Third Year Financial Economics 2012 Topic1a1

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Introduction to Financial

Economics

February 2012

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Financial economics applies the techniques of economic analysisto understand the savings and investment decisions of individuals,the investment, financing and payout decisions of firms, the level

and properties of interest rates and prices of financial derivativesand the economic role of financial intermediaries.

To be covered:

Financial Markets/Financial Development and Economic Growth

Decision making given uncertaintyrisk

Financial Instruments

Interest Rates


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Derivatives

Financial Intermediation

Asymmetric Information in Fin. Markets

Capital Structure Theory


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Financial Market

A financial market is a market where financial assets

are exchanged or traded.

Examples include:

1. Primary vs. Secondary markets

2. Debt and equity markets vs. derivative markets

3. Centralized exchanges vs. over-the-counter markets


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Role of Financial Markets Price discovery - The interactions of buyers and sellers in a

financial market determine the price of the traded asset.

Liquidity - A financial market offers liquidity. A buyer of an assetmust be assured that if one needs to sell the asset in future one willmanage to do so without any problems. The market facilitates this.

Reduction of transaction costs - A financial market helps in thereduction of transaction costs. The two costs associated withtransacting are search costs and information costs.

Search costs include such costs incurred as one advertises his

intention to sell or purchase an asset as well as the value of timespent locating a counterparty to the impending transaction.

Information costs are costs associated with assessing theinvestment merits of a financial asset, i.e., the likelihood of the

cash flow expected to be generated.


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Classification of Financial Markets

Financial markets can be classified by the type of financial claimsuch as debt markets or equity market. Examples would include

stock exchanges where ordinary shares are traded.

They can be classified by maturity of the claim money marketvs. capital markets. Money markets are markets where short-terminstruments are traded. Capital markets deals with long-term debt

instruments.

They can also be classified as those dealing with newly issuedinstruments (primary markets) or those dealing with alreadyexisting assets (secondary markets).

So an IPO would take place in a primary market while a seasonedoffering would occur in a secondary market.


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Financial Markets and the Real Economy

The real economy and financial markets are not unrelated.

We begin by distinguishing between real assets and financial

assets.

Real Assets

Real assets: represent a societys wealth.

Real assets produce output consumed by economy.

They determine the productive capacity of the economy.

Examples include: land, buildings, machinery & equipment,

knowledge, etc.

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Financial Assets

Financial assets are claims to the income generated by the real

assets.

They are just pieces of paper, or computer entries.

They contribute to the productive capacity indirectly.

Examples include: stocks, bonds, etc.


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Financial assets:

Allow for the separation of ownership and management

Facilitate the transfer of funds to enterprises with attractive

investment opportunities.

They are claims to the income generated by real assets.

Their value depends on the value of the underlying real

assets.


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The Relationship between Financial Assets and Real Assets

Real assets produce goods and services. Financial assets

determine the allocation of wealth among investors.

Money firms receive when they issue securities (financial assets)is used to purchase real assets.

The return on a financial asset comes from the income producedby a real asset.

Financial assets are destroyed in the course of doing business(e.g. loan). Real assets are only destroyed by accident or throughwearing out over time.


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Financial Markets and the Economy

-Financial assets and the markets in which they are traded do

play an important role in the economy.

-Financial assets allow us to make optimal use of the economys

real assets.

-These assets play 4 main roles:

Consumption Timing

Allocation of Risk

Separation of Ownership and Management Transfer of funds from surplus to deficit units.


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1. Consumption Timing

Some individuals in the economy earn more than they want to

spend. Others spend more than they earn

Financial assets allow us to time our consumption. They makeit possible for us to store our purchasing power.

Invest in high earning periods and spend in low earningperiods. Can allocate consumption to periods that providegreatest satisfaction.

Individuals can separate decisions concerning currentconsumption from constraints imposed by current earnings.


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2. Allocation of Risk

All real assets involve some risk. Cash flows are not certain

but can be assigned probabilities depending on differentscenarios.

Investors with different risk profiles are catered for: risk

averse, risk neutral, risk loving. Different financial assets caterfor this e.g. equities and bonds.

There is generally a positive relationship between risk and

return. This allows firms to optimally price assets depending

on the risk-return characteristics of investors. Facilitates

process of building stock of real assets.


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3. Separation of Ownership and Management

In todays business environment characterized by large

corporations owners do not necessarily manage firms.

Financial markets allow this separation of ownership andmanagement.

Holders of equity are the owners, they appoint a managementteam to run the firm on their behalf.

