The Relationship Between Risk and Return

1
The Relationship Between Risk and Return
2
Goals of Risk Analysis

• A good risk and return model
• Should apply to all assets
• Explain the types of risk that are rewarded
• Develop standardized risk measures
• Translate risk into a rate of return demanded by
  the investor
• Should do well explaining past returns and
  forecasting future returns.

3
Issues Relating to Risk

• Riskiness of the expected future cash flows
• Stand Alone vs. Portfolio Risk
• Diversifiable Risk vs. Non-Diversifiable (Market)
  Risk
• Higher Market Risk Implies Higher Return
• The same principles apply to physical assets

4
Stand Alone Risk

• The risk faced from owning the asset by itself.
  (there are no other assets which help to spread
  risk)
• The return from owning the asset varies based on
  outcomes in the market
• Need to look at the expected return and standard
  deviation

5
Probability Distributions

• Probability Distribution provides the
  combinations of outcomes and the probability that
  the outcome will occur
• Example Weather Forecast
• Outcome Probability
• Rain .6 60
• No Rain .4 40

6
Probability

• The probability tells the likelihood that it will
  rain. The probability is based upon the current
  conditions.
• Given 100 days with the current conditions (the
  history), it will rain on 60 of the following
  days.
• We want to use the same logic when discussing the
  possible return from owning the stock - what is
  the history?

7
An Example

• Intel has decided to introduce its new computer
  chip. There are three possible outcomes and
  three possible returns
• Outcome Return Prob
• 1) High Demand 90 40
• 2) Average Demand 30 20
• 3) Low Demand -80 40

8
Example Continued

• Assume MidAmerican Energy is also facing three
  outcomes
• Outcome Return Prob
• 1) High Demand 15 25
• 2) Average Demand 10 50
• 3) Low Demand 5 25
• How would you compare the two stocks?

9
Expected Rate of Return

• To compare the two stocks you would need to find
  the expected rate of return

10
Intel

• Demand Ret Prob Ret x Prob
• High 90 40 (.9)(.4) .36
• Average 30 20 (.3)(.2) .06
• Low -80 40 (-.8)(.4) -.32
• expected return 10

11
Mid American Energy

• Demand Ret Prob Ret x Prob
• High 15 25 (.15)(.25) .0375
• Average 10 50 (.1)(.5) .0500 Low
  5 25 (.25)(.05) .0125
• expected return 10
• The expected return for each stock is 10
• Which would you prefer to own?

12
Measuring Stand Alone Risk

• To compare the stand alone risk you need to look
  at the standard deviation
• To calculate Standard Deviation
• 1) Find Expected return
• 2) Subtract expected return from each outcomes
  return
• 3) Square the number in 2)
• 4) Multiply the squares by the probabilities and
  sum them together
• 5) Take the square root of the number in 4

13
Intel

• Demand (Ret-ExpectRet)2 x Prob
• High (90 - 10)2 x (.40) .2560
• Average (30 - 10)2 x (.20) .0080
• Low (-80 - 10)2 x (.40) .3240
• .5880
• take the square root (.5880)1/2
• standard deviation .7668 76.68

14
Mid American Energy

• Demand (Ret-ExpectRet)2 x Prob
• High (15-10)2 x (.25) .000625
• Average (10- 10)2 x (.50) 0.00
• Low (5 - 10)2 x (.25) .000625
• .00125
• take the square root (.00125)1/2
• standard deviation .035355 3.54

15
Interpreting Standard Deviation

• What does the standard deviation tell us?
• Assuming that the returns are normally
  distributed
• The actual return will be within one standard
  deviation 68.26 of the time.
• This means that we can expect the return to fall
  in a range between the expected return plus and
  minus the standard deviation 68 of the time

16
Prob Ranges for Normal Dist.
68.26
95.46
99.74
17
Our Example

• Intel had an expected return of 10 and standard
  deviation of 76.64. Therefore we expect the
  return to be between 10-76.64 - 66.64 and
  1076.64 86.64 68 of the time
• Mid American Energy had an expected return of 10
  and standard deviation of 3.536 implying an
  interval form 6.464 to 13.536
• Which would you rather own?

