QUARTA SETTIMANA

Dal 2 al 3 marzo 2015

1. Ruolo e funzionamento dei mercati finanziari 2. Equilibrio e efficienza dei mercati 3. I tassi corporate 4. Tassi a lunga nella zona-Euro e negli USA 5. Aspettative e comunicati della Banca Centrale 6. Il mercato del future sull'euribor e la BCE

7. Bolle e mode (Camerer)8. La caduta dei prezzi azionari di fine millennio 9. Bolle finanziarie e psicologia umana10. Effetto delle aspettative eterogenee

Casi in cui non vale l’efficienza valutativa (e in certi casi anche informativa)

• Bolle razionali

di rendimenti• Mode di opinioni

di utilità• Macchie solari• Bolle informative

fondamentale

prezzo

Un esempio di (probabile) bolla. L’andamento dell’indice S&P ind. 500la caduta del prezzo (-20,5%) è avvenuta in pochi minuti il 19

ott. 1987 (“lunedì nero”) nel biennio 2006-2007

200

240

280

320

360

1986:01 1986:07 1987:01 1987:07 1988:01 1988:07

la caduta del prezzo (-20,5%) è avvenuta in pochi minuti il 19 ott. 1987 (“lunedì nero”)

• Come si individua la presenza di una bolla?

• Premesso che individuare la presenza di una bolla non è agevole perché non è sempre distinguibile da altre irregolarità dei prezzi si possono dare alcune indicazioni:

• A proposito della stima del fondamentale si dimostra che la formula

Vt = + + + + …

può essere approssimata da:

Et [Dt+1] Et[Dt+2] Et[Dt+3] Et[Dt+4]

(1+rt) (1+rt)2 (1+rt)3 (1+rt)4

DNt

rt – gNt

Dove DtN è la stima in t del livello del dividendo “normale”

dell’esercizio t (= al netto delle componenti transitorie), gtN è la

crescita attesa tendenziale dei dividendi

Quest’ultima formula è equivalente a:

Vt = = Dt

N UtN

rt – gNt rt – g′Nt

Dove UtN è la stima in t del livello dell’utile “normale”

dell’esercizio t (= al netto delle componenti transitori, g’Nt è la

crescita attesa tendenziale “autonoma” (o “naturale”) degli utili (= crescita depurata per l’effetto del’autofinanziamento e dell’aumento dell’indebitamento)

Da questa relazione si ricava anche:

DtN / Vt = rt – gD,t

N

UtN / Vt = rt – g′Ut

N

E ipotizziamo (ipotesi nulla H0) che il prezzo sia uguale al fondamentale. Respingeremo poi quest’ipotesi se è palesemente contraddetta dai dati

P V ?

(P non significativamente diverso da V)

Oppure P V ?

(P significativamente diverso da V)

Se UtN / Vt = rt – g′Ut

N UtN / Pt ?

Se UtN / Pt è nell’intervallo di confidenza

della stima rt – g′UtN di Ut

N / Vt accettiamo l’potesi di Pt = Vt

Altrimenti analizziamo la differenza

UtN / Pt - rt – g′Ut

N

e cerchiamo di capire che cosa è successo

FIG.1 – L’evoluzione degli indici Dow-Jones, S&P500 e NASDAQ (scala logaritmica; dati giornalieri, periodo gen.1985-gen.2004)

5

6

7

8

86 88 90 92 94 94

96 98 00 02 04

Dow-Jones S&P NASDAQ

b o l l a d e l 1987

b o l l a d e l m i l l e n n i o

FIG. 3 – L’andamento dello S&P500 e dei relativi utili (scala logaritmica; dati mensili, periodo gen. 1985 - dic. 2003)

Fonte: Shiller, sito internet: http://www.econ.yale.edu/~shiller/data.htm

4

5

6

7

8

86 88 90 92 94 96 98 00 02

S&P500 utili

2

4

6

8

10

12

14

86 88 90 92 94 96 98 00 02

tasso a 10 anni

FIG.4 – Differenza fra il valore di equilibrio del rapporto utili/indice di borsa S&P500 e il suo valore effettivo

(dati mensili, periodo gen. 1985-dic. 2003)

Fonte: nostre elaborazioni su dati di Shiller, Fed e Federal Reserve Bank of Philadelphia

-2

-1

0

1

2

3

86 88 90 92 94 96 98 00 02

Dal questo grafico a scala logaritmica risulta che il prezzo è effettivamente più legato agli utili «normali» che a quelli correnti

