
Economy (P) Orl. Utility Orl. Tech
Recession % %
Normal % %
Boom % %
R = P(1)*R1 + P(2)*R P(n)*Rn
R (OT) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%

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

14. Have you considered
RISK?

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

16. What is Risk? Uncertainty in the distribution of possible outcomes.
Company A
return

17. What is Risk? Uncertainty in the distribution of possible outcomes.
Company A
return
Company B
return

18. 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.

19. 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.

20. Standard Deviation n
i=1 s S 2
= (Ri - R) P(i)

21. = (Ri - R) P(i) 2 s S n
i=1
Orlando Utility, Inc.

22. s S = (ki - k) P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 n n
( 4% - 10%)2 (.2) = 7.2

23. s S = (ki - k) P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0

24. s S = (ki - k) P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8

25. s S = (ki - k) P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance =

26. s S = (ki - k) P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2
( 4% - 10%)2 (.2) = 7.2
(10% - 10%)2 (.5) = 0
(14% - 10%)2 (.3) = 4.8
Variance =
Stand. dev. = = %

27. = (Ri - R) P(ki) 2 s S n
i=1
Orlando Technology, Inc.

28. s S = (ki - k) P(ki) Orlando Technology, Inc.2 s S n
i=1
Orlando Technology, Inc.
(-10% - 14%)2 (.2) =

29. s S = (ki - k) P(ki) Orlando Technology, Inc.2 s S n
i=1
Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =

30. s S = (ki - k) P(ki) Orlando Technology, Inc.2 s S n
i=1
Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =
(30% %)2 (.3) =

31. s S = (ki - k) P(ki) Orlando Technology, Inc.2 s S n
i=1
Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =
(30% %)2 (.3) =
Variance =

32. s S = (ki - k) P(ki) Orlando Technology, Inc.2 s S n
i=1
Orlando Technology, Inc.
(-10% - 14%)2 (.2) =
(14% %)2 (.5) =
(30% %)2 (.3) =
Variance =
Stand. dev. = = %

33. Which stock would you prefer?
How would you decide?

34. Which stock would you prefer?
How would you decide?

35. Summary Orlando Orlando Utility Technology Expected Return 10% 14%
Standard Deviation % %

36. It depends on your tolerance for risk!
Remember there’s a tradeoff between risk and return.
Return
Risk

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

38. Suppose we have stock A and stock B
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

39. Suppose we have stock A and stock B
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). RA
rate of
return
time

40. Suppose we have stock A and stock B
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). RA
rate of
return RB
time

41. Suppose we have stock A and stock B
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). Rp RA RB
rate of
return
time

42. What has happened to the variability of returns for the portfolio?Rp RA RB
rate of
return
time

43. 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.

44. 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.

45. Some risk can be diversified away and some can not.
Market Risk is also called Nondiversifiable risk (SYSTEMATIC RISK). This type of risk can not be diversified away.
Firm-Specific risk is also called diversifiable risk (UNSYSTEMATIC RISK). This type of risk can be reduced through diversification.

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

47. Firm-Specific 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.

48. As you add stocks to your portfolio, firm-specific risk is reduced.

49. As you add stocks to your portfolio, firm-specific risk is reduced.
number of stocks

50. As you add stocks to your portfolio, firm-specific risk is reduced.
Market risk
number of stocks

51. As you add stocks to your portfolio, firm-specific risk is reduced.
Market risk
number of stocks

52. Systematic Risk is the result of:
Interest Rate Change
Changes in Purchasing Power (Inflation)
Changes in investor expectations about the overall performance of the economy
Systematic Risk cannot be eliminated by diversification

53. Measure of Systematic Risk

54. Unsystematic Risk is the result of:
Management capabilities and decisions
Strikes
The availability of raw materials
The unique effects of government regulation, such as pollution control
The effect of foreign competition
The particular levels of financial and operating leverage the firm employs

55. Beta Coefficient: Index of Systematic Risk

56. 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

57. 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

58. Note
As we know, the market compensates investors for accepting risk - but only for market risk. Firm-specific risk can and should be diversified away.
So - we need to be able to measure market risk.

59. This is why we have BETA. Beta: a measure of market risk.
Specifically, it 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.

60. The market’s beta is 1
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: computer firms).
A firm with a beta < 1 is less volatile than the market (ex: utilities).

