Summary of Courses
in Finance
(Revision for the State Exam)
Mihály Ormos
Summary in finance, MBA2002
1
Business Economics & Corporate Finance
4. Markowitz’s portfolio theory
–Maximization of expected utility and risk-aversion
–Diversification, diversifiable and nondiversifiable risk
–Efficient portfolio, investor decision in the Markowitz model
5. CAPM by Sharpe
–Risk-free opportunity, homogeneous expectations
–Market portfolio and the capital market line
–Beta and the security market line
6. Market efficiency
–Definition of perfect efficiency, and its properties
–Forms of market efficiency (definitions, tests, reasons of
existence)
–Perfect vs. efficient, adaptive complex systems
Summary in finance, MBA2002
2
Business Economics & Corporate Finance
7. Basics of investment decisions
–Owner’s value maximisation, the opportunity cost approach
–Opportunity cost from the capital market, through CAPM
–Mini-firm approach
8. Taxation
–Principles of taxation, basic types
–Value Added Tax, Corporate Tax, Personal Income Tax
–Consideration of taxes in corporate financial analyses
9. Dividend policy
–Indicators of dividend, practices
–Indifference of dividend policy in perfect and imperfect market
–Significance of indifference of dividend policy in financial
analyses, consequences
Summary in finance, MBA2002
3
Markowitz’s portfolio theory
Maximization of expected utility, risk-aversion and rationality
Investors compare investment possibilities with different
risk and return.
How do investors decide in a risky situation?
Bernoulli was the first who argued that investors decide
upon the maximisation of expected value (return).
Investors’ decisions are made upon the expected utility
(satisfaction) of the wealth.
So investors try to maximise the expected utility, NOT
the expected value of the wealth
EU W    piU ( wi )  max
i
Summary in finance, MBA2002
4
Markowitz’s portfolio theory
Maximization of expected utility, risk-aversion and rationality
The expected utility of an output is not proportionally
related to expected value of the same output. The
relationship can be represented by the utility function
of the wealth.
Summary in finance, MBA2002
5
Markowitz’s portfolio theory
Maximization of expected utility, risk-aversion and rationality
MU(W)
U(W)
More money
is better...
W
Decreasing marginal utility of the wealth
Summary in finance, MBA2002
6
Portfolio theory
Diversification, diversifiable and nondiversifiable risk
E(r)
U5
U4
U3
U2
U1
σ(r)
Summary in finance, MBA2002
7
Portfolio theory
Diversification, diversifiable and nondiversifiable risk
By diversifying the investments (creating portfolio), the
risk (variance of the return) will be decreased.
E(r)
kij= 0,5
U5
j
3,3
3
U4
2,5
i
U3
2
U2
1
U1
11,4
Summary in finance, MBA2002
17,1
σ(r)
8
Portfolio theory
E(r)Diversification, diversifiable and nondiversifiable risk
U5
E(r)
U4
U3
U2
U1
σ(r)
Summary in finance, MBA2002
9
Portfolio theory
E(r)Diversification, diversifiable and nondiversifiable risk
U5
E(r)
U4
U3
U2
U1
σ(r)
Summary in finance, MBA2002
10
Portfolio theory
Diversification, diversifiable and nondiversifiable risk
E(r)
While the diversification is free, and useful, all
Uinvestors
5
hold efficient portfolios.
E(r)
Efficient portfolios
B
A
U4
U3
U2
U1
Summary in finance, MBA2002
σ(r)
11
Portfolio theory
Diversification, diversifiable and nondiversifiable risk
In a portfolio the (total) risk of an investment can be
divided into two parts:
– diversifiable (unique or non-systematic risk)
– non-diversifiable (market or systematic risk)
Summary in finance, MBA2002
12
Portfolio theory
Efficient portfolio, investor decision in the Markowitz model
E(r)
In the Markowitz model the portfolios held by the
(r)
E
investors cannot be identified, so as the non-
U 5 U5
diversifiable riskE(r)
.