18
Trade off Between Risk and Return
19
Risk Aversion

• Generally, people are risk averse. (They avoid
  risk)
• In our example the expected return is the same
  for both stocks, but Intel is much riskier (as
  measured by the standard deviation)
• What if the expected returns were not the same?

20
Which do you prefer?

• Project A expected return of 50 with standard
  deviation of 30
• Project B expected return of 8 with standard
  deviation of 15

21
Coefficient of Variation

• The amount of risk per unit of return which is
  equal to
• Calculating the Coefficient of Variation
• Project A 30/50 .6 Project B 15/8 1.875

22
Semi Variance

• If stocks are normally distributed they are
  symmetric about the mean.
• This teats upside and downside risk equally.
• An investor is often more concerned about the
  chance that a return falls below what is expected
  or in other words the downside risk.

23
Semi Variance
Where n number of periods where actual
returnltaverage return
24
Sources of Risk

• Project Risk Factors influencing the realized
  cash flows of the project error in estimation
• Competitive Risk Cash flows impacted by the
  actions of a competitor
• Industry-Specific Risk Technology, Legal, and
  Commodity Risk
• International risk Political risk and exchange
  rate risk
• Market Risk Impacts all firms, marcoeconomic
  changes such as inflation and interest rates

25
Risk Intuition

• Diversification It is possible to decrease the
  impact of some of the risks through
  diversification.
• Example Project risk can be offset by other
  projects undertaken by the firm.
• Which of the risks on the previous slide can be
  diversified? Which Cant?
• As an investor, which risks should you be more
  concerned with (which can be diversified)?

26
Risk and Diversification
Project Risk
Competitive Risk
Industry Wide Risk
International Risk
Market Risk
Firm Specific Affects One Firm
Market Risk Affects All Firms
Firm Can Reduce Risk By
Multiple Projects
Acquiring Competitors
Diversifying Across Sectors
Diversifying Across Countries
Cannot Affect
Investors Can Mitigate Risk By
Diversifying Across Domestic Firms Markets
Diversifying Globally
Diversifying Across Asset Classes
27
Quick Stats Review

• Covariance
• Combines the relationship between the stocks with
  the volatility.
• () the stocks move together
• (-) The stocks move opposite of each other

28
Stats Review 2

• Correlation coefficient The covariance is
  difficult to compare when looking at different
  series. Therefore the correlation coefficient is
  used.
• The correlation coefficient will range from
• -1 to 1

29
Risk in a Portfolio Context

• The expected return of a portfolio of assets is
  equal to the weighted average of the expected
  returns of the individual assets.
• Example four stocks 25 of your in each
• Intel 25 Disney 10
• BP 15 Citicorp 16
• Portfolio Expect Ret
• (.25)(2.5)(.1)(.25)(.15)(.25)(.16)(.25).165

30
Standard Deviation

• The standard deviation of the portfolio will not
  equal the weighted average of the standard
  deviations of the stocks in the portfolio.
• The standard deviation can be calculated from
  each years portfolio expected return just like
  for an individual asset.

31
Example 1

• Two stocks with correlation coefficient -1
• Year Stock A Stock B Portfolio
• 2004 26 -6 10
• 2005 6 14 10
• 2006 -4 24 10
• 2007 12 8 10
• Avg Ret 10 10 10
• Stand dev 10.86 10.86 0

32
Example 2

• Two stocks with correlation coefficient 1
• Year Stock A Stock B Portfolio
• 2004 16 19 17.5
• 2005 8 7 7.5
• 2006 12 13 12.5
• 2007 4 1 2.5
• Avg Ret 10 10 10
• Stand dev 4.47 6.71 5.59

33
Example 3

• Two stocks with correlation coefficient .571
• Year Stock A Stock B Portfolio
• 2004 18 22 20
• 2005 -4 12 4
• 2006 24 18 21
• 2007 2 -12 -5
• Avg Ret 10 10 10
• Stand dev 11.4 13.19 10.9

34
Real World

• Most stocks have a correlation between 0.5 and
  0.7
• Why is it usually positive?
• What type of risk does this represent?

