how financial markets works

7/30/2019 How Financial Markets Works

1/21

1

HOW FINANCIAL MARKETS WORK


2/21

2

Efficient markets

In this part we begin the study of the key working mechanisms of financial markets.

Actual markets are very complex entities, and how they work essentially depends on a

number of specific characteristics concerning the structure of the market and the

operational conditions of participants.

Here we begin with a set of characteristics that qualify financial markets as efficient

(the so-called Efficient Market Hypothesis (EMH)). Efficiency is a key concept of

modern finance. It relates to general economic principles of efficient allocation of

resources, in the particular context of financial resources.


3/21

3

Efficiency occurs with three necessary conditions

perfect competition

free entry/exitno dominant position (no market makers)

no transaction costs transations requires no extra cost (material or

immaterial) in addition to the market cost

perfect information all operators are freely and equally informed

about the prevailing market conditions (the marketinterest rate) at any point in time

Efficient financial markets achieve three fundamental properties:

market equilibrium: demand of financial funds equals supply

allocative efficiency: allocation of funds is optimal = given the market interest

rate each agent equates marginal cost and marginal benefit of funds solvency: all those who are funded are solvent.


4/21

4

1. Supply, demand, equilibrium

Supply and demand of funds

Let us start from the first fundamental function of financial markets: allow people to

choose their preferred time profile of resources and expenditure (intertemporal

problem)

Consider a person with available resources in two periods Y0, Y1

Supply of funds: Y0 can be spent currently (E0) or lent (L0) at the year interest rate (or

return rate) r. Time profile of available resources:

E0 = Y0L0E1 = Y1 + L0(1 + r)

A supplier shifts resources from the present to the future.

LSupply

curve

r

1+r measures the increase of future

resources for 1 of decrese of presentresources. A higher r is an incentive to

increase the supply of funds


5/21

5

Demand of funds:Y0 can be increased by borrowing (B0) at the year interest rate r.Time profile of available resources:

E0 = Y0 +B0

E1 = Y1 B0(1 + r)

A borrower shifts resources from the future to the present.

B

Demand

curve

r

1+r measures the decrease of future

resources for 1 of increse of present

resources. A higher r is an incentive todecrease the demand of funds


6/21

6

Market equilibrium

Market equilibrium obtains when demand equals supply at a single interest rate

(market interst rate)

Market equilibirium

Amount

of funds

Market interest

rate

Demand Supply


7/21

7

The market mechanisms

The adjustment of the market out of equilibrium

Funds Funds

S

D

r is too high: excess supply; supply(point S) exceeds demand (pointD);

suppliers' competition makes r fall

up to equilibrium E(note

movements alongthe curves)

E

r is too low: excess demand;denmand(pointD) exceeds supply (point S);

demanders' competition makes r rise

up to equilibrium E(note

movements alongthe curves)

D

S

E


8/21

8

The adjustment of the market: shifts of demand and supply

Funds Funds

increase in demand (D1) (the curve

shifts upw.): at the initial equilibri-

um rate E,D1 > S; demanders'competition makes r rise up to

equilibrium E1 (note the movement

along the supply curve)

E1

increase in supply (S1) (the curve

shifts upw.):at the initial equilibri-

um rate E, S1 >D; suppliers'competition makes r fall up to

equilibrium E1 (note the movement

along the demand curve)

D=S EE

S=D

D1S1

E1


9/21

9

Solvency

In equilibrium, all borrowers must be solvent (solvency or intertemporal constraint)

B0(1 + r) < Y1 E1

1 10

(1 )

Y EB

r

+

Borrowing must not exceed the present value of net future resources


10/21

10

2. Security markets and prices

Introducing security prices

Some financial instruments ("securities") whereby funds are exhanged are traded at a

price in organized markets. We know that for these instruments we should computethe rate of return (which may or may not include a fixed interest rate). In these

markets transactions modify the price of the security. How does the security market

mechanism work?

