1. INTRODUCTION TO CORPORATE FINANCE Laurence Booth • W. Sean Cleary
Prepared by
Ken Hartviksen

2. CHAPTER 8 Risk, Return, and Portfolio Theory

3. CHAPTER 8 – Risk, Return and Portfolio Theory
Lecture Agenda
Learning Objectives
Important Terms
Measurement of Returns
Measuring Risk
Expected Return and Risk for Portfolios
The Efficient Frontier
Diversification
Summary and Conclusions
Concept Review Questions
CHAPTER 8 – Risk, Return and Portfolio Theory

4. CHAPTER 8 – Risk, Return and Portfolio Theory
Learning Objectives
The difference among the most important types of returns
How to estimate expected returns and risk for individual securities
What happens to risk and return when securities are combined in a portfolio
What is meant by an “efficient frontier”
Why diversification is so important to investors
CHAPTER 8 – Risk, Return and Portfolio Theory

5. Important Chapter Terms
Arithmetic mean
Attainable portfolios
Capital gain/loss
Correlation coefficient
Covariance
Day trader
Diversification
Efficient frontier
Efficient portfolios
Ex ante returns
Ex post returns
Expected returns
Geometric mean
Income yield
Mark to market
Market risk
Minimum variance frontier
Minimum variance portfolio
Modern portfolio theory
Naïve or random diversification
Paper losses
Portfolio
Range
Risk averse
Standard deviation
Total return
Unique (or non-systematic) or diversifiable risk
Variance
CHAPTER 8 – Risk, Return and Portfolio Theory

6. Introduction to Risk and Return
Risk and return are the two most important attributes of an investment.
Research has shown that the two are linked in the capital markets and that generally, higher returns can only be achieved by taking on greater risk.
Risk isn’t just the potential loss of return, it is the potential loss of the entire investment itself (loss of both principal and interest).
Consequently, taking on additional risk in search of higher returns is a decision that should not be taking lightly.
CHAPTER 8 – Risk, Return and Portfolio Theory

7. Introduction to Risk and ReturnRF
Risk
Risk Premium
Real Return
Expected Inflation Rate
CHAPTER 8 – Risk, Return and Portfolio Theory

8. Measuring Returns Introduction
Ex Ante Returns
Return calculations may be done ‘before-the-fact,’ in which case, assumptions must be made about the future
Ex Post Returns
Return calculations done ‘after-the-fact,’ in order to analyze what rate of return was earned.
CHAPTER 8 – Risk, Return and Portfolio Theory

9. Measuring Returns Introduction
In Chapter 7 you learned that the constant growth DDM can be decomposed into the two forms of income that equity investors may receive, dividends and capital gains.
WHEREAS
Fixed-income investors (bond investors for example) can expect to earn interest income as well as (depending on the movement of interest rates) either capital gains or capital losses.
CHAPTER 8 – Risk, Return and Portfolio Theory

10. Measuring Returns Income Yield
Income yield is the return earned in the form of a periodic cash flow received by investors.
The income yield return is calculated by the periodic cash flow divided by the purchase price.
Where CF1 = the expected cash flow to be received
P0 = the purchase price
[8-1]
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11. Income Yield Stocks versus Bonds
The dividend yield is calculated using trailing rather than forecast earns (because next year’s dividends cannot be predicted in aggregate), nevertheless dividend yields have exceeded income yields on bonds
Reason – risk
The risk of earning bond income is much less than the risk incurred in earning dividend income
(Remember, bond investors, as secured creditors of the first have a legally-enforceable contractual claim to interest.)
CHAPTER 8 – Risk, Return and Portfolio Theory

12. Measuring Returns Common Share and Long Canada Bond Yield Gap
Table 8-1 illustrates the income yield gap between stocks and bonds over recent decades
The main reason that this yield gap has varied so much over time is that the return to investors is not just the income yield but also the capital gain (or loss) yield as well.
CHAPTER 8 – Risk, Return and Portfolio Theory

