1
Risk and Rates of
Return
Chapter 6
Interest Rate
4
Interest rate represents the cost of money
It is the opportunity cost of money:
It shows the return lost from not investing in a
comparable risk investment.
It is expected to compensate the investor for the time,
inflation, and risk.
5
Conceptually:
Interest Rates
6
Conceptually:
Nominal
risk-free
Interest
Rate
krf
Interest Rates
7
Conceptually:
Nominal
risk-free
Interest
Rate
krf
=
Interest Rates
8
Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
krf
=
Real
risk-free
Interest
Rate
k*
9
Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
krf
=
Real
risk-free
Interest
Rate
k*
+
10
Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
krf
=
Real
risk-free
Interest
Rate
k*
+
Inflationrisk
premium
IRP
11
Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
=
Real
risk-free
Interest
Rate
krf
Mathematically:
k*
+
Inflationrisk
premium
IRP
12
Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
=
Real
risk-free
Interest
Rate
krf
k*
+
Inflationrisk
premium
IRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)
13
Interest Rates
Conceptually:
Nominal
risk-free
Interest
Rate
=
Real
risk-free
Interest
Rate
krf
k*
+
Inflationrisk
premium
IRP
Mathematically:
(1 + krf) = (1 + k*) (1 + IRP)
This is known as the “Fisher Effect”
14
Interest Rates
Suppose the real rate is 3%, and the nominal
rate is 8%. What is the inflation rate premium?
(1 + krf) = (1 + k*) (1 + IRP)
(1.08) = (1.03) (1 + IRP)
(1 + IRP) = (1.0485), so
IRP = 4.85%
Term Structure of Interest Rates
The pattern of rates of return for debt
securities that differ only in the length
of time to maturity.
15
Term Structure of Interest Rates
16
The pattern of rates of return for debt
securities that differ only in the length
of time to maturity.
yield
to
maturity
time to maturity (years)
Term Structure of Interest Rates
17
The pattern of rates of return for debt
securities that differ only in the length
of time to maturity.
yield
to
maturity
time to maturity (years)
Term Structure of Interest Rates
18
The yield curve may be downward sloping or
“inverted” if rates are expected to fall.
yield
to
maturity
time to maturity (years)
Term Structure of Interest Rates
19
The yield curve may be downward sloping or
“inverted” if rates are expected to fall.
yield
to
maturity
time to maturity (years)
20
For a Treasury security, what is the
required rate of return?
21
For a Treasury security, what is the
required rate of return?
Required
rate of
return
=
22
For a Treasury security, what is the
required rate of return?
Required
rate of
return
=
Risk-free
rate of
return
Since Treasuries are essentially free of default
risk, the rate of return on a Treasury security
is considered the “risk-free” rate of return.
23
For a corporate stock or bond, what is the
required rate of return?
24
For a corporate stock or bond, what is the
required rate of return?
Required
rate of
return
=
25
For a corporate stock or bond, what is the
required rate of return?
Required
rate of
return
=
Risk-free
rate of
return
26
For a corporate stock or bond, what is the
required rate of return?
Required
rate of
return
=
Risk-free
rate of
return
+
Risk
premium
How large of a risk premium should we require
to buy a corporate security?
Returns
Expected Return - the return that an
investor expects to earn on an asset,
given its price, growth potential, etc.
Required Return - the return that an
investor requires on an asset given
its risk and market interest rates.
