Summary in finance, MBA20021 Summary of Courses in Finance (Revision for the State Exam) Mihály Ormos.

Summary in finance, MBA2002 1

Summary of Coursesin Finance

(Revision for the State Exam)

Mihály Ormos


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


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

Business Economics & Corporate Finance


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

i iwUipUE W max)(



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.


MU(W)

W

U(W)More money

is better...

Decreasing marginal utility of the wealth



Portfolio theory Diversification, diversifiable and nondiversifiable risk

U5

U4

U3

U2

U1

E(r)

σ(r)



By diversifying the investments (creating portfolio), the risk (variance of the return) will be decreased.

U5

U4

U3

U2

U1

E(r)

σ(r)

1

3

2

2,5

11,4

i

3,3

17,1

j

kij= 0,5



U5

U4

U3

U2

U1

E(r)

σ(r)σ(r)

E(r)



U5

U4

U3

U2

U1

E(r)

σ(r)σ(r)

E(r)



While the diversification is free, and useful, all investors hold efficient portfolios.

U5

U4

U3

U2

U1

E(r)

σ(r)σ(r)

E(r)

A

Efficient portfolios

B



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) U 5

U 4

U 3

U 2

U 1

E (r)

σ(r)σ(r)

E(r)

A

efficient portfolios

B


Portfolio theory Efficient portfolio, investor decision in the Markowitz model

In the Markowitz model the portfolios held by the investors cannot be identified, so as the non-diversifiable risk .

U5

U4

U3

U2

U1

E(r)

σ(r)σ(r)

E(r)

A

Efficient portfolios

B

E(r)

C


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 15σ(r)

E(r)

U5

U4

U3

U2

U1

E(r)

σ(r)

CAPM by Sharpe Risk-free opportunity, homogeneous expectations

By introducing the two additional assumptions: risk-free assets and homogeneous expectations, CAPM solves the problem of Markowitz model.

M

All investors hold the same risky portfolio (M),independently toits preferences.This risky portfolio will be combined with risk-free assets, by its preferences.


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.

Capital Market Line

rf

σ(r)

E(r)

Market Portfolio

E(rM)

σ(rM)


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.


CAPM by Sharpe Beta and the security market line

rM

ri

1

βiεi

ri

rM

2222 )()()( iMii rr

αi



So the CAPM is fMf rrErrE )()(

E(r)

market portfolio

security market line

E(rM)

1

rf

β

riskpremium

timepremium



E(r)

rf

β


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.


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.


Market efficiency Forms of market efficiency, definitions

Question: whether the actual price contains all public information.

If yes, then future events are unpredictable and randomly happen.If not, then future prices can be predicted

• using historical price (return) information (weak form)

• using public fundamental information (semi- strong form)

• based on unpublic (fundamental) information (strong form)

price

presentpast future

New information, accidentiallity


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.


Weak Market efficiencyform 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 random-walk.

–Runs tests

–Return patterns• January-December effect• Day of the week effect

–etc.


Weak Market efficiencyform Forms of market efficiency, tests

Conclusion:The prices are unpredictable by technical analyses

in Hungary as well.

The stock prices do not have memory.


Semi-strong Market efficiencyform 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.


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Daily return


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.


Basics of investment decisionsOwner’s value maximisation, the opportunity cost approachDevelopment 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.


Basics of investment decisionsOwner’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 value- this 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.


Basics of investment decisions Opportunity cost from the capital market, through CAPM

E(r)

rf

β

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 those investment decisions will be realised, which promises higher return than the normal.


E(F1)E(F2)

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FENPV altrIRR

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Shareholder

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Tőkepiaci alternatívaCapital m.alternative

Basics of investment decisions Opportunity cost from the capital market, through CAPM


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”.


TaxationPrinciples 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 solvencyDetermining 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)


TaxationValue 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)



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.



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.)


TaxationConsideration 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, MBA20021 Summary of Courses in Finance (Revision for the State Exam) Mihály Ormos.

Documents

expected utility satisfaction

riskaversion diversification

nondiversifiable risksummary

utility function

nondiversifiable riskin

nondiversifiable riskby

nondiversifiable riskwhile

different risk