The Relationship
Between Risk and Return
Goal of Financial Management:
Maximize the value of the firm as determined by:
the present value of its expected cash flows,
discounted back at a rate that reflects both the
riskiness of the firms projects and the
financing mix used to fund the projects.
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.
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
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
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%
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?
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%
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?
Expected Rate of Return
To compare the two stocks you would need to
find the expected rate of return
n
  (Prob t )(Return t )
t 1
Intel
Demand
High
Average
Low
Ret
Prob
Ret x Prob
90% 40%
(.9)(.4) = .36
30% 20%
(.3)(.2) = .06
-80% 40%
(-.8)(.4) = -.32
expected return 10%
Mid American Energy
Demand Ret
High
Average
Low
Prob Ret x Prob
15% 25% (.15)(.25) = .0375
10% 50% (.1)(.5) = .0500
5% 25% (.25)(.05) = .0125
expected return
10%
The expected return for each stock is 10%
Which would you prefer to own?
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
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%
Mid American Energy
Demand (Ret-ExpectRet)2
High
(15%-10%)2 x
Average (10%- 10%)2 x
Low
(5% - 10%)2 x
x Prob
(.25) = .000625
(.50) = 0.00
(.25) = .000625
.00125
take the square root (.00125)1/2
standard deviation = .035355 = 3.54%
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
Prob Ranges for Normal Dist.
68.26%
95.46%
99.74%
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 10+76.64 = 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?
Trade off Between
Risk and Return
Avg Ret
Stnd Dev
Excess Ret
Small Co Stocks
17.6%
33.6%
12.1%
Large Co Stocks
13.3%
20.1%
7.8%
L-T Corp Bonds
5.9%
8.7%
0.4%
L-T Gov Bonds
5.5%
9.3%
US Treas Bills
3.8%
3.2%
Inflation
3.2%
4.5%
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?
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%
Coefficient of Variation
The amount of risk per unit of return which is
equal to:
Standard Deviation
Expected Return
Calculating the Coefficient of Variation:
Project A 30/50 = .6 Project B 15/8 = 1.875
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.
Semi Variance
n

t 1
(R t  Average Return)
n
2
Where:
n = number of periods where actual return<average return
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
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 Can’t?
As an investor, which risks should you be
more concerned with (which can be
diversified)?
Risk and Diversification
Project
Risk
Competitive
Risk
Industry Wide
Risk
International
Risk
Firm
Specific
Affects
One Firm
Market
Risk
Market
Risk
Affects
All Firms
Firm Can Reduce Risk By:
Multiple
Acquiring
Projects
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
Quick Stats Review
Covariance:
Cov( AB ) 
 (r
Ai
 r A )( rBi  r B ) Pi
Combines the relationship between the stocks
with the volatility.
(+) the stocks move together
(-) The stocks move opposite of each other
Stats Review 2
Correlation coefficient: The covariance is
difficult to compare when looking at different
series. Therefore the correlation coefficient
is used.
 AB  Cov( AB) /( A B )
The correlation coefficient will range from
-1 to +1
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
BP
25%
15%
Disney
Citicorp
10%
16%
Portfolio Expect Ret
(.25)(.25)+(.1)(.25)+(.15)(.25)+(.16)(.25)=.165
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.
Example 1
Two stocks with correlation coefficient = -1
Year
Stock A
2004
26%
2005
6%
2006
-4%
2007
12%
Avg Ret
10%
Stand dev 10.86
Stock B
-6%
14%
24%
8%
10%
10.86
Portfolio
10%
10%
10%
10%
10%
0
Example 2
Two stocks with correlation coefficient =+1
Year
2004
2005
2006
2007
Avg Ret
Stand dev
Stock A
16%
8%
12%
4%
10%
4.47
Stock B
19%
7%
13%
1%
10%
6.71
Portfolio
17.5%
7.5%
12.5%
2.5%
10%
5.59
Example 3
Two stocks with correlation coefficient =+.571
Year
2004
2005
2006
2007
Avg Ret
Stand dev
Stock A
18%
-4%
24%
2%
10%
11.4
Stock B
22%
12%
18%
-12%
10%
13.19
Portfolio
20%
4%
21%
-5%
10%
10.9
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?
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
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:

2
portfolio 
2 2
w A A
2
2
 (1  wB ) B
 2w A (1  w A )  AB A B
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.
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.
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
Beta - Intuition
Beta measures the sensitivity of the individual asset to
movements in the market for similar assets.
Stock example:
Assume the S&P500 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.
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...
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).
CAPM
ri=rRF+Bi(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
ri=rRF+Bi(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
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
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.