27
Risk and Rates of Return
Two Components of return
Periodic cash flows
28
Risk and Rates of Return
Two Components of return
Periodic cash flows
Price Change (capital gains)
29
Risk and Rates of Return
Holding Period return
30
Risk and Rates of Return
Holding Period return
Pt + Dt
= ---------- - 1
Pt-1
31
Risk and Rates of Return
Holding Period return
Pt + Dt
= ---------- - 1
Pt-1
(Pt - Pt-1) + Dt
= ---------------Pt-1
32
Risk and Rates of Return
33
Expected Return
Expected return is based on expected cash flows (not
accounting profits)
Return can be expressed as Cash
Flows or Percentage Return
Risk and Rates of Return
34
Expected Return
Expected return is based on expected cash flows (not
accounting profits)
In an uncertain world future cash flows are not known
with certainty
Risk and Rates of Return
35
Expected Return
Expected return is based on expected cash flows (not
accounting profits)
In uncertain world future cash flows are not known with
certainty
To calculate expected return, compute the weighted
average of all possible returns
Risk and Rates of Return
36
Expected Return
Expected return is based on expected cash flows (not
accounting profits)
In uncertain world future cash flows are not known with
certainty
To calculate expected return, compute the weighted
average of possible returns
Calculating Expected Return:
k
N
 k iP( k i )
i1
Risk and Rates of Return
37
Expected Return
Expected return is based on expected cash flows (not
accounting profits)
In uncertain world future cash flows are not known with
certainty
To calculate expected return, compute the weighted
average of possible returns
Calculating Expected Return:
k
N
 k iP( k i )
i1
where
ki
= Return state i
P(ki) = Probability of ki occurring
N
= Number of possible states
38
Risk and Rates of Return
Expected Return Calculation
Example
You are evaluating ElCat Corporation’s common stock. You
estimate the following returns given different states of the
economy
State of Economy
Probability
Return
Economic Downturn
Zero Growth
Moderate Growth
High Growth
.10
.20
.40
.30
–5%
5%
10%
20%
39
Risk and Rates of Return
Expected Return Calculation
Example
You are evaluating ElCat Corporation’s common stock. You
estimate the following returns given different states of the
economy
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
k
N
 k iP(k i )
i 1
Probability
x
.10
.20
.40
.30
Return
–5%
5%
10%
20%
= –0.5%
40
Risk and Rates of Return
Expected Return Calculation
Example
You are evaluating ElCat Corporation’s common stock. You
estimate the following returns given different states of the
economy
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
k
N
 k iP(k i )
i 1
Probability
x
.10
x
.20
.40
.30
Return
–5%
5%
10%
20%
= –0.5%
=
1%
41
Risk and Rates of Return
Expected Return Calculation
Example
You are evaluating ElCat Corporation’s common stock. You
estimate the following returns given different states of the
economy
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
k
N
 k iP(k i )
i 1
Probability
x
.10
x
.20
x
.40
.30
Return
–5%
5%
10%
20%
= –0.5%
=
1%
=
4%
42
Risk and Rates of Return
Expected Return Calculation
Example
You are evaluating ElCat Corporation’s common stock. You
estimate the following returns given different states of the
economy
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
k
N
 k iP(k i )
i 1
Probability
x
.10
x
.20
x
.40
x
.30
Return
–5%
5%
10%
20%
= –0.5%
=
1%
=
4%
=
6%
43
Risk and Rates of Return
Expected Return Calculation
Example
You are evaluating ElCat Corporation’s common stock. You
estimate the following returns given different states of the
economy
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
k
N
 k iP(k i )
i 1
Probability
x
.10
x
.20
x
.40
x
.30
Return
= –0.5%
=
1%
=
4%
=
6%
k = 10.5%
–5%
5%
10%
20%
44
Risk and Rates of Return
Expected Return Calculation
Example
You are evaluating ElCat Corporation’s common stock. You
estimate the following returns given different states of the
economy
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
k
Probability
x
.10
x
.20
x
.40
x
.30
Return
= –0.5%
=
1%
=
4%
=
6%
k = 10.5%
–5%
5%
10%
20%
N
 k iP(k i )
i 1
Expected (or average) rate
of return on stock is 10.5%
Risk and Rates of Return
Risk
Risk is the uncertainty of future outcomes
45
Risk and Rates of Return
Risk
Risk is the uncertainty of future outcomes
Example
You evaluate two investments: ElCat Corporation’s
common stock and a one year Gov't Bond paying 6%. The
return on the Gov't Bond does not depend on the state of
the economy--you are guaranteed a 6% return.
46
Risk and Rates of Return
Risk
Risk is the uncertainty of future outcomes
Example
You evaluate two investments: ElCat Corporation’s
common stock and a one year Gov't Bond paying 6%. The
return on the Gov't Bond does not depend on the state of
the economy--you are guaranteed a 6% return.
Probability
of Return
100%
T-Bill
6%
Return
47
48
Risk and Rates of Return
Risk
Risk is the uncertainty of future outcomes
Example
You evaluate two investments: ElCat Corporation’s
common stock and a one year Gov't Bond paying 6%. The
return on the Gov't Bond does not depend on the state of
the economy--you are guaranteed a 6% return.
Probability
of Return
100%
T-Bill
Probability
of Return
ElCat Corp
40%
30%
20%
10%
6%
Return
–5% 5% 10% 20% Return
49
Risk and Rates of Return
Risk
Risk is the uncertainty of future outcomes
Example
You evaluate two investments: ElCat Corporation’s
common stock and a one year Gov't Bond paying 6%. The
return on the Gov't Bond does not depend on the state of
the economy--you are guaranteed a 6% return.
