Ontechnicalanalysis

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On Technical Analysis

?

It is well known that current spot prices of traded assets provide

information about future spot prices when market participants are

heterogeneously informed.

?

However,

spot

prices

generally

are

imperfect

aggregators

of

private information.

?

For example, if the current spot price depends on the unobserved current

supply

of

the

good

as

well

as

on

the

private

information

of

market

participants, then it is not a sufficient statistic for the private information.

?

Consequently,

market

participants

use

their

private

signals

in

addition to the observed price in forming their demands.

?

Noise

in

the

current

equilibrium

spot

price

also

makes

it

impossible

for

that

price

to

reveal

perfectly

the

private

information

from

earlier

periods.

As

a

result,

historical

prices

together with current prices allow more accurate inferences about

past and present signals than do current prices alone.

?

Because

current

spot

prices

are

not

fully

revealing,

past

prices,

that is, technical analysis, provide information to agents forming

their demands.

1

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?

Consider

a

three-date

model

in

which

the

time

1

aggregate

supply

of

the

risky

asset

is

uncertain,

and

investors

receive

private signals about the time 3 payoff of the asset.

?

In this setting, an individual is unable to infer the average value of

all

investors'

signals

(a

sufficient

statistic

for

the

aggregate

information set) by observing the time 1 price and his own private

signal.

?

Suppose that investors receive additional information at time 2. If

the

investors'

time

1

signals

remain

private,

and

the

time

2

aggregate supply also is uncertain, then each investor will find it

impossible to infer the average time 1 or time 2 signal from the

time

2

price.

The

time

1

price

is

useful

in

learning

about

the

aggregate information set because it is not perturbed by the noisy

variation in the time 2 supply; however it also is not influenced by

time 2 signals.

?

Hence, inferences about the signals from either the time 1 price or

the

time

2

price

alone

are

strictly

dominated

by

inferences

considering both prices.

2

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?

Individuals employ technical analysis (TA) even though the time

2 price is set competitively by rational investors using all public

information, including the time 1 price.

?

One

implication

is

that

financial

markets

are

not

weak-form

efficient in the sense that the current price reflects all information

contained in past prices.

?

However, the degree to which forecasts of future spot prices are

improved by the use of TA remains an open question.

3

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Equilibrium in a Dynamic Economy

with Endogenous Beliefs

?

Two

kinds

of

assets

:

A

riskless

asset

and

one

risky

asset

are

exchanged

in

markets

opening

at

times

t

=

1

and

t

=

2.

Consumption occurs only at

t

= 3 when each share of the riskless

asset pays 1 unit and the risky asset provides a random payoff of

u

.

?

Preference and endowment

: The riskless rate is assumed to be 0.

Investors

i

(

i

= 1, 2, 3, . . .) are a priori identical and countably

infinite in number. Each enters the first period with

n

0

units of

the

riskless

asset,

and

chooses

a

feasible

trading

strategy

to

maximize the expected utility of consumption at time 3:

where

R

is

the

common

absolute

risk

aversion

parameter

and

?

0

is the common prior information available to traders.

?

Information set

: Just prior to the opening of the market at time

t

,

each individual receives a private signal,

y

it

, of the time 3 payoff

of the risky asset. Competitive trading establishes the risky asset

price

P

t

at each date. The information available to investor

i

at

?

i

1

?

?

?< /p>

0

,

y

i

1

,

P

1

time

1

and

2

is

and

?

i

2

?

?

?

i< /p>

1

,

y

i

2

,

P

2

,

respectively.

Define

?

t

< br>?

?

?

1

t

,

?

2

t

,

?

3

t

,

?

as the information set available to the

market at time

t

.

4

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?

A feasible trading strategy

requires that planned asset holdings

be measurable with respect to the trader's available information

and satisfy the individual's budget at each trading date.

?

Let

d

it

, denote individual

i

's time

t

holding of the risky asset.

?

The payoff at time 3 is

n

0

?

d

i

?

P

2

?

P

1

?

?

d

i

2

?

u

?

P

2< /p>

?

?

The

optimal

trading

strategy

is

determined

by

sequentially

solving

and

?

A

rational

expectations

equilibrium

is

a

pair

of

demand

functions

?

d

i

1

,< /p>

d

i

2

?

for

each

investor

and

a

pair

of

equilibrium

price

functions

?

P

1

,

P

2

?

that

together

satisfy

the

following

conditions.

?

First,

the

P

,

are

functions

of

?

t

through

their

dependence

on

investors'

demands

and

per

capita

supplies,

and,

for

each

realization

of

?

t

,

traders'

price

conjectures

are

identical

to

P

t

?

?

t