61. Calculating Beta
XYZ Co. returns -5
-15 5 10 15
-10
S&P 500
returns

62. Calculating Beta
XYZ Co. returns
. . . -5
-15 5 10 15
-10
S&P 500
returns

63. Calculating Beta
Beta = slope
= 1.20
XYZ Co. returns
. . . -5
-15 5 10 15
-10
S&P 500
returns

64. 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.

65. What is the Required Rate of Return?
The return on an investment required by an investor given the investment’s risk.

66. Required
rate of
return =

67. Required
rate of
return =
Risk-free +

68. Risk-free Risk Premium
Required
rate of
return =
Risk-free +
Risk
Premium

69. Risk-free rate of return Risk Premium Market Risk
Required
rate of
return
Risk-free
rate of
return
Risk
Premium = +
Market
Risk

70. Risk-free Risk Premium Market Firm-specific
Required
rate of
return =
Risk-free +
Risk
Premium
Market
Firm-specific

71. Risk-free Risk Premium Market Firm-specific
Required
rate of
return
Risk-free
Risk
Premium
Market
Firm-specific
can be diversified
away = +

72. Let’s try to graph this relationship!
Required
rate of
return
Let’s try to graph this
relationship!
Beta

73. Required
rate of
return .
12%
Risk-free
rate of
return
(6%)
Beta 1

74. . security market line (SML) 1 12% Beta Required rate of return
Risk-free
rate of
return
(6%)
Beta 1

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

76. . SML Is there a riskless (zero beta) security? 1 12% Beta Required
rate of
return
SML
Is there a riskless
(zero beta) security? .
12%
Risk-free
rate of
return
(6%)
Beta 1

77. . SML Is there a riskless (zero beta) security? Treasury
Required
rate of
return
SML
Is there a riskless
(zero beta) security? .
12%
Treasury
securities are
as close to riskless
Risk-free
rate of
return
(6%)
Beta 1

78. . SML Where does the S&P 500 fall on the SML? 1 12% Beta Required
rate of
return
SML
Where does the S&P 500
fall on the SML? .
12%
Risk-free
rate of
return
(6%)
Beta 1

79. . SML Where does the S&P 500 fall on the SML? The S&P 500 is a good
Required
rate of
return
SML
Where does the S&P 500
fall on the SML? .
12%
The S&P 500 is
a good
approximation
for the market
Risk-free
rate of
return
(6%)
Beta 1

80. . SML Utility Stocks 1 12% Beta Required rate of return Risk-free
(6%)
Beta 1

81. . SML High-tech stocks 1 12% Beta Required rate of return Risk-free
(6%)
Beta 1

82. Rj = the Required Return on security j,
The CAPM equation:
Rj = Rf j (Rm - Rf)
where:
Rj = the Required Return on security j,
Rf = the risk-free rate of interest,
j = the beta of security j, and
Rm = the return on the market index. b b

83. 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?

84. Rj = Rf + (Rm - Rf) b Rj = .06 + 1.2 (.12 - .06) Rj = .132 = 13.2%
According to the CAPM, Disney stock should be priced to give a 13.2% return.

85. . SML Theoretically, every security should lie on the SML 1 12% Beta
Required
rate of
return
SML
Theoretically, every
security should lie
on the SML .
12%
Risk-free
rate of
return
(6%)
Beta 1

86. . SML Theoretically, every security should lie on the SML
Required
rate of
return
SML
Theoretically, every
security should lie
on the SML .
12%
If every stock
is on the SML,
investors are being fully
compensated for risk.
Risk-free
rate of
return
(6%)
Beta 1

87. . SML If a security is above the SML, it is underpriced. 1 12% Beta
Required
rate of
return
SML
If a security is above
the SML, it is
underpriced. .
12%
Risk-free
rate of
return
(6%)
Beta 1

88. . SML If a security is above the SML, it is underpriced.
Required
rate of
return
SML
If a security is above
the SML, it is
underpriced. .
12%
If a security is
below the SML, it
is overpriced.
Risk-free
rate of
return
(6%)
Beta 1

89. Practice Problem:
Find the intrinsic value of a common stock with the following information:
ROE = 20%
50% retention of earnings
Beta = 1.4
recent dividend = $4.30
Treasury bond yield = 7.5%
Return on the S&P 500 = 12%
Market price for common stock = $100
Should you buy the stock?