Part 3 Risk
Jilin university
College of economics
Ding zhaoyong
Outline of this part
This part examines the relationship between expected
return and risk for portfolios and individual assets,
When the capital markets are in equilibrium,they
determine a trade—off between expected return and
risk.
This part is composed by four chapters:
– 9 capital market theory,an overview( risk and
return)
– 10 CAPM
– 11 APT
– 12 risk,return and capital budgeting
Chapter 9 Risk and return
Chapter 9 Risk and return
9.1 Returns
– Dollar return
If you buy some kinks of assets,your gain or loss from
that investment is called the return on your investment,
This return will usually have tow components,
First,you may receive some cash directly while you own
the investment,This is called the income component of
your return,Second,the value of the asset you purchase
will often change,In this case,you have a capital gain or
capital loss on your investment.
Total dollar return= dividend income +capital gain(loss)
Total cash if stock is sold= initial investment+total return
Chapter 9 Risk and return
– Percentage return
It is usually more convenient to summarize information
about return in percentage terms,rather than dollar
return,because that way your return does not depend on
how much you actually invest,The question we want to
answer is,how much do we get for each dollar we invest.
Percentage return=(dividends paid at end of period+change
in market value over period)/beginning market value
9.2 Inflation and returns
– Real versus nominal returns
The returns we calculated in the previous section are called
nominal returns because they were not adjusted for
inflation.
Chapter 9 Risk and return
Returns that have been adjusted to reflect inflation are
called real return.
The difference between nominal return and real return is
important and bears repeating:
Your nominal return on an investment is the percentage
change in the number of dollars you have.
Your real return on an investment is the percentage change
in how much you can buy with your dollars,in other
words,the percentage change in your buying power.
– The fisher effect
The fisher effect is the relationship between nominal
returns,the real returns,and inflation.
Chapter 9 Risk and return
Let R stand for the nominal return and r stand for the
real return and h stand for the inflation rate.
(1+R)=(1+r)× (1+h)
9.3 Average returns,the first lesson
– Calculating average returns
– Risk premiums
Rate of return on government bonds is the risk-free return
because the government can always raise taxes to pay its
bills.
A particularly interesting comparison involves the
virtually risk-free return on T-bills and the very risky
return on common stocks.
Chapter 9 Risk and return
The difference between these two returns can be
interpreted as a measure of the excess return on the
average risky asset.
We call this the ―excess‖ return since it is the
additional return we earn by moving from a
relatively risk-free investment to a risky one,
Because it can be interpreted as a reward for
bearing risk,we will call it risk premium.
Risk premium is the excess return required from an
investment in a risky asset over a risk-free
investment.
So the first lesson is on average risky assets earn a
risk premium.
Chapter 9 Risk and return
9.4 The variability of returns,the second lesson
– Frequency distributions and variability
To get started,we can draw a frequency distribution for
the common stock returns like the figure.
What we need to do is to actually measure the spread in
returns,We now want to know how far the actual
return deviates from the average in a typical year,In
other words,we need a measure of how volatile the
future is,The variance and its square root,the standard
deviation,are the most commonly used measures of
volatility,
Chapter 9 Risk and return
Number
of years
Returns
16
14
12
10
8
6
4
2
0
-55 -45 -35 -25 -15 -5 5 15 25 35 45
Chapter 9 Risk and return
Variance is the average squared difference between the
actual return and the average return.
Standard deviation is the positive square root of the
variance
– The historical variance and standard deviation
– Normal Distribution
Normal distribution is a symmetric,bell—shaped
frequency distribution that is completely defined by its
mean and standard deviation.
)1(
2)(2)(2)(2)( 4321
T
RRRRRRRRV a r
Chapter 9 Risk and return
– The second lesson
Our observation concerning the year—to —year
variability in returns are the basis for our second lesson
from capital market history.
On average,bearing risk is handsomely rewarded,but
in a given year,there is a significant change of a
dramatic change in value.
Thus our second lesson is,The greater the potential
reward,the greater is the risk.
9.5 The discount rate for risky projects
– The case where risky is the same as the market
Chapter 9 Risk and return
Expected return on market portfolio = risky— free rate + expected
risk return
Expected return on the market = current risk— free rate +
historical risk premium
– The case where risk is different from the market
The relationship between project risk and market risk,
and there risks are not equal,can be provided in
figure like next,
Where the discount rate is positively related to the
project’s risk,that is because when investors demand
a high expected return on a project with a high risk.
