FIN2101
BUSINESS FINANCE II
Disclaimer
It is recommended that students complete the
course FIN1101 Business Finance I prior to
attempting FIN2101 Business Finance II.
Teaching Team
Rex Zeeman
Room L305
Phone 4631 2423
Consultation Times:
Mondays,2-4
Wednesdays,10-12
Thursdays,9-11
Kymberlee Simpson
Room T310
Phone 4631 5509
Consultation Times:
Mondays,9-11
Wednesdays,2-4
Lecture Slides
Lecture slides can be accessed in the
computer labs or through the course
discussion group.
Tutorials
Monday,2-4 (K213)
Wednesday,10-12 (K212)
Assessment
Assignment 1 (10%) due 02/09/03
Assignment 2 (10%) due 14/10/03
End-of-semester exam (80%)
Course Overview
Risk-Return Analysis
Capital Asset Pricing Model (CAPM)
Application of the CAPM
Working Capital Management (2 weeks)
Takeovers
Course Overview
Sources of Finance
Capital Structure
Leasing
Investment and Financing Decisions
Dividend Policy
International Financial Management
Module 1
Risk-Return Analysis
Student Activities
Reading
Text,Chapter 6 (pp,194-210 only)
Text Study Guide,Chapter 6 (part only)
Study Book,Module 1
Tutorial Work
Tutorial Workbook,Self Assessment Activity 1.1
Text Study Guide,Chapter 6,T/F 1 to 8,MC 1 to 12,
Problems 1 to 5
Objectives
At the end of today’s lecture you should be able to:
discuss the terms ‘risk’ and ‘expected return’;
distinguish between ‘ex ante’ and ‘ex post’ data;
calculate expected return and risk for a single asset and
a portfolio;
explain risk-return relationships;
discuss the concepts of utility theory and portfolio theory
and their application to investment decision making;
calculate covariance and the correlation coefficient; and
calculate the coefficient of variation.
Return
The financial outcome of an investment.
Represents the increase in investment value
over a given period of time.
1-t
t1-tt
t
P
C P - P
k
Return
Expected return and required rate of return
are ex ante values.
Actual return is an ex post value.
In an efficient market,expected return =
required rate of return.
Actual return may be >,= or < the expected
or required return.
Risk
Risk is the chance that the actual
outcome will differ from the expected
outcome.
An investment is considered to be RISKY
when its return could be any number of
possibilities.
Sources of Risk
Interest rate risk
Market risk
Inflation risk
Business risk
Financial risk
Liquidity risk
Exchange rate risk
Country risk
Ex Ante vs Ex Post
Ex ante means before the fact.
Ex ante return is the return the investor
expects to receive.
Ex post means after the fact.
Ex post returns are actual (historical) returns
earned.
Expected Return - Single Asset
Weighted average of the possible returns:
n
1i
ii
Pr k k
Example 1,Expected Return and
Risk - Single Asset
Po ss ible Re turn s
k
i
Probability of Occurre nce
Pr
i
- 0,10 0.1
0 0.1
0,30 0.5
0,60 0.3
Example 1 Solution
3 2 %o r 0,3 2
0,1 8 0,1 5 0 0,0 1 -
0,3 0,6 0 0,5 0,3 0 0,1 0 0,1 0,1 0-
Pr k k
n
1i
ii
Ex Post (Arithmetic Mean) Return
n
k
k
n
1i
i?
Risk - Single Asset
Measured by the variation of possible returns
from the expected return.
Returns assumed to be normally distributed
about the expected (mean) return.
Standard deviation is the most common
measure of the variation of outcomes or risk.
The greater the possible variation,the higher the
risk.
Ex Ante vs Ex Post Risk
Ex ante risk is future or before-the-fact
risk forecasted on the basis of the
probabilities assigned to each of the
possible outcomes.
Ex post risk is historical risk calculated
on the basis of an observed return
series.
