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 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

    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 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

    Opatija 2010 A. Urbn M. Ormos

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    Thank you for your attention!

    Opatija 2010 A. Urbn M. Ormos