How financial markets (should) work

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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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◼ Three fundamental goals

Financial markets are called efficient as they achieve

• Market equilibrium: demand of funds equals supply; at the prevailing market conditions, everyone can freely lend or borrow as much as wanted (no "rationing")

• Allocation efficiency: allocation of funds is the best possible one (minimal cost, maximal benefit, for each agent, and society as a whole)

• Information efficiency: the market transmits all the necessary information to achieve efficient allocations.

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◼ Three necessary conditions

Efficiency occurs with three necessary conditions • perfect competition -- free entry/exit

− no dominant position (no price makers)

• no transaction costs − transactions requires no extra cost (material or immaterial) in addition to the market cost

• perfect information − all operators are freely and equally endowed with "all relevant information" (to optimal decisions)

general (economy-wide) specific (sectoral) External information

All external factors affecting the payoffs of financial transactions

Internal information

All internal factors (specific to the parties) affecting the payoffs of financial transactions "characteristics" and "actions" of the borrower market conditions (security prices, interest rates)

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◼ Supply and demand of funds

Let us start from the first fundamental function of financial markets: allow people to borrow and lend. Remember that this amounts to choosing the preferred time profile of resources and expenditure, and this is an intertemporal choice.

The general principle is that this choice (as any rational choice) is driven by comparing its cost with its benefit. The optimal choice should have benefit (at least) equal to cost.

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•

Supply of funds

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

Y0 can be spent currently (E0) or lent (L0) at the year interest rate r. A supplier shifts

available resources from the present to the future. Time profile of available resources: E0 = Y0 − L0

E₁ = Y₁ + L₀(1 + r)

L

Supply curve

r

• 1+r measures the increase of future resources (benefit) for €1 of decrease of present resources (cost)

• Along the supply curve, the lender equates the benefit with the cost of lending. A higher 1 is an incentive to increase the supply of funds

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•

Demand for funds

Y0 can be increased by borrowing (B0) at the year interest rate r.. A borrower shifts

available resources from the future to the present.

Time profile of available resources: E0 = Y0 + B0

E1 = Y1 − B0(1 + r)

r

• 1+r measures the decrease of future resources (cost) for €1 of increase of present resources (benefit)

• Along the demand curve, the borrower equates the benefit with the cost of borrowing. A higher r is an incentive to decrease the demand for funds

B

Demand curve

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◼ Market equilibrium

Market equilibrium obtains when demand equals supply at a single interest rate (market interest rate). No transaction takes place at a different rate

Market equilibrium Amount of funds r Market interest rate Demand _Supply r*

At the market interest rate,

• each borrower/lender in the market can make his optimal transaction

• borrow/lend the exact amount of funds that equates cost and benefit for each

• any single borrower/lender can satisfy his/her plan (no shortages)

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•

The market mechanisms

The adjustment of the market out of equilibrium

Funds r Funds r S D

r is too high: excess supply;

supply (point A) exceeds demand (point B); suppliers' competition makes i fall up to equilibrium E

(note movements along the curves)

E

r is too low: excess demand;

(point A) exceeds supply (point B); demanders' competition makes i rise up to equilibrium E (note

movements along the curves)

A B E A B D S

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The adjustment of the market: shifts of demand and supply

Funds

r

Funds

r increase in demand (D1) (the

curve shifts upw.): at the initial equilibrium rate E, D1 > S;

demanders' competition makes i rise up to equilibrium E1 (note the

movement along the supply curve)

E1

r increase in supply (S1) (the

curve shifts upw.): at the initial equilibrium-um rate E, S1 > D; suppliers' competition makes i fall up to equilibrium E1 (note the

movement along the demand curve)

D=S E E S=D D1 S1 E1 S D r S D

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• Solvency

In equilibrium, all borrowers must be solvent (solvency or intertemporal constraint) Bo(1+r) <Y1-E1

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◼ Introducing security prices

We know that some financial instruments ("securities") are traded at a price in organized markets. In these markets, transactions modify the price of the security. We know that the interest rate on these instruments should be computed in a particular way − the rate of return − that takes the role of price into account. How does the security market mechanism work?

