Chapter Overview The main objective of people who invest in the stock market is to make a profit. However, the world is full of uncertainty. Many investment decisions made by investors are under conditions of uncertainty. Therefore, the risk of the investment has to be weighted against the probability of returns. For an investment decision, both probability and risk have to be incorporated in the decision making process. Numerous studies on the investment process are based on the expected utility theory by von-Neumann and Morgenstern (1953). Its framework considers the whole distribution of returns (including the risks) simultaneously. Suppose there are two alternative investment portfolios, A and B. If the expected utility of investment A is larger than the expected utility of investment B, then investment A will be preferred to investment B. When there is full information on preferences, we can simply calculate the expected utility of all the comparative investments and choose the one with the largest expected utility. However, in reality, we have only partial information on preferences. Hence, we are unable to calculate the expected utility directly. The partial information on preferences is that they are non-decreasing (more is preferred to less), there is risk aversion (dislike of risk) and there is also decreasing absolute risk aversion (positive skewness preferred). The Stochastic Dominance (SD) approach provides a simple method to choose among the uncertainty investments based on these three information sets. The main advantage of the SD approach is that it makes no assumptions about the investor’s utility function. It is nonparametric orientated because it examines the whole distribution of returns. The SD approach is developed on the foundation of von-Neumann and Morgenstern’s (1953) expected utility paradigm. The modern theoretical treatment of dominance begins in the 1960s (Masse 1962, Quirk and Saposnik 1962, Fishburn 1964). By the end of the 1960s and beginning of 1970s, four papers (Hadar and Russell 1969, Hanoch and Levy 1969, Rothschild and Stiglitz 1970, Whitmore 1970) pave the way for SD paradigm’s development. There are three major types of SD: the first-order SD, the second-order SD and the third-order SD. First-order SD is based on preferences by all investors with non-decreasing utility function. Second-order SD takes into account investors’ dislike for risk and third-order SD is based on decreasing absolute risk aversion. Since the publication of the four papers as mentioned above, many theoretical extensions and algorithms of SD have been developed. Fishburn (1974) introduces a type of SD applied to the mixture of, or convex linear combinations of probability distributions which is called the convex SD. In addition to the convex SD, Bawa, Bodurtha (Jr.), Rao and Suri (1985) propose superconvex SD for dominance of third order with discrete distributions and for continuous distributions. Both studies are important contributions to the traditional SD, which only focuses on individual distribution, whereas Fishburn and Bawa et al. introduce the concept of linear combination of distributions. Ten years after Bawa and his group’s work, Shalit and Yitzhaki (1994) make another significant contribution to SD literature. They introduced the concept of marginal conditional SD. However, marginal conditional SD is more restrictive than second-order SD because it considers only marginal changes in the holding of risky assets in a given portfolio. On the other hand, a decision based on the changes in wealth, which is more relevant to investors than one based on total wealth motivate the next two important studies. Levy (1998) develops Prospect SD that corresponds to the S-shaped value function. Levy and Levy (2002) employ the Markowitz SD for all reverse S-shaped value function. Recently, Leshno and Levy (2002) established the Almost SD rules which formally reveal a preference for “most” decision makers but not for “all”. SD approach has proven to be one of the most useful tools in investment decision making under conditions of uncertainty. Many literatures have implemented SD rules empirically in different areas. The work of Levy and Sarnat (1970, 1972), Porter (1973, 1974), and Kjetsaa and Kieff (2003) are the major studies to compare the efficient set between SD and Mean-Variance in various stock markets and mutual funds. Vickson (1977), and Vickson and Altman (1977) investigate the relative effectiveness of the Decreasing Absolute Risk Aversion (DARA) SD criterion, which is a SD criterion for decreasing absolute risk aversion utility. Levy and Kroll (1979) test SD with riskless asset criterion. Kroll and Levy (1979) relax the perfect market assumption and test the effectiveness of the various SD with riskless asset criteria when the borrowing rate is higher than the lending rate. Seyhun (1993) uses SD approach to test the January effect in New York Stock Exchange. Bernard and Seyhun (1997) apply SD approach to test market efficiency following earnings announcements. Larsen and Resnick (1999) compare SD analysis with the traditional event study methodologies and find that the former is better