growth optimal investments with transaction costs
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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 logreturn
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
i1
i+3
i+1g
g1
g2
g3
g4
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 logreturn
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 logreturn
X iGrowth Optimal
Estimation of Future Returns 5/10
Opatija 2010 A. Urbn M. Ormos

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nap
1.rszvny
d.rszvny
n1
n3
n5
n6
n2
n4g
g1
g2
g3
g4 n
Xn empirikusbecslsei Xnelzmnye
. . .
Urbn Andrs Zoltn Tams
6/10
Asset1
A
ssetd
day
Estimation of Future Returns
1TxTxEstimation for
Opatija 2010 A. Urbn M. Ormos

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Proportional transaction costs
tc=reduced stock / initial stock
Initial stock Reduced stock
Transaction Costs 8/10
Opatija 2010 A. Urbn M. Ormos

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Methodology 9/10
Dow Jones Industrial Average constituents inDecember 2005.Assets
January 1991 December 2005Interval
US Treasury Bill 1 monthRiskfree 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 tstatsModel evaluation
Opatija 2010 A. Urbn M. Ormos

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Threefactor model alfa beta smb hml momR2 0.663 Estimated coeff. 1.04 1.01 0.33 0.24Fstat 76.24 (tstat) (2.73) (11.75) (3.41) (1.89)pvalue 0.000 pvalue 0.007 0.000 0.001 0.061adj. R2 0.654Fourfactor model
R2 0.668 Estimated coeff. 1.14 1.06 0.31 0.26 0.09Fstat 58.09 (tstat) (2.96) (10.86) (3.18) (2.06) (1.37)pvalue 0.000 pvalue 0.003 0.000 0.002 0.042 0.172adj. R2 0.657Growthoptimal
Avg. monthly prem. 1.99% Std. dev. 11.44%
Empirikus eredmnyek Faktor modellek 10/10
SMB
HML
MOM
Opatija 2010 A. Urbn M. Ormos

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Thank you for your attention!
Opatija 2010 A. Urbn M. Ormos