Ex Ante Risk - Single Asset
n
1i
i
2
ik
2
kk
n
1i
i
2
i
2
k
Pr k - k
Pr k - k
Ex Post Risk - Single Asset
1 -n
k - k
n
1i
2
i
k
Example 1 Solution (Continued)
2 2,7 %o r 0,2 2 7
0,0 5 1 6
0,0 2 3 5 2 0,0 0 0 2 0,0 1 0 2 4 0,0 1 7 6 4
0,30,3 2-0,6 0 0,50,3 2-0,3 0
0,10,3 2-0 0,10,3 2-0,1 0-
Pr k - k
22
22
n
1i
i
2
ik
Coefficient of Variation
The ratio of the standard deviation to
expected return.
Indicates the amount of risk per dollar of
return.
Allows investors to compare assets with
differing expected returns.
Coefficient of Variation
k
C k
V
The higher the CV,the greater the risk.
Risk-Return Trade-Off
k
A B
C D
High Risk/
High Return
High Risk/
Lower Return
Investor Preferences
Each individual investor may have personal
preferences regarding risk and return.
An aggressive investor may be willing to bear
more risk in order to obtain additional return.
On the other hand,a conservative investor
may wish to avoid risk and might be willing to
forego additional return to escape risk.
These differences in investor preferences can
be illustrated graphically in expected
return/risk space by indifference curves.
Indifference Curves
A line connecting points,usually in
expected return/risk space,that are equally
preferred by investors.
Source,Kolb & Rodriguez,Principles of Finance,p,253.
Indifference Curves
The investor would prefer to be on the
highest possible curve,eg the conservative
investor prefers E to A.
The attainment of any position on any
curve will depend on the investment
opportunities available in the market,ie
the combinations of risk and return that
are available.
Indifference Curves
In general,an investor will do best by
holding the portfolio at the point of tangency
between an indifference curve and the
EFFICIENT FRONTIER (curve H-MR).
Portfolio Theory
Developed by Harry Markowitz as a
normative approach to investment choice
under uncertainty.
Describes how investors accommodate risk.
Investors can spread risk by investing in more
than one particular asset,ie in a PORTFOLIO.
Spreading of risk is called
DIVERSIFICATION.
Types of Risk
Diversifiable or Unsystematic or Avoidable
or Unique Risk
Non-diversifiable or Systematic or
Unavoidable or Market Risk
Expected Return - Portfolio
n
1j
jjp
k w k
Example 2 - Portfolio Theory
k i 1 k i 2 Pr i
0.25 0.01 0.5
0.10 - 0.05 0.3
- 0.25 0.35 0.2
Assume that 50% is invested in Asset 1 and
50% in Asset 2.
Calculate Expected Returns for
Assets 1 and 2
0,0 6
0,2 0,3 5 0,3 0,0 5- 0,5 0,0 1 k
0,1 0 5
0,2 0,2 5- 0,3 0,1 0 0,5 0,2 5 k
Pr k k
2
1
n
1i
ii
Calculate Expected Return of
Portfolio
0,0 8 2 5
0,0 6 0,5 0 0,1 0 5 0,5 0
k w k
n
1j
jjp
Risk - Portfolio of 2 Assets
A function of three (3) things:
the risk of the individual assets in the portfolio;
the weighting of each asset in the portfolio;
the relationship between the returns on the
assets that make up the portfolio.
Risk - Portfolio of 2 Assets
211,221
2
2
2
2
2
1
2
1k rw2w w w p
Calculate Risk of Assets 1 and 2
0,1 4 7 3
0,20,0 6-0,3 5
0,30,0 6-0,0 5- 0,50,0 6-0,0 1
0,1 8 9
0,20,1 0 5-0,2 5-
0,30,1 0 5-0,1 0 0,50,1 0 5-0,2 5
Pr k - k
2
22
k
2
22
k
n
1i
i
2
ik
2
1
Risk - Portfolio of 2 Assets
211,221
2
2
2
2
2
1
2
1k rw2w w w p
Correlation Coefficient
A measure of the relation between the rates
of return on two securities.
Can be +,-,or 0.
Value in the range -1.0 to +1.0.