Remember the formula of the return rate (RR) of any security k

pkt = purchase price at time t

pkt+1 = market price at time t+1 (e.g. one year); pkt+1 =1kt kt

kt

p p

p+

= capital gain/loss

ykt+1 = payoff (per euro) per time unit (a fixed interest rate i for bonds, a variable dt+1

dividend for equities)

1 1

11

kt ktkt

kt

y pr

p

+ ++

+=


11/21

11

The sum of the payoff and the future market price is the future value of the security,

Vkt+1 =ykt+1 +pkt+1 Therefore,

1

11

ktkt

kt

Vr

p

++ =

The RR of a security is inversely proportional to its price, for its given future

value

The relationship between the RR and the price of a security

RR

price

higher V

lower V

Vdetermines the position of

the curve. Given the price,higher (or lower) Vshifts the

curve upw. (or downw.) and

raises (or lowers) the RR


12/21

12

Example. The current price of the shares of company k is pkt = 2. The one-year

dividend is dkt+1 = 0.2 per share, and the resale price ispkt+1 = 2.1. Hence, Vkt+1 =

(0.2+2.1) = 2.3, and rkt+1 = (2.3 2)1= 0.15 = 15%. Now suppose thati) the price falls to 1.8. Hence rkt+1 = (2.3 1.8)1= 0.278 = 27.8%

ii) at the initial price, the one-year dividend is revised downwards to dkt+1 = 0.1.

Hence, Vkt+1 = 2.2, rkt+1 = 10%

Demand and supply w.r.t. price

We can now translate demand and supply of funds into demand and supply of

securities.

First, consider that

those who demand funds: issue (supply) securities

demand for funds is decreasing in the RR

RR is decreasing in the security price

security supply is increasing in its pricethose who supply funds: buy securities

demand for funds is increasing in the RR

RR is decreasing in the security price

security demand is decreasing in its price


13/21

13

Demand and supply of a security

price

equilibrium price

equilibrium RR

demand

supply

amount ofsecurity k

price

demand

supply

amount ofsecurity k

E

E1

How to get more funds from the market.

Suppose k is a bond issued by a company, andat the equilibrium price E, the company wishes

more funds. Its supply ofk should increase (the

supply curve shifts upw.). The market accepts

to buy the new issuance ofk at the new

equilibrium price E1, such that the RR ofk is

higher

Exercise. Draw an increase in the

demand for the security, anddetermine the new equilibrum price.

How has the RR changed? Do the

security suppliers receive more or

less funds than before?


14/21

14

Arbitrage across securities

Can the RR of any security be set independently of (and be different from) the RR ofother securities?. In an efficient market the answer is NO.

Let us use the EMH

perfect competition

no transaction costs

perfect information reformulated as follows: all operators are all freely and

equally informed about the prevailing market conditions

(the RRs of all securities), i.e. they posses the

"information set" {Vkt+1,pkt, all k} at any point in time t.

Under these conditions fund suppliers compare the RRs across securities and seek

higher RR. They sell low RR and buy high RR assets. This is called arbitrage.


15/21

15

Consider the following process

higher RR securities demand increases price rises RR fallslower RR securities demand decreases price falls RR rises

Arbitrage tends to make RRs convergent, and

in force of efficient arbitrage, security trading goes on until all securities pay aunique RR, the "market return rate" rt+1

1

1 11

ktkt t

kt

Vr r

p

++ +=

The equilibrium (arbitrage) price of securities

Security trading determines prices, not directly RRs. The price of each security that is

established at the arbitrage equilibrium is

1

11

ktkt

t

Vpr

+

+

=+

The equilibrium price of a security is the present value of its future market

value (payoff + sale price) discounted with the market RR


16/21

16

Relationship between security price and market return rate

Example 1. The year market RR is 5%. The stock company k has a prospective profit of

100 mln. and a sale price of 2 bln. Profits are entirely distributed to shareholders. Its

present market value ispkt = (2.1 bln 1.05) = 2 bln. 2 bln divided by the numberof shares gives the market price of equities k.