35
Portfolio Effects

• Each stock has two types of risk
• Market Related (Non diversifiable)
• Firm Specific (Diversifiable)
• Increasing the number of stocks in your portfolio
  should increase the diversification, lowering the
  portfolio risk.
• However there is a limit to the decrease in risk,
  since most stocks are positively correlated you
  can not eliminate all of the market risk

36
Calculations of Standard Deviation

• Variance and Standard Deviation can be calculated
  if you know the correlation coefficient and
  standard deviation of each asset.
• For two assets

37
Marginal Investor

• The investor trading at the margin who has the
  most influence on the price.
• The type of marginal investor plays a key role in
  determining how a firm may respond to different
  circumstances
• Usually it is assumed that the marginal investor
  is well diversified.

38
Measuring Market Risk and The Market Portfolio

• A market portfolio of all stocks available still
  has a positive standard deviation. The market
  portfolio would represent the return on the
  average stock.

39
Capital Asset Pricing Model

• CAPM relates an assets market risk to the
  expected return from owning the asset.
• Major components
• Risk Free Rate - the return earned on an asset
  that is risk free (US Treasuries)
• Beta - A measure of the firms market risk
  compared to the average firm
• Market Return - the expected return on a
  portfolio of all similar assets

40
Beta - Intuition

• Beta measures the sensitivity of the individual
  asset to movements in the market for similar
  assets.
• Stock example
• Assume the SP500 increases by 10
• If a stock also increase by 10 over the same
  period it would have a beta equal to 1.
• If a stock increases by more than 10 its beta
  will be greater than 1.

41
Beta - Intuition

• A higher beta implies that the stock is more
  sensitive to an economy wide fluctuation than the
  market portfolio.
• In other words the stock has a higher amount of
  Non-diversifiable risk.
• Since the Market risk for the stock is higher it
  should also have a higher return...

42
Risk and Return

• The CAPM compares the return on the market
  portfolio to a risk free rate, the difference is
  the market risk premium.
• The Market Risk Premium represents the extra
  return for accepting the market risk related to
  the riskier asset (the extra return on the
  average stock).

43
CAPM

• rirRFBi(rM-rRF)
• Where
• ri The return on asset i
• rRF The return on the Risk Free Asset
• rM The return on the Market Portfolio
• Bi the beta on asset i

44
rirRFBi(rM-rRF)

• Example
• Bank of America has a beta of 1.55
• Let If rRF 7 and rM 9.2
• The return on Bank of America stock is
• ri rRF Bi ( rM - rRF )r .07 1.55
  (.092-.07) .104

45
Market Risk Premium

• The Market Risk Premium is the extra return from
  investing in the average stock. In the CAPM
  this is equal to rM-rRF
• The market risk premium represents the market
  risk.
• If a stock had a beta of 1 it would earn
• ri rRF Bi ( rM - rRF )r .07 1.0
  (.092-.07) .092
• which is the market return

46
Risk and Return

• Given the inputs to the CAPM you can develop the
  relationship between the risk of an asset (as
  measured by beta) and its return.
• An easy way to demonstrate this is to graph the
  possible risk and return combinations.

47
Graphing the Security Market Line

• ri rRF Bi ( rM - rRF )
• Let risk (Bi) be on the horizontal axis and
  return (ri) be on the vertical axis.
• The slope of the line is then equal to the market
  risk premium (rm-rRF)
• Then you can graph all the possible combinations
  of risk and return.