Rate of return of Italian Bonds and a Stock Index in 2015

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•

The rate of return

Remember the formula of the RR of any security k

1 1 1 kt kt

1

y

p

r

p

=

+

−

− _pkt = purchase price at time t

− _{pkt+1 = market price at time} t+1 (e.g. one year);

− _{ykt+1 = payments (per euro) per time unit (a fixed interest rate} i for bonds, a variable _{dt+1 dividend for equities)}

•

Capital gains and losses

The formula can also be expressed as follows

1 1 1 1 1

=

y

p

p

r

p

p

y

p

p

−

=

+

+ 

rate of change of the price

- capital gain > 0 - capital loss < 0

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•

The future value

Another formulation is the following: The sum of the payments and the future market price yield the future value of the security

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

1

V

r

p

=

−

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

Note. The formula of the RR has the simple meaning that you invest €_pkt to get €_{Vkt+1 in} one year

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The relationship between the RR and the price of a security

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 is _pkt+1 = €2.1. Hence, _Vkt+1 = €(0.2+2.1) = €2.3, and _rkt+1 = €(2.3  2)−1= 0.15 = 15%.

Now suppose that

i) 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%.

rk

pk

higher V

lower V

V determines the position of the curve. Given the price, higher (or lower) V shifts the curve upw. (or downw.) and raises (or lowers) the RR

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◼ 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 RR RR is decreasing in the security price

security supply is increasing in its price those who supply funds: buy securities

supply of funds is increasing in RR RR is decreasing in the security price

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Demand and supply of a security

price equilibrium price → equilibrium RR demand _supply amount of security k price demand supply amount of security k E E1

How to get more funds from the market.

Suppose k is a bond issued by a company, and at the equilibrium price E, the company wishes more funds. Its supply of k should increase (the supply curve shifts upw.). The market accepts to buy the new issuance of k at the new

equilibrium price E1, such that the RR of k is higher

Exercise. Draw an increase in the demand for the security, and

determine the new equilibrium price. How has the RR changed? Do the security suppliers receive more or less funds than before?

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The relationship between the supply of bonds and the RR. The case of Italian State bonds

-15 -10 -5 0 5 10 15 1970 1975 1980 1985 1990 1995 Real return rate Deficit/GDP

The government deficit should be financed by borrowing (see Part 1), i.e. by selling bonds in the market.

The higher the deficit, the higher the RR required by lenders

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◼ Arbitrage across securities

Can the RR of any security be set independently of (and be different from) the RR of other

equivalent securities? In an efficient market the answer is NO. Let us use the efficiency conditions

 perfect competition  no transaction costs

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

equally informed about the prevailing market conditions (the price and 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 (high price) and buy high RR (low price) assets. This is called

arbitrage.

4. The equilibrium (arbitrage) price of securities

and informational efficiency

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Consider the following process

higher RR securities demand increases price rises RR falls lower 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 a unique RR, the "market return rate" r

1 1 kt

1

V

r

r

p

=

− →

The price of each security that is established at the arbitrage equilibrium is s.t. all _rk are equal to the market rate r, i.e.

1

₁

V

r

p

− =

₁

V

p

r

=

+

•The equilibrium price of a security (its "right price") is its future value discounted at the market rate

• Informational efficiency: observing the prices, given the market rate, the market transmits all available relevant information, i.e. the future value of each security

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•

Arbitrage at work

Consider a stock market session with the following data − Two securities, k = 1, 2

− Constant future value V₁ = 100, V₂ = 150 − Market rate of return r = 10%

→ equilibrium prices: p*₁ = V₁/(1 + r) = 90.9, p*₂ = V₂/(1 + r) = 136.3 − Opening price p₁₀ = 80, p₂₀ = 160

→ opening RR r₁₀ = V₁/p₁₀ – 1= 25%, r₂₀ = V₂/p₂₀ – 1 = −6,2%

Convergence to equilibrium prices Sales (−), purchases (+)

60 80 100 120 140 160 180 Titolo 1 Titolo 2 90,9 136,3 6 security 2 security 1 -20 -15 -10 -5 0 5 10 15 20 Titolo 1 Titolo 2 security 1 security 2

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Relationship between security price and market return rate

pkt

high future value 1

1

V

p

r

=

+

low future value

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Example 1. How to value a stock company.