13. Measuring Returns Dollar Returns
Investors in market-traded securities (bonds or stock) receive investment returns in two different form:
Income yield
Capital gain (or loss) yield
The investor will receive dollar returns, for example:
$1.00 of dividends
Share price rise of $2.00
To be useful, dollar returns must be converted to percentage returns as a function of the original investment. (Because a $3.00 return on a $30 investment might be good, but a $3.00 return on a $300 investment would be unsatisfactory!)
CHAPTER 8 – Risk, Return and Portfolio Theory

14. Measuring Returns Converting Dollar Returns to Percentage Returns
An investor receives the following dollar returns a stock investment of $25:
$1.00 of dividends
Share price rise of $2.00
The capital gain (or loss) return component of total return is calculated: ending price – minus beginning price, divided by beginning price
[8-2]
CHAPTER 8 – Risk, Return and Portfolio Theory

15. Measuring Returns Total Percentage Return
The investor’s total return (holding period return) is:
[8-3]
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16. Measuring Returns Total Percentage Return – General Formula
The general formula for holding period return is:
[8-3]
CHAPTER 8 – Risk, Return and Portfolio Theory

17. Measuring Average Returns Ex Post Returns
Measurement of historical rates of return that have been earned on a security or a class of securities allows us to identify trends or tendencies that may be useful in predicting the future.
There are two different types of ex post mean or average returns used:
Arithmetic average
Geometric mean
CHAPTER 8 – Risk, Return and Portfolio Theory

18. Measuring Average Returns Arithmetic Average
Where:
ri = the individual returns
n = the total number of observations
Most commonly used value in statistics
Sum of all returns divided by the total number of observations
[8-4]
CHAPTER 8 – Risk, Return and Portfolio Theory

19. Measuring Average Returns Geometric Mean
Measures the average or compound growth rate over multiple periods.
[8-5]
CHAPTER 8 – Risk, Return and Portfolio Theory

20. Measuring Average Returns Geometric Mean versus Arithmetic Average
If all returns (values) are identical the geometric mean = arithmetic average
If the return values are volatile the geometric mean < arithmetic average
The greater the volatility of returns, the greater the difference between geometric mean and arithmetic average.
(Table 8-2 illustrates this principle on major asset classes 1938 – 2005)
CHAPTER 8 – Risk, Return and Portfolio Theory

21. CHAPTER 8 – Risk, Return and Portfolio Theory
Measuring Average Returns Average Investment Returns and Standard Deviations
The greater the difference, the greater the volatility of annual returns.
CHAPTER 8 – Risk, Return and Portfolio Theory

22. Measuring Expected (Ex Ante) Returns
While past returns might be interesting, investor’s are most concerned with future returns.
Sometimes, historical average returns will not be realized in the future.
Developing an independent estimate of ex ante returns usually involves use of forecasting discrete scenarios with outcomes and probabilities of occurrence.
CHAPTER 8 – Risk, Return and Portfolio Theory

23. Estimating Expected Returns Estimating Ex Ante (Forecast) Returns
The general formula
Where:
ER = the expected return on an investment
Ri = the estimated return in scenario i
Probi = the probability of state i occurring
[8-6]
CHAPTER 8 – Risk, Return and Portfolio Theory

24. Estimating Expected Returns Estimating Ex Ante (Forecast) Returns
Example:
This is type of forecast data that are required to make an ex ante estimate of expected return.
CHAPTER 8 – Risk, Return and Portfolio Theory

25. CHAPTER 8 – Risk, Return and Portfolio Theory
Estimating Expected Returns Estimating Ex Ante (Forecast) Returns Using a Spreadsheet Approach
Example Solution:
Sum the products of the probabilities and possible returns in each state of the economy.
CHAPTER 8 – Risk, Return and Portfolio Theory

26. CHAPTER 8 – Risk, Return and Portfolio Theory
Estimating Expected Returns Estimating Ex Ante (Forecast) Returns Using a Formula Approach
Example Solution:
Sum the products of the probabilities and possible returns in each state of the economy.
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27. CHAPTER 8 – Risk, Return and Portfolio Theory
Probability of incurring harm
For investors, risk is the probability of earning an inadequate return.
If investors require a 10% rate of return on a given investment, then any return less than 10% is considered harmful.
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28. CHAPTER 8 – Risk, Return and Portfolio Theory
Risk Illustrated
Possible Returns on the Stock
Probability
-30% -20% -10% 0% 10% 20% 30% 40%
Outcomes that produce harm
The range of total possible returns on the stock A runs from -30% to more than +40%. If the required return on the stock is 10%, then those outcomes less than 10% represent risk to the investor. A
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29. CHAPTER 8 – Risk, Return and Portfolio Theory
Range
The difference between the maximum and minimum values is called the range
Canadian common stocks have had a range of annual returns of % over the period
Treasury bills had a range of 21.07% over the same period.
As a rough measure of risk, range tells us that common stock is more risky than treasury bills.
CHAPTER 8 – Risk, Return and Portfolio Theory