200

150

100

5040

30

20

15

10

586 88 90 92 94 96 98 00 02 04 06 08 10

indice borsautiliutili "normali"

fine

1. Ruolo e funzionamento dei mercati finanziari 2. Equilibrio e efficienza dei mercati 3. I tassi corporate 4. Tassi a lunga nella zona-Euro e negli USA 5. Aspettative e comunicati della Banca Centrale 6. Il mercato del future sull'euribor e la BCE7. Bolle e mode (Camerer)8. La caduta dei prezzi azionari di fine millennio

9. Bolle finanziarie e psicologia umana

“bolla” del millennio e psicologia degli azionisti (R. Shiller)

• Others sharply disagree with these bubble stories, and it is

precisely this intimation of foolishness that seems to bother

them. It seems to them just implausible that investors at

large have been foolish. Rather, it seems to them that the

high valuations the market has placed on the stock market

recently can be attributed to actions of rational investors who

are wrestling with hard-to-interpret evidence about such

issues as how much recent technological innovations will

promote future economic growth. Suggesting that investors at

large have been irrational seems arrogant and presumptuous.

• One of the most important arguments that it is not

foolishness that has brought us the high valuations in the

aggregate market is to observe the decisions of some

of the most august of investors, the real experts. One

may note, for example, that those who manage

university endowments had not withdrawn en masse

from the stock market before its peak in March 2000.

• Despite these arguments against calling a bubble, in my

recent book Irrational Exuberance I do argue that there has

indeed been a speculative bubble in the stock market in

recent years. But I argue that the kind of less-than-perfectly-

rational behavior that underlies it is not abject foolishness

(cioè, non è stata una vera “bolla razionale”, ma è stata

comunque una bolla speculativa che, anche se non del tipo

“razionale” non è dovuta a stupidità)

• Moreover, I do not think that it is presumptuous of me (or

anyone else) to argue that human error in evaluating the

available facts has created the high market valuations,

and to argue that it is an error that infects the thinking of

some of the most intelligent people in our society.

• There are many aspects to intuitive probability. One of them is

the representativeness heuristic, identified originally by Tversky

and Kahneman (1974). They showed that in forming

subjective judgments, people have a tendency to disregard

base rate probabilities [= le reali probabilità], and to make

judgments solely in terms of observed similarities to

familiar patterns.

• I think we can say that investors have overconfidence

in a complex culture of intuitive judgments about

expected future price changes, and an excessive

willingness to act on these judgments.

• Psychologists have documented that there is a social basis for

attention, that is, people tend to pay attention to what others

are paying attention to.

• Not surprisingly, speculative assets whose price has gone

up a lot recently gather a great deal of attention.

• People are more likely to buy assets that have their

attention just because they are thinking about them more.

Assets that have not had big price increases are less likely to

garner the attention.

• Another part of the mechanism by which the past price

increases affect the judgments that are actually made about

investing for the future have to do with the feelings of

confidence and self esteem that past successes in

investing has given successful investors. Success in

investing usually involves some acquired skills in understanding

the particular category of investment and in the strategy of

dealing with it. Acquiring such skills regarding that category

increases demand for it. Psychologists Heath and Tversky

(1991) have shown through experiments that holding

probabilities constant people prefer to bet in situations in

which their perceived competence is high.

• After a bubble has continued for a while, there are many people who have committed themselves to the investments, emotionally as well as financially.

• Investing for the long term means judging the

distant future, judging how history will be made, how

society will change, how the world economy will change.

• Reaching decisions about such issues cannot

proceed from analytical models alone;

• there has to be a major input of judgment that is

essentially personal and intellectual in origin.

• With such a confusion of factors, it is hard for

anyone to make objective judgments without being

influenced by the recent success behavior of the

market and the recent success of investments.

• The complex judgment that portfolio managers must

make about these factors, in turn, is inevitably

influenced by the judgments of others. In making

major allocation decisions, one almost inevitably

winds up trusting to a common view or consensus

view about the future.

• Professionals ultimately must end up generally assuming

that what their colleagues believe is true.

• The news media play a prominent role in generating

our conventional wisdom, more so among

nonprofessionals, but among investment

professionals as well. And the news media are

themselves in a fiercely competitive business for survival

as news media. They cannot be indifferent to the

public resonance with the stories they write. They

therefore help reinforce a conventional wisdom in

some dimensions, and help change it in others.

