The Relationship Between Risk and Return - PowerPoint PPT Presentation

1 / 127
About This Presentation
Title:

The Relationship Between Risk and Return

Description:

Explain the types of risk that are rewarded. Develop ... Major components: ... Equation of a line: Y = a bX. Graphing combinations of X and Y form a line. ... – PowerPoint PPT presentation

Number of Views:68
Avg rating:3.0/5.0
Slides: 128
Provided by: facult46
Category:

less

Transcript and Presenter's Notes

Title: 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
(No Transcript)
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
Write a Comment
User Comments (0)
About PowerShow.com