30. Differences in Levels of Risk Illustrated
The wider the range of probable outcomes the greater the risk of the investment.
A is a much riskier investment than B
Outcomes that produce harm
Probability B A
-30% -20% -10% 0% 10% 20% 30% 40%
Possible Returns on the Stock
CHAPTER 8 – Risk, Return and Portfolio Theory

31. Historical Returns on Different Asset Classes
Figure 8-2 illustrates the volatility in annual returns on three different assets classes from 1938 – 2005.
Note:
Treasury bills always yielded returns greater than 0%
Long Canadian bond returns have been less than 0% in some years, and the range of returns has been greater than T-bills but less than stocks
Common stock returns have experienced the greatest range of returns
(See Figure 8-2 on the following slide)
CHAPTER 8 – Risk, Return and Portfolio Theory

32. Measuring Risk Annual Returns by Asset Class, 1938 - 2005
FIGURE 8-2
CHAPTER 8 – Risk, Return and Portfolio Theory

33. Refining the Measurement of Risk Standard Deviation (σ)
Range measures risk based on only two observations (minimum and maximum value)
Standard deviation uses all observations
Standard deviation can be calculated on forecast or possible returns as well as historical or ex post returns
CHAPTER 8 – Risk, Return and Portfolio Theory

34. Measuring Risk Ex post Standard Deviation
[8-7]
CHAPTER 8 – Risk, Return and Portfolio Theory

35. Measuring Risk Example Using the Ex post Standard Deviation
Problem
Estimate the standard deviation of the historical returns on investment A that were: 10%, 24%, -12%, 8% and 10%.
Step 1 – Calculate the Historical Average Return
Step 2 – Calculate the Standard Deviation
CHAPTER 8 – Risk, Return and Portfolio Theory

36. Ex Post Risk Stability of Risk Over Time
Figure 8-3 demonstrates that the relative riskiness of equities and bonds has changed over time
Until the 1960s, the annual returns on common shares were about four times more variable than those on bonds
Over the past 20 years, they have only been twice as variable
Consequently, scenario-based estimates of risk (standard deviation) is required when seeking to measure risk in the future
Scenario-based estimates of risk is done through ex ante estimates and calculations
CHAPTER 8 – Risk, Return and Portfolio Theory

37. Relative Uncertainty Equities versus Bonds
FIGURE 8-3
CHAPTER 8 – Risk, Return and Portfolio Theory

38. Measuring Risk Ex ante Standard Deviation
A Scenario-Based Estimate of Risk
[8-8]
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39. CHAPTER 8 – Risk, Return and Portfolio Theory
Scenario-based Estimate of Risk Example Using the Ex ante Standard Deviation – Raw Data
GIVEN INFORMATION INCLUDES:
Possible returns on the investment for different discrete states
Associated probabilities for those possible returns
CHAPTER 8 – Risk, Return and Portfolio Theory

40. CHAPTER 8 – Risk, Return and Portfolio Theory
Scenario-Based Estimate of Risk Ex ante Standard Deviation Spreadsheet Approach: First Step – Calculate the Expected Return
Determined by multiplying the probability times the possible return.
Expected return equals the sum of the weighted possible returns.
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41. CHAPTER 8 – Risk, Return and Portfolio Theory
Scenario-Based Estimate of Risk Second Step – Measure the Weighted and Squared Deviations
Now multiply the square deviations by their probability of occurrence.
First calculate the deviation of possible returns from the expected.
Second, square those deviations from the mean.
The sum of the weighted and square deviations is the variance in percent squared terms.
The standard deviation is the square root of the variance (in percent terms).
CHAPTER 8 – Risk, Return and Portfolio Theory