E(r)
U4
Efficient portfolios
U4
C
U3
B
A
U
U
2
U1
Summary in finance, MBA2002
σ(r)13
CAPM by Sharpe
Risk-free opportunity, homogeneous expectations
The new assumptions and boundary conditions:
• Perfect competition (microeconomic conditions)
– lot of investors with small investments
– regulations and taxes have no effect on the decisions
– perfect information flow
– no transaction cost
• Investors
– are rational, and hold Markowitz type portfolio
– use the same type of analyses (together with the above conditions on
the competition gives the homogeneous expectations)
• Investment opportunities
– are restricted to risky securities traded on the security market
and to risk-free lending and borrowing
– the cost of risk-free lending and borrowing are the same
Summary in finance, MBA2002
14
CAPM by Sharpe
Risk-free opportunity, homogeneous expectations
E(r)
By introducing the two additional assumptions: risk-freeU
5
assets and homogeneous expectations, CAPM solves the
problem of Markowitz model.
E(r)
All investors hold the
same risky portfolio (M),
independently to
its preferences.
This risky portfolio will
be combined with riskfree assets, by its
preferences.
Summary in finance, MBA2002
U4
M
U3
U2
U1
σ(r)
15
CAPM by Sharpe
Market portfolio and the capital market line
While everyone hold the
same risky portfolio this
cannot be anything else
than the Market
Portfolio (M).
This will be combined
with the risk-free asset,
so all portfolios held by
the investors will be
placed on the Capital
Market Line.
Summary in finance, MBA2002
E(r)
Capital Market Line
Market Portfolio
E(rM)
rf
σ(rM)
σ(r)
16
CAPM by Sharpe
Market portfolio and the capital market line
After all the question is, that how a given security
affects the risk of the Market Portfolio.
– Only the affect on the market portfolio has to be examined,
because the risk free return does not influence the
diversification or the perception of the relevant risk.
This depends on what extent the given security gains in
average the deviation of the Market Portfolio.
This is shown by the slope of characteristic line.
Summary in finance, MBA2002
17
CAPM by Sharpe
Beta and the security market line
εi
ri
 (ri ) 2   i2 (rM ) 2   ( i ) 2
ri
βi
1
αi
rM
rM
Summary in finance, MBA2002
18
CAPM by Sharpe
Beta and the security market line
So the CAPM is

E (r )  r f   E (rM )  r f

E(r) security market line
market portfolio
risk
premium
E(rM)
rf
1
Summary in finance, MBA2002
time
premium
β
19
CAPM by Sharpe
Beta and the security market line
E(r)
rf
β
Summary in finance, MBA2002
20
Market efficiency
Definition of perfect efficiency, and its properties
The market is perfectly efficient if all available
information on securities (and everything that can be
connected to the securities) is immediately and in a
correct way built in to the prices.
In general this means that it is not possible that a
security bought or sold on the market price can
produce positive NPV.
Continuous buying and selling, and continuous information
collection and “in building” with zero transaction- and
information acquiring cost.
While the transactions, collection and processing information
can take cost the prices will reflect all information until the
marginal cost of transactions are less than the return
connected to the transaction.
Summary in finance, MBA2002
21
Market efficiency
Forms of market efficiency, definitions
Weak form of market efficiency:
all historical price (return) information available is
immediately built in,
Semi-strong form of market efficiency:
also all public (fundamental) information is immediately built
in the securities’s price,
Strong form of market efficiency:
all public and non-public information is immediately built in
the prices as well.
Summary in finance, MBA2002
22
Market efficiency
Forms of market efficiency, definitions
Question: whether the actual price contains all public
information.
If not,
prices can
be predicted and
yes, then future events
are unpredictable
randomly happen.