This brings about the principal-agent problem.

P i i l bl


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Principal-agent problem Agency problems: empire building, risk avoidance to protect jobs,

excessive consumption of luxuries.

Different ways used by mgt. to increase their welfare atthe expense of shareholders

1. Excessive consumption of perquisitesthey use firm resources to

make expenditures that provide them with personal benefits

(private jets, holding meeting in exotic resorts doubling asvacation spots).

2. Maximizing firm size rather than its valuein the labor market

for the mgt. compensation is highly related with firm size. Mgt

has an incentive to maximize the size of the firm and not firmvalue. This is known as overinvestment and mgt. that overinvest

is said to be engaging in empire building.

3. Siphoning corporate assets - E.g., mgt. can establish a separate

shell firm which they own and then direct cash flow from themain firm to the shell.15


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4. Risk-avoidance to protect jobsmgt. may be

so self-serving as to be biased against more risky

projects and favouring less risky ones.

Solutions:

1. Tie compensation to performance (stockoptions);

2. Outside monitors (security analysts).

3. Etc.

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Risks faced by Mgt vs. Risk faced by

Shareholders Mgt. and shareholders may be exposed to different risks associated

with the firm.

If shareholders are fully diversified then they are exposed just to

the systematic or firm-specific risk. If one particular firm doesnt

do so well there may be others doing well, gains and losses may

cancel out, reducing risk.

But if the managements income is largely from their

compensation then they may be exposed to the firms total risk.

Therefore management tends to take action to reduce the firms

total risk, even if such action may not be in the shareholders

interests. 17

S M t t t


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Sc emes use y Mgt. to re uce exposure tofirm risk

1. Excessive diversificationMgt can diversify the firms operations

across industries, even though this may be of little value to the

already diversified shareholders. This excessive diversification

serves to reduce the probability of the firms failure and thus

reduces the probability that the mgt would be out of a job.

2. Bias toward investment with near-term payoffsif mgt

compensation is tied to the firms earnings, then mgt has an

incentive to bias their selection of capital projects toward

investments that payoff well in a short period of time. This can

happen even when the investments may not maximize shareholder

value in the long-run.3. Mgt. Entrenchmentthe CEO can steer the firm towards

investments that reflect his/her unique talents. Overtime, this policy

will make it difficult for shareholders to fire the CEO even if he/she

is not optimally performing. 18


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4. Transfer of funds from surplus to deficit

units

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Risks associated with investing in financial assets

Purchasing Power risk- this is the risk that is due to the

uncertainty of the buying power of the cash flow you may

receive from the financial assets.

Default or credit risk the issuer of the financial asset may

fail to pay the lender i.e. the borrower may default on the

obligation.

Foreign exchange risk for assets whose cash flow is not

denominated in SA Rands there is the risk that the exchange

rate will change adversely resulting in losses in SA Rands.


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Users of the Financial System

The needs of the users of the financial system will determine what

financial assets are available.

3 main groups:

The Household Sector

The Business Sector

The Government Sector


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The Household Sector

The consumption timing function of financial assets is most

relevant to households

2 factors have a significant effect on the financial needs ofhouseholds: taxes and risk preferences.

Taxes: high-tax bracket investors will seek tax-free securities.Financial services providers will endeavor to offer such assets.

Risk preference: differences in risk preference lead to demandfor a diverse set of investment alternatives. Also leads to demandfor easy portfolio diversification.


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The Business Sector

Businesses need to raise money to finance investment in real assets.

2 ways for businesses to raise money:

-borrow from banks or households (issuing bonds) this is

referred to as debt.

-issuing stocks (allowing new owners)

this is referred to asequity.

- firms issue to get best possible price, to minimize cost of

issuing. To achieve this they use of investment banks.

Low cost implies simplicity of securities. But households want

variety. Intermediaries address this mismatch.


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The Government Sector

Government requires money for investment, social services,

salaries etc.

When revenue < expenditure governments need to borrow.

The government cannot sell shares to raise capital. It can:

- print money (inflationary pressure)

- issue treasury bills and other fixed income securities. These arehighly liquid: quickly converted to cash with low transaction

costs.

Because of governments taxing power it is very credit worthy. Can

therefore borrow at lowest interest rates.


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The Role of Capital Markets:

An Illustration

using Inter-temporalConsumption Choice


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Back to Basics: Economics 101

In ECO101 we assume a unique happiness function for

every individual (utility function).

We call such a function the individuals subjective

preference. Every economic agent is trying tomaximize his/her happiness subject to some

constraints.