48
ri rRF Bi ( rM - rRF )

• Lets put in some numbers for beta and ki
• beta 0 ri .070(.092-.07).07 rRF
• beta 1 ri .071(.092-.07).092 rM
• beta 1.55 ri .07 1.55(.092-.07) .104

49
B0,rrRF B1,r0.092 B1.55,r.104
Return
Security Market Line
.104
0.092
rRF
0
1.0
1.55
Beta
50
Note

• The market risk premium measures the risk
  aversion of the investors. If investors become
  more risk averse the risk premium widens
  (investors require a higher return to accept
  risk)
• In this case the slope of the security market
  line will become steeper.

51
Increased Risk Aversion

Return
rRF
Beta
Bi
52
Estimating the Components of the CAPM

• Risk Free Return
• Usually long Term treasury bonds are used to
  approximate the risk free return
• Market return
• The market return uses historical data on a
  market index, the SP 500 is a commonly used

53
Estimating Beta

• Two main approaches to estimating beta
• Historical Data (Top Down Beta)
• Utilizes the price history for the stock to
  estimate beta. Problems?
• Bottom Up Beta
• Comparing the firm to others in the same
  industry.

54
Estimating a Top Down Beta

• The most common approach is to use linear
  regression analysis.
• Regression -- Attempts to explain the
  relationship between two variables by estimating
  the line that best describes the relationship.

55
Regression Review

• Equation of a line Y a bX
• Graphing combinations of X and Y form a line.
• X is the independent variable and placed on the
  horizontal axis. Y the dependent variable and
  placed on the vertical axis (The value of Y
  depends upon X)
• a is the Y intercept and b the slope of the line.

56
Observations of X and Y variables

Y
X
57
Regression Estimates the line that best explains
the relationship between the variables

58
The Line is the one that minimizes the sum of
the squared residuals

59
Estimating the Regression

• The slope of the line is then equal to
• The Intercept is

60
Confidence in the ResultsR-Squared (R2)

• R2 will range up to one. It is the portion of
  the relationship explained by the regression
• R-Squared (R2) correlationYX2b2sx2/sY2
• Examples
• An R2 of one implies all the points are on the
  line
• An R2 of 0.5 would mean that half of the
  relationship is explained by the line.

61
Confidence in the ResultsT-statistic

• The t-statistic tells us whether or not we can
  reject the hypothesis that the variable is equal
  to zero.
• The higher the t-statistic the higher the
  confidence that we can reject the hypothesis that
  the slope is zero.
• If you cannot reject the hypothesis -- It implies
  that the dependent variable has no impact on the
  independent variable.

62
T-Statistic

• A Rule of Thumb
• The confidence levels are based upon the number
  of observations, but in general
• If you have a t-statistic above 2.0 you can
  reject the null hypothesis at the 95 level.
• (With 120 observations a t-statistic of 2.36
  allows rejection at the 99 level)

63
Standard Error

• Provides a measure of spread around each
  variable.
• Provides a confidence band similar to standard
  deviation)
• We can use standard error to estimate the T-
  Statistic (Assuming a normal distribution)
• T-StatinterceptA/SEA T-Statslope B/SEB

64
Quick Review

• Linear Regression - Provides line the best
  describes the relationship between two variables
• R2 - Portion of relationship explained by the
  estimated line
• T-Statistic - Confidence in the estimate of the
  variable (Is is statistically significant?)
• Standard Error - Confidence Interval

65
Estimating Beta

• The basic CAPM can be rearranged to allow the use
  of regression analysis to estimate Beta.
  rirRFBi(rM-rRF)
• rirRFBirM -BirRF
• rirRF-BirRF BirM
• rirRF(1-Bi)BirM

66
Estimating Beta

• rirRF(1-Bi)BirM
• We know that rRF(1-Bi) is a constant let it a
• riaBirM
• Dependent Independent
• Variable Variable

67
Estimating Beta

• Given Historical data on the return of the market
  portfolio and the individual asset we can
  estimate Beta.