• using historical price (return) information
price
(weak form)
• using public fundamental information (semistrong form)
• based on unpublic (fundamental) information
(strong form)
New information,
accidentiallity
Summary in finance, MBA2002
past
present
future
23
Market efficiency
Forms of market efficiency, tests
Two types of analyses:
– technical analyses
– fundamental analyses
If the technical analyses proved to be useless this verifies
the weak form of market efficiency.
By the examination of the fundamental analyses the
semi-strong and strong form of market efficiency can
be tested.
Summary in finance, MBA2002
24
Weak
form
Market efficiency
Forms of market efficiency, tests
The technical analyses try to find some kind of
stochastic relation between sec’s historical prices and
other “things”.
Predictability testes:
–Correlation tests
• auto-correlation
• cross-correlation (with other sec’s, indexes, volumes)
The correlation coefficients are very small, almost randomwalk.
– Runs tests
– Return patterns
• January-December effect
• Day of the week effect
–etc.
Summary in finance, MBA2002
25
Weak
form
Market efficiency
Forms of market efficiency, tests
Conclusion:
The prices are unpredictable by technical analyses
in Hungary as well.
The stock prices do not have memory.
Summary in finance, MBA2002
26
Semi-strong
form
Market efficiency
Forms of market efficiency, tests
Testing of consultants companies and managed mutual
founds past forecasts and compared them to the later
reality.
The results are:
–
–
–
–
on the long run: nothing
on the short run: nothing
by industrial segment, region, etc.: nothing
the managed portfolios gives the same nothing in average
There is no consistent winner.
Summary in finance, MBA2002
27
Event
studies
Market efficiency
Accumulated
abnormal hozam
return
Kumuláltátlagos
abnormális
Összegzett
többlethozam
Forms of market efficiency, tests
-30
8
10
9
6
Daily return
4
2
0
5
4
-2
-4
-20
-10
0
10
20
30
-6
-8
-20
Summary in finance, MBA2002
8
7
6
Day of
publication
30
-10
0
10
20
Napok a bejelentés előtt és után
Days before and after the events
3
2
1
40
28
Market efficiency
Forms of market efficiency, reasons of existence
If the markets are proved to be efficient, than any kind
of analyses are proved to be useless.
If these are useless, no one would do them,
but the markets are efficient because lot of analysts
work on,
If the number of analysts decreases they would have the
opportunity to gain excess profit, so the number will
increases.
Summary in finance, MBA2002
29
Basics of investment decisions
Owner’s value maximisation, the opportunity cost approach
Development of public limited corporations
Early capitalism
• individuals and families, with unlimited liability
• the owner and the manager is the same
• Development of technology and mass production required
the concentration of capital
Limited liability
• more owner one company
• legal entity
• management and ownership are separated, but
• the goals are different
• shares are tradable
• stock exchange
• agency problem
However, the management makes the decisions, as a
starting point we presume, that the decisions will be
made upon the theory of shareholder’s value.
Summary in finance, MBA2002
30
Basics of investment decisions
Owner’s value maximisation, the opportunity cost approach
The goal of the owners’ is the maximisation value, that is
the maximisation of the value of the corporation.
– If this is the goal of the owner -by the shareholder’s valuethis will be goal in any business decision.
The wealth of the owner can be increased through
dividend pay off or stock price increase.
Only those investment decisions suits to the value
maximisation approach, which promise higher return
than others.
Others means in investment decisions the opportunity
cost.
Opportunity cost is the return of other investments on
the capital market with similar risk.
Summary in finance, MBA2002
31
Basics of investment decisions
Opportunity cost from the capital market, through CAPM
E(r)
Stock prices are
continuously adjusted by the efficient capital
market itself- to the
expected risks and
returns, so the expected
returns (fitting to the
risk) tends to the
normal return. Only
rf
those investment
decisions will be
realised, which
promises higher return
than the normal.