42. CHAPTER 8 – Risk, Return and Portfolio Theory
Scenario-Based Estimate of Risk Example Using the Ex ante Standard Deviation Formula
CHAPTER 8 – Risk, Return and Portfolio Theory

43. CHAPTER 8 – Risk, Return and Portfolio Theory
Portfolios
A portfolio is a collection of different securities such as stocks and bonds, that are combined and considered a single asset
The risk-return characteristics of the portfolio is demonstrably different than the characteristics of the assets that make up that portfolio, especially with regard to risk
Combining different securities into portfolios is done to achieve diversification.
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44. CHAPTER 8 – Risk, Return and Portfolio Theory
Diversification
Diversification has two faces:
Diversification results in an overall reduction in portfolio risk (return volatility over time) with little sacrifice in returns
Diversification helps to immunize the portfolio from potentially catastrophic events such as the outright failure of one of the constituent investments
(If only one investment is held, and the issuing firm goes bankrupt, the entire portfolio value and returns are lost. If a portfolio is made up of many different investments, the outright failure of one is more than likely to be offset by gains on others, helping to make the portfolio immune to such events.)
CHAPTER 8 – Risk, Return and Portfolio Theory

45. Expected Return of a Portfolio Modern Portfolio Theory
The Expected Return on a Portfolio is simply the weighted average of the returns of the individual assets that make up the portfolio:
The portfolio weight of a particular security is the percentage of the portfolio’s total value that is invested in that security.
[8-9]
CHAPTER 8 – Risk, Return and Portfolio Theory

46. Expected Return of a Portfolio Example
Portfolio value = $2,000 + $5,000 = $7,000
rA = 14%, rB = 6%,
wA = weight of security A = $2,000 / $7,000 = 28.6%
wB = weight of security B = $5,000 / $7,000 = (1-28.6%)= 71.4%
CHAPTER 8 – Risk, Return and Portfolio Theory

47. Range of Returns in a Two Asset Portfolio
In a two asset portfolio, simply by changing the weight of the constituent assets, different portfolio returns can be achieved
Because the expected return on the portfolio is a simple weighted average of the individual returns of the assets, you can achieve portfolio returns bounded by the highest and the lowest individual asset returns
Example 1:
Assume ERA = 8% and ERB = 10%
(See the following 6 slides based on Figure 8-4)
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48. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Portfolio Return Affect on Portfolio Return of Changing Relative Weights in A and B
Expected Return %
Portfolio Weight
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
FIGURE 8-4
ERA=8%
ERB= 10%
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49. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Portfolio Return Affect on Portfolio Return of Changing Relative Weights in A and B
FIGURE 8-4
Expected Return %
Portfolio Weight
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
ERA=8%
ERB= 10%
A portfolio manager can select the relative weights of the two assets in the portfolio to get a desired return between 8% (100% invested in A) and 10% (100% invested in B)
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50. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Portfolio Return Affect on Portfolio Return of Changing Relative Weights in A and B
Expected Return %
Portfolio Weight
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
FIGURE 8-4
ERA=8%
ERB= 10%
The potential returns of the portfolio are bounded by the highest and lowest returns of the individual assets that make up the portfolio.
CHAPTER 8 – Risk, Return and Portfolio Theory

51. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Portfolio Return Affect on Portfolio Return of Changing Relative Weights in A and B
Expected Return %
Portfolio Weight
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
FIGURE 8-4
ERA=8%
ERB= 10%
The expected return on the portfolio if 100% is invested in Asset A is 8%.
CHAPTER 8 – Risk, Return and Portfolio Theory

52. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Portfolio Return Affect on Portfolio Return of Changing Relative Weights in A and B
FIGURE 8-4
Expected Return %
Portfolio Weight
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
ERA=8%
ERB= 10%
The expected return on the portfolio if 100% is invested in Asset B is 10%.
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53. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Portfolio Return Affect on Portfolio Return of Changing Relative Weights in A and B
FIGURE 8-4
Expected Return %
Portfolio Weight
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
ERA=8%
ERB= 10%
The expected return on the portfolio if 50% is invested in Asset A and 50% in B is 9%.
CHAPTER 8 – Risk, Return and Portfolio Theory