68
Estimating Jensens Alpha

• We can also gain insight by looking at the
  intercept term.
• The goal is to compare the intercept term to the
  value we should have gotten for it given the
  historical data.
• From the rearranged CAPM the intercept should
  equal
• rRF(1-B)

69
Jensens Alpha

• rRF(1-B)
• Given the historical data to estimate kRF and the
  B we found from the regression we can find an
  estimate of the intercept
• The difference between the estimate in the
  regression and the one from the historical data
  is called Jensens Alpha.

70
Jensens Alpha

• The estimate from the regression comes from the
  historical data on the returns on the market and
  stock -- It is an estimates of the actual return
  received.
• The theoretical estimate of Jensens Alpha comes
  form the risk free rate and the assets beta - It
  measures what you would have expected to receive.

71
Interpreting Jensens Alpha

• If
• a gt rRF(1-B) The intercept from the regression
  is higher than what we would have expected. This
  implies that the stock did better than expected.
• a lt rRF(1-B) The intercept from the regression
  is less than what we would have expected. This
  implies that the stock worse than expected.

72
Issues in Estimation

• What estimation period should be used?
• What interval should be used to calculate the
  returns (monthly, weekly, daily)?
• Calculating Dividends in the return

73
Estimating Beta An example

• Disney 5 years of monthly returns Example
• March 37.87
• April 36.42 Dividend in April 0.05
• Return((36.42.05)-37.87)/37.87 -3.69
• Monthly return over the same period on the SP
  500 served as the market return

74
Regression Results

• rDisney -0.00011.40(rM)e
• Beta 1.40
• rM(1-B) -.0001-.01
• R2.32
• Standard error of Beta .27

75
Interpreting the results

• Beta, The stock is more responsive to market
  risk than the market average.
• R2.32 The line explains 32 of the relationship
  between the variables (32 of the Disneys return
  is explained by market risk factors the rest is
  firm or industry risk).
• SE .27 Beta ranges from 1.4.27 1.67 to
  1.4-.27 1.13 with 68 confidence

76
Interpreting Jensens Alpha

• During the 5 years, the average monthly return on
  long term treasuries was .4
• rRF(1-B) .004(1-1.4) -.0016 a -.01
• Jensens Alpha
• a- rRF(1-B) -.0001 - (-.0016) .0015
• On average Disney performed .15 better than
  expected each month.
• That translated into (1.0015)12-1 .01811.81
  better than expected each year.

77
Adjusted Beta

• Many analysts adjust the regression estimate of
  beta.
• Beta has been shown to move toward one over time
  as the firm matures. The data would not
  represent this well.
• A common adjustment is the following is to find a
  weighted average beta as follows .67(regression
  estimate).33(1)
• Disney .67(1.4).33(1) 1.27

78
Regression Example (2)
79
Regression Results

• The coefficient on SP 500 is the beta,
• Beta 1.2847, Intercept .0335
• Standard Error on Beta 0.2995
• T-Statistic on Beta 4.2889
• R2.2439
• Can you explain each of these?
• Can you Calculate Jensens Alpha?

80
Financial Leverage and Beta

• The amount of borrowing that the firm uses to
  finance its capital projects plays a key role in
  determining beta.
• A higher use of debt should increase the
  riskiness of the firm and increase its beta.
• The use of debt concentrates risk on the
  shareholder (the residual claimant).

81
Financial Leverage and Risk

• Given the same level of earnings, increasing the
  use of debt creates a fixed payment that must be
  paid prior to the shareholder claims
• Because of this the return required by the
  shareholders increases to compensate them for
  extra risk.
• The firm is more responsive to market changes
  (implying a higher beta..)