If the project’s risk were judged to be high,the
discounted rate should be selected more higher than
the market expected rate of return,
Chapter 9 Risk and return
9.6 Risk and beta
– Diversification
The difference between the standard deviation of an
individual stock and the standard deviation of a
portfolio or an index is due to the well—known
phenomenon of diversification,
Diversification is very effective at reducing risk,
– Beta
Beta is defined as the covariance of the return of an
individual stock with the ―market proxy‖ portfolio
return divided by the variance of the of the market’s
proxy return.
Chapter 12
Risk,return and capital budgeting
12.1 The cost of equity capital
– From the firm’s respective,the expected return is
the cost of equity capital,
That is,
The risk—free rate,
The market—risk premium,
The company beta,
)( FMF RRRR
FR
FM RR
Chapter 12
Return,risk,and capital budgeting
12.2 Calculation of the beta
Problems of beta
Beta may vary over time
The sample size may be inadequate
Betas are influenced by changing financial
leverage and business risk
2
,
)(
),( is e c u r i t y of
M
I
Mt
Mtit M
RV a r
RRC o v
Chapter 12
Return,risk,and capital budgeting
Solution
Problems 1 and 2 can be moderated by more
sophisticated statistical
Problem 3 can be lessened by adjusting for
changes in business and financial risk
Look at average beta estimates of several
comparable firms in the industry.
12.3 Determinants of beta
– Cyclicality of revenues
Chapter 12
Return,risk,and capital budgeting
– Operating leverage
Cash flow = revenue –fixed cost – variable cost
PV(asset)= PN(revenue)-(fixed cost)-PV(variable)
PV(revenue)= (fixed cost) +PV(variable) +PV(asset)
Those who receive the fixed costs are like debtholders in
the project; they simply get a fixed payment,Those who
receive the net cash flows from the asset are like holders
of common stocks; they get whatever is left after
payment of the fixed costs.
So we can now figure out the asset’s beta is related to the
beta of the values of revenue and costs.
Chapter 12
Return,risk,and capital budgeting
In other words,the beta of the value of the revenues is simply
a weighted average of the beta of its components parts,
Now the fixed—cost beta is zero by definition,the betas of
revenues and variable costs should be approximately the
same,because they respond to the same underlying
variable,the rate of output,Therefore,
P V ( R )
P V ( A )
P V ( R )
P V ( V C )
P V ( R )
P V ( FC )
a s s e tc o s t v a r i a b l ec o s t f i x e dr e v e n u e
])( )(1[)(PV ( V C )-PV ( R )r e v e n u ea s s e t APV
FCPV
APV R
Chapter 12
Return,risk,and capital budgeting
– Financial leverage and beta
In practice the beta of debt is very low,so we can
assumption the beta of debt is zero,and
E q u i t yD e b tA s s e t E q u i t yD e b t
E q u i t y
E q u i t yD e b e
D e b t
E q u i t yA s s e t E q u i t yD e b t
E q u i t y
Chapter 12
Return,risk,and capital budgeting
Because Equity/(Debt + Equity) must be below 1 for a
levered firm,so we can rearranging the above equation
like this:
12.4 Extensions of the basic model
– The firm versus project,vive la difference
– The cost of capital with debt
Suppose a firm uses both debt and equity to finance its
investments.
A s s e tE q u i t y )
E q u i t y
D e b t 1(
Chapter 12
Return,risk,and capital budgeting
If the firm pays rb for its debt financing and rs for its equity,
what is the overall or average cost of its capital?
So the cost of capital to be,
Because interest is tax deductible at the corporate level,the
after—tax cost of debt is
rbBS BrsBS S
)1( t a xc or po r a t ea f t e r d e b t ofC o s t CTrb
Chapter 12
Return,risk,and capital budgeting
Assembling these results,we get the average cost of capital
(after tax) for the firm:
Because the average cost of capital is a weighting of its cost of
equity and its cost of debt,it is usually referred to as the
weighted averaged cost of capital,rWACC and from now we
will use this term.
)1()()(c a p i t a l ofc o s t a v e r a g e CTrbBS BrsBS S
Chapter 12
Return,risk,and capital budgeting
12.5 Summary and conclusions
– A firm with excess cash can either pay a dividend or
make a capital expenditure.
– The expected return on any asset is dependent upon its
beta.
– We considered the case of a project whose beta risk was
equal to that of the firm,if the firm is unleveled the
discounted rate on the project is equal to
– If the project’s beta differs from that of the firm,the
discounted rate should be based on the project’s beta.
– The beta of a company is a function of a number of
factors,Perhaps have three most important factors.