Maximise utility subject to some constraints:

E.g., U(x, y) subject to PxX + PyY W


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Economics 101

We can represent an individuals preference,

U(x, y), by indifference curves on thex-y diagram.

x

y

U0

U1

U2

Represent higher levels of utility

U0 < U1 < U2


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Economics 101

The constraint ofPxX + PyY Wcan be

shown as the budget line.

x

y

Budget line (Slope = Px/Py)

W/Py

W/Px

Feasible Consumption Set


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Maximizing utility means picking the best feasibleconsumption point (C*). The equilibrium condition is:

(slope of indifference curve)MRS = Px/Py (Slope of

budget line)

WhereMRS = MUx/MUy

x

y

U0

U1

U2

W/Py

W/Px

C* (with consumption of x* and y*)

x*

y*


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Inter-temporal Consumption Choice

For inter-temporal consumption choice, we employ the samerationale. Now, x becomes current consumption (C0) and ybecomes future consumption (C1). That means, our happinessdepends on two things: current and future consumption.

C0

C1

U0

U1

U2


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In order to have the indifference curves (ICs) asdescribed with nice concave shapes, we assume that:

More is better than less.Diminishing marginal utility of consumption for a

single period.

U(C0,C1)

C0

U = U(C0,C1=constant)

MU > 0(U /C0) > 0

MU is diminishing

i.e., (2U /C2) < 0


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With the assumptions, we have the following diagram.

The slope of the IC represents the individuals

subjective rate of time preference (SRTP).

We call the slope the marginal rate of substitution

between current consumption and future consumption.

The math expression is:

MRS = MU(C0)/MU(C1)= (U /C0) / (U /C1)

C0

C1

U0

Th C i


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The Constraint Recall that an individual maximizes his happiness subject to constraints.

What are the constraints?

It depends on the options available for the individual to allocate his wealth

across different time periods. We study two options: [1] Production opportunity and [2] participation in

the capital market.

We assume the individual has endowment ofY0 and Y1 in the current andfuture periods, respectively. So, we can plot the endowment point on thediagram.

Constraint A: With no wealth allocation across periods, his utility is U0.

C0

C1

U0

Y0

Y1

You basically consume what

you get each period,

C*0=Y0, C*1=Y1

P d i O i


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Production Opportunity Constraint B: The individual can only invest in production

opportunities to allocate wealth across periods

Now, we introduce production opportunities that allow a unit of current

savings/investment to be turned into more than one unit of futureconsumption.

Assume the individual faces a schedule of productive investmentopportunities. We line them up from the highest return to the lowest andplot them as follows:

Such decreasing marginal rate of return means diminishing marginal

returns to investment because the more an individual invests, the lowerthe rate of return on the MARGINAL investment.

Total investment

Marginal rate of return


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Total investment in the current period is equal to currentperiod endowment minus current consumption (i.e., Investment= Y0-C0)

With this in mind, we can plot the constraint on the C0-C1

space. We call this constraint the production opportunity set (POS).

The slope of the POS is now called the Marginal Rate ofTransformation (MRT) offered by the production/investmentopportunity set.

Investment means the individual can move its consumptionpoint along POS.

C0

C1

Y0

Y1

Production Opportunity


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Production Opportunity At the endowment point, the individual is not maximizing his

utility subject to Constraint B. He can do better by investing more(i.e., move north-west along the POS) because at the endowment

point, the return offered by investing is higher than his SRTPneeded to make him feel indifferent.

The equilibrium is when he invests until the return offered by themarginal investment is just equal to its SRTP. We have: (slope ofPOS)MRT = MRS(slope of indifference curve).

C0

C1

Y0

Y1U0

U1

C*0

C*1

P d ti O t it


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Production OpportunityPoints to Note:

This individual can achieve a higher utility (U1>U0) by investing in productionopportunities (i.e. reallocating consumption over time).

His feasible consumption set expands with the introduction of productionopportunities. With constraint A, he can only consume at the endowment point.With the introduction of production opportunity (a less restrictive constraint B),his feasible consumption set becomes all the points along the POS.

This gives the rationale for inter-temporal consumption choice which also explainsinvestment. If exposed to various investment opportunities, individuals want to takesome of them in order to allocate wealth. Doing so would allow them to achieve

higher utility level.

C0

C1

Y0

Y1U0

U1

C*0

C*1

Capital Market


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Capital Market Now, instead of one individual, lets assume there are many individuals in the

economy. Some are lenders, while others are borrowers.