82
Fundamental Beta

• The fundamental beta is the beta the firm would
  have if it used no debt to finance its
  operations.
• When we ran the regression, the firm most likely
  was using debt. Therefore the data does not
  provide us with a measure of risk that is
  independent of the use of debt.

83
UnLevered Beta

• Assume that the impact of financial leverage is
  fairly straight forward.
• BL BU(1(1-t)Debt/Equity)
• BL Levered Beta BU Unlevered Beta
• t corporate tax rate

84
Disneys Unlevered Beta

• bL bU(1(1-t)(D/E))
• we estimated the leveraged beta to be 1.4
• historically its Debt to equity ratio is 14 and
  its marginal corporate tax rate is 36
• We can find the unlevered beta
• 1.4 bU(1(1-.36)(.14)) the solve for bU
  1.2849
• Then we could find the Beta based upon different
  levels of debt/equity.

85
Disneys Unlevered Beta

• BL BU(1(1-t)Debt/Equity)
• we estimated the leveraged beta to be 1.4
• Historically Disneys Debt to Equity ratio is 14
  and its marginal corporate tax rate is 36.
• 1.4 bU(1(1-.36)(.14))
• then solve for bU 1.2849
• As the Debt/Equity ratio changes we can estimate
  the levered beta.

86
Bottom Up Beta

• The bottom up beta is a weighted average of the
  average beta in the firms core industries.
• The bottom up beta will usually provide a better
  estimate of market risk when
• There is a high standard error in the regression
• There have been structural changes in the firm
  (reorganization or merger for example)
• When the firms equity is not traded or traded
  infrequently.

87
Calculating Bottom up Beta

• Determine the key industries in which the firm
  operates
• Find the average unlevered beta of other firms in
  the key industries
• Calculate a weighted average of the unlevered
  betas (weighted by the of the firm in each
  industry)
• Use the firms debt equity ratio to find the
  current beta

88
Calculating Bottom Up Beta

• Look at the firms financial statements to
  breakdown the firm into business units.
• Estimate the average unlevelered beta of other
  publicly traded firms
• Calculate the weighted average of the unlevered
  betas
• Calculate the debt/equity ratio of the firm
• Combine 3 and 4 to find the levered beta.

89
Financial Statements

• Look at the annual report and or 10-K (firms
  website or Edgar, or Mergent)
• From Disney 10-K
• The Walt Disney Company, together with its
  subsidiaries, is a diversified worldwide
  entertainment company with operations in four
  business segments Media Networks, Parks and
  Resorts, Studio Entertainment, and Consumer
  Products.

90
Calculating unlevered beta

• To find the unlevered beta for each business unit
  you would need to find the unleverd beta of firms
  who are concentrated in the same business as the
  business unit.
• As an example we will use the parks and resorts
  business line.
• Disneys parks are destination resorts, family
  friendly, focus on amusement rides etc. They
  also have a small portion of their business in
  cruise lines.

91
Disney Parks and Resorts Comparable firms
92
Other business units

• Media- Time Warner (enterprise competitor),
  Univision, ACME communications, Gray Television
• Consumer goods (toys) Matel, Hasbro, Action
  Products, Action Games
• Studios Marvel (X-Men movie),Lions Gate,
  Graymark, Image (DVD production intermediary),
  Time Warner (enterprise competitor)

93
Calculating the weight in each business unit

• Simple approaches - revenue, assets,
  capital expenditure
• Multiple approach Use industry averages for
  revenue multiple.
• enterprise value (EV)MVequityBVdebt-Cash
• EV/sales multiple used to aggregate revenues
• RevEV/Sales est. value per business unit
• then find of total est. value

94
of BusinessSimple approaches
95
D/E Book or Market Value?

• Book Value is based on the balance sheet
• Market Value would be based upon the current
  value. For equity this is easy it is the
  market capitalization of the firm. For Debt it
  is much harder due to a lack of pricing data for
  debt. It is possible to estimate a market value
  for debt, based on a portion of debt- if you can
  find a price.
• Book value often over emphasizes the impact of
  debt, since market value of equity will be more
  undervalued by book value .