The market RR rises to 7%: check thatpkt falls to 1.97 bln.

pkt

rt+1

low future value

high future valueSecurities with higher future

value command a higher price

than those with lower future

value


17/21

17

Example 2. News and prices. Consider again Example 1.

i) News arrive that raise the prospective profits of the company to 150 mln. The future

value is now 2.15 bln., and hence the present market value rises to 2.05 bln. In fact,at the initial value of 2 bln., holding the shares ofk would yield more than the market

rate, rkt+1 = (2.15 bln./2 bln) 1 = 7.5%. Arbitrage shifts demand towards shares k

and raises their price until the RR is 5% again.

ii) At the initial market value of 2.0 bln., company k has 100 mln. shares of 20 each

in the market. News arrive that their price will rise by 10% on a year basis. Hence the

current price rises to 22.1 (compute this by means of the formula ofpkt applied to unit

values per share).

A trading day of "Telecom Italia" at the Milan Stock Exchange


18/21

18

3. Fundamental valuation

We have seen that, givent the market RR, th equilibrium price of a security depends

on its future value. This is typically a forecast based on available information

The future value of a security is given by its prospective payoff as well as its future

price. What is the economic rationale of having the present price to depend on the

future price? How can the future price be forecast?

The Rational Expectations Method (REM)

The REM is a sophisticated method that explains how forecasts of future variables

can be obtained in a rational manner, where "rational" means

to make the best use of all available knowledge and information to obtain a (statistically) correct forecast (not systematically wrong, correct "on

average")


19/21

19

Consider again the equilibium security price formula in a simple reformulation

1 1

1 1

1 1kt kt ktp y pr r+ += ++ + = PV of next payoff + PV of next price

As a first approximation the market RR is taken as a constant r.

To determine pkt+1, use "all available knowledge", i.e. "the model" that generates the

price. Hence project the formula into the future,

1 2 2

1 1

1 1kt kt kt

t t

p y pr r

+ + += ++ +

Back to the present

1 2 2

1 2 2

1 1 1 1

1 1 1 1

1 1 1

1 1 12 2

=( ) ( )

kt kt kt kt

kt kt kt

p y y pr r r r

y y pr r r

+ + +

+ + +

= + +

+ + + +

+ ++ + +

Nowpkt depends onpkt+2, the price two years hence. If you repeat the operation with

pkt+2, you will get thatpkt depends on pkt+3, and so on. This is an "infinite regress"

problem. How can it be solved?


20/21

20

At the Tth period forward, the fomula looks like the following

( )1

1 1

(1 )1

T

kt kt n kt T n Tn

p y prr+ +

== + ++

Note that the discount factor 1/(1 + r)T tends to zero as time Tgrows to infinity, so

that the future price term vanishes. Therefore,

( )

1

1kt kt nn np y

r+= +

Under the REM, the equilibrium price of a security is the compound present

value of the sum of all its future payoffs ("intrinsic" or "fundamental"evaluation)


21/21

21

Conclusion

Arbitrage + Equilibrium pricing + REH = "fundamental" evaluation =Informational Efficiency

Fundamental evaluation implies that only all future payoffs matter (no conjectures or

"speculations" about future prices). Indeed, payoffs measure the intrinsic income

generation of the asset. Hence proposition of Informational Efficiency (the mkt. price of

an asset reveals all is necessary for lenders to know)

Relatedly, efficient prices only react to unexpected news about future payoffs.

Therefore, efficient prices move randomly. Arandom walk is a process such thatpkt =pkt-1 + ut

where ut is a random variable unpredictable at t-1, and is uncorrelated with previous or

future random news. In other words,pkt-1 contains all value information as oft-1, but it

contains no information aboutpkt.

In an efficient financial market, the best predictor of the future price of an assetis its current price

how financial markets works

Documents