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.
ri= rRF + Bi ( rM - rRF )
Lets put in some numbers for beta and ki
beta = 0
ri = .07+0(.092-.07)=.07= rRF
beta = 1
ri = .07+1(.092-.07)=.092= rM
beta =1.55 ri = .07 +1.55(.092-.07) = .104
B=0,r=rRF
B=1,r=0.092
B=1.55,r=.104
Return
Security
Market
Line
.104
0.092
rRF
0
1.0
1.55
Beta
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.
Increased Risk Aversion
Return
rRF
Bi
Beta
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 S&P 500 is a commonly
used
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.
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.
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.
Observations of X and Y variables
Y
X
Regression Estimates the line that best explains the
relationship between the variables
The Line is the one that minimizes the
sum of the
squared residuals
Estimating the Regression
The slope of the line is then equal to
Cov(x, y)
Variance X
The Intercept is:
AverageY  slope ( AverageX )
Confidence in the Results
R-Squared (R2)
R2 will range up to one. It is the portion of
the relationship explained by the regression
R-Squared (R2) = correlationYX2=b2x2/Y2
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.
Confidence in the Results
T-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.
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)
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 TStatistic (Assuming a normal distribution)
T-Statintercept=A/SEA T-Statslope = B/SEB
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
Estimating Beta
The basic CAPM can be rearranged to allow
the use of regression analysis to estimate
Beta.
ri=rRF+Bi(rM-rRF)
ri=rRF+BirM -BirRF
ri=rRF-BirRF +BirM
ri=rRF(1-Bi)+BirM
Estimating Beta
ri=rRF(1-Bi)+BirM
We know that rRF(1-Bi) is a constant let it = a
ri=a+BirM
Dependent
Variable
Independent
Variable
Estimating Beta
Given Historical data on the return of the
market portfolio and the individual asset we can
estimate Beta.
Cov(rM , ri )
Beta 
Variance(r M )
Estimating Jensen’s 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)
Jensen’s 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 Jensen’s Alpha.
Jensen’s 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 Jensen’s Alpha
comes form the risk free rate and the assets
beta - It measures what you would have
expected to receive.
Interpreting Jensen’s Alpha
If
a > 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 < rRF(1-B) The intercept from the regression is
less than what we would have expected. This
implies that the stock worse than expected.
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
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
S&P 500 served as the market return
Regression Results
rDisney= -0.0001+1.40(rM)+e
Beta = 1.40
rM(1-B) = -.0001=-.01%
R2=.32
Standard error of Beta = .27
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
Disney’s 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
Interpreting Jensen’s 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%
Jensen’s 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 =.0181=1.81%
better than expected each year.
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
Regression Example (2)
SUMMARY OUTPUT
Cisco
Regression Statistics
R Square
Observations
0.24397973
59
Intercept
S&P500
Coefficients Standard Error
t Stat
0.03358372
0.01311694 2.56033182
1.28470379 0.299540417 4.28891635
Regression Results
The coefficient on S&P 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 Jensen’s Alpha?
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).
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..)
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.
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
Disney’s 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.
Disney’s Unlevered Beta
BL = BU(1+(1-t)Debt/Equity)
we estimated the leveraged beta to be 1.4
Historically Disney’s 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.
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 firm’s equity is not traded or traded
infrequently.
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 firm’s debt equity ratio to find the
current beta
Calculating Bottom Up Beta
1.
2.
3.
4.
5.
Look at the firm’s 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.
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.”
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.
Disney’s parks are destination resorts, family
friendly, focus on amusement rides etc. They also
have a small portion of their business in cruise lines.
Disney –Parks and Resorts Comparable firms
Firm
6 Flags
Cedar Fair
Royal Caribbean
Carnival
Great Wolf
Average
Beta
2.87
1.28
1.88
1.71
0.59
D/E
3.33
1.52
0.82
0.42
0.53
All data from Yahoo - D/E are book
values
Unlevered
Beta
0.91
0.64
1.22
1.34
0.44
0.91
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)
Calculating the weight
in each business unit
Simple approaches - % revenue, % assets, % capital
expenditure
Multiple approach – Use industry averages for revenue
multiple.
enterprise value (EV)=MVequity+BVdebt-Cash
EV/sales multiple used to aggregate revenues
Rev*EV/Sales = est. value per business unit
then find % of total est. value
% of Business
Simple approaches
Revenues (2005)
Identifiable Assets
13,207
41.3%
26,926
54.3%
2,228
74.2%
9,023
28.2%
15,807
31.9%
726
24.2%
Studio
7,587
23.8%
5,965
12.0%
37
1.2%
Consumer
2,127
6.7%
877
1.8%
10
0.3%
Media
Networks
Parks and
Resorts
Capital Expenditures
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 .