• Stock market price increases generate news stories

about new era theories just as much as the news

stories themselves do. Stories about new era

economics surged around 1997

• If one believes in efficient markets, one believes that

the marketplace of ideas somehow works out optimally,

and hence, by inference one might suppose that the

prominent theories that appear to move investors’

decisions are based on the best possible

information too.

• Irving Janis, in his book Groupthink about professionals’

herd behavior, refers to a number of reasons why

professionals operating in groups may be unwilling

to deviate from the group consensus. His book

reviewed a number of case studies in which professional

groups made serious errors.

• Janis refers to a tendency for people to try to conform

to the consensus of the group in order to preserve

their status within the group.

• In judging whether the stock market remains a good

investment despite high price earnings ratios,

organizations must somehow judge whether we are

entering a new era as some claim. Organizations are

fundamentally ill-equipped to make such judgments,

just as organizations are ill-equipped to write books on

history.

• One reason that institutional investors may not do better is

that they feel that they are dealing with clients who have

expectations of them that make it difficult to pursue their own

best judgment. The clients expect them to invest in

accordance with certain fads.

• Another reason I believe that the differences are so small is that

institutional investors do not feel that they have the

authority to make trades in accordance with their own best

judgments. Their obediance to conventional wisdom hampers

their investment ability.

• Psychologists have argued that human thinking that leads

to action, even individual human thinking, tends to be

motivated by qualitative reasons and justifications, rather

than abstract weighing of probabilities and scenarios.

fine

1. Ruolo e funzionamento dei mercati finanziari 2. Equilibrio e efficienza dei mercati 3. I tassi corporate 4. Tassi a lunga nella zona-Euro e negli USA 5. Aspettative e comunicati della Banca Centrale 6. Il mercato del future sull'euribor e la BCE7. Bolle e mode (Camerer)8. La caduta dei prezzi azionari di fine millennio 9. Bolle finanziarie e psicologia umana

10.Effetto delle aspettative eterogenee

Et[Pt+1 + Dt+1]

Pt

1 +Et[rt]Supponiamo per semplicità che dividendo e tasso siano nulli

Et[Pt+1 + Dt+1]

Pt = Et[Pt+1]

1 +Et[rt]

Pt = Et[Pt+1]

Pt – Pt-1 = Et[Pt+1] – Pt-1

Pt = Et[Pt+1] – Pt-1

Da che cosa dipendono le aspettative dei vari

individui h, Et,h[Pt+1] , la cui media

ponderata corrisponde a Et[Pt+1] ???

• Da che cosa dipendono le aspettative dei vari individui h, Et,h[Pt+1] , la cui media ponderata corrisponde a Et[Pt+1] ???

• Una soluzione semplice è supporre che esistano due categorie di individui e ciascuna categoria basi le sue previsioni su un tipo di modello diverso da quello dell’altra categoria

• Perché questo è importante?

Andamento del Dow Jones

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9,000

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11,000

12,000

13,000

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15,000

99 00 01 02 03 04 05 06 07 08

DJADJCLOSE

Variazioni del Dow Jone

-.12

-.08

-.04

.00

.04

.08

.12

99 00 01 02 03 04 05 06 07 08

DLOG(DJADJCLOSE)

Istogramma delle variazioni del Dow Jones

0

100

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300

400

500

600

-0.05 0.00 0.05 0.10

Series: DLOG(DJADJCLOSE)Sample 1/01/1999 27/02/2009Observations 2448

Mean -4.46e-05Median 0.000277Maximum 0.105083Minimum -0.082005Std. Dev. 0.012692Skewness 0.074522Kurtosis 11.04229

Jarque-Bera 6599.469Probability 0.000000

Problemi della mancata considerazione dell’eterogeneità delle aspettative

• The empirical literature demonstrates that very often the macroeconomics fundamentals are not able to explain the large and persistent movements of some economic

variables such as securities prices or exchange rates.

Principali casi di eterogeneità nelle aspettative

(1) rational and irrational agents (De Long et al. 1990, 1991),

(2) informed versus uninformed agents (Genotte and Leland, 1990; Lyons, 1991),

(3) chartists versus fundamentalists (Frankel and Froot, 1988; De Grauwe, 1993)

(4) sophisticated versus naive agents (Day and Huang, 1990).

La difficoltà di conoscere come funzione il mondo

• Indeed, the literature on bounded rationality [= razionalità limitata] has put

forward two important criticisms.

• It is unrealistic to assume that agents know the “economic model”; it

seems more reasonable to assume that their expectations are based on time

series observations.