than the latter. Best, Best and Yoder (2000) employ the SD approach to compare value portfolios and low book- to-market portfolios. These studies show that SD is a popular tool used to examine the market’s efficiency. In summary, Bawa (1982) and Levy (1992, 1998) provide a detailed survey on the empirical studies of SD in economics and finance. Since the SD approach has been used widely in various areas in empirical finance, there is no doubt that it can be employed effectively in international momentum strategies and Internet stocks as well. This thesis examines the application of SD approach in the stock market. The thesis is organized into three parts. Chapter reviews and extends previous studies on SD tests. Empirical investigation using SD will be conducted in the following two chapters. The first objective of the thesis, which will be presented in the second chapter, is to perform size and power tests on some commonly used SD tests, namely, the Kaur-Rao-Singh (1994) test, the Anderson (1996) test and the Davidson-Duclos (2000) test when the underlying distributions are correlated, and either homoskedastic or heteroskedastic. Although the SD methodology has been developed for more than three decades, while powerful SD tests have been only available recently. McFadden (1989) starts SD testing using the minimum/maximum statistic. On the other hand, there are several studies (e.g. Anderson 1996; Davidson and Duclos 2000) which rely on the comparison of the distributions at a finite number of grid points. Although there have been difference in SD test methods in prior studies, the literature is rather silent on the performance of SD tests. Recently, Tse and Zhang (2004) present Monte Carlo studies to examine the size and power of some SD tests when the underlying distributions are independent. However, little is known about the size- and power- performance of SD tests when the underlying distributions are correlated. As the dependency between two sets of distributions is important in empirical finance and economics, this study attempts here to fill that gap. Monte Carlo simulations are used to perform the test. Specifically, this study attempts to determine which SD test is more appropriate to use for empirical researches when the underlying distributions are correlated. Results of this study may suggest a simpler and powerful test for future research in the economics and finance literature. The aim of the third chapter is to re-examine the profitability of momentum strategies in international stock markets using the SD approach. Since the landmark study on momentum profits by Jegadeesh and Titman (1993), there have been numerous extensions by other researchers (e.g. Fama and French 1996, Hong and Stein 1999 and Cooper, Gutierrez and Hameed 2004). Despite many extensive studies, the actual causes for momentum profits are still controversial and inconclusive. Standard asset pricing models such as CAPM and Fame-French three-factor models fail to explain the existence of momentum profits. The SD approach is applied to test the momentum portfolios in international stock markets in this study. By applying the SD approach, this study would like to distinguish between the hypothesis that there exists some (more general) asset pricing model that can explain the momentum effect versus the alternative hypothesis that there is no asset pricing model consistent with risk-averse investors that can rationalize the momentum effect. Chapter four will provide an alternative view on the “new economy” Internet stocks. Specifically, the SD approach is used to examine whether the new economy dominates the old economy or vice versa. In addition, stock preference of different types of investors will also be examined in this chapter. Many studies have attempted to explain the downfall of Internet stocks especially since the bubble burst in the spring of 2000. Some studies value Internet stocks from the fundamental accounting system (Ofek and Richardson 2002). Others examine this downfall from investors’ behavior (Wheale and Amin 2003). Although many studies have examined misperceptions on Internet stocks, there is still a persistent lack of literature on the comparisons between the old and new economy stocks and the linkage with utility maximization. In this study, a different approach, namely the SD approach is employed to investigate whether investors’ enthusiasm for Internet stocks in recent years is consistent with utility maximization. Investors may use the results of this part of the study as a reference for their decisions on Internet stocks. . of dominance begins in the 19 60s (Masse 19 62, Quirk and Saposnik 19 62, Fishburn 19 64). By the end of the 19 60s and beginning of 19 70s, four papers (Hadar and Russell 19 69, Hanoch and Levy 19 69,. 1 Chapter 1 Overview The main objective of people who invest in the stock market is to make a profit. However, the world is full of uncertainty. Many investment decisions made by investors. attempted to explain the downfall of Internet stocks especially since the bubble burst in the spring of 2000. Some studies value Internet stocks from the fundamental accounting system (Ofek