Jilin university
College of economics
Ding zhaoyong
Outline of this part
This part examines the relationship between expected
return and risk for portfolios and individual assets,
When the capital markets are in equilibrium,they
determine a trade—off between expected return and
risk.
This part is composed by four chapters:
– 9 capital market theory,an overview( risk and
return)
– 10 CAPM
– 11 APT
– 12 risk,return and capital budgeting
Chapter 9 Risk and return
Chapter 9 Risk and return
9.1 Returns
– Dollar return
If you buy some kinks of assets,your gain or loss from
that investment is called the return on your investment,
This return will usually have tow components,
First,you may receive some cash directly while you own
the investment,This is called the income component of
your return,Second,the value of the asset you purchase
will often change,In this case,you have a capital gain or
capital loss on your investment.
Total dollar return= dividend income +capital gain(loss)
Total cash if stock is sold= initial investment+total return
Chapter 9 Risk and return
– Percentage return
It is usually more convenient to summarize information
about return in percentage terms,rather than dollar
return,because that way your return does not depend on
how much you actually invest,The question we want to
answer is,how much do we get for each dollar we invest.
Percentage return=(dividends paid at end of period+change
in market value over period)/beginning market value
9.2 Inflation and returns
– Real versus nominal returns
The returns we calculated in the previous section are called
nominal returns because they were not adjusted for
inflation.
Chapter 9 Risk and return
Returns that have been adjusted to reflect inflation are
called real return.
The difference between nominal return and real return is
important and bears repeating:
Your nominal return on an investment is the percentage
change in the number of dollars you have.
Your real return on an investment is the percentage change
in how much you can buy with your dollars,in other
words,the percentage change in your buying power.
– The fisher effect
The fisher effect is the relationship between nominal
returns,the real returns,and inflation.
Chapter 9 Risk and return
Let R stand for the nominal return and r stand for the
real return and h stand for the inflation rate.
(1+R)=(1+r)× (1+h)
9.3 Average returns,the first lesson
– Calculating average returns
– Risk premiums
Rate of return on government bonds is the risk-free return
because the government can always raise taxes to pay its
bills.
A particularly interesting comparison involves the
virtually risk-free return on T-bills and the very risky
return on common stocks.
Chapter 9 Risk and return
The difference between these two returns can be
interpreted as a measure of the excess return on the
average risky asset.
We call this the ―excess‖ return since it is the
additional return we earn by moving from a
relatively risk-free investment to a risky one,
Because it can be interpreted as a reward for
bearing risk,we will call it risk premium.
Risk premium is the excess return required from an
investment in a risky asset over a risk-free
investment.
So the first lesson is on average risky assets earn a
risk premium.
Chapter 9 Risk and return
9.4 The variability of returns,the second lesson
– Frequency distributions and variability
To get started,we can draw a frequency distribution for
the common stock returns like the figure.
What we need to do is to actually measure the spread in
returns,We now want to know how far the actual
return deviates from the average in a typical year,In
other words,we need a measure of how volatile the
future is,The variance and its square root,the standard
deviation,are the most commonly used measures of
volatility,
Chapter 9 Risk and return
Number
of years
Returns
16
14
12
10
8
6
4
2
0
-55 -45 -35 -25 -15 -5 5 15 25 35 45
Chapter 9 Risk and return
Variance is the average squared difference between the
actual return and the average return.
Standard deviation is the positive square root of the
variance
– The historical variance and standard deviation
– Normal Distribution
Normal distribution is a symmetric,bell—shaped
frequency distribution that is completely defined by its
mean and standard deviation.
)1(
2)(2)(2)(2)( 4321
T
RRRRRRRRV a r
Chapter 9 Risk and return
– The second lesson
Our observation concerning the year—to —year
variability in returns are the basis for our second lesson
from capital market history.
On average,bearing risk is handsomely rewarded,but
in a given year,there is a significant change of a
dramatic change in value.
Thus our second lesson is,The greater the potential
reward,the greater is the risk.
9.5 The discount rate for risky projects
– The case where risky is the same as the market
Chapter 9 Risk and return
Expected return on market portfolio = risky— free rate + expected
risk return
Expected return on the market = current risk— free rate +
historical risk premium
– The case where risk is different from the market
The relationship between project risk and market risk,
and there risks are not equal,can be provided in
figure like next,
Where the discount rate is positively related to the
project’s risk,that is because when investors demand
a high expected return on a project with a high risk.
