An Evolutionary Approach in Financial Forecast

(A Random thought)

VEAM 2010 at Cualo Le Hong Nhat

The Classical Theory of FinanceRisk and Return: A Brief Review

• Investors prefer high expected levels of return and dislike risk.

• It would be a mistake to ask the question as: Which investments are most attractive?

• By creating a portfolio, one can achieve the same level of return as any single asset, but with a less volatility.

The Classical Theory of FinanceThe One-Fund Portfolio: Illustration

Mean return

Standard deviation (Risk)

One fund M

C (CAPM):

_

MR

_

R

A (Single Asset)

AS

}1|),...,(:{)(1

21 J

jJJ r

)()(

),()( rR

RVar

RRCovrR M

M

M

The Classical theory of FinanceImplication of The One Fund: CAPM

• CAPM:

Which says that the expected return of a security equals the riskless rate of interest, r, plus a risk premium, associated with the security’s beta.

• Rationally, If this expected return does not meet or beat the required return, then investors should not hold this asset or security.

)( rRrR M

The Classical theory of FinanceMatching CAPM with the Real World

• Assumption on rational expectation.

• Rational behavior and adjustment mechanism.

• Embedded in the mechanism is EMH: prices can never be too far out of line.

The Classical theory of FinanceRandom Walk (EMH) & ARCH paradigm

time

EMH:

),0(~,:)1( 2 Ndp ttt

tEp:)2( (unbiased)

ttt exdp ^

':)3(

ARCH

210

221 )|(:)4( ttt eeE

t 1t

Pricing error

Variance is time varying:

An evolutionary ApproachBounded rationality and learning

• Bounded Rationality• Adaptive Learning and Risk Dominance• Stochastically Stable State• Forecast in Adaptive Learning Environments.• EMH in Adaptive Learning