We now have opportunities to borrow and lend at the market-determined

interest rate (r).Constraint C: No production opportunity. But individuals can lend/borrow at r.

We can graph the borrowing and lending opportunities along the capital marketline.

Now, we introduce the concept of wealth. Wealth of an individual is the presentvalue of his current and future endowment. Thus:

W0 = Y0 + Y1/(1+r)and W1 = (1+r)Y0 + Y1

C0

C1

Y0

Y1

W0

Capital market line with Slope = -(1+r)

Y0(1+r) + Y

1

Capital Market Line


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Capital Market LineLooking at points A and B:

Point A: You consume your current and future endowments now. So,

C0 = current endowment + PV of future endowment, i.e., C0 = Y0+Y1/(1+r)

Point B: You consume nothing now and everything in future. So C1 = Y0(1+r)+Y1

Slope of capital line = C1/C0=[Y0(1+r)+Y1 ]/[Y0+Y1/(1+r)] = -(1+r)

Therefore, equation of capital market line: C1=Y0(1+r)+Y1 - (1+r)C0

Thus: C1=W1- (1+r)C0

C0

C1

Y0

Y1

W0

Capital market line with Slope = -(1+r)

W1=Y0(1+r) + Y1B

A

Capital Market


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Capital Market The feasible consumption set is now all the points along the

capital market line.

Moving north-west along the capital market line, the individual

can achieve a higher utility (U2>U0).

This individual is now lending (Y0-C*0) amount of money, andwill get back(1+r)(Y0-C*0) in the next period so that he canconsume a total of C*1= Y1+(1+r)(Y0-C*0).

C0

C1

Y0

Y1

W0

Y0(1+r) + Y

1

U0U2

C*0

C*1

NB: One should be able to

determine C*0 and C*1

(i.e., optimal consumption

path)

Production and Capital Market


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Production and Capital MarketConstraint D: Individuals can now borrow/lend at r & invest in production opportunities.

-With only production opportunity, the individual achieves U1 only (see point D in diagram below). But if

capital market is introduced, he can do better.

-At D the borrowing rate is less than the rate of return on the marginal investment. Since further

investment returns more than the cost of borrowed funds we increase investment. That is we move

up the POS until when point B is reached (at which point return on investment is equal to the

borrowing rate).

-At point B we receive output from production (P0, P1) and the present value of wealth is W*.

-At this point, his wealth is maximized.

-Now his wealth is W*0 = P*0 + P*1/(1+r) which is larger than W0.

-Once we are on the market line we can move along it as we search for a utility maximizing point (i.e.

(C*0, C*1) ). With his wealth maximized, he chooses (C*0, C*1) to consume and yield him U3.

C0

C1

Y0

Y1U0

U3

(C*0, C*1)

P*1

P*0

U1

W*0

A

D

B

Fi h S ti Th


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Fisher Separation TheoremPoints to note:

The decisions of production and consumption involve 2 distinct steps.1st Step: Choosing production point by moving along POS and produce at the point where the

return on the marginal investment is just equal to market interest rate.

2nd Step: Choosing consumption point by moving along the capital market line and consume at thepoint where MRS (subjective rate of time preference) is equal to market interest rate.

We call this the FISHER SEPARATION THEOREM. The important point is theproduction point is governed solely by objective criteria, namely, the set of opportunitiesavailable and the market interest rate. This is independent of individuals subjective rateof time preferences.

C0

C1

Y0

Y1U0

U3

(C*0, C*1)

P*1

P*0

U1

W*0

A

D

B

Fisher Separation Theorem


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Fisher Separation TheoremImplication 1:

As the graph below shows, with two different individuals

that differ only in their subjective preferences, given thesame opportunity set, both of them would choose theexact same point of production regardless of thedifference of their preferences.

C0

C1

Y0

Y1

P*1

P*0 W*0

Individual 1

Individual 2

Implication 2:


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Implication 2:

Consider two investors investing all their money on the stocks of a single firm.Their well-being is thus tied to the well-being of the firm. Consider the firm ismaking a decision on what to produce.

Fisher Separation Theorem implies that even though the two investors differ in

their subjective perception of how to consume between now and future, they bothhas one unified objective, i.e, to maximize their current wealth.

Doing so means the firm can maximize its value. This is the same as investinguntil the return on the marginal investment is just equal to the cost of capital, i.e,the market interest rate.

And the firm knows that its shareholders will unanimously agree on what it does.

C0

C1

Y0

Y1

P*1

P*0 W*0

Individual 1

Individual 2

li i 2


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Implication 2:

MRT = (1 + r) is the point where both of the two individuals wouldagree for the firm to produce.