Correlation Coefficient
21
kk
21
1,2
k,kC o v
r
Covariance (Ex Ante)
n
1i
i2i2,1i1,21 Pr k - k k - k k,kC o v
Covariance (Ex Post)
1 -n
k - k k - k
k,kC o v
n
1i
2i2,1i1,
21
Calculate Covariance
0.0 240 5-
0.2 0.0 6-0.3 5 0.1 05-0.2 5-
0.3 0.0 6-0.0 5- 0.1 05-0.1 0
0.5 0.0 6-0.0 1 0.1 05-0.2 5 k,kC o v
21
Calculate Covariance
k
1,i
– k
1
(1)
k
2,i
- k
2
(2)
(1) x (2)
(3)
(3) x P r
i
0.145 - 0.05 - 0.00725 - 0.003625
- 0.005 - 0.11 0.00055 0.000165
- 0.355 0.29 - 0.10295 - 0.02059
- 0.02405
Calculate Correlation Coefficient
0.86 -
0.1473 0.189
0.02405-
k,kC ov
r
21
kk
21
1,2
Covariance & Correlation
Coefficient
21
21
kk1,221
kk
21
1,2
r k,kC ov
k,kC ov
r
Calculate the Portfolio Risk
20,0 4 8 8 2 1 1 1
10,0 0 2 3 8 3 5 0
10,0 1 1 9 7 1 0 7 - 250,0 0 5 4 2 4 3 2 0,0 0 8 9 3 0 2 5
0,1 4 7 3 0,1 8 9 0,8 6- 0,5 0,5 2 0,1 4 7 3 0,5 0,1 8 9 0,5
rw2w w w
2222
211,221
2
2
2
2
2
1
2
1k p
Correlation Coefficient & Diversification
Diversification is of greatest benefit in risk
reduction when the correlation between the
returns on two securities is NEGATIVE.
Investor’s OBJECTIVE is to find two assets
whose returns are negatively correlated.
Public companies tend to have positive
correlation coefficients in the range +0.2 to
+0.7,averaging around +0.4.
Example 3 - Risk Reduction
Through Diversification Inv est me nt A Inv est me nt B
k 10% 15%
Risk? k 10% 30%
Alt e r n at ive P or t f olio We igh t in gs
P or t f olio w
A
w
B
1 100% 0%
2 50% 50%
3 0% 100%
Co r r e lation Coe f f icie n t s
Ca se 1 r
A,B
= + 1.0
Ca se 2 r
A,B
= + 0.2
Re q u ire d,Calc ula te the e x pe c ted r e turn a nd r isk f or e a c h of the 3
por tfolios unde r c a se s 1 a nd 2,
Example 3 Solution
C A SE 1 (r
A,B
= +1,0)
P or tf oli o 1 (100% In ve stm e n t A )
k
p
= k
A
= 10%
k p
=?
kA
= 10%
P or tf oli o 3 (100% In ve stm e n t B)
k
p
= k
B
= 15%
k p
=?
k B
= 30%
Example 3 Solution (Continued)
P ort f ol io 2 (50 % In vestm ent A,5 0% In vestm ent B )
12,5 %or 0,12 5 =
0,15 0,5 + 0,10 0,5 =
k w = k
n
1j
jjp
Example 3 Solution (Continued)
20%o r 0,2 0
0,0 4
0,0 1 5 0,0 2 2 5 0,0 0 2 5
0,3 0 0,1 0 1,0 0,5 0,5 2 0,3 0 0,5 0,1 0 0,5
rw2w w w
2222
BABA,BA
2
B
2
B
2
A
2
Ak
p
Example 3 Solution (Continued)
C A SE 2 (r
A,B
= +0,2)
P ort f oli o 1 (100% In vest m e n t A)
Un ch an ge d,ie k
p
= k
A
= 10%
k p
=?
k A
= 10%
P ort f oli o 3 (100% In vest m e n t B)
Un ch an ge d,ie k
p
= k
B
= 15%
k p
=?
k B
= 30%
P or tf oli o 2 (50% In ve stm e n t A,50% In ve stm e n t B)
k
p
is unaf fe c ted by the c ha ng e in t he c orr e lation coe ff icie nt and r e mains at 12.5%,
16.73%or 0.1673 =
0.028
0.003 0.0225 0.0025 =
0.30 0.10 0.2 0.5 0.5 2 + 0.30 0.5 + 0.10 0.5 =
rw2w + w+ w =
2222
BABA,BA
2
B
2
B
2
A
2
Ak
p
BUSINESS FINANCE II
Disclaimer
It is recommended that students complete the
course FIN1101 Business Finance I prior to
attempting FIN2101 Business Finance II.