Probability
of Return
100%
T-Bill
ElCat Corp
Probability
There is risk in of
Owning
Return ElCat stock,
no risk in owning the Treasury Bill
40%
30%
20%
10%
6%
Return
–5% 5% 10% 20% Return
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
50
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
51
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
52
53
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Probability
Return
Economic Downturn
Zero Growth
Moderate Growth
High Growth
.10
.20
.40
.30
–5%
5%
10%
20%
54
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
Probability
x
.10
.20
.40
.30
Return
( –5% – 10.5%)2 =
5%
10%
20%
24.025%2
55
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
Probability
x
.10
x
.20
.40
.30
Return
( –5% – 10.5%)2 =
( 5% – 10.5%)2 =
10%
20%
24.025%2
6.05%2
56
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
Probability
x
.10
x
.20
x
.40
.30
Return
( –5% – 10.5%)2 =
( 5% – 10.5%)2 =
( 10% – 10.5%)2 =
20%
24.025%2
6.05%2
0.10%2
57
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
Probability
x
.10
x
.20
x
.40
x
.30
Return
(
(
(
(
–5% – 10.5%)2 = 24.025%2– -6.05%2
5% 10.5%)2 =
0.10%2
10% – 10.5%)2 =
20% – 10.5%)2 = 27.075%2
58
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
Probability
x
.10
x
.20
x
.40
x
.30
Return
(
(
(
(
–5% – 10.5%)2
5% – 10.5%)2
10% – 10.5%)2
20% – 10.5%)2
s2 =
=
=
=
=
24.025%2
6.05%2
0.10%2
27.075%2
57.25%2
59
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
Probability
x
.10
x
.20
x
.40
x
.30
Return
( –5% – 10.5%)2
( 5% – 10.5%)2
( 10% – 10.5%)2
( 20% – 10.5%)2
s2 =
s =
=
=
=
=
24.025%2
6.05%2
0.10%2
27.075%2
57.25%2
57.25%2
60
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Economic Downturn
Zero Growth
Moderate Growth
High Growth
Probability
x
.10
x
.20
x
.40
x
.30
Return
( –5% – 10.5%)2
( 5% – 10.5%)2
( 10% – 10.5%)2
( 20% – 10.5%)2
s2 =
s =
s =
=
=
=
=
24.025%2
6.05%2
0.10%2
27.075%2
57.25%2
57.25%2
7.57%
61
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Probability
x
.10
x
.20
x
.40
x
.30
Return
( –5% – 10.5%)2
Economic Downturn
( 5% – 10.5%)2
Zero Growth
( 10% – 10.5%)2
Moderate Growth
( 20% – 10.5%)2
High Growth
s2 =
s =
Higher standard deviation, higher risk
s =
=
=
=
=
24.025%2
6.05%2
0.10%2
27.075%2
57.25%2
57.25%2
7.57%
62
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
NOTE: The
s
N
 (k i  k )
i 1
2
P(k i )
standard
deviation of the
T-Bill is 0%
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Probability
x
.10
x
.20
x
.40
x
.30
Return
( –5% – 10.5%)2
Economic Downturn
( 5% – 10.5%)2
Zero Growth
( 10% – 10.5%)2
Moderate Growth
( 20% – 10.5%)2
High Growth
s2 =
s =
Higher standard deviation, higher risk
s =
=
=
=
=
24.025%2
6.05%2
0.10%2
27.075%2
57.25%2
57.25%2
7.57%
63
Risk and Rates of Return
Measuring Risk
Standard Deviation (s) measure the dispersion of
returns.
s
N
2
(k

k
)
P(k i )
 i
i 1
Example
Compute the standard deviation on ElCat common stock.
the mean (k) was previously computed as 10.5%
State of Economy
Probability
x
.10
x
.20
x
.40
x
.30
Return
( –5% – 10.5%)2
Economic Downturn
( 5% – 10.5%)2
Zero Growth
( 10% – 10.5%)2
Moderate Growth
( 20% – 10.5%)2
High Growth
2 =
s
Can compare the s of 7.57 to another
s =
stock with expected return of 10.5%
s =
=
=
=
=
24.025%2
6.05%2
0.10%2
27.075%2
57.25%2
57.25%2
7.57%
Risk and Rates of Return
64
Measuring Risk
Standard Deviation (s) for historical data can be used
to measure the dispersion of historical returns.
N
1
2
s
( ki  k )

(n  1) _ i 1
Risk and Rates of Return
65
Use the following data to calculate the historical return
of XYZ
Year
Return
1992
12%
1993
16%
1994
-8%
1995
6%
Risk and Rates of Return
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
66
Risk and Rates of Return
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
67
Risk and Rates of Return
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
Stock price will most likely fall if a major government
contract is discontinued unexpectedly.
