Value versus Growth: Stochastic Dominance Criteria

Value versus Growth:Stochastic Dominance Criteria

Abhay AbhyankarUniversity of Edinburgh

Keng-Yu HoNational Central University

Huainan ZhaoCity University, London

NTU International Conference on Finance Taipei, Taiwan

December 13-14, 2006

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Introduction• Evidence of value-based investment

strategy.– Even back from the 1930s. (Graham and

Dodd, 1934)• Why value stocks earn higher returns

than growth stocks?– Risk-based explanation.– Behavioral explnantion.

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Previous Research• Numerous empirical studies find that

value stocks outperform growth stocks worldwide.– Risk-return tradeoff.

• Fama and French (1992, 1993).• Petkova and Zhang (2005).

– Investor sentiment.• Debondt and Thaler (1985).• Lakonishok, Shleifer, and Vishny (1994).

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Motivation• Apply a new approach in testing the

value premium.• Advantages of stochastic dominance

tests:– Compare the entire return distributions

of two portfolios.– No need to specify asset pricing model

to estimate expected returns and adjust for risk.

– Allow for minimal assumptions about investor’s utility function.

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Stochastic Dominance Tests• First-order stochastic dominance－

Non-satiation.

• Second-order stochastic dominance－ Risk-aversion.

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);();( 22 FzGz

)();(1 zFFz

zz

dtFtdttFFz0 102 );()();(

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Stochastic Dominance Tests• Third-order stochastic dominance－

Positive skewness preference.

• Kolmogorov-Smirnov type tests at all observation points in the sample.

);();( 33 FzGz

dtFtdsdtsFFzzz t

0 20 03 );()();(

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Stochastic Dominance Tests• Hypothesis

H0:

H1:– The null hypothesis is that the CDF G

stochastically dominates CDF F for the jth order (including the case where the two CDFs are equal), while the alternative is that stochastic dominance fails at some points.

zFzGz jj somefor );();(

zFzGz jj allfor );();(

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Stochastic Dominance Tests• Barrett and Donald (2003) tests:

– P-values for FOSD have closed-form distribution: .

– P-values beyond FOSD (e.g. SOSD and TOSD) do not have closed-form distribution.• Two simulation methods.• Three bootstrap methods

))ˆ;()ˆ;((supˆNjMj

zj FzGz

MNMNS

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Stochastic Dominance Tests• Two-step test for the first and second order stochastic dominance.

– First Step: Test whether the CDF of the value portfolio return stochastically dominates the CDF of growth portfolio return.

– Second Step:Test whether the CDF of the growth portfolio return stochastically dominates the CDF of the value portfolio return.

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Stochastic Dominance Tests• If we fail to reject the first step

(second step) but can reject the second step (first step), we conclude that the value (growth) portfolio stochastically dominates the growth (value) portfolio.

• If we reject or fail to reject both steps of the test, we conclude that there is no stochastic dominance relation between the two portfolio returns.

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Data• Monthly returns on the U.S. value

and growth portfolios from 1951-2003.– Book-to-market ratio.– Earnings-to-price ratio.– Cash flow-to-price ratio.

• In general, value stocks have larger mean but lower standard deviation than growth stock.

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Descriptive Statistics

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Empirical Results• For first-, second-, and third-order stochastic dominance tests, we find that value stocks are preferred to growth stocks.• The results are found for both full sample period (1951-2003) and LSV sample period (1963-1990).• The results based on stochastic dominance tests cast doubt on the risk-based argument that value premium may due to omitted risk factors in existing asset pricing models.

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Empirical Results: 1951-2003

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Empirical Results: 1963-1990

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Empirical Results• Results during economic booms.

– For first-, second-, and third-order stochastic dominance tests, we find that value stocks are preferred to growth stocks.

– The results are found for both full sample period (1951-2003) and LSV sample period (1963-1990).

• Results during economic booms.– For first-, second-, and third-order stochastic

dominance tests, we find no stochastic dominance relation between value and growth stocks.

– The results are found for both full sample period (1951-2003) and LSV sample period (1963-1990).

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Empirical Results: Boom, 1951-2003

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Empirical Results: Boom, 1963-1990

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Empirical Results: Recession, 1951-2003

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Empirical Results: Recession, 1963-1990

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Conclusion• Re-examine the value premium using stochastic dominance test. • In general, the value premium exists for non-satiation, risk-averse and positive skewness preference investors.• However, value premium cannot be simple explained by misspecified models.• Behavioral explanation seems to be preferred to risk-based explanation.