Teaching Team
Rex Zeeman
Room L305
Phone 4631 2423
Consultation Times:
Mondays,2-4
Wednesdays,10-12
Thursdays,9-11
Kymberlee Simpson
Room T310
Phone 4631 5509
Consultation Times:
Mondays,9-11
Wednesdays,2-4
Lecture Slides
Lecture slides can be accessed in the
computer labs or through the course
discussion group.
Tutorials
Monday,2-4 (K213)
Wednesday,10-12 (K212)
Assessment
Assignment 1 (10%) due 02/09/03
Assignment 2 (10%) due 14/10/03
End-of-semester exam (80%)
Course Overview
Risk-Return Analysis
Capital Asset Pricing Model (CAPM)
Application of the CAPM
Working Capital Management (2 weeks)
Takeovers
Course Overview
Sources of Finance
Capital Structure
Leasing
Investment and Financing Decisions
Dividend Policy
International Financial Management
Module 1
Risk-Return Analysis
Student Activities
Reading
Text,Chapter 6 (pp,194-210 only)
Text Study Guide,Chapter 6 (part only)
Study Book,Module 1
Tutorial Work
Tutorial Workbook,Self Assessment Activity 1.1
Text Study Guide,Chapter 6,T/F 1 to 8,MC 1 to 12,
Problems 1 to 5
Objectives
At the end of today’s lecture you should be able to:
discuss the terms ‘risk’ and ‘expected return’;
distinguish between ‘ex ante’ and ‘ex post’ data;
calculate expected return and risk for a single asset and
a portfolio;
explain risk-return relationships;
discuss the concepts of utility theory and portfolio theory
and their application to investment decision making;
calculate covariance and the correlation coefficient; and
calculate the coefficient of variation.
Return
The financial outcome of an investment.
Represents the increase in investment value
over a given period of time.
1-t
t1-tt
t
P
C P - P
k
Return
Expected return and required rate of return
are ex ante values.
Actual return is an ex post value.
In an efficient market,expected return =
required rate of return.
Actual return may be >,= or < the expected
or required return.
Risk
Risk is the chance that the actual
outcome will differ from the expected
outcome.
An investment is considered to be RISKY
when its return could be any number of
possibilities.
Sources of Risk
Interest rate risk
Market risk
Inflation risk
Business risk
Financial risk
Liquidity risk
Exchange rate risk
Country risk
Ex Ante vs Ex Post
Ex ante means before the fact.
Ex ante return is the return the investor
expects to receive.
Ex post means after the fact.
Ex post returns are actual (historical) returns
earned.
Expected Return - Single Asset
Weighted average of the possible returns:
n
1i
ii
Pr k k
Example 1,Expected Return and
Risk - Single Asset
Po ss ible Re turn s
k
i
Probability of Occurre nce
Pr
i
- 0,10 0.1
0 0.1
0,30 0.5
0,60 0.3
Example 1 Solution
3 2 %o r 0,3 2
0,1 8 0,1 5 0 0,0 1 -
0,3 0,6 0 0,5 0,3 0 0,1 0 0,1 0,1 0-
Pr k k
n
1i
ii
Ex Post (Arithmetic Mean) Return
n
k
k
n
1i
i?
Risk - Single Asset
Measured by the variation of possible returns
from the expected return.
Returns assumed to be normally distributed
about the expected (mean) return.
Standard deviation is the most common
measure of the variation of outcomes or risk.
The greater the possible variation,the higher the
risk.
Ex Ante vs Ex Post Risk
Ex ante risk is future or before-the-fact
risk forecasted on the basis of the
probabilities assigned to each of the
possible outcomes.
Ex post risk is historical risk calculated
on the basis of an observed return
series.
