7/29/2019 GROWTH OPTIMAL INVESTMENTS WITH TRANSACTION COSTS

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GROWTH OPTIMAL INVESTMENTS WITH

TRANSACTION COSTS

Andrs Urbn

Mihly Ormos PhD.

Opatija 2010 A. Urbn M. Ormos

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Overview 1/10

Investment Strategies

Classical approach

Growth Optimal approach

Growth Optimal Investment Theory

Practise

Empirical Results

CAPM, Factor models

Growth Optimal strategy

Opatija 2010 A. Urbn M. Ormos

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A logoptimlis stratgia Expected return

Heuirstic methods

Naive

Mean return - variance

A, Markowitz, Sharpe,

Treynor- Black

Mean log-return

X iGrowth Optimal

The Growth Optimal Policy 2/10

Opatija 2010 A. Urbn M. Ormos

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nap

1.rsz

vny

d.r

szvny

i+4

i+2i

i-1

i+3

i+1g

g-1

g-2

g-3

g-4

i+5. . .

xi(1)

xi(d) 101%

100,6%

Pl.:

3/10Price relatives

day

Ass

et1

As

setd

Opatija 2010 A. Urbn M. Ormos

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A logoptimlis stratgia Expected return

Heuirstic methods

Naive

Mean return - variance

A, Markowitz, Sharpe,

Treynor- Black

Mean log-return

X iGrowth Optimal

The Growth Optimal Policy 4/10

Maximizing wealth level:

011...= WxxxW

TTT

TTG

tx

T

t

t

T

t

TeWeWxWW

0

ln

1=

0

1=

0=== .ln

1=

=1

t

T

t

Tx

TG

Opatija 2010 A. Urbn M. Ormos

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A logoptimlis stratgia

Estiamtion of expected return and risk:

Unconditionalprobability denstity function of return

Expected return ~mean of historical returnsExpected risk ~historical standard deviation

Conditional estimation future returns

Estimation ofnext day returns based on previous observations

Expected return

Heuirstic methods

Naive

Mean return - variance

A, Markowitz, Sharpe,

Treynor- Black

Mean log-return

X iGrowth Optimal

Estimation of Future Returns 5/10

Opatija 2010 A. Urbn M. Ormos

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nap

1.rszvny

d.rszvny

n-1

n-3

n-5

n-6

n-2

n-4g

g-1

g-2

g-3

g-4 n

Xn empirikusbecslsei Xnelzmnye

. . .

Urbn Andrs Zoltn Tams

6/10

Asset1

A

ssetd

day

Estimation of Future Returns

1TxTxEstimation for

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Proportional transaction costs

tc=reduced stock / initial stock

Initial stock Reduced stock

Transaction Costs 8/10

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Methodology 9/10

Dow Jones Industrial Average constituents inDecember 2005.Assets

January 1991 December 2005Interval

US Treasury Bill 1 monthRisk-free rate

NYSE, AMEX and NASDAQ capitalization

weighted average, including dividendsMarket index

Center for Research in Security Prices (CRSP)databaseSource of data

0.1%Transaction cost

Factor modelsEquilibrium models

R2, adjusted R2 and t-statsModel evaluation

Opatija 2010 A. Urbn M. Ormos

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Three-factor model alfa beta smb hml momR2 0.663 Estimated coeff. 1.04 1.01 -0.33 -0.24F-stat 76.24 (t-stat) (2.73) (11.75) (-3.41) (-1.89)p-value 0.000 p-value 0.007 0.000 0.001 0.061adj. R2 0.654Four-factor model

R2 0.668 Estimated coeff. 1.14 1.06 -0.31 -0.26 -0.09F-stat 58.09 (t-stat) (2.96) (10.86) (-3.18) (-2.06) (-1.37)p-value 0.000 p-value 0.003 0.000 0.002 0.042 0.172adj. R2 0.657Growth-optimal

Avg. monthly prem. 1.99% Std. dev. 11.44%

Empirikus eredmnyek Faktor modellek 10/10

SMB

HML

MOM

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Thank you for your attention!

Opatija 2010 A. Urbn M. Ormos