54. CHAPTER 8 – Risk, Return and Portfolio Theory
Range of Returns in a Two Asset Portfolio Example 1: (r)A= 14%, E(r)B= 6%
A graph of this relationship is found on the following slide.
CHAPTER 8 – Risk, Return and Portfolio Theory

55. Range of Returns in a Two-Asset Portfolio E(r)A= 14%, E(r)B= 6%
CHAPTER 8 – Risk, Return and Portfolio Theory

56. Expected Portfolio Returns Example of a Three Asset Portfolio
CHAPTER 8 – Risk, Return and Portfolio Theory
K. Hartviksen 5

57. Modern Portfolio Theory (MPT)
Prior to the establishment of Modern Portfolio Theory (MPT), most people only focused upon investment returns—they ignored risk
With MPT, investors had a tool that they could use to dramatically reduce the risk of the portfolio without a significant reduction in the expected return of the portfolio
CHAPTER 8 – Risk, Return and Portfolio Theory

58. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Return and Risk For Portfolios Standard Deviation of a Two-Asset Portfolio using Covariance
[8-11]
Risk of Asset A adjusted for weight in the portfolio
Risk of Asset B adjusted for weight in the portfolio
Factor to take into account co-movement of returns. This factor can be negative.
CHAPTER 8 – Risk, Return and Portfolio Theory

59. CHAPTER 8 – Risk, Return and Portfolio Theory
Expected Return and Risk For Portfolios Standard Deviation of a Two-Asset Portfolio using Correlation Coefficient
[8-15]
Factor that takes into account the degree of co-movement of returns. It can have a negative value if correlation is negative.
CHAPTER 8 – Risk, Return and Portfolio Theory

60. Grouping Individual Assets into Portfolios
The riskiness of a portfolio that is made of different risky assets is a function of three different factors:
the riskiness of the individual assets that make up the portfolio
the relative weights of the assets in the portfolio
the degree of co-movement of returns of the assets making up the portfolio
The standard deviation of a two-asset portfolio may be measured using the Markowitz model:
CHAPTER 8 – Risk, Return and Portfolio Theory

61. Risk of a Three-Asset Portfolio
The data requirements for a three-asset portfolio grows dramatically if we are using Markowitz Portfolio selection formulae
Needed: Three correlation coefficients between A and B; A and C; and B and C A
ρa,b
ρa,c B C
ρb,c
CHAPTER 8 – Risk, Return and Portfolio Theory

62. Risk of a Four-asset Portfolio
The data requirements for a four-asset portfolio grows dramatically if we are using Markowitz Portfolio selection formulae
Needed: Six correlation coefficients between A and B; A and C; A and D; B and C; C and D; and B and D A C B D
ρa,b
ρa,d
ρa,c
ρb,d
ρb,c
ρc,d
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63. CHAPTER 8 – Risk, Return and Portfolio Theory
Covariance
A statistical measure of the correlation of the fluctuations of the annual rates of return of different investments.
[8-12]
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64. CHAPTER 8 – Risk, Return and Portfolio Theory
Correlation
The degree to which the returns of two stocks co-move is measured by the correlation coefficient (ρ).
The correlation coefficient (ρ) between the returns on two securities will lie in the range of +1 through - 1.
+1 is perfect positive correlation
-1 is perfect negative correlation
[8-13]
CHAPTER 8 – Risk, Return and Portfolio Theory

65. Covariance and Correlation Coefficient
Solving for covariance given the correlation coefficient and standard deviation of the two assets:
[8-14]
CHAPTER 8 – Risk, Return and Portfolio Theory

