how financial markets works
TRANSCRIPT
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HOW FINANCIAL MARKETS WORK
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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.
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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.
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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
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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
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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
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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
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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
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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
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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
+ ++
+=
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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
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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
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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?
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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.
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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
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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
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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
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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")
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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?
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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)
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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