Ex Ante Risk - Single Asset
n
1i
i
2
ik
2
kk
n
1i
i
2
i
2
k
Pr k - k
Pr k - k
Ex Post Risk - Single Asset
1 -n
k - k
n
1i
2
i
k
Example 1 Solution (Continued)
2 2,7 %o r 0,2 2 7
0,0 5 1 6
0,0 2 3 5 2 0,0 0 0 2 0,0 1 0 2 4 0,0 1 7 6 4
0,30,3 2-0,6 0 0,50,3 2-0,3 0
0,10,3 2-0 0,10,3 2-0,1 0-
Pr k - k
22
22
n
1i
i
2
ik
Coefficient of Variation
The ratio of the standard deviation to
expected return.
Indicates the amount of risk per dollar of
return.
Allows investors to compare assets with
differing expected returns.
Coefficient of Variation
k
C k
V
The higher the CV,the greater the risk.
Risk-Return Trade-Off
k
A B
C D
High Risk/
High Return
High Risk/
Lower Return
Investor Preferences
Each individual investor may have personal
preferences regarding risk and return.
An aggressive investor may be willing to bear
more risk in order to obtain additional return.
On the other hand,a conservative investor
may wish to avoid risk and might be willing to
forego additional return to escape risk.
These differences in investor preferences can
be illustrated graphically in expected
return/risk space by indifference curves.
Indifference Curves
A line connecting points,usually in
expected return/risk space,that are equally
preferred by investors.
Source,Kolb & Rodriguez,Principles of Finance,p,253.
Indifference Curves
The investor would prefer to be on the
highest possible curve,eg the conservative
investor prefers E to A.
The attainment of any position on any
curve will depend on the investment
opportunities available in the market,ie
the combinations of risk and return that
are available.
Indifference Curves
In general,an investor will do best by
holding the portfolio at the point of tangency
between an indifference curve and the
EFFICIENT FRONTIER (curve H-MR).
Portfolio Theory
Developed by Harry Markowitz as a
normative approach to investment choice
under uncertainty.
Describes how investors accommodate risk.
Investors can spread risk by investing in more
than one particular asset,ie in a PORTFOLIO.
Spreading of risk is called
DIVERSIFICATION.
Types of Risk
Diversifiable or Unsystematic or Avoidable
or Unique Risk
Non-diversifiable or Systematic or
Unavoidable or Market Risk
Expected Return - Portfolio
n
1j
jjp
k w k
Example 2 - Portfolio Theory
k i 1 k i 2 Pr i
0.25 0.01 0.5
0.10 - 0.05 0.3
- 0.25 0.35 0.2
Assume that 50% is invested in Asset 1 and
50% in Asset 2.
Calculate Expected Returns for
Assets 1 and 2
0,0 6
0,2 0,3 5 0,3 0,0 5- 0,5 0,0 1 k
0,1 0 5
0,2 0,2 5- 0,3 0,1 0 0,5 0,2 5 k
Pr k k
2
1
n
1i
ii
Calculate Expected Return of
Portfolio
0,0 8 2 5
0,0 6 0,5 0 0,1 0 5 0,5 0
k w k
n
1j
jjp
Risk - Portfolio of 2 Assets
A function of three (3) things:
the risk of the individual assets in the portfolio;
the weighting of each asset in the portfolio;
the relationship between the returns on the
assets that make up the portfolio.
Risk - Portfolio of 2 Assets
211,221
2
2
2
2
2
1
2
1k rw2w w w p
Calculate Risk of Assets 1 and 2
0,1 4 7 3
0,20,0 6-0,3 5
0,30,0 6-0,0 5- 0,50,0 6-0,0 1
0,1 8 9
0,20,1 0 5-0,2 5-
0,30,1 0 5-0,1 0 0,50,1 0 5-0,2 5
Pr k - k
2
22
k
2
22
k
n
1i
i
2
ik
2
1
Risk - Portfolio of 2 Assets
211,221
2
2
2
2
2
1
2
1k rw2w w w p
Correlation Coefficient
A measure of the relation between the rates
of return on two securities.
Can be +,-,or 0.
Value in the range -1.0 to +1.0.
