N^th Order Stochastic Dominance Test With Applications

Stochastic dominance (SD) test describes a set of relations that hold between two distributions. This paper extends the traditional stochastic dominance test results to Nth order stochastic dominance for both risk-averse and risk-seeking investors. When N ? 3, we introduce the definition and tests of SD for both risk averters and risk seekers. In addition, we compare the preference of the S&P 500 index and 3 Month Treasury Bill (3M-Tbill) at the sense of the first three orders SD test. We conclude that in the entire period as well as in the two sub-periods, risk-averse investors prefer 3 Month Treasury Bill, while risk-seeking investors prefer S&P 500 index.In this paper, we will apply SD theory to the issues of market efficiency and gold preference. Financial crises are normally associated with negative effects on financial markets. In this article, we investigate whether the most recent global fi-nancial crisis (GFC) had any positive impact on the G7 (Canada, France, Germany,Italy, Japan, the United Kingdom and the United States) indices. To conduct the analysis, we employ the mean-variance (MV) analysis, CAPM statistics, Hurst exponent, runs test, multiple variance ratio test and stochastic dominance (SD)tests. Our MV and CAPM results indicate that most of the G7 stock indices are significantly less volatile. The results from Hurst exponent, run tests and multiple variance ratio confirm that efficiency improved in the post-GFC period. Finally,our SD results indicate that there is no arbitrage opportunity and the markets are efficient due to the GFC, and, in general, investors prefer investing in the indices after the GFC. Overall, we conclude that the GFC led markets to be more effi-cient and mature, confirming that crises can also have positive impacts on stock markets.The objective of this paper is to assess the effect of gold quoted at the Shanghai Gold Exchange (SGE) in Chinese portfolios composed of stocks, government, and corporate bonds. With the 2004-2014 period, our results show that in general,risk-averse investors prefer not to include gold while risk-seeking investors prefer to include it in their stock-bond portfolios, especially in crisis periods. This result is found to be time-varying but not time frequency dependent and the inclusion of the risk-free asset does not induce relevant impacts. Furthermore, risk-seekers prefer including gold in an equal-weighted portfolio while risk averters prefer including gold in efficient portfolios. These findings can provide important information for Chinese banks, fund managers and individual investors regarding to the portfolio diversification with gold.