96
Disney Bottom Up Beta
97
Other methods

• Beta can also be estimated in other ways for
  example
• Accounting Betas -- found by analyzing the
  financial statement of the firm and similar firms
• Alternate regression -- You can replace equity
  returns with a proxy ( change in earnings or
  cash flows for example)

98
Measuring Beta - Summary

• Two main methods Top Down (regression) and Bottom
  Up. Bottom up is better when we do not have good
  data.
• Beta is an estimate of the firms sensitivity to
  market risk.
• The use of financial leverage plays a key role in
  determining the beta

99
Whats Next?

• CAPM measures the impact of market risk on the
  return of an individual security.
• So far we have concentrated on Stand Alone Risk,
  but we know that combining assets into a
  portfolio can reduce stand alone risk.

100
Portfolios

• We showed earlier that it was possible to reduce
  risk by combining assets into a portfolio.
• There is a limit to the amount of risk a
  portfolio can eliminate
• Given a set of assets, different weighting of the
  assets will produce different returns for the
  portfolio (and different risk)

101
Efficient Frontier

• By changing the weights in a portfolio you get
  different return and risk combinations.
• It is often possible to rearrange a portfolio and
  produce a higher return without changing the
  risk.
• The efficient frontier provides the set of
  portfolios that produces the highest return at
  each level of risk.

102
Efficient Frontier

• Given four assets, the next slide shows a graph
  of 76 different portfolios created by changing
  only the weights in the portfolio.
• The vertical axis is the return on the portfolio
  , the horizontal axis represents the standard
  deviation of the portfolio.
• The efficient frontier is the set of points that
  provides the highest return for each level of
  risk.

103
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104
Arbitrage Pricing Model

• The CAPM and APM both make a distinction between
  stand alone and market risk
• The CAPM assumes that the market risk is captured
  by the market portfolio.
• The APT assumes that there are many risk factors
  that help to determine the market risk.

105
Arbitrage Pricing Model

• APM assumes that several factors contribute to
  market risk (interest rate, inflation, exchange
  rates ). Just like the CAPM it assumes we can
  measure the sensitivity of an asset to each
  factor (Beta did this in the case of the CAPM)
• In the APM let Bi represent the sensitivity of
  the asset to factor i

106
Arbitrage Pricing Model

• The expected return of the asset is then
• E(R)RRFB1(E(R)1-rRF) B2(E(R)2-rRF)
  Bn(E(R)n-rRF) e
• The CAPM is actually a one factor version of the
  APM
• The APM is difficult to implement due to need to
  identify the relevant factors and returns.

107
Arbitrage Pricing Model

• Assumptions
• Equal portfolios of risk should provide equal
  expected returns
• Investors will drive the return of those that do
  not compensate for their risk up and those that
  provide too much return down.
• Sources of Market Wide Risk
• There are different sources of market risk
  relating to the different factors investigated.

108
Arbitrage Pricing Model

• Arbitrage illustration
• Assume one factor and 3 portfolios
• bA2.0 bB1.0 bC1.5
• Portfolio with 50 in A and 50 in B has same
  beta as C
• What is portfolio of A and B paid 16 but
  Portfolio C paid 15?

109
APM in practice

• Use of factor analysis to determine the factors
  that impact a broad group of stocks
• Benefits
• Specifies number of factors
• Measures beta relative to the common factors
• of factors, factor betas, factor risk premium
• Weaknesses
• The factors are unspecified

110
Multifactor Models

• of factors of identified by the APM a
  multifactor model attempts to identify the
  factors
• Possible factors
• Industrial production
• Unanticipated inflation
• Shifts in term structure of interest rates
• Real rate of return

111
Proxy Models

• Attempting to identify financial or other
  multiples that are linked to returns
• Example Fama and French low price to book
  ratios and low market capitalization result in
  higher returns.
• Rt1.77 - .11ln(MV).35ln(MV/MV)
• (-1.99) (4.44)

112
The Risk in Borrowing

• The risk of default is a primary concern for the
  debt market.
• Again with added risk there should be added
  return.
• Default risk includes firm specific risk, unlike
  the equity risk model we have been discussing.
• Bonds have a much larger downside potential than
  upside potential.

