# Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly

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## Abstract

**:**

## 1. Introduction

## 2. Definitions of Stochastic Dominance and Omega Ratios

**Definition**

**1.**

## 3. Consistency Results

**Property**

**1.**

**Example**

**1.**

**Property**

**2.**

**Example**

**2.**

**Proposition**

**1.**

**Theorem**

**1.**

**Theorem**

**2.**

## 4. Testing Market Efficiency, Arbitrage Opportunity and Anomaly

#### 4.1. Arbitrage Opportunity and Anomaly

#### 4.2. Market Efficiency and Rationality

## 5. Illustration

## 6. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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1. | |

2. | We note that our proof is different from that of Balder and Schweizer (2017). |

**Figure 1.**The plots of Omega ratios of rental yields of Class A and Class E. The dotted and solid line represent the results of Class A and Class E, respectively.

**Figure 2.**The plots of Omega ratios of the price yield of Class A and Class E. The dotted and solid line represent the results of Class A and Class E, respectively.

Class | Mean | std | Skewness | Kurtosis | JBtest | t-test/F-test |
---|---|---|---|---|---|---|

A | 0.0041 | 0.0008 | −0.1957 | 1.9615 | 1 | 0.0000 |

E | 0.0028 | 0.0008 | 0.4521 | 1.8709 | 1 | 0.7059 |

Class | A | B | C | D | E |
---|---|---|---|---|---|

A | OD | OD | OD | OD | |

B | ND | OD | OD | OD | |

C | ND | ND | OD | OD | |

D | ND | ND | ND | OD | |

E | ND | ND | ND | ND |

Class | Mean | std | Skewness | Kurtosis | JB test | t-test/F-test |
---|---|---|---|---|---|---|

A | 0.0054 | 0.0233 | −0.2194 | 3.6554 | 0 | 0.5327 |

E | 0.0056 | 0.0308 | −0.1495 | 3.9346 | 1 | 0.0001 |

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**MDPI and ACS Style**

Guo, X.; Jiang, X.; Wong, W.-K.
Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly. *Economies* **2017**, *5*, 38.
https://doi.org/10.3390/economies5040038

**AMA Style**

Guo X, Jiang X, Wong W-K.
Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly. *Economies*. 2017; 5(4):38.
https://doi.org/10.3390/economies5040038

**Chicago/Turabian Style**

Guo, Xu, Xuejun Jiang, and Wing-Keung Wong.
2017. "Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly" *Economies* 5, no. 4: 38.
https://doi.org/10.3390/economies5040038