Correlation Coefficient
21
kk
21
1,2
k,kC o v
r
Covariance (Ex Ante)
n
1i
i2i2,1i1,21 Pr k - k k - k k,kC o v
Covariance (Ex Post)
1 -n
k - k k - k
k,kC o v
n
1i
2i2,1i1,
21
Calculate Covariance
0.0 240 5-
0.2 0.0 6-0.3 5 0.1 05-0.2 5-
0.3 0.0 6-0.0 5- 0.1 05-0.1 0
0.5 0.0 6-0.0 1 0.1 05-0.2 5 k,kC o v
21
Calculate Covariance
k
1,i
– k
1
(1)
k
2,i
- k
2
(2)
(1) x (2)
(3)
(3) x P r
i
0.145 - 0.05 - 0.00725 - 0.003625
- 0.005 - 0.11 0.00055 0.000165
- 0.355 0.29 - 0.10295 - 0.02059
- 0.02405
Calculate Correlation Coefficient
0.86 -
0.1473 0.189
0.02405-
k,kC ov
r
21
kk
21
1,2
Covariance & Correlation
Coefficient
21
21
kk1,221
kk
21
1,2
r k,kC ov
k,kC ov
r
Calculate the Portfolio Risk
20,0 4 8 8 2 1 1 1
10,0 0 2 3 8 3 5 0
10,0 1 1 9 7 1 0 7 - 250,0 0 5 4 2 4 3 2 0,0 0 8 9 3 0 2 5
0,1 4 7 3 0,1 8 9 0,8 6- 0,5 0,5 2 0,1 4 7 3 0,5 0,1 8 9 0,5
rw2w w w
2222
211,221
2
2
2
2
2
1
2
1k p
Correlation Coefficient & Diversification
Diversification is of greatest benefit in risk
reduction when the correlation between the
returns on two securities is NEGATIVE.
Investor’s OBJECTIVE is to find two assets
whose returns are negatively correlated.
Public companies tend to have positive
correlation coefficients in the range +0.2 to
+0.7,averaging around +0.4.
Example 3 - Risk Reduction
Through Diversification Inv est me nt A Inv est me nt B
k 10% 15%
Risk? k 10% 30%
Alt e r n at ive P or t f olio We igh t in gs
P or t f olio w
A
w
B
1 100% 0%
2 50% 50%
3 0% 100%
Co r r e lation Coe f f icie n t s
Ca se 1 r
A,B
= + 1.0
Ca se 2 r
A,B
= + 0.2
Re q u ire d,Calc ula te the e x pe c ted r e turn a nd r isk f or e a c h of the 3
por tfolios unde r c a se s 1 a nd 2,
Example 3 Solution
C A SE 1 (r
A,B
= +1,0)
P or tf oli o 1 (100% In ve stm e n t A )
k
p
= k
A
= 10%
k p
=?
kA
= 10%
P or tf oli o 3 (100% In ve stm e n t B)
k
p
= k
B
= 15%
k p
=?
k B
= 30%
Example 3 Solution (Continued)
P ort f ol io 2 (50 % In vestm ent A,5 0% In vestm ent B )
12,5 %or 0,12 5 =
0,15 0,5 + 0,10 0,5 =
k w = k
n
1j
jjp
Example 3 Solution (Continued)
20%o r 0,2 0
0,0 4
0,0 1 5 0,0 2 2 5 0,0 0 2 5
0,3 0 0,1 0 1,0 0,5 0,5 2 0,3 0 0,5 0,1 0 0,5
rw2w w w
2222
BABA,BA
2
B
2
B
2
A
2
Ak
p
Example 3 Solution (Continued)
C A SE 2 (r
A,B
= +0,2)
P ort f oli o 1 (100% In vest m e n t A)
Un ch an ge d,ie k
p
= k
A
= 10%
k p
=?
k A
= 10%
P ort f oli o 3 (100% In vest m e n t B)
Un ch an ge d,ie k
p
= k
B
= 15%
k p
=?
k B
= 30%
P or tf oli o 2 (50% In ve stm e n t A,50% In ve stm e n t B)
k
p
is unaf fe c ted by the c ha ng e in t he c orr e lation coe ff icie nt and r e mains at 12.5%,
16.73%or 0.1673 =
0.028
0.003 0.0225 0.0025 =
0.30 0.10 0.2 0.5 0.5 2 + 0.30 0.5 + 0.10 0.5 =
rw2w + w+ w =
2222
BABA,BA
2
B
2
B
2
A
2
Ak
p