If the project’s risk were judged to be high,the
discounted rate should be selected more higher than
the market expected rate of return,
Chapter 9 Risk and return
9.6 Risk and beta
– Diversification
The difference between the standard deviation of an
individual stock and the standard deviation of a
portfolio or an index is due to the well—known
phenomenon of diversification,
Diversification is very effective at reducing risk,
– Beta
Beta is defined as the covariance of the return of an
individual stock with the ―market proxy‖ portfolio
return divided by the variance of the of the market’s
proxy return.
Chapter 12
Risk,return and capital budgeting
12.1 The cost of equity capital
– From the firm’s respective,the expected return is
the cost of equity capital,
That is,
The risk—free rate,
The market—risk premium,
The company beta,
)( FMF RRRR
FR
FM RR
Chapter 12
Return,risk,and capital budgeting
12.2 Calculation of the beta
Problems of beta
Beta may vary over time
The sample size may be inadequate
Betas are influenced by changing financial
leverage and business risk
2
,
)(
),( is e c u r i t y of
M
I
Mt
Mtit M
RV a r
RRC o v
Chapter 12
Return,risk,and capital budgeting
Solution
Problems 1 and 2 can be moderated by more
sophisticated statistical
Problem 3 can be lessened by adjusting for
changes in business and financial risk
Look at average beta estimates of several
comparable firms in the industry.
12.3 Determinants of beta
– Cyclicality of revenues
Chapter 12
Return,risk,and capital budgeting
– Operating leverage
Cash flow = revenue –fixed cost – variable cost
PV(asset)= PN(revenue)-(fixed cost)-PV(variable)
PV(revenue)= (fixed cost) +PV(variable) +PV(asset)
Those who receive the fixed costs are like debtholders in
the project; they simply get a fixed payment,Those who
receive the net cash flows from the asset are like holders
of common stocks; they get whatever is left after
payment of the fixed costs.
So we can now figure out the asset’s beta is related to the
beta of the values of revenue and costs.
Chapter 12
Return,risk,and capital budgeting
In other words,the beta of the value of the revenues is simply
a weighted average of the beta of its components parts,
Now the fixed—cost beta is zero by definition,the betas of
revenues and variable costs should be approximately the
same,because they respond to the same underlying
variable,the rate of output,Therefore,
P V ( R )
P V ( A )
P V ( R )
P V ( V C )
P V ( R )
P V ( FC )
a s s e tc o s t v a r i a b l ec o s t f i x e dr e v e n u e
])( )(1[)(PV ( V C )-PV ( R )r e v e n u ea s s e t APV
FCPV
APV R
Chapter 12
Return,risk,and capital budgeting
– Financial leverage and beta
In practice the beta of debt is very low,so we can
assumption the beta of debt is zero,and
E q u i t yD e b tA s s e t E q u i t yD e b t
E q u i t y
E q u i t yD e b e
D e b t
E q u i t yA s s e t E q u i t yD e b t
E q u i t y
Chapter 12
Return,risk,and capital budgeting
Because Equity/(Debt + Equity) must be below 1 for a
levered firm,so we can rearranging the above equation
like this:
12.4 Extensions of the basic model
– The firm versus project,vive la difference
– The cost of capital with debt
Suppose a firm uses both debt and equity to finance its
investments.
A s s e tE q u i t y )
E q u i t y
D e b t 1(
Chapter 12
Return,risk,and capital budgeting
If the firm pays rb for its debt financing and rs for its equity,
what is the overall or average cost of its capital?
So the cost of capital to be,
Because interest is tax deductible at the corporate level,the
after—tax cost of debt is
rbBS BrsBS S
)1( t a xc or po r a t ea f t e r d e b t ofC o s t CTrb
Chapter 12
Return,risk,and capital budgeting
Assembling these results,we get the average cost of capital
(after tax) for the firm:
Because the average cost of capital is a weighting of its cost of
equity and its cost of debt,it is usually referred to as the
weighted averaged cost of capital,rWACC and from now we
will use this term.
)1()()(c a p i t a l ofc o s t a v e r a g e CTrbBS BrsBS S
Chapter 12
Return,risk,and capital budgeting
12.5 Summary and conclusions
– A firm with excess cash can either pay a dividend or
make a capital expenditure.
– The expected return on any asset is dependent upon its
beta.
– We considered the case of a project whose beta risk was
equal to that of the firm,if the firm is unleveled the
discounted rate on the project is equal to
– If the project’s beta differs from that of the firm,the
discounted rate should be based on the project’s beta.
– The beta of a company is a function of a number of
factors,Perhaps have three most important factors.