68
Risk and Rates of Return
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
Market related Risk - Risk due to overall market
conditions
69
Risk and Rates of Return
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
Market related Risk - Risk due to overall market
conditions
Stock price is likely to rise if overall stock market is
doing well.
70
Risk and Rates of Return
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
Market related Risk - Risk due to overall market
conditions
Diversification: If investors hold stock of many
companies, the firm specific risk will be canceled out:
Investors diversify portfolio.
71
Risk and Rates of Return
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
Market related Risk - Risk due to overall market
conditions
Diversification: If investors hold stock of many
companies, the firm specific risk will be canceled out:
Investors diversify portfolio.
Firm specific risk also called diversifiable
risk or unsystematic risk
72
Risk and Rates of Return
73
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
Market related Risk - Risk due to overall market
conditions
Diversification: If investors hold stock of many
companies, the firm specific risk will be canceled out:
Investors diversify portfolio.
Even if hold many stocks, cannot eliminate the market
related risk
Risk and Rates of Return
74
Risk and Diversification
Risk of a company's stock can be separated into two
parts:
Firm Specific Risk - Risk due to factors within the firm
Market related Risk - Risk due to overall market
conditions
Diversification: If investors hold stock of many
companies, the firm specific risk will be canceled out:
Investors diversify portfolio.
Even if hold many stocks, cannot eliminate the market
related risk Market related risk is also called non-diversifiable
risk or systematic risk
Risk and Rates of Return
Risk and Diversification
If an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually
eliminated
75
Risk and Rates of Return
Risk and Diversification
If an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually
eliminated
Variability
of Returns
Market
Related Risk
Number of stocks in Portfolio
76
Risk and Rates of Return
Risk and Diversification
If an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually
eliminated
Variability
of Returns
Firm Specific
Risk
Number of stocks in Portfolio
77
Risk and Rates of Return
Risk and Diversification
If an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually
eliminated
Variability
of Returns
Total
Risk
Number of stocks in Portfolio
78
Risk and Rates of Return
Risk and Diversification
If an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually
eliminated
Variability
of Returns
20
Number of stocks in Portfolio
79
Risk and Rates of Return
Risk and Diversification
If an investor holds enough stocks in portfolio (about
20) company specific (diversifiable) risk is virtually
eliminated
Holding a general stock mutual fund (not a specific
industry fund) is similar to holding a well-diversified
portfolio.
Variability
of Returns
20
Number of stocks in Portfolio
80
Risk and Rates of Return
Measuring Market Risk
Market risk is the risk of the overall market. To
measure the market risk we need to compare
individual stock returns to the overall market returns.
81
Risk and Rates of Return
Measuring Market Risk
Market risk is the risk of the overall market. To
measure the market risk we need to compare
individual stock returns to the overall market returns.
A proxy for the market is usually used: An index of
stocks such as the S&P 500
82
Risk and Rates of Return
83
Measuring Market Risk
Market risk is the risk of the overall market, so to
measure need to compare individual stock returns to
the overall market returns.
A proxy for the market is usually used: An index of
stocks such as the S&P 500
Market risk measures how individual stock returns are
affected by this market
Risk and Rates of Return
84
Measuring Market Risk
Market risk is the risk of the overall market, so to
measure need to compare individual stock returns to
the overall market returns.