Disney Bottom Up Beta
Unlevered Beta Revenue
Media Networks
Parks and
Resorts
Studio
Consumer
Source of Weights
Identifaible
Capital
Assets
Expenditures Damodaran
1.120
46.31%
60.83%
83.15%
49.25%
0.911
25.72%
29.04%
22.03%
20.09%
1.081
25.67%
13.00%
1.33%
25.62%
1.182
7.87%
2.09%
0.39%
5.04%
Unlevered Beta
1.123
1.111
1.151
1.071
D/E Yahoo
Disney
0.389
1.399
0.389
1.383
0.389
1.433
0.389
1.334
D/E Damodaran
Disney
0.250
1.306
0.250
1.292
0.250
1.338
0.250
1.245
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)
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
What’s 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.
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)
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.
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.
7
6
5
4
3
2
1
0
0
2
4
6
8
10
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.
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
Arbitrage Pricing Model
The expected return of the asset is then:
E(R)=RRF+B1(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.
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.
Arbitrage Pricing Model
Arbitrage illustration
Assume one factor and 3 portfolios
bA=2.0 bB=1.0 bC=1.5
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%?
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”
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
*Chen, Roll, & Ross 1986 J of Business
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.
Rt=1.77% - .11ln(MV)+.35ln(MV/MV)
(-1.99)
(4.44)
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.
Default Risk and Bond Ratings
Moody’s investors services and Standard and
Poor’s 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.
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”.
Summary of Bond Ratings
Moody’s
S&P
Fitch
Aaa
AAA
AA
Maximum safety
Aa
AA
AA
Very High Grade
A
A
A
Upper Med Grade
Baa
BBB
BBB
Lower Med Grade
Ba
BB
BB
Low Grade Speculative
B
B
B
Highly Speculative
Caa
CCC
CCC
In poor standing
Ca
CC
CC
May be in default
C
C
C
More risky than CC
D
D
and Straegies 2004
D Fabozzi Bond Markets
In Analysis
Default
Investment Grade
Low Credit
Worthiness
Substantial Risk
close to default or
in default
In default
Yield Spread Monthly Data
Jan 1919 – June 2004 (Moodys)
20
18
16
14
%
12
10
8
6
4
2
0
9/8/1913
1/24/1941
Aaa
Baa
6/11/1968
Date
10/28/1995
Long Term Average Yearly Yields Over Time
(Moody’s)
18
16
14
(%)
12
10
8
6
4
1980
1985
1990
Aaa
Aa
1995
A
2000
Baa
Yield Spreads 1994 - 2003
10
6
5
8
7
4
6
AAA
5
4
3
3
BBB
Treas
AAA-Treas
2
BBB-Treas
2
1
1
0
Jan-94 Nov-94 Sep-95
0
Jul-96 May-97 Mar-98 Jan-99 Nov-99 Sep-00 Jul-01
Date
May-02 Mar-03
Spread
Yield
9
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
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
Bond Rating Criteria
Financial Ratios
Mortgage Provisions
Guarantee Provisions
Sinking funds
Maturity
Stability
Regulation
Others
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
Bond Ratings and Average
Yield Spreads vs. US Treasuries (long term bonds
Jan 2004)
Rating
AAA
AA
A+
A
ABBB
BB
Spread
.30%
.50%
.70%
.85%
1.00%
1.5%
2.5%
Rating
B+
B
BCCC
CC
C
D
Spread
3.25%
4.00%
6.00%
8.00%
10.00%
12.0%
20.0%
Relative Yield Spreads
Spreads are also measured relative to a base rate
relative
yield on bond A - yield on bond B
yield 
yield on bond b
spread
yield yield on bond A

ratio yield on bond B
General Factors
Impacting Yield Spreads
1.
2.
3.
4.
5.
6.
7.
Type of issuer
Issuers creditworthiness
Maturity
Embedded options
Taxability
Liquidity
Other risks associated with
previously discussed premiums
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.
Bond Rating Criteria and
Financial Ratios 1998-2000
AAA
EBIT int cov
17.5
EBITDA Int Cov 21.8
NetCF/TotDebt 90%
FCF/TotDebt
41%
ROC
28.2%
LTDebt/TotCap 15%
TotDebt/TotCap 27%
AA
10.8
14.6
67%
22%
22.9%
26.4%
36%
A
6.8
9.6
50%
17%
19.9%
32.5%
40%
BBB
3.9
6.1
32%
6%
14%
41%
47.4%
BB
B
2.3
1.0
3.8
2.0
20% 11%
1%
-4%
11.7% 7.2%
56% 71%
61% 75%