Value versus Growth: Stochastic Dominance Criteria

1. Value versus Growth:Stochastic Dominance Criteria Abhay Abhyankar University of Edinburgh Keng-Yu Ho National Central University Huainan Zhao City University, London NTU International Conference on Finance Taipei, Taiwan December 13-14, 2006

2. 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. NTU International Conference on Finance

3. 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). NTU International Conference on Finance

4. 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. NTU International Conference on Finance

5. Stochastic Dominance Tests • First-order stochastic dominance－Non-satiation. • Second-order stochastic dominance－Risk-aversion. NTU International Conference on Finance

6. Stochastic Dominance Tests • Third-order stochastic dominance－Positive skewness preference. • Kolmogorov-Smirnov type tests at all observation points in the sample. NTU International Conference on Finance

7. 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. NTU International Conference on Finance

8. 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 NTU International Conference on Finance

9. 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. NTU International Conference on Finance

10. 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. NTU International Conference on Finance

11. 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. NTU International Conference on Finance

12. Descriptive Statistics NTU International Conference on Finance

13. 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. NTU International Conference on Finance

14. Empirical Results: 1951-2003 NTU International Conference on Finance

15. Empirical Results: 1963-1990 NTU International Conference on Finance

16. 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). NTU International Conference on Finance

17. Empirical Results: Boom, 1951-2003 NTU International Conference on Finance

18. Empirical Results: Boom, 1963-1990 NTU International Conference on Finance

19. Empirical Results: Recession, 1951-2003 NTU International Conference on Finance

20. Empirical Results: Recession, 1963-1990 NTU International Conference on Finance

21. 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. NTU International Conference on Finance