• It has been shown that, in several economic areas, naïve forecasting tends

to give more accurate predictions than forecasts based on models even if

it cannot as a rule predict turning point.

• The agents also need to have perfect knowledge about the beliefs of all

the other agents in the economy to coordinate their actions on the same RE

[RE=sigla per “aspettative razionali”]

Cambio dollaro/euro

1.16

1.20

1.24

1.28

1.32

1.36

1.40

2004:01 2004:07 2005:01 2005:07 2006:01

cambio $/€

1 Gen.2006 30 Giu. 2006

• Challenging the RE [=aspettative razionali] hypothesis leads

to two questions.

• The first question is how we should model expectations given

the fact that it is hard to observe or obtain information

about [other] individual expectations in real markets.

• The second question is whether heterogeneity in

expectations does contribute to excess price volatility as

that observed in stock market or exchange rate. In other

words, the question is whether agents are able to learn and

coordinate on a RE equilibrium in a heterogeneous world.

• on which criteria we could distinguish between both groups of agents.

• Evidence from survey data shows that:• at short horizons, respondents tend to forecast by

extrapolating recent trends (es. analisi tecnica) while • at long horizons they tend to forecast a return to a

long-run equilibrium (esempio: analisi del fondamentale)

Con quali criteri si possono distinguere le diverse classi di agenti

• Therefore, they associated the longer-term expectations, which are consistently stabilizing, with the fundamentalists,

• and the short-term forecasts, which seem to have a destabilizing nature, with the chartists.

• The behaviour of both groups can be explained in two ways:

• First, both groups behave in different manner because they have different information sets. Therefore, each agent is acting rationally subject to certain constraints.

• Even when agents have the same information set they may act differently. This may be the case because either they draw a different set of inferences from the same information set or they have different goals, including different attitudes to contending with risk or uncertainty.

Aspettativa dei fondamentalisti sul prezzo futuro:

• Fundamentalists look for fundamental determinants of the price. They calculate an equilibrium price p* consistent with these fundamentals, and expect that the current price will gradually move towards its equilibrium value:

p^ft = pt-1 + f(p*- pt-1)

(p^ft - pt-1) = f(p*- pt-1)

Ma: (p^ft - pt-1) ≡ Δp^f

t (variazione attesa del prezzo per i fondamentalisti), da cui:

Δp^ft = f(p*- pt-1)

Aspettative dei chartisti sul prezzo futuro

• Chartists base their forecasts on technical analysis, which is mainly a study of past prices to detect patterns that can be projected in the future. They use various extrapolative models that can be summarised under the following general formulation:

p^ct = φ(pt-1, pt-2 , …)

Ovvero:

Δ p^ct = Φ(pt-1, pt-2 , …)

Aspettive medie del mercato

• The change in the price expected by the market can be written as a weighted average of the two groups’ expectations:

p^t = αt p^f

t + (1-αt) p^ct

(date le aspettative il prezzo di equilibrio non è univoco: dipende dalle percentuali αt )

Ovvero, in termini di variazione (il prezzo passato lo conoscono tutti):

Δp^t = αt Δp^f

t + (1-αt) Δp^ct

(α è il peso sei fondamentalisti)

Come varia la % αt ?

• If α is constant over time, this means that the weight of the two groups remains the same

• However, much evidence supports the possibility of switching:

• Once the weighting factor α is admitted to be able to vary, it remains to explain how it could change. Several

strategies have been adopted.

La % delle varie classi

• the proportion of each class of agents fluctuates due to

mimetic contagion phenomena. The probability of

switching from one group to the other can be formalize

as

• a stochastic process of random meetings (Kirman,

1993; Topol, 1991)

• or can be grounded on microeconomic foundations

(Orlean, 1995, Lux, 1995,1998, Laurent, 1995). This

strategy is based on endogenous switching. Several

cases are possible.

1. Portfolio managers are considered to be the only persons who

actually buy and sell on the market. They form their expectations

as a weight average of chartists and fundamentalists. Therefore,

they update the weights over time according to whether the

fundamentalists or the chartists have recently been doing

the better forecasting.

2. The second case is derived from Frankel and Froot (1990a) and

from the empirical observation that the relative weight of the

two groups depends on the forecasting horizons. For shorter

forecasting horizons, more weight is placed on chartists while the

opposite is true for longer forecasting horizons.