113
Default Risk and Bond Ratings

• Moodys investors services and Standard and
  Poors Corporation provide ratings for corporate
  bonds based upon the quality of the bond.
• The ratings allow investors to compare the safety
  of bonds to each other. A large part of the
  rating is based upon default risk.
• The highest rating, AAA or Aaa, represents a very
  low probability of default.

114
Bond Ratings

• As the probability of default increases, the
  rating drops from AAA to AA (or Aaa to Aaa).
• After A the ratings go to BBB then BB etc.
• Bonds rated below BB are considered high risk or
  Junk Bonds.

115
Summary of Bond Ratings
116
Yield Spread Monthly Data Jan 1919 June 2004
(Moodys)
117
Long Term Average Yearly Yields Over Time
(Moodys)
118
Yield Spreads 1994 - 2003
119
Determination of Default Risk

• Generally
• Higher cash flow generation relative to financial
  obligation lowers default risk
• More stability in cash flows lowers default
  risk
• Higher liquidity of assets lowers default risk

120
Yield Spreads

• Yield Spreads
• The difference in required return between two
  assets, the difference in required return
  represents the difference in risk.
• Often bonds that are the same except for the
  possibility of default are compared, implying
  that the yield spread is a measure of the default
  risk

121
Bond Rating Criteria

• Financial Ratios
• Mortgage Provisions
• Guarantee Provisions
• Sinking funds
• Maturity
• Stability
• Regulation
• Others

122
Yield Spreads and Risk Premiums

• The difference in yield between any two assets
  should represent differences in risk. The extra
  return earned on a riskier security is termed the
  risk premium.
• Generally the risk premium is quoted in basis
  points.
• Yield Spread Yield on Bond A Yield on Bond B
• Where yield on bond B is being used as a benchmark

123
Bond Ratings and Average Yield Spreads vs. US
Treasuries (long term bonds Jan 2004)

• Rating Spread Rating Spread
• AAA .30 B 3.25
• AA .50 B 4.00
• A .70 B- 6.00
• A .85 CCC 8.00
• A- 1.00 CC 10.00
• BBB 1.5 C 12.0
• BB 2.5 D 20.0

124
Relative Yield Spreads

• Spreads are also measured relative to a base rate

125
General Factors Impacting Yield Spreads

• Type of issuer
• Issuers creditworthiness
• Maturity
• Embedded options
• Taxability
• Liquidity
• Other risks associated with previously discussed
  premiums

126
Linking Yield Spreads to Financial Performance

• One of the key things impacting the rating is the
  financial condition of the firm.
• Changes in the financial condition obviously
  impact the ability of the firm to pay its debt
  obligations.
• Often the most commonly used measure is an
  interest coverage ratio. However use of interest
  coverage by itself may mislead. Therefore
  composite scores of credit risk may be used.

127
Bond Rating Criteria and Financial Ratios
1998-2000

• AAA AA A BBB BB B
• EBIT int cov 17.5 10.8 6.8 3.9 2.3 1.0
• EBITDA Int Cov 21.8 14.6 9.6 6.1 3.8 2.0
• NetCF/TotDebt 90 67 50 32 20 11
• FCF/TotDebt 41 22 17 6 1 -4
• ROC 28.2 22.9 19.9 14 11.7 7.2
• LTDebt/TotCap 15 26.4 32.5 41 56 71
• TotDebt/TotCap 27 36 40 47.4 61 75