A proxy for the market is usually used: An index of
stocks such as the S&P 500
Market risk measures how individual stock returns are
affected by this market
Regress individual stock returns on Market index
85
Risk and Rates of Return
Measuring Market Risk
Regress individual stock returns on Market index
PepsiCo 15%
Return
10%
5%
S&P
Return
-15%
-10%
-5%
5%
-5%
-10%
-15%
10%
15%
86
Risk and Rates of Return
Measuring Market Risk
Regress individual stock returns on Market index
PepsiCo 15%
Return
10%
5%
S&P
Return
-15%
-10%
-5%
Jan 1992
PepsiCo -0.37%
S&P
-1.99%
5%
-5%
-10%
-15%
10%
15%
87
Risk and Rates of Return
Measuring Market Risk
Regress individual stock returns on Market index
PepsiCo 15%
Return
10%
5%
S&P
Return
-15%
-10%
-5%
5%
-5%
Plot Remaining
Points
-10%
-15%
10%
15%
88
Risk and Rates of Return
Measuring Market Risk
Regress individual stock returns on Market index
PepsiCo 15%
Return
10%
Fit Regression
Line
5%
S&P
Return
-15%
-10%
-5%
5%
-5%
-10%
-15%
10%
15%
89
Risk and Rates of Return
Measuring Market Risk
Regress individual stock returns on Market index
PepsiCo 15%
Return
10%
5%
S&P
Return
-15%
-10%
-5%
5%
10%
15%
-5%
-10%
Slope =
-15%
rise 5.5%
=
= 1.1
run
5%
Risk and Rates of Return
Measuring Market Risk
Market Risk is measured by Beta
90
91
Risk and Rates of Return
Measuring Market Risk
Market Risk is measured by Beta
Beta is the slope of the characteristic line
PepsiCo 15%
Return
10%
5%
S&P
Return
-15%
-10%
-5%
5%
10%
15%
-5%
-10%
Slope =
-15%
rise 5.5%
=
= 1.1
run
5%
= Beta (b)
Risk and Rates of Return
Measuring Market Risk
Market Risk is measured by Beta
Beta is the slope of the characteristic line
Interpreting Beta
Beta = 1
Market Beta = 1
Company with a beta of 1 has average risk
92
Risk and Rates of Return
Measuring Market Risk
Market Risk is measured by Beta
Beta is the slope of the characteristic line
Interpreting Beta
Beta = 1
Market Beta = 1
Company with a beta of 1 has average risk
Beta < 1
Low Risk Company
Return on stock will be less affected by the market than average
93
Risk and Rates of Return
Measuring Market Risk
Market Risk is measured by Beta
Beta is the slope of the characteristic line
Interpreting Beta
Beta = 1
Market Beta = 1
Company with a beta of 1 has average risk
Beta < 1
Low Risk Company
Return on stock will be less affected by the market than average
Beta > 1
High Market Risk Company
Stock return will be more affected by the market than average
94
Risk and Rates of Return
Required
Minimum rate of return necessary to
Rate of = attract investors to buy funds
Return
95
Risk and Rates of Return
Required
Minimum rate of return necessary to
Rate of = attract investors to buy funds
Return
Required rate of return, K, depends on the risk-free
rate(Krf) and the risk premium(Krp)
96
Risk and Rates of Return
Required
Minimum rate of return necessary to
Rate of = attract investors to buy funds
Return
Required rate of return, K, depends on the risk-free
rate(Krf) and the risk premium(Krp)
Using the capital asset pricing model (CAPM) the
risk premium(Krp) depends on market risk
97
Risk and Rates of Return
Required
Minimum rate of return necessary to
Rate of = attract investors to buy funds
Return
Required rate of return, K, depends on the risk-free
rate(Krf) and the risk premium(Krp)
Using the capital asset pricing model (CAPM) the
risk premium(Krp) depends on market risk
Security Market Line
Kj = Krf + bj ( Km – Krf )
where:
Kj = required rate of return on the jth security
Bj = Beta for the jth security
98
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
99
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
100
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
15%
10%
5%
Risk Free Rate
.50
1.0
1.5
Beta
101
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
15%
12%
10%
Risk & Return
on market
5%
.50
1.0
1.5
Beta
102
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
SML
15%
Market
10%
Connect Points for
Security Market Line
5%
.50
1.0
1.5
Beta
103
104
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
SML
15%
Market
10%
5%
.50
1.0
1.5
Beta
If b of security j =1.2
105
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
SML
15%
j
Market
10%
Kj = 5%+1.2(12% – 5%)
5%
.50
1.0 1.2
If b of security j =1.2
1.5
Beta
106
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
SML
15%
13.4%
j
Market
10%
Kj = 5%+1.2(12% – 5%)
=13.4%
5%
.50
1.0 1.2
If b of security j =1.2
1.5
Beta
107
Risk and Rates of Return
Security Market Line
Kj = Krf + bj ( Km – Krf )
Example:
If the expected return on the market is 12% and the risk
free rate is 5%:
Kj = 5% + bj (12% – 5% )
SML
15%
13.4%
j
Market
10%
Kj = 5%+1.2(12% – 5%)
=13.4%
5%
.50
1.0 1.2
If b of security j =1.2
1.5
Beta
If b = 1.2, investors will
require a 13.4% return
on the stock
Risk and Rates of Return
ki : Expected (or required) rate of return from an
investment i.
KRF : Risk free rate of return (e.g., 3 moth T-Bill rate)
kM : Expected return from a market (e.g., S&P500)
portfolio
(kM - kRF) : Market Risk Premium
b(kM - kRF) : Risk Premium on asset i
108
Risk and Rates of Return
Portfolio Return = S wi x ki
Return of a portfolio is the weighted average return of
individual securities in the portfolio.
Portfolio beta = S wi x bi
Beta of a portfolio is the weighted average beta of
individual securities in the portfolio.
109