This is exactly the famous project selection rule, the positive NetPresent Value rule. The firm value is maximized by taking allprojects that have positive NPV.

NPV = -initial investment + present value of future payoutdiscounted by cost of capital.

Cost of capital = r

C0

C1

Y0

Y1

P*1

P*0 W*0

Individual 1

Individual 2

H t h h ld lth?


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How to max shareholders wealth? We again uses Fisher Separation Theorem

Given perfect and complete capital markets, the owners of the firm(shareholders) will unanimously support the acceptance of all projects until the

least favourable project has return the same as the cost of capital.

In the presence of capital markets, the cost of capital is the market interest rate.

The project selection rule, i.e., equate

marginal rate of return of investment = cost of capital (market interest rate)

Is exactly the same as the positive net present value rule:

Net Present Value Rule

Calculate the NPV for all available (independent) projects. Those with positiveNPV are taken.

At the optimum:

NPV of the least favourable project ~= zero

This is a rule of selecting projects of a firm that no matter how individualinvestors of that firm differ in their own opinion (preferences), such rule is stillwhat they are willing to direct the manager to follow.

Fi h S ti Th


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Fisher Separation Theorem The separation principle implies that the maximization of the

shareholders wealth is identical to maximizing the present value

of lifetime consumption Since borrowing and lending take place at the same rate of

interest, then the individuals production optimum is independentof his resources and tastes

If asked to vote on their preferred production decisions at ashareholders meeting, different shareholders will be unanimousin their decision

unanimity principle

Managers of the firm, as agents for shareholders, need not worry

about making decisions that reconcile differences in opinionamong shareholders i.e there is unanimity

The rule is therefore

take projects until the marginal rate of return equals the

market interest rate = taking all projects with +ve NPV


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An exercise for self-study

Consider the following utility function:

U= U(C0) + 1/(1+ )U(C1)

We now take a total derivative:

U'(C0)dC0 + [1/(1+ )]U'(C1)]dC1 = 0

Rearranging,

dC1/dC0 = -(1- ) [U'(C0)/ U'(C1)] slope ofindifference curve

- the slope of the indifference curve depends upon the relative marginalutilities as well as the subjective rate of time preference

A i


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An Exercise

450U0

C0 =C1

C0

C1

1

1

As C0 MU As C

1 MU

Slope of the indifference curve

along the 450 is -(1+ ) as

[U'(C0)/ U'(C1)] = 1To the right of the 450 line, the slopeis less than 1 as

[U'(C0)/ U'(C1)] < 1

To the left of the 450 line, the slopeis greater than 1 as

[U'(C0)/ U'(C1)] > 1dC1/dC0 = -(1- ) [U'(C0)/ U'(C1)]slope of indifference curve

Therefore, even if > 0, the tradeoff between C0 and C1 can be < 1if C0 is sufficiently high

Another Numerical Example


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Another Numerical Example

Assume individuals can borrow and lend, but no production

Suppose that the utility function for consumption isU = log(C

0) + [1/(1+ )] log(C

1)

The individuals wealth is given by the equation

W = y0 + [1/(1+R)]y1 where R is the rate of interest and

is the subjective rate of time preference If an individual is to maximize utility, then we know that the present

value of consumption must equal wealth: W = y0 + [1/(1+R)]y1

Derive the optimal consumption paths, assuminga) W=100, R=10%, =10%

b) W=100, R=5%, =10%c) W=100, R=10%, =5%

We are ignoring production opportunities in this example


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The Optimization Problem Set up the constrained optimization problem

L = log(C0) + [1/(1+ )] log(C1) + [ WC0C1/(1+R)] The first order conditions

L/C0 = (1/C0) - = 0 = 1 / C0 L/C1 = (1/(1+ )) (1/C1) - /(1+R) = 0 = [(1+R)/(1+)] (1/

C1)]

[1 / C0] = [(1+R)/(1+)] (1/ C1)] C0

* = [(1+ )/(1+ R)] C1* If = R C0* = C1* If > R C0* > C1*

If < R C0* < C1*

C0

C1

U

C0

*

C1*


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Optimal Consumption Paths Solve for the following three cases a) W=100, R=10%, =10%

C0 = (1.10/1.10)C1 W = C0 + C1 /(1+R) = 100

C0* = C1* = C* = 52.38

b)W=100, R=5%, =10%

c)=100, R=10%, =5%

Third Year Financial Economics 2012 Topic1a1

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