66. Importance of Correlation
Correlation is important because it affects the degree to which diversification can be achieved using various assets.
Theoretically, if two assets returns are perfectly positively correlated, it is possible to build a riskless portfolio with a return that is greater than the risk-free rate.
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67. CHAPTER 8 – Risk, Return and Portfolio Theory
Affect of Perfectly Negatively Correlated Returns Elimination of Portfolio Risk
Time
If returns of A and B are perfectly negatively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be riskless. There would be no variability
of the portfolios returns over time.
Returns on Stock A
Returns on Stock B
Returns on Portfolio
Returns %
10% 5%
15%
20%
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68. CHAPTER 8 – Risk, Return and Portfolio Theory
Example of Perfectly Positively Correlated Returns No Diversification of Portfolio Risk
Returns %
If returns of A and B are perfectly positively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be risky. There would be no diversification (reduction of portfolio risk).
20%
15%
Returns on Stock A
Returns on Stock B
Returns on Portfolio
10% 5%
Time
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69. CHAPTER 8 – Risk, Return and Portfolio Theory
Affect of Perfectly Negatively Correlated Returns Elimination of Portfolio Risk
Returns %
If returns of A and B are perfectly negatively correlated, a two-asset portfolio made up of equal parts of Stock A and B would be riskless. There would be no variability
of the portfolios returns over time.
20%
15%
Returns on Stock A
10%
Returns on Stock B
Returns on Portfolio 5%
Time
CHAPTER 8 – Risk, Return and Portfolio Theory

70. Affect of Perfectly Negatively Correlated Returns Numerical Example
Perfectly Negatively Correlated Returns over time
CHAPTER 8 – Risk, Return and Portfolio Theory

71. Diversification Potential
The potential of an asset to diversify a portfolio is dependent upon the degree of co-movement of returns of the asset with those other assets that make up the portfolio
In a simple, two-asset case, if the returns of the two assets are perfectly negatively correlated it is possible (depending on the relative weighting) to eliminate all portfolio risk
This is demonstrated through the following series of spreadsheets, and then summarized in graph format
CHAPTER 8 – Risk, Return and Portfolio Theory

72. Example of Portfolio Combinations and Correlation
Perfect Positive Correlation – no diversification
Both portfolio returns and risk are bounded by the range set by the constituent assets when ρ=+1
CHAPTER 8 – Risk, Return and Portfolio Theory

73. Example of Portfolio Combinations and Correlation
Positive Correlation – weak diversification potential
When ρ=+0.5 these portfolio combinations have lower risk – expected portfolio return is unaffected.
CHAPTER 8 – Risk, Return and Portfolio Theory

74. Example of Portfolio Combinations and Correlation
No Correlation – some diversification potential
Portfolio risk is lower than the risk of either asset A or B.
CHAPTER 8 – Risk, Return and Portfolio Theory

75. Example of Portfolio Combinations and Correlation
Negative Correlation – greater diversification potential
Portfolio risk for more combinations is lower than the risk of either asset
CHAPTER 8 – Risk, Return and Portfolio Theory

76. Example of Portfolio Combinations and Correlation
Perfect Negative Correlation – greatest diversification potential
Risk of the portfolio is almost eliminated at 70% invested in asset A
CHAPTER 8 – Risk, Return and Portfolio Theory

77. The Effect of Correlation on Portfolio Risk:
Diversification of a Two Asset Portfolio Demonstrated Graphically
The Effect of Correlation on Portfolio Risk:
The Two-Asset Case
Expected Return
Standard Deviation 0%
10% 4% 8%
20%
30%
40%
12% B
rAB= +1 A
rAB = 0
rAB = -0.5
rAB = -1
CHAPTER 8 – Risk, Return and Portfolio Theory

78. Impact of the Correlation Coefficient
Figure 8-7 illustrates the relationship between portfolio risk (σ) and the correlation coefficient
The slope is not linear a significant amount of diversification is possible with assets with no correlation (it is not necessary, nor is it possible to find, perfectly negatively correlated securities in the real world)
With perfect negative correlation, the variability of portfolio returns is reduced to nearly zero.
CHAPTER 8 – Risk, Return and Portfolio Theory

79. Expected Portfolio Return Impact of the Correlation Coefficient
FIGURE 8-7 15 10 5
Standard Deviation (%) of Portfolio Returns
Correlation Coefficient (ρ)
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80. CHAPTER 8 – Risk, Return and Portfolio Theory
Zero Risk Portfolio
We can calculate the portfolio that removes all risk.
When ρ = -1, then
Becomes:
[8-15]
[8-16]
CHAPTER 8 – Risk, Return and Portfolio Theory