The stock company k has a prospective profit of €20 mln. and its assets (buildings, machineries, know-how, etc.) have a sale price of €190 mln. The future value of the company is €210 mln. The market RR is 5%. Hence the present market value of k is _pkt = €(210 mln  1.05) = €200 mln. €200 mln divided by the number of shares gives the market price of equities k.

The market rate rises to 7%: check that _pkt falls to €196 bln.

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

i) News arrive that raise the prospective profits of the company to €30 mln. The future value is now €220 mln., and hence the present market value rises to €210 mln. In fact, at the initial value of €200 mln., holding the shares of k would yield more than the market rate, _rkt+1 = €(220 mln./200 mln) − 1 = 10%. Arbitrage shifts demand towards shares k and raises their price until the RR is 5% again.

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◼ Three important questions and explanations

1) Why are security prices different?

They reflect the (market information of) future value of securities; securities with

higher future value command a higher price than those with lower future value. This is called informational efficiency

2) Why are security prices so variable ("volatile")?

They react quickly to changes in r and V. "News" about changes in V are the most important factor. Note: V are future, unobservable variables, assessed by investors

3) If you're so smart, why aren't you so rich?

"Smart traders" present themselves as being able to make systematically higher RR than the others. Arbitrage and informational efficiency make this impossible (at least on average), or: "you can't beat the market". In fact, the equilibrium price formula means that anyone in the market who buys security k at price _pkt upon the information that its future value is _{Vkt+1 will earn no more (no less) than the market rate} r.

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◼ Fundamental valuation

Arbitrage and informational efficiency have another important implication: the truly smart trader is the one who chooses high yield securities given all available information, not the one who seeks to speculate (i.e. make conjectures) on unknowable future prices. This is a.k.a the principle of fundamental valuation

Can we aim (rationally) at pure "speculative" capital gains? Recall that the RR can be re-expressed as follows

1 1 1 kt kt kt kt kt kt

y

p

p

r

p

p

=

+

−

rate of change in the price, or "speculative" component.

yield rate of the security on the basis of all available information at t

(rem.: all investors are freely endowed with the same information, hence they all believe in the same

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Changes in future prices are unpredictable (rationally)

Now let us extend our view beyond one year. The investor who buys the security k in t and holds it for a number of years up to T, can expect to obtain the compound value of its stream of future payoffs net of changes in the price each year. Is there a rational basis to foresee the future price?

Here is one: you know (everybody knows) the security price formula where we use a more correct notation for the future value V

1 1 ( _{kt t} kt V |I ) p r + = +

(_Vkt+1|It) reads: the t+1 value of k is computed according to all available information _It, and is the best possible forecast, as of t.

What then will _{pkt+1 be? By the same reasoning,}

2 1 1

1

(

V

|I

)

p

r

=

₊

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Hence, to foresee _{pkt+1 you would need foresee (Vkt+2|It+1). This is the future value of} k

recomputed in t+1 if news arrive (_{It+1) that are unknown in} t. Hence, to foresee _pkt+1 as of t, you would need know now the information that will arrive in t+1. This is clearly impossible! Indeed, if _{It+1 were predictable in} t, it would be used immediately, and the price would rise in t, not t+1 (see Example 2(ii) p. 21). Therefore,

in an efficient market, the only source of the RR to a security that investors can rationally expect is its stream of future payments

As a result, the equilibrium price formula for any number of years n = 1, …, T is

(

1

)

y

p

r

=

+



The fundamental equilibrium price of a security reflects the present value of the stream of its future payments

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

• What determines price movements?

• Are instantaneous prices, equilibrium prices? • Is arbitrage going on?