Summary in finance, MBA2002
β
32
Basics of investment decisions
Opportunity cost from the capital market, through CAPM
Firm
Project
E(F1)
E(Fn)
E(F2)
0
1
2
E(FN)
…
n
…
N
F0
Shareholder
Investment
decision
βproject
IRR

E ( Fn )
0
n
n 0 (1  ralt )
NPV  
IRR  ralt
Dividend
E(r) értékpapír-piaci egyenes
Capital
Tőkepiaci
m.
alternative
alternatíva
piaci portfolió
ralt
E(rM)
rf
1
Summary in finance, MBA2002
β
33
Basics of investment decisions
Mini-firm approach
All investments will be implemented which is better than
the similar risk capital market investment.
Better means positive NPV or IRR exceeds ralt.
The opportunity cost is estimated through CAPM.
The risk (so the opportunity cost) of any arbitrary
elements of the shareholder’s portfolio depend on the
stochastic relationship with the market portfolio but
not each other.
So, if the CAPM is used than the risk of any single entity
-as well as the risk of any project- individually with
respect to the market portfolio will be examined, i.e.
independently from its corporate environment.
The single projects will be considered as “mini-firms”.
Summary in finance, MBA2002
34
Taxation
Principles of taxation, basic types
Two basic principles of taxation:
–Principle of benefit
The value of contribution “to the common” is fair if it is proportional to
the received benefit form the “common”.
–Principle of solvency
Determining the value contribution, the income and the financial position
should be considered
Two basic types of taxation was settled:
–Indirect types
These do not consider the personal conditions, these are connected to the
consumption and to the turnover (e.g. VAT)
–Direct types
• These are strictly connected to the individual conditions (like income, or
profit) of the person or corporation (e.g. PIT, or CT)
Summary in finance, MBA2002
35
Taxation
Value Added Tax, Corporate Tax, Personal Income Tax
Connected to almost all products and services.
In this case the authority does not have any connection to the
taxing individuals, because the supplier pays after all transaction,
actually the purchaser pays the tax but the price contains it.
If the purchased good or service will be used for business activity the tax
payable can be reduced with the shifted tax, so only the added value will be
charged by this tax.
The general degree of VAT in Hungary is 25%.
Advantages:
– if a wide black market exists, than from the income side it is difficult to
collect the tax
– strengthening the documentation of transactions
– the consumer does not sense, “hidden tax”
Disadvantages:
– higher administrative task
– intellectual crimes (negative tax)
– not proportional contribution (with higher income, the less amount will be
used for consumption)
Summary in finance, MBA2002
36
Taxation
Value Added Tax, Corporate Tax, Personal Income Tax
The tax base is coming form the accounting pre-tax
profit.
This accounting pre-tax profit has to be modified
according to the differences between the law of
accounting and taxation.
From the corrected positive pre-tax profit 18%
corporate tax has to be paid.
Summary in finance, MBA2002
37
Taxation
Value Added Tax, Corporate Tax, Personal Income Tax
In case of private domestic individuals the sum of all
income (money or payments in kind) forms the tax
base
There are two types of income tax
–aggregated income
• tax brackets (higher income – higher tax rate)
–separated income
• revenue on capital investment: 20% tax rate (the interest is 0%, price
earnings 20%, dividend tax 20%, etc.)
Summary in finance, MBA2002
38
Taxation
Consideration of taxes in corporate financial analyses
VAT: net amounts are used in the calculations (the company
actually just an intermediary)
Other taxes, which are not connected to the accounting profit e.g.
consumption tax are considered in the cash flow as simple costs
(cash outflow)
Corporate tax and personal income tax:
These types reduce the shareholder’s value, the main difference is
the level on which they act.
The two tax types are summarized in the so called effective tax rate
teff=1-(1-tc)(1-tp)
As a basic principle in determination of the expected cash-flows
and opportunity cost, that the same taxation should be
considered.
If the opportunity cost were determined after all tax liability, than the cash
flows should be calculated on the same way.
Summary in finance, MBA2002
39