81. An Exercise using T-bills, Stocks and Bonds
Historical averages for returns and risk for three asset classes
Each achievable portfolio combination is plotted on expected return, risk (σ) space, found on the following slide.
Historical correlation coefficients between the asset classes
Portfolio characteristics for each combination of securities
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82. Results Using only Three Asset Classes
The efficient set is that set of achievable portfolio combinations that offer the highest rate of return for a given level of risk. The solid blue line indicates the efficient set.
The plotted points are attainable portfolio combinations.
CHAPTER 8 – Risk, Return and Portfolio Theory

83. Two-Security Portfolios Modern Portfolio Theory
FIGURE 8-9
Expected Return %
Standard Deviation (%) 13 12 11 10 9 8 7 6
This line represents the set of portfolio combinations that are achievable by varying relative weights and using two non-correlated securities.
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84. CHAPTER 8 – Risk, Return and Portfolio Theory
Dominance
It is assumed that investors are rational, wealth-maximizing and risk averse
If so, then some investment choices dominate others
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85. Investment Choices The Concept of Dominance IllustratedB C
Return %
Risk
10% 5%
To the risk-averse wealth maximizer, the choices are clear, A dominates B,
A dominates C.
A dominates B because it offers the same return but for less risk.
A dominates C because it offers a higher return but for the same risk.
20%
CHAPTER 8 – Risk, Return and Portfolio Theory

86. Efficient Frontier Modern Portfolio Theory
FIGURE 8-10
Expected Return %
Standard Deviation (%) A E B C D
A is not attainable
B,E lie on the efficient frontier and are attainable
E is the minimum variance portfolio
C, D are attainable but are dominated by superior portfolios
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87. Efficient Frontier Modern Portfolio Theory
FIGURE
Expected Return %
Standard Deviation (%) A E B C D
Rational, risk averse investors will only want to hold portfolios such B.
The actual choice will depend on her/his risk preferences.
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88. CHAPTER 8 – Risk, Return and Portfolio Theory
Diversification
Risk of a portfolio can be reduced by spreading the value of the portfolio across, two, three, four or more assets
The key is to choose assets whose returns are less than perfectly positively correlated
Even with random or naïve diversification, risk of the portfolio can be reduced
This is illustrated in Figure 8-11 and Table 8-3 found on the following slides
As the portfolio is divided across more and more securities, the risk of the portfolio falls rapidly at first, until a point is reached where, further division of the portfolio does not result in a reduction in risk
Going beyond this point is known as superfluous diversification
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89. Diversification Domestic Diversification
FIGURE 8-11 14 12 10 8 6 4 2
Standard Deviation (%)
Number of Stocks in Portfolio
Average Portfolio Risk
January 1985 to December 1997
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90. Diversification Domestic Diversification
CHAPTER 8 – Risk, Return and Portfolio Theory

91. Average Portfolio Risk
Total Risk of an Individual Asset Equals the Sum of Market and Unique Risk
Standard Deviation (%)
Number of Stocks in Portfolio
Average Portfolio Risk
This graph illustrates that total risk of a stock is made up of market risk (that cannot be diversified away because it is a function of the economic ‘system’) and unique, company-specific risk that is eliminated from the portfolio through diversification.
Diversifiable (unique) risk
[8-19]
Nondiversifiable (systematic) risk
[8-19]
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92. International Diversification
Clearly, diversification adds value to a portfolio by reducing risk while not reducing the return on the portfolio significantly
Most of the benefits of diversification can be achieved by investing in 40 to 50 different ‘positions’ (investments)
However, if the investment universe is expanded to include investments beyond the domestic capital markets, additional risk reduction is possible
(See Figure on the following slide.)
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93. Diversification International Diversification
FIGURE 8-12
100 80 60 40 20
Percent risk
Number of Stocks
International stocks
U.S. stocks
11.7
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94. Summary and Conclusions
In this chapter you have learned:
How to measure different types of returns
How to calculate the standard deviation and interpret its meaning
How to measure returns and risk of portfolios and the importance of correlation in the diversification process
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95. CHAPTER 8 – Risk, Return and Portfolio Theory
Copyright
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CHAPTER 8 – Risk, Return and Portfolio Theory