3. When the price deviates from the equilibrium value (in one

sense or the other), the two groups of fundamentalists and

chartists are numerically different so their excess demand is

not nil and then they influence the price.

Nel terzo caso quindi:

• Their weight is thus an increasing function of the deviation of the price from its equilibrium value:

αt = 1/[(1 + (pt-1 - p* )2 ]

ESEMPIO DI Simulazione per il cambio s

• Expectations formation

• Fundamentalists’ forecast:

• Ef,t(∆st+1) = -ψ(st – s*t)

• Chartists’ forecast

• Ec,t(∆st+1) = βΣTi=0 αi∆st-i

• The role of transaction Costs (per i fondamentalisti)

• If st - s*t < C then Ef,t(∆st+1) = 0

• If st - s*t > C then fundamentalists’

forecast rule applies

Attenzione: C può essere interpretato non solo come un costo di transazione ma anche come un “intervallo di incertezza” in cui giace il fondamentale

Quindi:

Ef,t(∆st+1) = -ψ(st – s*t) se abs[-ψ(st – s*

t)]>C

altrimenti

Ef,t(∆st+1) =0

Numero chartisti e fondamentalisti nel tempo

• Learning the forecasting rulesNumber of chartists and fundamentalists is endogenous

• Probabilities of switching

• Ppfct = ….. (probability of switching from fundamentalists to

chartists)• Ppcf

t = ….. (probability of switching from chartists to fundamentalists)

• Probabilities of switching are determined by relative utilities of chartists and fundamentalists

cfttct

fctftctc pnpnnn 1,1,1,,

fcttf

cfttctftf pnpnnn 1,1,1,,

Risultato delle simulazioni

Fondamentale poco variabile

(da +2 a -4 circa)

Fondamentale molto variabile

(da +35 a -25 circa)

Conseguenze…

• Fat tailsexchange rate returns exhibit fat tails compared to the normal distribution. This has been observed first by Mandelbrot for prices of commodities. Our model mimicks this empirical regularity

• We also find excess kurtosis, which is declining with time aggregationThis has also been found in reality

• Thus exchange rate movements in normal times are small

• Once in a while there is turbulence in the market• Our model generates this dynamics.

Esempio del cambio• PPP-dynamics (= valore di equlibrio del

fondamentale) is a strong force• Thus, the relation between exchange rate and

fundamentals dominates; there is little complexity• When shocks are small, exchange rates are mostly

within transactions cost band

• PPP-dynamics (= valore di equlibrio del fondamentale) is weak force

• Chartist behaviour becomes important because link between exchange rate and fundamental is weak

• The interaction between fundamentalist and chartist forecasts creates strong non-linearity and thus complexity

• These features of the dynamics of exchange rates have been confirmed empirically

• When there are few chartists (a lot of fundis), – profitability of chartism is low; – profitability of fundamentalism is high

• When number of chartists increase relative to number of fundis– Profitability of chartism increases exponentially– Profitability of fundamentalism collapses

• There seems to be a self-fullfilling evolutionary dynamics• An invasion by chartists creates noise around the

fundamental; • Noise is what chartists thrive on. • Thus the invasion creates the conditions that makes

chartism profitable, reinforcing the attraction. • Chartists create informational environment which makes

it rational to use chartists’ rules. • … ma se il prezzo si allontana troppo dal fondamentale

aumentano I fondamentalisti e quindi…• This does not lead to corner solution, though,

because risk also increases when chartists become more numerous.

(Al diminuire della % di fondamentalisti il prezzo diventa più slegato dal fondamantale)

-40

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P R E Z Z O F O N D A M E N T A L E

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40

10 20 30 40 50 60 70 80 90 100 110

% f o n d a m e n t a l i s t i = 1 % % f o n d a m e n t a l i s t i = 9 9 %

Costo = 20, b = 0.8,

(Al crescere del costo di transazione il prezzo si allontana maggiormente dal fondamentale)

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P R E Z Z O F O N D A M E N T A L E

C o s t o = 0

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10 20 30 40 50 60 70 80 90 100 110

c o s t o = 4 0

% fondamentalisti = 50%, b=0.8

(Nel lungo periodo il prezzo diventa meno slegato dal fondamentale)

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P R E Z Z O F O N D A M E N T A L E

o s s e r v a z i o n i = 1 0 0

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250 500 750 1000

o s s e r v a z i o n i = 9 9 0

1 0 1 1 0

% fondamentalisti = 1%, costo = 40, b=0.8

FINE

Della quarta settimana